HIGH POWER PULSED FIBER LASER SOURCES AND THEIR USE IN TERAHERTZ GENERATION by Matthew A. Leigh
_____________________
A Dissertation Submitted to the Faculty of the DEPARTMENT OF PHYSICS In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA
2008
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THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dissertation prepared by Matthew A. Leigh entitled “High Power Pulsed Fiber Laser Sources and their Use in Terahertz Generation” and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy. _______________________________________________________________________
Date: 8/18/2008
Nasser Peyghambarian
_______________________________________________________________________
Date: 8/18/2008
Shibin Jiang
_______________________________________________________________________
Date: 8/18/2008
William Bickel
_______________________________________________________________________
Date: 8/18/2008
Ewan Wright
_______________________________________________________________________
Date: 8/18/2008
Sumit Mazumdar Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. ________________________________________________ Date: 8/18/2008 Dissertation Director: Nasser Peyghambarian
3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.
SIGNED: Matthew A. Leigh
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ACKNOWLEDGMENTS First I would like to acknowledge my dissertation director, Dr. Nasser Peyghambarian. He has been my adviser throughout my enrollment at the University of Arizona, and has been an invaluable mentor and guide. I would like to acknowledge Dr. Shibin Jiang, who has served on my committee, and was the manager of my research group at NP Photonics. I would like to acknowledge my other committee members, Dr. Ewan Wright, Dr. William Bickel, and Dr. Sumit Mazumdar for their flexibility, vision, and helpful suggestions. Additionally, I really appreciate what I learned in each of their classes. I would like to acknowledge my co-workers in my research group, Dr. Wei Shi and Dr. Jie Zong. I have learned much from working with them, and they have supported me in my professional development goals. I would also like to acknowledge Dr. Jianfeng Wu and Dr. Jiafu Wang who were both instrumental to my success. I would like to acknowledge the support of a few close friends Jim, Jimmy, and Ray who helped me at critical times in my graduate career. I also thank Gary Rasmussen for his spiritual guidance and friendship. Finally, I would like to recognize the contributions and patience of my dear wife, Jennifer, and two sons, Christian and Zachary. They have supported and helped me throughout my graduate career, and have given meaning to my efforts. I could not have made it without them.
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DEDICATION
To my wife, for being my eternal companion.
To Christian and Zach, for being my sons, providing inspiration, and cheering me in my darkest hours.
To my Father and Mother, for their wonderful examples and encouragement.
To my brother Lew, for a life of teaching, for working late hours on holidays with me, and being my accountability partner.
To my sisters Becky, Ruth, and Jen, for guiding and encouraging me.
To my forefathers, who have provided these opportunities.
Finally, to my God, for granting me sufficient grace to finish.
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TABLE OF CONTENTS
LIST OF FIGURES.......................................................................................................10 LIST OF TABLES........................................................................................................13 ABSTRACT..................................................................................................................14 CHAPTER 1: GENERAL INTRODUCTION.............................................................16 1.1. Lasers and fiber optics.....................................................................................16 1.2. Brief introduction to optical fibers...................................................................17 1.3. Brief introduction to lasers and fiber lasers.....................................................18 1.4. THz Technology...............................................................................................21 1.4.1. Terahertz Applications.............................................................................22 1.4.2. Terahertz Generation Systems.................................................................23 1.5. Research Overview..........................................................................................24 CHAPTER 2: FUNDAMENTALS OF ION-DOPED GLASS FIBER AND ACTIVE OPTICAL FIBER..........................................................................................................27 2.1. Introduction......................................................................................................27 2.2. Spectral properties of Rare-Earth Ions in glasses............................................29 2.2.1. Electronic configuration and energy levels of ions.................................29 2.2.2. Optical transitions .................................................................................30 2.2.3. Nonradiative transitions..........................................................................32 2.3. Active Optical Fibers.......................................................................................33 2.3.1. Types of Ions and Glass used in active optical fiber...............................33 2.3.2. Erbium ions in glass................................................................................35 2.4. Future Possibilities in Doped Optical Fibers...................................................38 CHAPTER 3: LASERS USING OPTICAL FIBERS..................................................39 3.1. Introduction......................................................................................................39
7 TABLE OF CONTENTS – Continued 3.2. Basic Structure of Conventional Lasers...........................................................40 3.2.1. Stimulated Emission...............................................................................40 3.2.2. Optical Amplification..............................................................................41 3.2.3. Optical Cavities.......................................................................................42 3.3. Basic Structure of Fiber Lasers........................................................................43 3.3.1. Construction of fiber lasers.....................................................................43 3.3.2. Advantages of Fiber Lasers.....................................................................44 3.3.3. Review of Current Fiber Lasers..............................................................45 3.3.4. Physics of fiber lasers.............................................................................47 3.4. Free-Space behavior of laser beams.................................................................49 3.4.1. Mode Quality..........................................................................................49 3.4.2. Gaussian Beam Parameters.....................................................................49 CHAPTER 4: ACTIVELY Q-SWITCHED ALL-FIBER LASERS............................53 4.1. Introduction......................................................................................................53 4.2. Methods for actively Q-switching all-fiber chains...........................................53 4.3. Design and Construction of actively Q-switched all-fiber laser .....................54 4.3.1. Average Power output of the Q-Switched fiber laser..............................59 4.3.2. Pulse width characterization of the Q-switched fiber laser.....................62 4.3.3. Peak power performance of the fiber laser.............................................65 4.3.3.1. Calculating the peak power from empirically measured quantities .....................................................................................................................65 4.3.3.2. Characterization of the peak power................................................67 4.3.4. Narrow linewidth spectral performance..................................................71 4.4. Dual Q-switched fiber lasers using a single piezoelectric...............................72 CHAPTER 5: OPTICAL FIBER AMPLIFIERS AND HIGH POWER OPTICAL FIBER LASER SYSTEMS...........................................................................................73 5.1. Motivation for Using Fiber Amplifiers............................................................73 5.2. Fundamentals of Optical Amplifiers................................................................73
8 TABLE OF CONTENTS - Continued 5.2.1. Amplifier Gain........................................................................................73 5.2.2. Noise in fiber amplifiers.........................................................................76 5.3. Modeling of Er/Yb co-doped large core active fiber amplifier .......................77 5.3.1. Er/Yb codoped fiber amplifier ...............................................................77 5.3.2. Rate equations for Er/Yb fiber................................................................79 5.3.3. Modeling for optimizing final amplifier stage........................................83 CHAPTER 6: HIGH POWER AMPLIFIED FIBER LASER SYSTEMS..................86 6.1. Introduction......................................................................................................86 6.2. High power fiber lasers and amplifiers............................................................86 6.3. High power fiber lasers in the 1.5 µm region..................................................87 6.4. Seed pulse generation systems.........................................................................88 6.4.1. Amplified Q-switched seed pulses..........................................................89 6.4.2. Seed pulses using electro-optic modulators and CW lasers....................91 6.5. Fiber Amplifier System....................................................................................92 6.5.1. Performance of first two amplifier stages...............................................92 6.5.2. Large Core Er-Yb doped Phosphate Glass Fiber for final stage.............93 6.5.3. Temporal performance of fiber amplifier system....................................95 6.5.4. Power performance of fiber laser system................................................95 6.6. Beam quality for fiber laser amplifier system..................................................99 CHAPTER 7: TECHNOLOGICAL DEVELOPMENTS IN THE TERAHERTZ ELECTROMAGNETIC FREQUENCY REGION.....................................................105 7.1. Introduction....................................................................................................105 7.1.1. Motivation.............................................................................................105 7.1.2. Chapter overview..................................................................................105 7.2. Terahertz Generation......................................................................................106 7.2.1. Terahertz Sources using RF Electronics................................................106 7.2.2. Terahertz pulses using ultrashort pulses................................................107
9 TABLE OF CONTENTS - Continued 7.2.3. Terahertz Sources using nanosecond pulses..........................................108 7.2.4. Terahertz Sources using quantum cascade lasers..................................109 7.3. Generation of Terahertz Using Difference Frequency Generation.................110 7.3.1. Crystals for difference frequency generation........................................110 7.3.2. Phase matching......................................................................................111 7.3.3. Backward THz generation.....................................................................112 CHAPTER 8: TERAHERTZ GENERATION WITH FIBER LASERS....................114 8.1. Chapter Overview..........................................................................................114 8.2. Fiber sources of THz radiation.......................................................................114 8.3. Terahertz generation system...........................................................................119 8.3.1. Overview...............................................................................................119 8.3.2. Single Frequency Fiber Laser System...................................................119 8.3.2.1. Pulse Generation system..............................................................119 8.3.2.2. Pulse Amplifiers...........................................................................122 8.3.3. THz Generation and Detection..............................................................124 8.4. Results of THz generation using pulsed amplifier system.............................125 8.4.1. Performance of dual wavelength fiber amplifier .......................................125 8.4.2. Performance of THz generation..................................................................128 8.5. Summary of THz generation..........................................................................131 CHAPTER 9: CONCLUSION...................................................................................132 9.1. Summary of research results..........................................................................132 9.2. Future research and development directions..................................................133 9.3. Frontiers in narrowband fiber lasers and terahertz.........................................135 REFERENCES............................................................................................................136
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LIST OF FIGURES Figure 1.1. Schematic representation of different types of standard telecommunications fiber.........................................................................................17 Figure 1.2. Schematic representation of different types of standard telecommunications fiber. HR stands for high reflection (often more than 99%), and OC for the output coupler, which generally has lower reflectance to allow for higher output............................................................................................................19 Figure 2.1. Schematic of the splitting of ionic energy levels for rare earth ions in a glass matrix..............................................................................................................28 Figure 2.2. Simplified schematic of the plitting of energy levels for an Er3+ ion in a glass matrix. ...........................................................................................................36 Figure 2.3. Fairly typical absorption and emission cross section spectra of Er+3 ions in silica glass. ..........................................................................................................37 Figure 3.1. Energy level diagrams for a three level laser such as a ruby laser (left), and a four level laser, such as a Nd:YAG (right)......................................................41 Figure 3.2. Schematic of a Gaussian beam around the beam waist with typical parameters labeled. ..................................................................................................51 Figure 4.1. Schematic of actively Q-switched all-fiber laser at 1064 nm. The direction of motion of the piezo is rotated 45° from the polarization axis of the PM fiber.. . .55 Figure 4.2. Square wave driving the piezoelectic transducer, and the ringing caused by the piezo being a capacitive element. The optical pulse is emitted when the induced birefringence allows the cavity to be dumped............................................57 Figure 4.3. (a) Q-switched pulse chain, illustrating a consistent period defined by the piezo signal, and typical pulse-height variations. (b) Typical near-Gaussian pulse shape.........................................................................................................................58 Figure 4.4. Relatively linear increase in average power with increasing pulse repetition rate. The curve flattens out as the inversion starts to saturate.................................60 Figure 4.5. Variation of average power with pump power, showing different slopes at different repetition rates. .........................................................................................61
11 LIST OF FIGURES - Continued Figure 4.6. Variation of pulse width with repetition rate (points) and fit (lines)..........63 Figure 4.7. Variation of pulse width with pump power, indicating that higher pump powers lead to shorter pulse widths.........................................................................64 Figure 4.8. Variation of peak power with pump power, illustrating near linear increase. ..................................................................................................................................69 Figure 4.9. Variation of peak power with pulse repetition rate (points) and fit (curves). ..................................................................................................................................70 Figure 4.10. Spectra from Q-switched laser. (a) Narrow-linewidth trace. (b) Wideband trace showing 980 nm pump, and sideband suppression.........................................71 Figure 5.1. Spectra of large core fiber showing various absorption bands dominated by Er and Yb ions.....................................................................................................78 Figure 5.2. Schematic of process in which an excitation from an excited Yb ion is transferred to an Er ion, and possible resulting transitions......................................80 Figure 5.3. Er-Er ion interaction in which a neighboring excited ion absorbs an emitted photon, and then emits a higher energy photon through the parasitic process of upconversion. ......................................................................................................81 Figure 5.4. Optimization of length for output power. Simulation was run with 30W of pump power and various powers of input pulses.................................................84 Figure 5.5. Optimization of length for signal gain. Simulation was run with 30W of pump power and various Er ion concentrations.......................................................85 Figure 6.1. Seed pulse and fiber amplifier schematic for high-power pulsed fiber laser system.......................................................................................................................90 Figure 6.2. Cross section of the LC-EYDF. The core size is 15 µm in diameter, with the dark, round objects being the stress rods............................................................94 Figure 6.3. Peak power and average power as the repetition rate is varied. The peak power saturates below 5 Khz, while the average power saturates above 100 KHz. 97
12 LIST OF FIGURES - Continued Figure 6.4. Performance as a function of pump power. Peak power (points) and fit (line). Pulse energy (triangles) and fit (line)............................................................98 Figure 6.5. Beam quality measurements (points) and fit (lines) in orthogonal directions. The beam showed good mode quality and the overlapping points indicate excellent symmetry...................................................................................100 Figure 6.6. OSA scan of fiber amplifier system output, demonstrating nearly 40dB of sideband suppression..............................................................................................101 Figure 6.7. Measurement of linewidth using a Fabry-perot cavity. The width of the envelope is compared against the spacing of the lines. The individual fringes are spaced by the pulse repetition rate of the laser.......................................................102 Figure 6.8. Oscilloscope trace in persistent mode showing Fabry-Perot piezo signal and fiber laser envelope..........................................................................................103 Figure 7.1. Schematic of a THZ source using a photoconductive switch with interdigitated electrodes. (Grün, 2005, Creative Commons image.)......................107 Figure 8.1. Schematic of the pulse generation system. The electrical generation system is in blue, while the optical train is in yellow.............................................121 Figure 8.2. Pulse amplification and THz generation system. The system starts with a pre-amp (1), isolator (I), and filter (F). This is followed by another amp (2), isolator, and filter. These beams are then combined in the beam combiner, before entering the final amplification stage. The pulses are then filtered and focused on the crystal, and the resultant THz light is detected by the bolometer.....................123 Figure 8.3. Dual-wavelength fiber laser average power. It shows a roughly linear profile with very little roll-over..............................................................................126 Figure 8.4. Dual Wavelength fiber laser power as a function of diode pump.............127 Figure 8.5. Quadratic dependence of THz Average power on fiber laser power........129 Figure 8.6. Dependence of THz peak power on fiber laser power. ............................130
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LIST OF TABLES Table 1.1: The Terahertz frequency range, and corresponding wavelength, wavenumber, photon energy, and photon temperature.............................................21 Table 2.1: Summary of various rare earth elements that have been used in fiber lasers. Included in the table are common host fibers and emission bands. (Adapted from Paschotta, 2008).......................................................................................................33 Table 8.1: Table of fiber-based THz sources in reverse chronological order. Peak emission is graphically estimated where it is not explicitly stated.........................112 Table 8.2: Reverse chronological table of THz sources pumped by eyesafe wavelength fiber lasers. .........................................................................................114
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ABSTRACT In this dissertation I report the development of high power pulsed fiber laser systems. These systems utilize phosphate glass fiber for active elements, instead of the industry-standard silica fiber. Because the phosphate glass allows for much higher doping of rare-earth ions than silica fibers, much shorter phosphate fibers can be used to achieve the same gain as longer silica fibers. This single-frequency laser technology was used to develop an all-fiber actively Q-switched fiber lasers. A short cavity is used to create large spacing between longitudinal modes. Using this method, we demonstrated the first all-fiber Q-switched fiber laser in the 1 micron region. In addition to creating high peak powers with Q-switched lasers, created even higher powers using fiber amplifier systems. High power fiber lasers typically produce spectral broadening through the nonlinear effects of stimulated Raman scattering, stimulated Brullion scattering, and self-phase modulation. The thresholds for these nonlinearities scale inversely with intensity and length. Thus, we used a short phosphate fiber gain stage to reduce the length, and a large core fiber final stage to reduce intensity. In this way we were able to generate high peak power pulses while avoiding visible nonlinearities, and keeping a narrow bandwidth. The immediate goal of developing these high power fiber laser systems was to generate narrowband terahertz radiation. Two different wavelengths were combined into the final amplifier stage at orthogonal polarizations. These were collimated and
15 directed into a GaSe crystal, which has a very high figure of merit for THz generation. The two wavelengths combined in the crystal through the process of nonlinear difference frequency generation. This produced a narrowband beam of THz pulses, at higher powers than previous narrowband THz pulses produced by eyesafe fiber lasers.
