LASERS Introduction In the interference of light we have used the term coherence between two sources of light. The two sources are coherent, when they vibrate in the same phase (or) constant phase difference. We know that light comes from a source comes as the sum of total radiations by billions and billions of atoms or molecules in the source. The phase is different at different times. Now, the question is that to what extent may the radiation from different atoms of a given source be related in phase in direction of emission and in polarization ie the coherence of a given source .In recent years, some sources are developed which are highly coherent. These sources are called LASERS. The word LASER stands for Light Amplification by Stimulated Emission of Radiation. The theoretical basis for the development of laser was provided by Albert Einstein in1917. In 1954, the prediction of Einstein was put to practical use by C.H. Townes and his co-workers. In 1960, the first laser device was developed by T.H.Maiman. It is often called as Ruby laser. The ruby laser emits red light of wavelengths 694.3 nm. Soon after, it is called Helium-Neon laser. It emits visible light at wavelength 632.8 nm. and also in Infrared region at 1150 nm. with the advancement of technology, laser has revolutionized the world of industry and technology. Characteristics of laser: (1) Monochromanicity: In laser radiation, all photons emitted between discrete energy levels will have same wavelength. As a result, the radiation is monochromatic in nature. If the higher energy level has closely spaced energy levels then from the transition from each level to lower energy level emits photons of different frequencies and wavelengths. Let the spread in frequency and wavelength be and .The frequency spread is related to its wavelength spread as c = 2 For lasers =0.001 nm. It is clear that laser