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CHAPTER 1:
GENERAL INTRODUCTION
1.1 Lasers and fiber optics Lasers have often captured the imagination of scientists, engineers, and the general public. Lasers have been a staple of popular culture science fiction stories involving “death rays” and other futuristic weapons. In the real world, lasers have provided powerful sources of photons that have been used in many industrial settings. They have also been used in many high precision settings, such as spectroscopy, metrology, and gravitational wave detection. Thus, the search for more powerful and useful laser sources continues to be an area of great interest, far apart from science fiction. Optical fibers have traditionally been used to transport laser light from one point to another with minimal disruption from the environment in telecommunications and networking applications. They have also been used in a variety of other applications to transport light from one point to another, both in technical and nontechnical fields. However, more recent developments in optical fibers have changed them from being passive transporters of light into powerful laser sources. This union has created a very interesting area for research and development in optical physics.
17 1.2 Brief introduction to optical fibers The invention of fiber optics in the mid 20th century has been a very important technological development. It has permitted the high-speed transmission of information between continents, and they have also been used in many sensing applications. Standard telecom optical fibers are continuously produced in large volume, with extremely high quality.
Figure 1.1. Schematic representation of different types of standard telecommunications fiber.
The general physics of optical fibers guiding light are discussed in various general books, such as Verdeyen (1994), Agrawal (2007) and Guenther (1990). Light is guided through the difference in index of refraction between the core and the
18 cladding of the fiber. In the ray optical model, the light is confined in the fiber through total internal reflection, at the core cladding interface. sin critical=n2 / n1
(1.1)
The numerical aperture is a commonly referenced parameter of optical fibers. It describes the index contrast between the core and cladding index, and can be directly related to the critical angle. NA=n core cos critical =n 2core−n2cladding
(1.2)
The wave model of light can be used to determine the number of modes in an optical fiber. For the highest spatial beam quality, such as for long distance telecom applications, a single optical mode is preferred. A further advancement is to guide only a single polarization, as opposed to both linear polarizations. Polarization maintaining (PM) fiber has been successfully developed for this purpose, with the panda configuration shown in figure 1.1 being a common implementation. For short range communication or high optical powers, multi-mode configurations of optical fibers can be used, as also shown in figure 1.1. 1.3 Brief introduction to lasers and fiber lasers Early scientists, such as Newton, were limited to optical sources such as sunlight and candles. While great discoveries on the nature of light were made with these sources, useful optical power was limited. The development of arc lamps provided much more powerful optical sources. However, the collimating of arc lamps is limited by the divergent nature and lack of coherence of the sources, and their
19 spectrum is limited by the available atomic transitions and phosphors. The development of lasers has addressed many of the shortcomings of these early sources. The basic principles of lasers can be found in general optics textbooks such as by Fowles (1972), and Guenther (1990). There are also a number of textbooks focusing strictly on lasers such as Milonni and Eberly (1988), and Verdeyen (1994) that provide more detail. While there is an extremely wide variety of laser types, each type of laser has a feedback mechanism and an optical gain medium.
Figure 1.2. Schematic representation of different types of standard telecommunications fiber. HR stands for high reflection (often more than 99%), and OC for the output coupler, which generally has lower reflectance to allow for higher output. For common solid state lasers, the feedback is provided by two mirrors, as shown in figure 1.2. The laser rod is typically a crystal or glass doped with active ions. These laser rods are optically pumped by either flashlamps or diode lasers, which excite the optically active ions in the rod. A few of these optically excited ions
20 then spontaneously decay to a lower energy level, and in the process emit a photon. Those photons emitted along the axis of the rod are reflected by the mirrors and stay in the optical cavity defined by the mirros. When these photons pass by other excited ions they stimulate the ions to emit a photon with the same direction, energy, polarization, and phase. In this way, many photons with the same parameters are built up, and a highly directional and coherent light source is produced. Fiber lasers are extremely similar to solid state lasers as they also use ions embedded in glass as the gain medium, and are typically pumped by diode lasers. However, instead of the mirrors that solid state lasers use for optical feedback, fiber lasers use fiber Bragg gratings to form the feedback cavity. These gratings, which are written into the fiber by ultraviolet radiation, act as high quality mirrors through the principle of interference. While fiber lasers have the same general schematic of solid state lasers, their construction gives them many technological advantages. The small diameter and mechanical flexibility of optical fibers permit miniaturized and conformal cavities. While bulk mirrors require sensitive alignment, fiber bragg gratings can be spliced, decreasing loss and greatly simplifying construction. Further, the laser rods used in solid state lasers have issues with thermal lensing (Song, 2002). The small diameter of optical fiber permits a very large surface to volume ratio, greatly simplifying thermal conductivity.
21 1.4 THz Technology The teraherz frequency range is variously described as the frequency area around 1 THz, the area from 1-10 THz, or the mm wavelength region. Table 1 provides an overview of the wavelengths, wavenumbers, and photon energies in this range. Photon temperatures are defined using the Bolzman constant. T photon=
E photon kB
(1.3)
Table 1.1: The Terahertz frequency range, and corresponding wavelength, wavenumber, photon energy, and photon temperature. Frequency [THz]
Wavelength [µm]
Wavenumber [cm-1]
Photon Energy [meV]
Photon Temperature [K]
0.1
3000
3
0.4
4.8
0.3
1000
10
1.2
14
1
300
33
4.1
48
3
100
100
12.4
144
10
30
334
41.4
480
THz is an area of the electromagnetic spectrum in which it has proven difficult to create efficient and powerful sources of radiation. It is generally regarded as too high a frequency for traditional radio frequency (RF) sources using electronics to be effective. On the other hand, the THz frequency region is low for optical frequencies, and by extension low for optical photon energies. Because of the low transition
22 energies, it has traditionally been regarded as inefficient for optical methods of generation. Thus, the creation of THz sources has proven to be difficult. 1.4.1 Terahertz Applications There is a great deal of interest in THz technology due to the many possibilities it presents. One of the most important aspects of THz radiation is that many substances are transparent to terahertz radiation, just as many substances are relatively transparent to radio waves and x-rays. However, unlike radio waves, the smaller wavelength of THz allows for more accurate imaging. Unlike x-rays, THz photons are nonionizing, reducing the potential for damage and safety problems. There are many interesting applications of THz technology that have already been implemented. In far infrared spectroscopy, THz spectroscopy offers the potential for higher signal to noise ratios and unique measurements compared to other far infrared techniques such as Fourier transform spectroscopy (Han, et. al. 2001). The ability of THz to penetrate packaging like x-rays but without ionizing the contents makes it potentially useful for nondestructive law enforcement applications such as detecting explosives (Fitch, et. al., 2007) and illegal drugs (Kwase, et. al. 2003, Lu, et. al., 2006). Many polymer molecules have structural resonances in the THz region, providing the possibility for the quality control of medicines (Taday, et. al., 2003), and DNA analysis and manipulation (Markelz, et. al., 2000). THz technology and imaging has many potential medical applications, such as tumor detection (Smye, et. al., 2001, Löffler, et. al., 2001).
23 The development of THz imaging systems has allowed the inspection of opaque packages and permitted the ability to spatially resolve the concentration of molecules such as water (Hu and Nuss, 1995). Though initial systems were relatively slow, recently developed THz imaging systems can obtain video-rate image acquisition (Yasuda, et. al., 2007, Lee, et. al., 2006). Other recent systems have focused on using line scan techniques to improve speed (Yasui, et. al., 2008) and developing sensitive detector arrays that work at higher speeds and do not require cryogenic cooling (Behnken, et. al., 2008). 1.4.2 Terahertz Generation Systems The development of terahertz sources using ultrafast lasers has been a significant advancement for the entire terahertz field (Reimann, 2008). The short pulse widths from ultrafast lasers are helpful in producing high peak power THz pulses, but they also necessarily produce very broad bandwidths. This limits effectiveness in spectrally resolved imaging, and due to water's strong absorption bands in the THz region, pulses with broad bandwidth lose effectiveness in freespace applications. Another popular method for producing THz is using Quantum Cascade Lasers (QCLs), which are capable of producing much narrower bandwidth THz light. QCLs are similar to typical diode lasers, and are made by depositing semiconductor layers in multiple quantum well structures. However, due to their structure of cascaded quantum wells, they are able to reach much longer wavelengths than standard
24 semiconductor lasers. QCLs have been extended into the THz region, providing extremely compact sources that can directly and efficiently generate THz radiation. The main problem with QCLs is their requirement for a low operating temperature, as currently most require cryogenic cooling. The development of QCL THz sources with higher operating temperatures is an ongoing research pursuit. DFG has also been used for generating narrow band THz radiation using ns pulses and solid-state Q-switched lasers (Zernike and Berman, 1965). The much smaller bandwidth of the ns pulses can produce significantly reduced linewidth compared to fs pulses, while still allowing high peak powers without the excessive cooling high power continous wave (cw) systems require (Nishizawa, et. al., 2008). Using solid state Q-switched lasers and DFG, scientists have produced very high power THz pulses over a very broad THz tuning range (Schaar, et. al., 2007, Shi, et. al., 2002, Shi, et. al., 2004). Difference frequency generation to generate narrowband THz has also been demonstrated using gas lasers (Tochitsky, et. al., 2007), and distributed feedback diode lasers (Deninger, et. al., 2008). Research groups have also endeavored to develop more compact solid-state pumped THz systems (Hayashi, et. al., 2007). 1.5 Research Overview In this dissertation, I report recent improvements in high power, narrow bandwidth pulsed fiber laser systems, and their use in THz generation. Actively Qswitched fiber lasers were developed, and also fiber amplifiers seeded by seeded by
25 ns Q-switched fiber lasers and ns pulses from electro-optic modulators. These systems provided high power while maintaining narrow bandwidth and a fixed polarization. Finally, ns pulses at two eyesafe wavelengths were combined in a nonlinear crystal to produce narrowband THz radiation. The complete system produced the highest THz power produced by a narrowband, eyesafe fiber laser system. In Chapter 2, the basics of active ions in glass fibers are reviewed. Active fibers are essential to fiber laser and amplifier systems, and thus the optical physics of the active ions are critically important to these systems. Chapter 3 reviews the fundamentals of solid state and fiber lasers. The properties of beams coming out of fiber lasers are also reviewed, as spatial beam quality is critical to free-space applications and beam focusing. Chapter 4 reports the development of actively Q-switched all-fiber lasers. I discuss the development of these lasers in the 1µm region, and at much higher repetition rates. Chapter 5 reviews the physics of amplification in optical fibers, in which a seed pulse passes through active fiber. This process is extremely useful for high power laser systems. Chapter 6 reports optical amplifiers that produce high powers while still maintaining good spatial and spectral beam quality. The power produced was the highest for amplified single frequency fiber lasers. Chapter 7 reviews current developments in terahertz technology. The various methods of production and detection serve to give perspective to our work.
26 Chapter 8 reports the use of fiber lasers to generate THz radiation using difference frequency generation. I report several groundbreaking results achieved by our team in the area of fiber pumped narrowband THz generation.
27
CHAPTER 2:
FUNDAMENTALS OF ION-DOPED GLASS FIBER AND ACTIVE OPTICAL FIBER
2.1 Introduction Optical fiber usually comes in doped and undoped variates. Undoped fiber is generally made to have extremely low losses, and is typically used to transport light. Telecom fiber and other fiber used for optical communication is generally considered undoped fiber. Doped fiber has the apparent disadvantage of being doped by photoactive ions. While the doping increases optical absorption, it also allows for optical emission. Thus an ion will absorb pump light at an absorption band, and re-emit it at a different wavelength. Active fiber makes fiber lasers possible. The optical spectra of ions are given a concise overview by Fowles (1975) and Wu (2005), and discussed more extensively by Digonnet (2001).
28
Figure 2.1. Schematic of the splitting of ionic energy levels for rare earth ions in a glass matrix.
29 2.2 Spectral properties of Rare-Earth Ions in glasses
2.2.1 Electronic configuration and energy levels of ions The rare earth ions are often considered to be elements 57 through 70, the Lanthanoid series, along with Scandium (21) and Yttrium (39). However, for doped optical systems, usually just the Lanthanoid series are considered. Also, the rare earth ions in glass are usually triply ionized, which is their most stable state. This gives them the electronic configuration of [Xe] 4fN-15S25p6 (Wu 2005). Because of this electronic configuration, the electrons in the f orbital will be somewhat shielded by the electrons in the outer 5s and 5p orbitals. This means that when the ions are in different hosts they will be perturbed, but their spectra will not dominated by the host. Thus, an ion will have similar spectral bands in different hosts. The Hamiltonian of the ion can be written as a sum of the Hamiltonian for a free ion (Hfree ion), the interaction of the ion and the host ( Vion-static lattice and Vion-dynamic lattice), the interaction of the ion with the electromagnetic field (VEM), and the interaction of the ions with other ions in the matrix (Vion-ion). The dominant term is the first, with the others serving as perturbations (Miniscalco, 2001). H =H free ion V ion− static latticeV ion−dynamic lattice V EM V ion−ion
(2.1)
While the ion-lattice terms are relatively small, they do provide a useful function. As can be seen in figure 2.1, the ion-lattice terms stark split the degeneracy of the spin-orbit band into discrete levels. Further, glass is a fairly random media, and the electronic conditions for each ion will be slightly different. This changes the
30 discrete lines into an entire energy band. Thus, photon absorption and emission can take place anywhere in the band, greatly increasing the ease of pumping and the wavelengths that can be emitted. Further, the ion-ion interactions can lead to the excitation of different energy levels through processes such as upconversion and cross-relaxation. 2.2.2 Optical transitions For fiber lasers, the interaction of the ion with the electromagnetic field is the most interesting as it controls the rates at which photons are emitted and absorbed. The derivation of the optical transition properties are worked out in Miniscalco (2001), and this section will summarize and discuss his method of derivation. In a transition between two levels, a and b, the strength of the transition can be given by the operator Sa,b: 2
S a ,b =∑ ∣〈 b j∣ D∣ a j 〉∣ i,j
(2.2)
The interaction operator controls the transition strength, with the electric and magnetic dipoles being the most probable. D Electric =ed =∑ e r i i
D Magnetic =ed =∑ i
e l 2 s j 2m i
(2.3) (2.4)
For these formulas e and m are the charge and mass of an electron in the ion. The quantities r, l, and s represent the position, orbital operator, and spin operator. The
31 sums are over all the f electrons in the outer shell, which to a large approximation are the only ones involved in photonic transitions. The use of these operators permits the calculation of the probability for rates of transition between the two levels. The probability for a spontaneous transition is given by the Einstein A coefficient:
4 3 1 64 n ave E local A a , b= 3 4 o E 3hc
2
1 S g a a ,b
(2.5)
In this form the rate is directly dependent on the value of the strength operator between the two levels. It also depends on the index of refraction of the host, n, the average photon frequency, νave, and the degeneracy of the initial state, ga. The ratio of the local field felt by the electron to the overall electric field is given by the polarizability of the glass host, and can take the more familiar symbol of χ. Using the Einstein A coefficient, the oscillator strength can also be computed. The oscillator strength is a dimensionless quantity that is roughly unity for an electric dipole transition, and orders of magnitude lower for other transitions. f a ,b=4 o
mc3 Aa , b 8 2 n e 2 2ave
(2.6)
The Einstein A coefficients can then be summed over all transitions to give a lifetime for the state, τa. 1 = Aa ,b a ∑ b
(2.7)
32 Through spectroscopy, the quantities can be measured. The oscillator strength can be determined by integrating the spectral line, and measuring various bulk quantities. f a ,b=4 o
mcn mcn d ≈ 4 o FWHM peak 2 ∫ a, b 2 e e
(2.8)
The Einstein A coefficient can be determined through the integral of the spectral line. With the addition of the branching coefficient, βa,b, the lifetime can be measured. A a , b=
a ,b = I d =∫ I a ,b d a ∫ a ,b
(2.9)
2.2.3 Nonradiative transitions Nonradiative transitions are vital in the operation of fiber lasers. Electrons optically excited from the ground state to a high state will quickly decay to a lower state of intermediate energy through nonradiative transitions. This will result in the intermediate state building up a population inversion, which can then lead to optical gain. Nonradiative transitions can also take place between different ions. For example, fiber co-doped with Er and Yb will be pumped at a wavelength where Yb will absorb the light, then transfer the excitation to a nearby Er ion. The Er ion will then undergo the stimulated radiative decay leading to gain at different wavelengths than those allowed by Yb.
33 2.3 Active Optical Fibers
2.3.1 Types of Ions and Glass used in active optical fiber For telecom applications, most active fibers were composed of Er ions in a silica glass host. For current high power lasers the active ion of choice has moved to Yb, though still in a silica host (Galvanauskas, 2004). However, many ions and different glasses have been used in the construction of fiber lasers and amplifiers. Nonsilica glasses, such as phosphate glasses, can have advantages such as higher ion solubility and lower photodarkening. Table 2 summarizes most of the reported ions and glasses, as well as their typical operating regions.
34
Atomic Number
Table 2.1: Summary of various rare earth elements that have been used in fiber lasers. Included in the table are common host fibers and emission bands. (Adapted from Paschotta, 2008) Common Element Ion Fiber Hosts Emission Bands
59
Praseodymium
Pr3+
Silicate, Fluoride
1.3 μm, 0.60.635 μm
60
Neodymium
Nd3+
Silicate, Phosphate
1.03–1.1 μm, 0.9– 0.95 μm, 1.32–1.35 μm
63
Europium
Eu3+
Silicate, Flourozirconate, Polymer
0.55-0.75 μm
67
Holmium
Ho3+
Silicate, Fluorozirconate
2.1 μm, 2.9 μm
68
Erbium
Er3+
Silicate, Phosphate, Fluoride
1.5–1.6 μm, 2.7 μm, 0.55 μm
69
Thulium
Tm3+
Silicate, Germanate, Fluoride
1.7–2.1 μm, 1.45– 1.53 μm
70
Ytterbium
Yb3+
Silicate
1.0–1.1 μm
35
2.3.2 Erbium ions in glass Erbium ions have historically been the most widely used ions in active fiber laser systems due to their optical transitions in the 1.5 µm telecommunications bands. The Er3+ ion takes an electronic structure of [Xe]4f11 for its optically active electrons. Most of the lasers and amplifiers reported in this dissertation used the 4I13/2 to 4
I15/2 transition highlighted in figure 2.2. The glass host splits the 4I15/2 level into eight
sublevels, and the 4I13/2 level into seven sublevels. These are further broadened by homogeneous and inhomogeneous broadening into continuous bands.
36
Figure 2.2. Simplified schematic of the plitting of energy levels for an Er 3+ ion in a glass matrix.
37 The most common pump band for these transitions is using ~980 nm pumping from the 4I15/2 level to the 4I11/2 level. This can be done through direct optical pumping of the Er ion, or by using a Er/Yb co-doped fiber and pumping the Yb with 980 nm, which will then transfer the excitation to the Er ions.
Figure 2.3. Fairly typical absorption and emission cross section spectra of Er+3 ions in silica glass. The absorption bands for Er in glass take on a characteristic shape, as shown in figure 2.3. The broad bandwidth of the Er emission permits lasing and amplification throughout the 1530-1570 nm region. However, the broad bandwidth can create some problems with the spectral purity of amplifiers. The entire emission band will be emitted through spontaneous emission, and some of these photons will then cause
38 stimulated emission of further photons in the process of amplified stimulated emission (ASE). Thus, for our narrowband systems we used spectral filters and isolators to filter out and block the ASE. 2.4 Future Possibilities in Doped Optical Fibers Current research in doped optical fibers include expanding the range of wavelengths that can be used. One possible future development is the use of semiconductor quantum dots as the doping agent in active optical fibers. The size of the dot determines the emission wavelength (Leigh, 2000). Due to the spread in quantum dot size, glass doped by quantum dots can have a broad bandwidth. Waveguides have been written in quantum dot doped glass, paving the way for the possibility of other photonic devices (Auxier, et. al., 2006; 2006a). Another possible development in active fibers would be the development of fibers suitable for the transmission and generation of THz radiation. The cross section of the fibers would need to be on the orders of hundreds of microns to millimeters to provide a waveguide. The development of flexible materials that are largely transparent could lead to effective THz guiding. Then, by doping the fiber material with a substance that is optically active in the THz region devices such as THz fiber lasers could be developed.
39
CHAPTER 3:
LASERS USING OPTICAL FIBERS
3.1 Introduction The invention of lasers in 1960 (Maiman) ushered in a new era of optical physics and technology, which has been utilized in many different areas of physics. The high intensities produced by lasers has led to the field of nonlinear optics (Boyd 1992). The short pulse-widths that can be produced by lasers have led to timeresolved spectroscopy and increased understanding of the dynamics of chemical reactions (Koeberg, et. al., 2007). The long coherence length of lasers has led to novel interferometry schemes, such as gravitational wave detection (Höfer, 2001). Finally, the narrow linewidths possible with lasers have led to a variety of remote sensing technologies in which individual transitions in gas are probed (Shi and Ding, 2004). New developments in laser technology have resulted in physics breakthroughs and commercially successful products. Thus, new and different laser sources have been a productive and necessary area of research. Section 1.2 of this dissertation briefly covered the setup of solid state lasers and references to general texts discussing laser theory. This section will cover laser theory in more detail, as well as addressing fiber lasers and spatial mode structure which are pertinent to the developments reported in this dissertation.
40 3.2 Basic Structure of Conventional Lasers
3.2.1 Stimulated Emission An excited atom can drop to a lower energy level by emitting a photon either on its own through spontaneous emission or by having the transition induced by an external photon in a process known as stimulated emission. The rate of spontaneous emission is given by the Eintein A coefficient as covered in chapter 2 of this dissertation. The rate of stimulated emission is given by the Einstein B coefficient which can be defined through the rate equation for stimulated emission. dN 1 =B21 N 2 I dt
(3.1)
Here Ni is the population concentration at the energy level, B21 is the Einstein B coefficient connecting the two levels, and I(ω) is the spectral radiance of the transition. For a simplified two-level system in equilibrium, the rates of transition from the upper state must equal the rates of transition to lower states. The spontaneous emission and stimulated emission from the upper state must equal the stimulated emission from the lower state. Fowles (1975) uses this principle to derive a balanced rate equation. N 2 A21 N 2 B 21 I =N 1 B12 I
(3.2)
For nondegenerate transitions, the stimulated emission rate must be the same, with B21 = B12. Further, the ratio of the stimulated emission to the spontaneous emission will be the number of photons per optical mode.
41 A21 8 h 3 = 3 B21 c
(3.3)
3.2.2 Optical Amplification To obtain optical amplification, the rate of downward transitions must be higher than the rate of upward transitions. For this to happen, the population of the upper level must be higher than the population of the lower level, in what is known as a population inversion. For a simple two level system, population inversion will not happen because the thermal distribution of electrons only leads to equal distribution in the high temperature limit (e.g. Verdeyen, 1994). However, for three and four level systems such population inversions will take place if the lifetime of the excited state is shorter than the lifetime of the lasing state.
Figure 3.1. Energy level diagrams for a three level laser such as a ruby laser (left), and a four level laser, such as a Nd:YAG (right).
To determine the gain in a general laser, assume that a laser wavefront is traveling in the gain medium. Each downward transition adds a photon to the optical field, and each upward transition takes away a photon from the field. Using the speed
42 of light to convert from time rates to spatial rates, the intensity can be determined through solving a differential equation. dI h = N – N ground B21 I dx c upper
(3.4)
This equation can be directly integrated in the spatial coordinate, giving the intensity an exponential dependence on length. The gain coefficient will then be given by the argument of this exponent. =
h N – N ground B21 c upper
(3.5)
The gain coefficient can be either negative or positive, depending on the relative magnitudes of N1 and N2. The optical pumping must be strong enough to create the inversion, and thus produce gain. 3.2.3 Optical Cavities To control and direct the photons in the gain medium optical feedback of some kind is necessary, separating a laser from an optical amplifier. A simplified schematic of a laser cavity was included in Chapter 1. In most lasers the feedback mechanism consists of a pair of mirrors forming an optical cavity. This cavity reflects the photons, forcing the gain media to amplify photons of the energy and direction it feeds back into the optical cavity. From a technological perspective, the optical cavity often requires exceptional stability and proper placement to both form and maintain the laser. Methods of improving cavity stability often can greatly decrease the noise and variability of the
43 laser. While semiconductor lasers can have a monolithic cavity with mirrors consisting of the diode end facets, solid state and gas lasers can have multiple mirrors and lenses in the cavity to obtain the proper beam shape and cavity length. The laser cavity will have a large effect on the characteristics of the laser. The reflection spectra of the mirrors will determine which wavelengths will be emitted. The cavity length will also determine which optical modes form a standing wave. While the reflectivity of the mirrors and the emission spectra of the gain media will usually define a broad envelope of possible wavelengths, the optical cavity will usually define the narrow linewidths that will actually lase. The spacing of optical nodes is given by the free spectral range, where d is the length of the cavity. FSR=
c 2d
(3.6)
Because the cavity length is inversely proportional to mode spacing, it provides a method to produce a “single frequency” laser which oscillates on only a single longitudinal mode. By making the cavity short and choosing appropriate mirror reflection bands, the laser can be made to oscillate in only a single cavity mode, greatly decreasing the bandwidth of the laser (Spiegelberg, et. al., 2004). 3.3 Basic Structure of Fiber Lasers
3.3.1 Construction of fiber lasers A schematic for a typical setup of a fiber laser was pictured in figure 1.2. Fiber lasers have the same basic components as other lasers, such as a gain medium and
44 optical feedback, but their use of optical fiber produces some advantages. The gain section is usually a section of doped optical fiber which can usually be spliced to the pump source. Meanwhile, the optical cavity is usually formed by Bragg gratings written directly into the fiber. With this setup, lasers can be constructed in a single fiber chain by fusion splicing the active fiber, gratings, and pump diodes. 3.3.2 Advantages of Fiber Lasers The single fiber chain construction permits the development of fiber lasers that have many advantages over traditional free-space aligned solid state lasers. A fiber laser cavity does not require the alignment of mirrors, significantly improving the ease of manufacturing, and can significantly decrease the effects of environmental conditions such as dust, humidity, and vibration. The relatively small diameter and flexibility of optical fiber allows much greater freedom in the construction and integration of fiber laser systems as the laser cavity can bend without the need for additional mirrors. Also, in solid-state lasers the crystal used for the gain medium is subject to thermal lensing, while a fiber laser can dissipate the same heat over a much longer length (Song, et. al., 2002). Fiber lasers have the same thermal advantage over semiconductor lasers, where the heat can dissipate over a large surface area, instead of the very small surface area of semiconductor lasers. Fiber lasers also have a significant mode quality advantage over most semiconductor lasers. Semiconductor lasers typically have an elliptical spatial mode, and require beam-shaping optics for fiber coupling. Fiber lasers are
45 inherently single mode, and can be spliced or easily coupled to other optical fibers. While semiconductor lasers are typically smaller than fiber lasers, fiber lasers are much smaller than other types of lasers such as gas lasers. However, similar to other lasers, fiber lasers have both advantages and disadvantages. The small size that makes fiber lasers so desirable for commercial products also prevents fiber lasers from achieving the extremely high powers reached by large chemical and gas lasers. Also, fiber lasers are limited to wavelengths in which glass can be made that has low optical loss. Finally, the glass used in fiber lasers must be able to be spliced to silica fibers to realize the full advantage of these lasers. Glass with a melting point much lower than silica can be problematic when splicing. 3.3.3 Review of Current Fiber Lasers Currently, research into fiber lasers has focused on higher powers, newer wavelengths, and novel fiber materials (Galvanauskas, 2004). The commercial development of fiber lasers has moved far beyond their beginnings as fiber amplifiers for telecom systems. The fiber laser field is currently expanding into new powers and wavelengths (Li, 2005a; Wu, 2005). Advances in materials and optical components, such as phosphate fibers and high power combiners, are two examples of technologies that are enabling the growth of the fiber laser area. Critical to the development of high power fiber lasers has been the development of large-core fibers (Offerhaus, et. al., 1998; Hebling, et. al. 2002). By
46 using a larger core, more pump light is able to be inserted into the fiber. Also, with larger cores there is the potential for increased mode sizes, reducing the chance of damage and parasitic nonlinear effects (Agrawal, 2007). The availability of highpower diode pump lasers and high power fiber combiners have driven these developments. Specialized fibers with noncircular cross sections have also been developed to increase pump absorption and improve mechanical properties, such as fibers with D profiles and hexagonal profiles (Galvanauskas, 2004; Ortac, et. al., 2008). Researchers are also using photonic crystal fibers to build high-power fiber lasers (Brooks and Di Teodoro, 2006; Song, et. al., 2008). Most high power fiber lasers are in the 1 micron wavelength region, where Ybdoped glass is pumped by 980 nm light (Gray, et. al., 2007; Lee, et. al., 2006). The small quantum defect allows for the possibility of very high efficiency, which is vital for high power systems where heat can distort or destroy the system. This wavelength contrasts with most early fiber lasers, which were commonly based on Er-doped fiber, and operated in the optical telecom bands around 1.5 µm. Recently, there has been a great deal of interest in fiber lasers around 2 µm, which use Ho and Tm doping (Wu, 2005; Barnes, et. al., 2007; Ashraf and King, 2003). These lasers can have the advantage of cross-relaxation in which one pump photon can produce 2 laser photons. This effect can overcome the inefficiencies caused by the large quantum defects, producing lasers that are similar to 1 µm lasers in efficiency, while still being eyesafe (Spuler and Mayor, 2007, defines eyesafe wavelengths).
47 There is great interest in developing fiber lasers at even longer IR wavelengths, into the 4 µm region and beyond, though technical challenges remain. There has been demonstrations of fiber lasers in the 3 µm region (Talavera and Mejia, 2006; Zhu and Jain, 2007; Zhu and Jain, 2007a). These fiber laser used ZBLAN fiber, which uses a specialized Floride glass. The small core of optical fibers combined with relatively long path lengths of fiber lasers lead to large nonlinear interactions. Various fiber lasers have been designed to take advantage of these nonlinearities. Brullion and Raman scattering have been used to make Brullion and Raman lasers with shifted wavelengths (Agrawal 2001; Wang, et. al., 2004; Zhao and Jackson, 2006). Silica fiber has been used to make passively Q-switched and modelocked lasers (Lin and Stolen, 1976 ). Ultrafast fiber lasers take advantage of Raman scattering and self-phase modulation to produce fs pulses with broad bandwidths (Chang, et. al., 2006). Further, fiber lasers based on nonlinear effects do not require external crystal, prisms, or gratings to produce their effects, eliminating a great deal of alignment complexity and materials expense. 3.3.4 Physics of fiber lasers The general principles governing fiber lasers are the same as those that govern solid-state and other types of lasers. Agrawal (2001) works out a derivation that is more specific to fiber lasers, and will be followed here. The small signal gain of a laser can be written as the product of the inversion in the fiber and the transition cross section of the fiber, σs .
48 g z= z N 2 z −N 1 z
(3.7)
For any laser to operate at threshold, the gain must equal the loss. For a fiber laser with two Bragg grating mirrors (R1 and R2), and length L this gives the equation (3.8). G is the single pass gain, and αinternal represents all internal losses. G2 R1 R2 e−
internal
L
(3.8)
=1
The integral of the small signal gain will give the overall gain for the cavity. At threshold the overall gain will equal the losses due to the gratings and any other internal loss processes. 1 L g z dz = cavity = internal gratings L ∫0
(3.9)
To reach threshold will require a minimum pumping power to produce the desired inversion. Assuming the pump is absorbed in an exponential fashion with coefficient αpump , the threshold pump power is given by equation 3.10. It can also be expressed in terms of the pump overlap. P Threshold =Cavity L
Pump Pump h pump P Sat pump =Cavity L Emission S S T 1
(3.10)
Using the approximation that the intracavity laser power is constant, the intracavity and output laser power can take simplified analytic forms. P s =P sat S
P absorption −1 P th
P out = 1− R1 P s= s P absorption− Pth
(3.11) (3.12)
49 In characterizing lasers it is important to consider the slope efficiency. It is the ratio of output power to absorbed pump power while the laser is above threshold. Using the above relations, the slope efficiency can be given by the fiber laser parameters. s =
dP out 1− R1 = dP absorption cavity L
s s p p
(3.13)
3.4 Free-Space behavior of laser beams
3.4.1 Mode Quality For free-space applications such as focusing and collimation, the spatial quality of fiber lasers becomes important. In order to tightly focus a beam or propagate it through space while maintaining high intensity, it is necessary to have a high quality beam. Figure 3.2 demonstrates the lowest order modes. For free-space purposes, a TEM00 mode is the most desirable. Modern fiber lasers with large cores must take special precautions to produce such a mode (Galvanauskas, 2004). 3.4.2 Gaussian Beam Parameters Fiber lasers typically produce Gaussian beams. The electric field of Gaussian beams is given by the following equation (Milonni and Eberly, 1988; Verdeyen, 1994). E x , y , z =E o
[ ] {[
wo −r 2 z kr 2 exp 2 exp −i kz−tan−1 w z z R 2R z w z
]}
(3.14)
50 This equation consists of multiple parts. The first is the beam waist, w(z). The second involves a space dependent phase with terms involving the Rayleigh range, zR, and the radius of curvature of the wave front, R(z).
2
2
(3.15)
[ ] [ ]
(3.16)
w z = w o 1
z z = w o 1 zR w 2o
zR R z = z 1 z
2
w 2o = z 1 z
2
w2o
(3.17)
w ±z R =w o 2
(3.18)
z R=
The Rayleigh range, zR, is defined as the axial distance from the beam waist to the point where the beam diameter is twice as large. The combination of both Rayleigh ranges define the confocal parameter of the beam, and gives a good estimate of the distance through which the beam can be focused.
51
Figure 3.2. Schematic of a Gaussian beam around the beam waist with typical parameters labeled.
52 The power is given by the square of the electric field. This is shown in figure 3.3. The power within a given radius can be computed by performing a Gaussian integral.
[ ] 2
P r = P total 1−exp −2
r w2o
(3.19)
In measuring the width of the beam there are multiple methods. The first is to take the 1/e2 points of the distribution. However, in practice this involves only three points. Thus, the standard way of measuring beam width has moved to a measure that includes all measured points, usually the 4σ beam width, as given in equation 3.21. For a perfect Gaussian beam, the 1/e2 width of the beam will be equal to the 4σ beam width, though they will be different for real beams. P w =1−e−2≈0.865 Po
D 4 =4
[
∞
∞
∫−∞ ∫−∞ I x , y x−x ave dxdy ∞ ∞ ∫−∞ ∫−∞ I x , y dxdy
(3.20)
]
1 2
(3.21)
A beam which contains multiple spatial modes will diverge more rapidly in free space applications, and be focused to a larger spot in focal applications. The common measure for beam quality is the beam parameter product. It is also known as the M2, and it is important for THz generation using fiber lasers for it to be as close to unity as possible. M 2=
wo 4
(3.22)
53 CHAPTER 4:
ACTIVELY Q-SWITCHED ALL-FIBER LASERS
4.1 Introduction Fiber-based Q-switched lasers are currently a very active area of research, and have many potential applications in such areas as fiber-based sensing and nonlinear frequency generation. Many groups have built Q-switched fiber lasers using acoustooptical and electro-optical modulators, though these lasers have involved bulk components in the laser cavity that increase loss, size, and complexity (Myslinkski, et. al., 1992; Wang, et. al., 2004; Morkel, et. al., 1993; Alvarez-Chavez, et. al., 2000) . Bulk components in the laser cavity have also been used by various groups that have reported passive Q-switched fiber lasers using saturable absorbers (Zenteno, et. al., 1990; Paschotta, et. al., 1999; Filippov, et. al., 2004). All-fiber Q-switched lasers using nonlinearities, such as Raman backscattering, have been constructed, but these are emitted at multiple wavelengths, and their pulse repetition rate is unstable and pump power dependent (Chernikov, et. al., 1997; Zhao and Jackson, 2006). This chapter reports an actively Q-switched all-fiber laser capable of high repetition rates while operating at a single frequency. The results were initially published in Leigh, et. al., 2007. 4.2 Methods for actively Q-switching all-fiber chains There is a definite technological interest in active Q-switching, which allows for adjusting the pulse repetition rate and power, and all-fiber chains which allow for
54 robust construction, high efficiency, and fiber splicing. To achieve both of these objectives methods that are different from standard solid-state Q-switched lasers must be used. Recently, methods for actively Q-switching all-fiber lasers have been developed for communications wavelengths around 1550 nm (Pérez-Millán,et. al., 2004; Russo, et. al., 2002; Huang, et. al., 2000; Chandonnet, et. al., 1993). Reported methods include magnetostriction modulation of fiber Bragg gratings (FBGs), stretching of FBGs with piezoelectric elements, acoustically generated microbending, and evanescent field coupling. All-fiber Q-switched lasers using fiber birefringence induced by stress have recently been developed (Kaneda, 2004). In this method, a piezoelectric compresses a fiber creating stress birefringence, and this birefringence acts as a waveplate, changing the polarization state of the light in the fiber. This Qswitch mechanism is similar to using an electro-optic modulator, where the polarization is modulated to switch the laser between high and low feedback states. 4.3 Design and Construction of actively Q-switched all-fiber laser I used the method of piezo-induced birefringence to develop an all-fiber actively Q-switched laser at 1064 nm. To the best of my knowledge, this is the first report of this type of laser in the 1 µm region. The gain medium of the laser consists of 2 cm of NP Photonics proprietary phosphate glass fiber that is highly Yb doped (6% wt) as shown in Figure 4.1. Yb has a broad absorption spectra, and NP Photonics typically builds cw fiber lasers from 1030 to 1070 nm using this active fiber.
55
Figure 4.1. Schematic of actively Q-switched all-fiber laser at 1064 nm. The direction of motion of the piezo is rotated 45° from the polarization axis of the PM fiber.
56 The high doping concentration creates a strongly absorbing active fiber, allowing for a 3.5 cm cavity length that is significantly shorter than other Q-switched fiber lasers, which can have cavity lengths of meters to kilometers. This short cavity length creates a large longitudinal mode spacing, helping to maintain lasing on a single longitudinal mode. The active fiber is spliced between two FBGs and a short section of standard nonpolarization-maintaining (non-PM) fiber as shown in Figure 4.1. A wavelength-stabilized, commercially available 976 nm diode laser pumps the cavity. This configuration allows a laser cavity where there is no coupling to external bulk components, such as acousto-optic modulators, while also eliminating fiber components within the cavity. The polarization-dependent reflection permits Q-switching if the internal birefringence of the cavity can be modulated. We can control the polarization in the cavity by using a 2 mm long piezoelectric element to stress the fiber, with the compression axis rotated 45° relative to the axis of the PM fiber. This stress induced birefringence acts as a waveplate, which rotates the polarization of the light inside the laser. Figure 4.2 shows an oscilloscope trace of the piezo driving signal and corresponding optical pulse. Figure 4.3 shows a typical pulse trains and a typical pulse shape.
57
Figure 4.2. Square wave driving the piezoelectic transducer, and the ringing caused by the piezo being a capacitive element. The optical pulse is emitted when the induced birefringence allows the cavity to be dumped.
58
Figure 4.3. (a) Q-switched pulse chain, illustrating a consistent period defined by the piezo signal, and typical pulse-height variations. (b) Typical near-Gaussian pulse shape
59
4.3.1 Average Power output of the Q-Switched fiber laser To characterize the Q-switched laser, we varied the repetition rate of the square wave to the piezo over a wide range of values. Unlike passively Q-switched lasers, we were able to adjust the repetition rate. We were able to achieve Q-switching at a peak repetition rate of 700 KHz, which is significantly faster than other all-fiber actively Qswitched lasers. As can be seen in Figure 4.4, the average power measured with multiple power meters varied linearly with average power over approximately seven orders of magnitude, and displayed consistent performance at six different pump powers. We varied the pump power of the diode from 30 to 185 mW and characterized the performance, as shown in Figure 4.5. At high pump powers or low repetition rates, we observed parasitic pulses, multiple optical pulses for each electrical pulse of the piezo, which would be troublesome for sensing applications. By proper adjustment of the piezo offset and electrical signal, we were able to eliminate the parasitic pulses and maximize the power in the single pulse. In general, different settings of repetition rate and pump power required adjusting the offset and piezo signal to optimize performance.
60
Figure 4.4. Relatively linear increase in average power with increasing pulse repetition rate. The curve flattens out as the inversion starts to saturate.
61
Figure 4.5. Variation of average power with pump power, showing different slopes at different repetition rates.
62
4.3.2 Pulse width characterization of the Q-switched fiber laser We measured both pulse width and the deviation in the pulse width using a digital oscilloscope. The Q-switched fiber laser produced narrower pulses at lower repetition rates as shown in Fig. 4.6. However, below ~500 Hz there was little change in pulse width, as the gain media likely had time to saturate. Higher pumping power also led to narrower pulse widths as shown in Figure 4.7. The pulse-width dependence with the repetition rate was well fit by a quadratic across all pump powers tested. The shortest average pulse width was 18.8 ns, and occurred at 185mW pump power at a 5000 Hz repetition rate. The pulse width measurements had a relative standard deviation of 3.1% on average, indicating good pulse-width stability for this laser. We measured the average power of the laser with multiple fiber-coupled Newport integrating sphere detectors, and subtracted out the background pump and amplified spontaneous emission. The average power for the laser when Q-switching showed a roughly linear increase with repetition rate, and the slope efficiency also increased with repetition rate. However, the average power would saturate at high repetition rates. We interpret this as indicating that the usable inversion was saturated by the pulses, and further increases would likely result in little more useful power. The maximum average power was 31 mW, and occurred at the highest pump power 185mW and highest repetition rate 700 KHz tested. The efficiency of the Q-switched
63 laser increased with pump power, with a useful maximum slope efficiency, measured after the isolator and connector, of 22% at 185mW pump.
Figure 4.6. Variation of pulse width with repetition rate (points) and fit (lines).
64
Figure 4.7. Variation of pulse width with pump power, indicating that higher pump powers lead to shorter pulse widths.
65
4.3.3 Peak power performance of the fiber laser The peak power is often more important in fiber sensing and nonlinear generation applications than average power and pulse energy. The peak power can be calculated from the average power and pulse width, and also from a calibrated photodiode and oscilloscope. In this way, powers can be cross-correlated. 4.3.3.1 Calculating the peak power from empirically measured quantities To calculate the peak power from the average power and pulse width, we start by defining average power as the total energy divided by the time. P ave ≡
E t
(4.1)
Alternately, the energy can be thought of as the power integrated over time. For a pulse, the energy in the pulse is the power in the pulse integrated over one period, T. t =T
E=∫ P t dt E pulse =∫t =0 P t dt
(4.2)
If there is a single pulse in each period, as opposed to some more complex repeating pulse pattern, then the integration only needs to be carried out over the pulse width, and not the entire period. The average power will then be the energy received in a single pulse, divided by the time between the pulses. P ave =
1 t=t P t dt T ∫t=0 pw
(4.3)
66 It has become relatively common in research to then approximate the power in the pulse as roughly constant, essentially treating the output as a square pulse. For this case the power is equal to the maximum power when the pulse is on, and zero when the pulse is off. This leads to an approximation of the peak power that is relatively easy to calculate using an oscilloscope and a relatively slow power meter. P ave =
P max t pw T P max =P ave T t pw
(4.4)
The pulses from the Q-switched fiber laser were fairly well approximated in shape by Gaussian functions. Thus, by using a Gaussian shape instead of a square pulse, a more accurate analytic formula can be obtained. The average power effectively integrates the energy in the laser pulse over the period of one repetition rate. P ave =
1 P e − t dt T ∫ max 2
(4.5)
The pulses were well separated in time, allowing us to approximate the time duration of the repetition rate to be infinite for the purposes of integration. The peak power is constant, and can be moved outside the integral. We can then use the closedform solution for Gaussian integrals. P ave =
P max 1 T 2 2
(4.6)
On an oscilloscope, it is much easier to measure the full width at half maximum of the pulse, or FWHM. Thus, it is necessary to convert the formula into a
67 form in which the measured quantities can be directly entered. The first step is to set the value of the power at half width equal to half the power. − t 1 1 P t FWHM = P max e 2 2 2
2
FWHM
=1
2
(4.7)
Taking the log of both sides reduces the exponential, and eliminates the negative sign.
2 2 t FWHM =ln 2 t FWHM = ln 2 = ln 2 2 2 t FWHM
(4.8)
This can then be substituted back into the formula for average power. Also, the pulse repetition rate, which is the inverse of the pulse period, is the quantity set by the laser operator. This gives us the final form for the peak power of a Gaussian pulse. P max =
P Ave ln2 2 t FWHM f RR
(4.9)
In this formula, Pmax is the peak power, Pave is the average power, tFWHM is the temporal full-width at halfmaximum of the pulse, and fRR is the pulse repetition rate. This provides a more accurate approximation than if assuming the pulse is is rectangular. The peak power obtained using average power and pulse width generally agreed with the results obtained with the photodiode. 4.3.3.2 Characterization of the peak power Experimentally, the peak power was relatively constant below a repetition rate of 500 Hz, similar to the pulse width. However, the peak power decreased at higher repetition rates as shown in Figure 4.8. A shifted negative power law fit the repetition
68 rate versus peak power data better than various exponential and rational functions while maintaining a minimum of fitting coefficients. The variation of the peak power with the pump power was roughly linear as shown in Figure 4.9. The highest average peak power obtained was 13.6 W at a pump power of 185mW and a repetition rate of 100 Hz. The pulse energy of the laser followed a very similar pattern, with a shifted power law being an acceptable fit. The maximum average pulse energy was 0.4 J, which occurred at 185mW pump power and 200 Hz repetition rate.
69
Figure 4.8. Variation of peak power with pump power, illustrating near linear increase.
70
Figure 4.9. Variation of peak power with pulse repetition rate (points) and fit (curves).
71
4.3.4 Narrow linewidth spectral performance The compact cavity of the laser leads to single frequency behavior due to wide spacing of the longitudinal modes. We estimate the longitudinal mode spacing of our laser cavity to be 3 GHz. The large mode spacing of the cavity allows few modes in the reflection band of the narrowband grating, and suppresses the oscillation of multiple longitudinal modes. Similar lasers at different wavelengths have also demonstrated extremely narrow linewidths. Using an Optical Spectrum Analyzer, we observed the narrow linewidth and lack of sidebands, as shown in Figure 4.10.
Figure 4.10. Spectra from Q-switched laser. (a) Narrow-linewidth trace. (b) Wideband trace showing 980 nm pump, and sideband suppression.
72
4.4 Dual Q-switched fiber lasers using a single piezoelectric In addition to developing all-fiber actively Q-switched fiber lasers in the 1 µm region, we also further developed actively Q-switched fiber lasers in the 1.5 µm region, which is a typical telecom band. Using a single piezoelectric transducer to span two fibers, we demonstrated the first example of multiple, simultaneous all-fiber actively Q-switched lasers (Shi, et. al., 2007). We also produced the highest peak powers for all-fiber, actively Q-switched fiber lasers. In this way we were able to create single frequency pulsed laser sources that were correlated in time that could be used in THz generation.
73
CHAPTER 5:
OPTICAL FIBER AMPLIFIERS AND HIGH POWER OPTICAL FIBER LASER SYSTEMS
5.1 Motivation for Using Fiber Amplifiers Oscillators, in both photonics an electronics, have limited power. They require amplification to obtain the highest powers. Thus, it is common to have an oscillator, in this case a laser, seed an amplifier system which then increases the power to a more desirable level. The ease of constructing fiber amplifiers has made this the primary technique to achieve high powers in fiber laser systems. There are many reviews and books which cover fiber amplifiers. In addition to the books by Agrawal (2001, 2007), Desurvire provides an informative review (2001). This section will discuss the basic operational physics of optical amplifiers using fiber optics. Then, a computer model for the co-doped Er/Yb fiber we used in our fiber amplifier systems will be discussed. 5.2 Fundamentals of Optical Amplifiers
5.2.1 Amplifier Gain A fiber amplifier is a relatively simple device, consisting only of a length of active fiber, and some means of coupling in the pump light and the optical signal to be amplified. However, the high powers achieved by this simple design can lead to much
74 more complicated behavior. The theoretical development is adapted from Chapter 4 of Agrawal (2001). The small signal gain for a fiber amplifier will be the same as the small signal gain for a fiber laser, as discussed in chapter 3. It is defined in terms of cross section and inversion. g = N 1− N 2
(5.1)
Fiber lasers are largely homogeneously broadened. Thus, their gain coefficient can be written in terms of the peak gain, go, dipole relaxation time, T2, the atomic transition frequency, ωa, optical power of the signal being amplified, P, and the saturation power of the amplifier, Ps. In the unsaturated regime, the equation can be additionally simplified. g =
g =
go 2
(5.2) 2 2
1− a T P / P s go 1− a 2 T 22
(5.3)
For an amplifier with Lorentzian linewidth, the gain bandwidth will be inversely proportional to the dipole relaxation time. Similarly, the dipole relaxation time can be computed from the bandwidth. g =
g 1 1 2 = T 2= = 2 T 2 g g
(5.4)
In general, the signal power at any point along the amplifier will depend on both position and the frequency being amplified. The resulting differential equation
75 can be integrated, and assuming gain does not change along the length, an analytic expression is obtained. dP z , = g P z , dz P in G= =exp Pout
∫
(5.5)
L
g dz =e
0
g L
(5.6)
With this analytic expression the full-width half-max (FWHM) of the amplifier bandwidth can be computed. With G0 being the peak value of the gain, the amplifier bandwidth, υA, will be directly related to the small signal gain bandwidth. A= g
ln 2 ln G o−ln 2
(5.7)
When the pump light is directly on resonance the frequency-dependent term in equation 5.2 is eliminated. This permits setting up a simplified differential equation for the power. dP P =g o dz 1P / P s
(5.8)
This equation can then be integrated with the initial power being Pin and the output power being Gpin .
G=Go exp −
P out G−1 Ps G
(5.9)
Another useful quantity that can be computed from this is the output saturation power. This is the power at which the overall gain is reduced by a factor of two from
76 the unsaturated value, and provides a convenient number for indicating the power at which further pumping brings diminishing returns. P sout =
G o ln 2 P G o−2 s
(5.10)
5.2.2 Noise in fiber amplifiers By comparison to other types of amplifiers, fiber amplifiers are comparatively clean, and can have very low distortion of the input signal. However, like other amplifiers, optical fiber amplifiers do introduce some noise into the signal. This noise comes about through the process of spontaneous emission. The spontaneous emission factor is related to the optical inversion, and defined below. n sp=
N2 N 2− N 1
(5.11)
The amplifier noise can then be written as a product of the spontaneous emission factor. In the limiting case of high gain, it is just twice the spontaneous emission factor. F n = 2 nsp
G−1 ≈2 n sp G
(5.12)
This sets a limit for the noise of a fiber laser. For an ideal amplifier with nsp=1, the noise is still increased by a factor of two.
77 5.3 Modeling of Er/Yb co-doped large core active fiber amplifier
5.3.1 Er/Yb codoped fiber amplifier For high power amplifiers in the 1.5 µm band, the use of co-doped Er and Yb fibers has become a very useful option (Hu, et. al., 2001; Jeong, et. al., 2005; Li, 2005). The Yb ions efficiently absorb the 980 nm pump light, and then transfer the excitation to the Er ions, which then emit the light in the desired 1.5 µm band. A schematic for this process is depicted in figure 5.2. For the final stage of our amplifier used a specialized NP Photonics, Inc. phosphate glass fiber that permitted doping with high concentrations of Er and Yb. It also had a large core to increase the mode area, resulting in less chance of damage and nonlinear parasitic effects. The fiber also had a dual cladding design which permitted multimode pumping and also served to expand the effective mode area. The spectra of the fiber, showing strong Yb and Er bands, is shown in figure 5.1.
78
Figure 5.1. Spectra of large core fiber showing various absorption bands dominated by Er and Yb ions.
79
5.3.2 Rate equations for Er/Yb fiber The computational model was developed by Nguyen, et. al., and used to model a variety of Er/Yb fibers (2007). Nguyen mentions that there are typically there are two types of computer models commonly used to study active fiber for optical amplifiers. Beam propagation method (BPM) models are typically used to accurately calculate the propagation of light in a waveguide. Meanwhile, propagation and rate equation models (PREM) worked well for single-mode pumped fiber amplifiers. Nguyen developed an “effective beam propagation model” in which the propagation of the optical field is modeled by a BPM equation, while also at each step the gain is determined from the rate equations. It includes the Yb to Er transitions depicted in Figure 5.1, as well as the Er-Er transitions depicted in figure 5.2. The rate equations lay out the possible transitions that take place in the amplified fiber. The occupation of the energy levels are given by Ni, the transition rates by Wi, and lifetimes by τ. The double-energy transfer process between Yb and Er is represented by KD while KC describes the net effect of an excitation transfer and relaxation followed by the second excitation transfer. The rates for the upconversion process are given by C22 and C33. Cross-relaxation between levels 1 and 4 is given by C14.
80
Figure 5.2. Schematic of process in which an excitation from an excited Yb ion is transferred to an Er ion, and possible resulting transitions.
81
Figure 5.3. Er-Er ion interaction in which a neighboring excited ion absorbs an emitted photon, and then emits a higher energy photon through the parasitic process of upconversion.
82
For the emission of 1.5 µm light, the levels of primary interest are the ground state, level 1, and the first excited state, level 2. dN 1 1 =− W 12W 13 N 1 W 21 N 2C 22 N 22−C 14 N 1 N 4 21 dt 2 C 33 N 3 – K F N 1 N 6K C N 2 N 6 K D N 3 N 6
(5.13)
dN 2 N 1 =W 12 N 1− W 21 N 2 3 −2 C 22 N 222C14 N 1 N 4 dt 21 32 −K C N 2 N 6
(5.14)
The levels for optical pumping are also of large importance. These are given by level 3 for the Er ion and level 6 for the Yb ion. dN 3 N N =W 13 N 1− 3 4 −2 C 33 N 23K F N 1 N 6−K D N 3 N 6 32 43 dt
(5.15)
dN 6 1 =W 56 N 5− W 65 N – K F N 1 N 6− K C N 2 N 6 65 6 dt −K D N 3 N 6
(5.16)
The transitions to level 4 are largely parasitic processes that reduce the efficiency of the system. The transitions to and from this band take place through upconversion and cross-relaxation. dN 4 N =− 4 C 22 N 22C 33 N 23−C 14 N 1 N 4 43 dt
(5.17)
The transition rates for the other bands considered can be obtained from the approximation that each Er and Yb ion will be in one of these energy levels. N Er= N 1N 2 N 3N 4
(5.18)
N Yb =N 5N 6
(5.19)
83 The total concentration of Er and Yb ions is a design parameter, and assumed known. Thus, equations 5.13 through 5.19 give a complete and solvable set of equations for the energy levels considered. 5.3.3 Modeling for optimizing final amplifier stage This computational model was successfully used to help optimize the length of the fiber amplifier. In many amplifiers there is a rollover with length. As length of fiber is increased beyond an optimal point, the pumping of the fiber is not high enough to invert the fiber, resulting in absorption of signal light. The input pulses had a relatively high repetition rate compared to the absorption of the ions. Thus, the amplifier was modeled for a continuous wave input, which is generally a good approximation for Er/Yb amplifiers when the pulse repetition rate is above 10 KHz. The model predicted that a length of approximately 12 cm would be the optimal length for our setup. The amplifier produced powers very similar to those predicted by the model when accounting for splice loss (Shi et. al., 2007a; Leigh et. al., 2007a; Leigh 2007b).
84
Figure 5.4. Optimization of length for output power. Simulation was run with 30W of pump power and various powers of input pulses.
85
Figure 5.5. Optimization of length for signal gain. Simulation was run with 30W of pump power and various Er ion concentrations.
86
CHAPTER 6:
HIGH POWER AMPLIFIED FIBER LASER SYSTEMS
6.1 Introduction High power fiber lasers have generated a great deal of interest due to their many advantages over other high power lasers such as thermal management, efficiency, compactness, and fiber splices eliminating alignment. While fiber lasers are capable of general high power laser tasks such as machining, they are also capable of high precision tasks, such as gravitation wave detection (Hofer, et. al., 2001), and as reported in this dissertation, terahertz generation (Leigh et. al., 2008). We have developed high power fiber laser systems in the C-band by using a highly-doped phosphate glass fiber. The scientific results for this chapter were published and presented in Leigh, et. al., 2008a and Leigh, et. al., 2008b. 6.2 High power fiber lasers and amplifiers High power fiber laser systems are typically made by having a relatively low power laser oscillator, and then amplifying that initial laser. Both cw and pulsed high power systems can be made this way. Fiber lasers offer the possibility of power scaling by simply splicing a combiner to the end of the current fiber laser, adding diode pump lasers, and adding another section of active fiber. In this way, fiber lasers offer the possibility of easy, compact power scaling.
87 A common obstacle to the creation of fiber laser systems with both high quality and high power is the onset of nonlinearities which can greatly broaden the spectrum and modify the laser’s temporal properties, even in large-mode area fibers. The main nonlinearities that affect fiber lasers are Brullion scattering, Raman scattering, self-phase modulation, and self-focusing. Many methods have been developed to improve the quality of high power fiber lasers such as altering index profiles (Sahu, et. al., 2006), using photonic crystal fibers (Brooks and Di Teodord, 2006), and suppressing stimulated Brillouin scattering and stimulated Raman scattering (Weßels, et. al., 2004; Zenteno, et. al., 2005). Much of the research in single-mode high power fiber lasers has focused on the 1 µm region where Yb-doped fibers have reached kilowatt continuous wave (cw) powers (Jeong, et. al., 2004), and hundreds of watts with narrow linewidths (Gray, et. al., 2007). The high efficiency of Yb greatly eases the constraints of high-power fiber laser systems . 6.3 High power fiber lasers in the 1.5 µm region While much of the development of high powered fiber lasers has been in the 1 µm region, there is considerable interest in the 1.5 µm region, which is relatively eyesafe, and where there are many commercially available fiber components (Desmoulins, et. al., 2008; Alegria, et. al., 2004; Jeong, et. al., 2005; Codemard, et. al., 2006; Savage-Leuchs, et. al., 2006). The highest output power for a 1.5 µm fiber laser system was a multimode system that produced 1.2 MW peak power at 1567 nm with a
88 65 µm fiber, and an M2 of 8.5. Single mode 1.5 µm systems have produced cw powers of over 100 W with single frequency operation. Pulsed single mode fiber laser systems at 1.5 µm have produced millijoule pulse energies and peak powers of 170 kW, but without any report of single frequency output. These systems used silica fiber, which can be problematic as Er–Yb doping often requires additives that increase numerical aperture. Instead of using Er–Yb doped silica fiber, the amplifier had an Er–Yb doped phosphate glass fiber for the final power stage of our amplifier chain. Phosphate glass fibers have higher rare-earth ion solubility than silica fibers, thus enabling shorter systems with lower nonlinearities (Lee, et. al., 2006; Qiu, et. al., 2005; Shi, et. al., 2008). Phosphate glass also has other interesting properties, such as decreasing in optical index of refraction when densified with an ultrafast laser, as opposed to the increase in silica glass (Leigh, et. al., 2005). Phosphate fibers have previously been used to produce high cw power per unit length at 1 µm and 1.5 µm, as well as high peak pulse powers at 1.5 µm. By using a polarization maintaining (PM), double-clad, large core, highly Er–Yb doped phosphate fiber (LC-EYPF), we were able to create single frequency pulses at higher peak powers than previous single frequency systems. 6.4 Seed pulse generation systems The phosphate glass technology developed by NP Photonics has led the development of single-frequency fiber laser systems with very low noise. These provide excellent seed sources for amplified fiber laser systems. We used the
89 previously developed Q-switched fiber lasers, as well as using cw lasers that were modulated with electro-optic modulators to produce the seed pulses. 6.4.1 Amplified Q-switched seed pulses Initially, we used the dual-wavelength Q-switched seed lasers as the source for our fiber laser amplifier system. Because the Q-switched fiber lasers had very high input power they could saturate the amplifier stages, resulting in very small amplified stimulated emission (ASE). However, even though both Q-switched fiber lasers were driven by the same piezo, there was still significant jitter between the two pulses. Also, with the pulse widths over 10 ns, there was build-up of Brullion scattering. Thus, despite the successes of the amplified Q-switched fiber laser systems we looked for alternative pulse generation methods that had lower jitter and shorter pulse widths.
90
Figure 6.1. Seed pulse and fiber amplifier schematic for high-power pulsed fiber laser system
91
6.4.2 Seed pulses using electro-optic modulators and CW lasers Our master oscillator-power amplifier (MOPA) system consists of a singlefrequency, high stability cw seed laser, a seed pulse generation system, and a threestage amplifier system, as shown in Figure 6.1. The seed laser is an NP Photonics Inc. fiber laser that utilizes highly Er–Yb doped phosphate fibers, producing a single frequency with an extremely narrow linewidth of 2 kHz, providing an excellent seed source. Our seed laser has a wavelength of 1550.67 nm at up to 100 mW. The seed laser is spliced to a PM isolator, which is then spliced to the first electro-optic modulator (EOM) in the pulse generation system. The pulse generation system starts with an EOM to directly modulate the fiber laser. This is follwed by an Er doped preamplifier to boost the power of these pulses, and a narrow bandpass filter (featuring a PM circulator and fiber Bragg grating) for removing out-of-band amplified stimulated emission (ASE) generated by the amplifier. The fiber path is then spliced to a second EOM (time synchronized to the first EOM) to remove the inband ASE, increase the extinction ratio, and clean the pulse temporal profile. A lowfrequency electrical function generator triggers home-made pulse generators, which are capable of generating electrical pulses from 0.7 ns to 12 ns at repetition rates up to 38 MHz. These nanosecond electrical pulses are then fed into rf driver amps, providing the electrical signal to drive the EOMs, which then modulate the seed laser.
92 6.5 Fiber Amplifier System The output fiber from the second EOM was fusion spliced to an all-fiber chain of three amplifier stages separated by interstage commercial fiber-coupled PM bandpass filters (for ASE rejection), isolators, and fiber taps (for pulse shape, spectrum, and power diagnostics). The first amplifier stage consisted of 0.5 m of commercial, PM, Er-doped silica fiber with a 7 µm core, the second stage used 1 m of commercial, PM, double-clad Er–Yb codoped silica fiber, also with a 7 µm core, and the final stage being a PM large core Er/Yb doped phosphate fiber (LC-EYPF). 6.5.1 Performance of first two amplifier stages Using a chain of multiple amplifiers optimized the amplifier performance through improved ASE management and distribution of the thermal load (Wang, et. al., 2004), and the short lengths reduced nonlinear interactions. We used high power single mode pumps for the first stage, and multimode diodes for the pumping of the second stage, while keeping the pump power low enough to avoid visible nonlinearities. At 20 kHz, the system produced pulses with ~3.5 µJ of pulse energy, 70 mW of average power, and 356 W of peak power, with minimal pulse steeping and the linewidth was <50 MHz, providing a high quality input into the final stage of the amplifier chain.
93 6.5.2 Large Core Er-Yb doped Phosphate Glass Fiber for final stage The LC-EYPF fiber for the final power amplifier was designed and drawn inhouse using phosphate fiber technology developed by NP Photonics. The fiber has a 15 µm core, currently the largest core for a single mode phosphate fiber, with an outer diameter of 122 µm. The cross section of the fiber can be seen in Figure 6.2. The core is doped with 3.01×1020 cm−3 of Er3+ and 14.6×1020 cm−3 of Yb3+. The bulk glass had a core index of 1.5606, a cladding index of 1.5597, and a lifetime of 7.2 ms. In use, it was also coated with a high index coating, which acted as a second cladding, further contained the pump light. The fiber contains stress rods to produce a birefringence that maintains the polarization of the seed pulse. We used a length of 12 cm, which greatly reduces distortions compared to silica fiber amplifiers that can have lengths on the order of meters or tens of meters. One end of the 12 cm LC-EYPF was fusion spliced to commercial large core silica fiber, and then to its pump diodes and the second amplifier stage. The output end was angle-polished to reduce feedback. The fiber was co-pumped from the input end with multimode diodes, with a maximum total pump power for the final stage of 34 W.
94
Figure 6.2. Cross section of the LC-EYDF. The core size is 15 µm in diameter, with the dark, round objects being the stress rods.
95
6.5.3 Temporal performance of fiber amplifier system This pumping leads a large inversion of the final stage LC-EYPF, which also leads to pulse steepening due to gain compression. At lower powers of pump, 10 W and under, the pulse widths decreased relatively linearly with pump power. Meanwhile, above 10 W the pulse width gradually flattened out to 2–3 ns. Thus, for our MOPA system, in order to produce pulse widths at a few nanoseconds, it is necessary to start with pulse widths around 10 ns. 6.5.4 Power performance of fiber laser system To measure the power output of a laser, we used an Ophir PE9F-SH pyroelectric energy meter that handles pulse repetition rates up to 20 kHz. The detector measures only the pulsed output, eliminating cw components such as ASE, stray pump, and in-band cw. We also used a fast optical detector, digitizing oscilloscope, and Newport power meter as a second measurement source at repetition rates below 20 kHz, and to measure the power at higher repetition rates. Both types of measurements were in good agreement. To characterize the power amplifier system, we used the maximum pump of 34 W and varied the repetition rate from 500 Hz to 1 MHz, as shown in Figure 3.3. The highest peak power was 51.5 kW at a repetition rate of 5 kHz, which is an improvement by a factor of 12.6 over previous 1.5 µm single frequency pulsed fiber
96 lasers (Dilley, et. al., 2007; Shi, et. al., 2007; Shi, et. al., 2008). The highest average power was 1.66 W at 20 kHz. After setting the repetition rate to 5 kHz, we varied the pump power from 2 to 34 W. As shown in Figure 6.4, both the pulse energy and peak power curves were well fit by a three parameter logistic function. The lack of a pronounced rollover indicates that higher output powers are possible.
97
Figure 6.3. Peak power and average power as the repetition rate is varied. The peak power saturates below 5 Khz, while the average power saturates above 100 KHz.
98
Figure 6.4. Performance as a function of pump power. Peak power (points) and fit (line). Pulse energy (triangles) and fit (line).
99
6.6 Beam quality for fiber laser amplifier system In fiber amplifier systems for THz generation it is important to not only generate high power, but to achieve high power while keeping the linewidth narrow and maintaining a single spatial mode. For THz conversion, poor mode and spectral quality decreases efficiency and can unnecessarily heat the nonlinear crystal. The spectrum was measured with an optical spectrum analyzer, and we observed sideband suppression of ~40 dB. The sideband was likely generated by residual ASE in the amplifiers. The beam maintained excellent single mode output, with an M2 of ~1.2 in each direction as measured by a commercial beam profile apparatus. This is important for collimating and focusing the fiber laser output for free-space applications. While using larger mode areas and permitting lower beam quality can certainly increase power, it will also lead to a beam that is not able to focus as tightly. The linewidth was estimated by using a scanning Fabry-Pérot interferometer with a 1.001 GHz free spectral range (FSR) and a digitizing oscilloscope, as shown in Figure 6.7 and 6.8. We determined the linewidth from the FSR of the Fabry-Pérot and the envelope width of the interference fringes (Zadler,et. al., 2005; Leigh, et. al., 2007) . For small pump powers and a final pulse width of 9.82 ns, the linewidth was 50 MHz, but broadened to 500 MHz when the pulse was compressed to 2.1 ns at higher pump powers. The resulting time-bandwidth products varied from 0.5 to 1, indicating near-transform limited linewidth.
100
Figure 6.5. Beam quality measurements (points) and fit (lines) in orthogonal directions. The beam showed good mode quality and the overlapping points indicate excellent symmetry.
101
Figure 6.6. OSA scan of fiber amplifier system output, demonstrating nearly 40dB of sideband suppression.
102
Figure 6.7. Measurement of linewidth using a Fabry-perot cavity. The width of the envelope is compared against the spacing of the lines. The individual fringes are spaced by the pulse repetition rate of the laser.
103
Figure 6.8. Oscilloscope trace in persistent mode showing Fabry-Perot piezo signal and fiber laser envelope.
104
6.7 Summary of amplified fiber laser system We used a PM, highly doped, large core phosphate glass fiber to produce 51.5 kW single frequency 1.5 µm pulses, demonstrating a significant improvement in performance over previous narrowband amplified fiber laser systems. The performance of our demonstrated source is of special interest for nonlinear wavelength conversion, which generally requires a pump beam of high peak power and spectral brightness, linear polarization, and excellent beam quality.
105
CHAPTER 7:
TECHNOLOGICAL DEVELOPMENTS IN THE TERAHERTZ ELECTROMAGNETIC FREQUENCY REGION
7.1 Introduction
7.1.1 Motivation The development of Q-switched fiber lasers and amplified fiber laser systems are valuable research directions. However, there is a variety of such systems available both commercially and in multiple labs. Meanwhile, in the terahertz region there is a lack of high power, narrowband sources. High quality, narrow bandwidth fiber lasers are ideal for developing compact, narrow-linewidth THz sources as they combine high power and high purity with compact size. 7.1.2 Chapter overview A brief overview of terahertz technology was given in Chapter 1. This chapter will review THz sources in greater depth. Reviews on various aspects of THz sources have been written by Smye, et. al., (2001), Ferguson and Zhang (2002), Kimmitt (2003), Williams (2006), Hoffmann and Hoffman (2007a), Thomson, et. al., (2007), Tonouchi (2007), and Vodopyanov (2008). Since terahertz is a rapidly developing field, the “state of the art” is in a period of rapid improvement.
106 7.2 Terahertz Generation
7.2.1 Terahertz Sources using RF Electronics Electronic implementations of THz sources have been limited by the ability of electronics to operate at THz frequencies. Metals and semiconductors tend to absorb THz radiation, making the generation of THz from these devices problematic (Kimmitt, 2003; Williams, 2006; Tonouchi, 2007) . There have been some advances in electronically generated THz by using novel materials. Diamond grown by chemical vapor deposition has been pursued by various groups due to the large thermal conductivity and other unique aspects of diamond (Chen, et. al., 2003; Gurbuz, et. al., 2005; Suzuki, et. al., 2006). Carbon nanotubes also have promise as possible THz sources (Wang, et. al., 2008). However, electrical solutions are still much lower power than optical sources, especially as the frequency goes above 1 THz (Tonouchi, 2007).
107
Figure 7.1. Schematic of a THZ source using a photoconductive switch with interdigitated electrodes. (Grün, 2005, Creative Commons image.)
7.2.2 Terahertz pulses using ultrashort pulses As previously mentioned, ultrashort pulses are currently the most common method for generating THz. Most methods of ultrashort THz pulse generation use an ultrafast laser with interdigitated electrodes (e. g. Mittleman, et. al., 1999), as depicted in figure 7.1. There have also been other advances in ultrafast THz generation, such as using tilted pulse fronts (Hebling, et. al., 2002; Stepanov, et. al., 2005), using a linear focal point through a cylindrical lens, (Stepanov, et. al., 2005a), optical filimentation and plasma generation (D'Amico, et. al., 2007; Thompson, et. al., 2007) and using optical rectification in a variety of specialized crystals (Vodopyanov, et. al., 2006;
108 Blanchard, et. al., 2007; Hoffmann, et. al., 2007b; Ascazubi, et. al., 2005; Löffler, et. al., 2005). Ultrashort pulses have some large advantages in terahertz generation. They are able to pack a high peak power into a low average power, resulting in terahertz generation without significant heating. Ultrashort pulses are useful for terahertz time resolved spectroscopy as their short temporal length allows for high resolution. This property has been used in various forms of terahertz imaging to obtain thicknesses. However, the short pulse widths have high spectral bandwidth. The high number of atmospheric absorption bands in the THz region indicate that much of the light of a broadband source would be absorbed in the atmosphere. It is possible that a narrow band source optimized for a transmission band would be more effective in these applications. 7.2.3 Terahertz Sources using nanosecond pulses Nanosecond pulse terahertz sources are typically generated with solid state Qswitched lasers. These have been quite successful with Q-switched lasers generating up to 389 watts of peak power (Shi and Ding, 2006). While these setups do not have the high peak power of ultrafast pulses, the pulses do possess a higher energy. Thus nanosecond pulsed terahertz sources may be better suited to terahertz machining, terahertz surgery, and terahertz lidar than femtosecond sources.
109 7.2.4 Terahertz Sources using quantum cascade lasers Semiconductor diode lasers have been an extremely important advance in lasers. They have provided high efficiency, high power, small size, and are much more economical when compared to other lasers both in cost per watt of output, and in total operating cost over laser lifetime. These are desirable attributes for a terahertz source. However, laser diodes perform best in the near IR. As the wavelengths increase to far IR and terahertz wavelengths, standard laser diodes are effectively useless. Quantum cascade lasers have been developed to address effective diode lasers in the mid and far IR. However, to reach terahertz wavelengths, QCLs still require extensive cooling (Ferguson and Zhang, 2002; Nguyen, et. al. 2006). Despite the cooling limitation, quantum cascade lasers have been successfully used in terahertz imaging systems (Darmo, et. al., 2004; Chamberlin, et. al., 2005; Lu, et. al., 2005; Bründermann, et. al., 2006; Behnken et. al., 2008). Further efforts have also produced narrower bandwidths (Marshall, et. al., 2008), lower frequencies (Worrall, et. al., 2006; Scalari, et. al., 2006) and higher operational temperatures (Williams, et. al., 2003). The development of intercavity difference frequency generation (Belkin et. al., 2007) will likely prove to be a significant advance in developing more practical quantum cascade lasers for terahertz generation. An alternative and promising solution for diode-based THz generation is development of p-Ge THz lasers (Bergner, et. al., 2005). This type of laser has achieved a peak power of 10 W (Muravjov, et. al., 2008). Further, the demonstrated
110 emission frequency range is fairly decent, with emission from 1.5 to 4.3 THz (Tonouchi, 2007). Though these sources are still rare, they appear to be very interesting from a technological perspective due to their high power. 7.3 Generation of Terahertz Using Difference Frequency Generation
7.3.1 Crystals for difference frequency generation Most nanosecond sources of terahertz radiation use difference frequency generation or optical rectification in a nonlinear crystal to generate terahertz radiation. To select an optimized crystal, it can be convenient to use a figure of merit. Vodopyanov (2007) suggests a figure of merit involving the effective nonlinear coefficient, deff, the absorption at the terahertz wavelength, αTHz , and the index of refraction nopt. d 2eff FOM = 2 nopt THz
(7.1)
Shi and Ding have improved on this figure of merit by more heavily weighting index of refraction and absorption. d 2eff FOM = 3 2 n opt THz
(7.2)
The second index of refraction has been found to be more useful in crystal selection. Other considerations for selecting a crystal include its damage threshold, its absorption at the pump wavelength, its optical quality, and its thermal conductivity.
111 7.3.2 Phase matching For difference frequency generation, different crystals will require different polarizations and angles (Milonni and Eberly, 1988; Boyd, 1992). A uniaxial crystal will have two different indices of refraction depending on the propagation direction in the crystal. For positive uniaxial crystals, such as ZnGeP2, the two types of phase matching (type I and type II) are given by (Shi, et al., 2002): Type I :
no 3 n e 2, ne 1, − = 3 2 1
(7.3)
Type II :
n o 3 ne 2, n o 1 − = 3 2 1
(7.4)
For these phase matching conditions λ3 is the pump wavelength, λ2 is the signal wavelength, while λ1 is the terahertz signal. A similar expression can be written for negative uniaxial crystals, in which the extraordinary index is less than the ordinary index. Type I :
ne 3 no 2, no 1, − = 3 2 1
(7.5)
Type II :
ne 3 n o 2, n e 1 − = 3 2 1
(7.6)
A photon going through the crystal at an arbitrary polarization and angle will see an index of refraction that is a combination of both the ordinary and extraordinary index. n e , =ne
n o
n sin n cos 2 o
2
2 e
2
(7.7)
112 Similarly, the effective nonlinear coefficient will vary depending on the angle. For type I and type II phase matching in ZnGeP2 the effective nonlinear coefficients are given below. Adjusting the angle will have a large effect on the output power. Type I :
oe−e
d eff
=d 36 sin 2 cos 2
oe−o
Type II : d eff
=d 36 sin cos 2
(7.8) (7.9)
The efficiency of the conversion process will depend on the length of the crystal, the effective nonlinear coefficients, P3 is the power at the pump wavelength, wo is the beam waist, and λ1 is the ouput THz wavelength. L2 P 3 4 d2 o c n1 n2 n 3 21 w 2o eff
=
(7.10)
7.3.3 Backward THz generation While difference frequency generation is usually performed in the forward direction, it can also be performed in the backward direction through proper phase matching (Shi and Ding, 2005). In this case, GaSe, a negative uniaxial crystal, was used as the nonlinear crystal. The phase matching was type II with a negative direction for the THz. The effective nonlinear coefficient for this case dictates different angles to maximize the effective nonlinear coefficient. ne 3 no 2, ne 1 − =− 3 2 1 2
d eff =d 22 cos sin 3
(7.11) (7.12)
113 Backwards THz generation is less efficient than forward generation. However, due to the high pump power of the solid-state laser and good alignment, a peak THz power of 217 W was obtained in this way, and the output wavelength was tuned from 167.6 µm to 2060 µm. Shi and Ding also derived analytic forms for the output THz power, and the threshold intensity for backward parametric generation.
4 PI wP
P THz =
i
THz
o
I th= THz i
p
th
e
i 2 i
(7.13) e
n i nTHz n p 2 2 8 o d eff L
(7.14)
114
CHAPTER 8:
TERAHERTZ GENERATION WITH FIBER LASERS
8.1 Chapter Overview As discussed earlier, there have been a variety of methods used to generate THz radiation. The two principal approaches to generate THz are photonic approaches, and electrical approaches. Photonic approaches use lasers and optics to generate the radiation, whereas electrical methods try to frequency-scale current radiofrequency electronic methods. The optical sources can be further divided into fiberbased THz sources, and nonfiber THz sources. This chapter reports the development of a fiber-based system for THz generation. The results for this chapter were published and presented in Leigh, et. al. (2008, 2008a), and Shi, et. al. (2008a). 8.2 Fiber sources of THz radiation Both fiber lasers and terahertz technology are relatively recent developments. Thus, very few groups have developed fiber-based terahertz sources. Because the core size of optical fiber is much smaller than the ~mm wavelength of THz radiation, no one has reported a fiber source that directly generates THz radiation. Instead, groups have used fiber lasers as replacements for benchtop lasers (Reimann, 2007), using methods such as photoconduction (e.g. Sigmund, et. al., 2005) and difference frequency generation (e. g. Ding and Shi, 2006a).
115 Groups using fiber lasers in the 1 µm region have produced pulsed THz using both fs and ps pulse widths. Groups have also reported generating THz with ultrafast fiber lasers in the eyesafe 1.5 and 2 µm wavelength regions. Narrowband fiber laser pumped THz sources are rare, due in part to the competing requirements of high power, single frequency and single mode. Table 8.1 summarizes various papers.
116
Table 8.1: Table of fiber-based THz sources in reverse chronological order. Peak emission is graphically estimated where it is not explicitly stated. Fiber laser Seed Pulse Estimated Peak Pulse Width Reference region [µm] Generation Emission [THz] [ns] Leigh, et. al., 2008b
1.5
Electro-optic Modulator
1.49
2.5 ns
Shi, et. al., 2007b
1.5
Electro-Optic Modulator
0.27
20 ns
Chang, et. al., 2007b
1
Ultrafast
0.6
110 fs
Shi, et. al., 2007a
1.5
Q-switched
1.5
2.03 ns
Creeden, et. al., 2007
1
Gainswitched Diode
2.45
500 ps
Chang, et. al., 2007a
1
Ultrafast
0.7
300 fs
Chang, et. al., 2006
1
Ultrafast
0.7
210 fs
Imeshev, et. al., 2006
2
Ultrafast
2
120 fs
Nagai, et. al., 2004
1.5
Ultrafast
2
150 fs
Sasaki, et. al., 2004
1.5
Gainswitched diode
1.5
100 ps
117 Eyesafe fiber lasers are desirable for commercial applications due to the much improved safety factor, as broken fibers or misaligned optics will not create a reflection that can damage the operator's vision. However, the 1 µm laser region is too short to be eyesafe (Spuler and Mayor, 2007). Also, most nonlinear crystals absorb more at 1 µm than at the longer eyesafe wavelengths, making the development of eyesafe fiber sources potentially more efficient at THz generation. Eyesafe fiber laser-pumped THz sources have been built using 1.5 µm lasers in the telecom C-band, and also at the 2 µm wavelength region, which is viewed as a region of great future interest in fiber lasers (Wu, 2005). However, outside of our research group, all reports of fiber lasers in the eyesafe range used to pump THz have been broadband sources. The performance of narrowband fiber-based THz sources are summarized in table 8.2. Some quantities were calculated using a “square pulse” approximation, as the values were not reported directly. One paper only reported relative intensities, making the power impossible to calculate, though it is likely that it had lower power than the other papers.
118
Paper
Table 8.2: Reverse chronological table of THz sources pumped by eyesafe wavelength fiber lasers. THz Peak THz Average THz Pulse Repetition Power Power Energy Rate
Type
Leigh, et. al., 2008b
26.4 mW
1.32 µW
66 pJ
20 KHz
Narrowband
Shi, et. al., 2007b
48.1 µW
38.5 nW
963 fJ
40 KHz
Narrowband
Shi, et. al., 2007a
530 µW
430 nW
10.8 pJ
40 KHz
Narrowband
Imeshev, et. al., 2006
275 mW
3.3 µW
33 fJ
100 MHz
Broadband
Nagai, et. al., 2004
N/A
N/A
N/A
50 MHz
Broadband
Sasaki, et. al., 2004
100 µW
10 nW
10 fJ
1 MHz
Broadband
119
8.3 Terahertz generation system
8.3.1 Overview The terahertz generation system consisted of two basic parts. The first part was the fiber laser amplifier system, and the second part was the nonlinear crystal system, in which the generation actually took place. 8.3.2 Single Frequency Fiber Laser System The master oscillator power amplifier (MOPA) system is seeded by two NP Photonics, Inc. single-frequency fiber lasers, which can have linewidths of less than 2 KHz, low noise, and high stability (Spiegelberg, et. al., 2004). The fiber lasers have a complete monolithic fiber construction with a short phosphate glass gain region spliced to fiber gratings, unlike fiber-stabilized diode lasers in which the cavity includes the diode-fiber coupling (Creeden, et. al., 2007). The basic cavity design has also been used to produce monolithic single frequency Q-Switched fiber lasers at various wavelengths (Kaneda, et. al., 2005; Leigh, et. al., 2007; Shi, et. al., 2007, 2007a). 8.3.2.1 Pulse Generation system These seed lasers are modulated by fiber-coupled electro-optic modulators (EOMs), as shown in figure 8.1, and similar to previous high-power single frequency
120 fiber laser systems. The EOMs are chosen for high extinction ratio, PM outputs, and high power handling capability. The EOMS have a 10 GHz bandwidth, and permit independent adjustment of pulse width and repetition rate. The first EOM chops the cw optical signal from the seed laser into ~ns optical pulses, with the pulse shape and timing defined by the electrical system. These optical pulses are amplified by an erbium doped fiber pre-amplifier, and filtered by a narrowband ~0.3 nm filter to remove Amplified Spontaneous Emission (ASE). The trigger pulse for the second EOM is timed to coincide with the arrival of the pulse, eliminating in-band ASE. The two seed laser wavelengths were chosen to be 1538.63 nm and 1550.50 nm, which is in the optical communications C-band. Compared with fiber lasers in the 1 µm region, the 1500 nm region has advantages for THz generation by difference frequency generation. One advantage of using C-band pumping is that it has approximately one third the quantum defect of 1 µm when generating terahertz radiation. Another advantage is that it has lower absorption in most nonlinear crystals.
121
Figure 8.1. Schematic of the pulse generation system. The electrical generation system is in blue, while the optical train is in yellow.
122
8.3.2.2 Pulse Amplifiers Both of the pulses were amplified through separate two-stage amplifier channels, as shown in figure 8.2. Filters and isolators helped to maintain the spectral quality of the beam, and fiber-coupled taps were spliced between each stage to both check the spectra and temporal profile of the pulse. To suppress the nonlinearities common in fiber lasers, short lengths of 50cm were used for the active fiber in each stage. Each wavelength was then combined into a single fiber using a fiber-spliced polarization beam combiner. As power increases, it becomes more important to use short lengths and large cores to suppress nonlinearities. For the final stage amplifier we used a large core codoped phosphate glass fiber that had 3% Er and 15% Yb by weight. This allowed us to realize high gain while keeping the fiber length to only 12 cm. This was computed to be the optimal length using the “effective beam propagation method,” as discussed in chapter 5 (Nguyen, et. al., 2007). This fiber is one to two orders of magnitude shorter than amplifiers using silica fiber, limiting nonlinearities and realizing a compact system. The core size was 15 µm, which is the largest core for single mode polarization maintaining phosphate glass fibers. The fiber was end polished to help reduce feedback and decrease the chance of end damage.
123
Figure 8.2. Pulse amplification and THz generation system. The system starts with a pre-amp (1), isolator (I), and filter (F). This is followed by another amp (2), isolator, and filter. These beams are then combined in the beam combiner, before entering the final amplification stage. The pulses are then filtered and focused on the crystal, and the resultant THz light is detected by the bolometer.
124
8.3.3 THz Generation and Detection We chose z-cut 15 mm thick GaSe as our nonlinear crystal because it has low absorption in the C-band, has a relatively high nonlinear coefficient of d22=54 pm/V, and has been used to generate THz power up to 389 W. GaSe is a positive uniaxial crystal, requiring type I phase matching with crossed polarizations. no 3 n e 2, n e 1 − = 3 2 1
(8.1)
In this configuration, the 1538 nm was the pump with o-polarization, while both the 1550 and the THz had e-polarization. We set the crystal at a phase matching angle of 15°, which agreed well with the theoretical value of 14.8°, and set the azimuthal angle to satisfy |cos3φ|=1 to maximize the emission. 2
d eff =d 22 cos cos3
(8.2)
∣cos3 ∣=1 =0,±30,±60,±90
(8.3)
To separate the THz output from the residual 1538 and 1550nm laser light we used a black polyethylene filter. A picarin lens focused the generated THz into an liquid He cooled bolometer made by IR Labs, Inc. The output was measured by using a lock-in detector and optical chopper.
125 8.4 Results of THz generation using pulsed amplifier system
8.4.1 Performance of dual wavelength fiber amplifier For the fiber laser system we used a pulse repetition rate of 20 KHz, which provided a good balance of high peak power and sufficient average power. Narrow linewidth operation was verified with a fiber fabry-perot interferometer. We estimated a pump linewidth of less than 400 MHz at higher pump powers with a 2 ns pulse width, demonstrating transform-limited operation (Zadler, et. al., 2005; Leigh, et. al. 2007). As shown in figure 8.3, the average power of the fiber laser system increased quite linearly with pump power, reaching 1.66W at maximum pumping. The peak power increased in a roughly Gaussian manner with pump power, reaching a 33.2 KW maximum. Figure 8.4 shows the plotted results. While the onset of rollover for peak power was observed, it was incomplete, indicating that increasing the pump power will likely lead to higher peak fiber laser power.
126
Figure 8.3. Dual-wavelength fiber laser average power. It shows a roughly linear profile with very little roll-over.
127
Figure 8.4. Dual Wavelength fiber laser power as a function of diode pump.
128
8.4.2 Performance of THz generation The calculated wavelength for the THz radiation was 1.49 THz, which agreed well with the wavelength measured with a metal grating fabry-perot of 1.5 THz. The linewidth of the generated THz is determined by the linewidth of the pumping laser and the nature of the THz process, producing a transform-limited linewidth of <400 MHz. The average power of the THz generation system showed a strong quadratic dependence on the fiber laser power, as shown in figure 8.5. The straight line on the log-log plot is a quadratic fit to the data. This is to be expected since difference frequency generation is a second-order nonlinear process, and thus will be related quadratically to power. Peak power had a similar quadratic dependence, as shown in figure 8.6. We achieved a peak power of 26.4 mW, corresponding to an average power of 1.32 µW. This is a factor of over 49 times more than previous results for narrowband THz sources pumped by eyesafe lasers. The power conversion efficiency for the THz generation was 8 x 10-7, and the photon conversion efficiency was at least 1 x 10-4. The GaSe crystal used for the DFG was uncooled, and the fiber amplifier did not use liquid or thermoelectric cooling, only requiring forced air, and indicating the efficiency of the system.
129
Figure 8.5. Quadratic dependence of THz Average power on fiber laser power.
130
Figure 8.6. Dependence of THz peak power on fiber laser power.
131
8.5 Summary of THz generation We developed the highest power THz source pumped by an eyesafe, narrowband fiber laser system, with an output of 26.4 mW. Further improvements could be realized through the development of phosphate fibers with larger cores for the final amplifier stage, and higher pumping. This system shows the potential of developing narrowband fiber-laser pumped THz systems that would be more portable and robust than solid-state pumped THz generation systems, perhaps leading to THz sources that can be used for trace-level hazardous materials due to its high spectral resolution.
132
CHAPTER 9:
CONCLUSION
9.1 Summary of research results There were many significant results in the field of fiber optics that were accomplished in the course of the research reported in this dissertation. These developments will be a significant aid in the development of high power, high purity fiber laser systems. First were the developments in actively Q-switched fiber lasers, a field in which there have been few reported demonstrations, papers, and presentations. I used a recently developed technique to Q-switch fiber lasers, and then greatly extended the repetition rates possible in these lasers. This was done through constructing a specialized electrical amplifier capable of sinking the large amounts of currents needed when putting high voltage into almost purely capacitive elements at high frequencies. Our research group also greatly improved the mechanical stability of this class of Q-switched fiber lasers, which also resulted in much better control over the pulsing characteristics of this type of laser. We were then able to demonstrate new wavelengths for actively Q-switched fiber lasers, higher powers, and multiple fibers being simultaneously Q-switched. Second were the developments in high power pulsed fiber laser systems in which an EOM was used as the active modulating element, followed by amplifier stages. By starting with a single frequency fiber laser, the use of spectral filtering, and
133 using a second EOM we were able to maintain a narrow bandwidth. Then, by using a unique Er/Yb co-doped phosphate fiber, we were able to generate higher narrowband powers than other fiber laser systems. The techniques we used can be applied to other types and frequencies of fiber laser systems, resulting in increased power and decreased linewidth. The short length of the fiber amplifiers also makes more compact systems possible. Third, we developed terahertz sources using fiber lasers as the pump. There are relatively few groups developing fiber laser-based THz systems with narrow bandwidth due to the conflicting requirements of narrow linewidth and high power. In developing a system in which both high power and narrow linewidth were achieved, it indicates an effective direction for those developing THz systems. Moving in the direction of higher spectral quality also opens up different THz applications than moving in the direction of “power at all costs.” By achieving 26 mW of peak THz power in a collimated beam it is possible to demonstrate interesting THz applications with this system. 9.2 Future research and development directions While much has been accomplished, there is still a great deal of headroom for future research. There are also many technical details to work out in the development of higher powers, higher purity, and using these systems in developing new methods for scientific quantization and analysis.
134 For Q-switched lasers, there are a number of new wavelengths that would be interesting to investigate, such as those in the 2 µm area. Further development of high powers in the 1 µm area would also be of interest, as time and resources did not permit the development of higher power actively Q-switched 1 µm lasers. Both of these bands offer the advantage of higher efficiency than the 1.5 µm band, with the 2 µm band also having the advantage of being an eyesafe wavelength. Also, when multiple fibers were simultaneously Q-switched, the 2 fibers were relatively close in wavelength. Interesting sensing applications could be developed for a system with narrowband 1 µm, 1.5 µm, and 2 µm lasers that were simultaneously Q-switched. There are also many improvements that could be made to the pulsed EOM and fiber amplifier system. Phosphate fibers with larger cores and lower losses would be very useful in producing higher powers. Also, phosphate fibers are very difficult to splice to silica fibers due to the differences in melting point. By polishing the silica fiber the reliability of the splice would be greatly improved, there would be a significant reduction in losses due to scatter at the silica/phosphate splice, and the launching condition would be improved. Also, the amplifier temporally distorts the pulse profile due to gain saturation. By preshaping the pulse instead of using a square pulse, the final output pulse could be near-Gaussian, possibly narrowing the linewidth. There are also improvements that can be made to the THz system. A fundamental problem of THz generation by difference frequency generation is the energy lost due to the quantum defect. By using a longer wavelength, such as 2 µm, this defect can be decreased. Further, longer wavelengths also have less loss in many
135 nonlinear crystals. As developments continue in 2 µm fiber lasers and components, it will likely become a promising option. 9.3 Frontiers in narrowband fiber lasers and terahertz There are many scientific uses for compact, high-efficiency, narrow linewidth, high power pulsed fiber laser systems. The continuing development of these sources is an important area of research. A key to these systems is concentrating large powers in small fiber cores while minimizing nonlinear effects. While the fiber lasers were used to generate THz radiation in this project, there is also great potential for fiber lasers in LIDAR and space-based laser systems. Terahertz also has huge potential for scientific uses. While these preliminary results demonstrated successful generation, there are multiple ways to increase the output power. Larger core fibers, higher diode pump powers, and enhancement cavities are all ways to increase the power of the THz radiation. These developments can lead to high power THz applications in trace gas detection and medical processing.
136
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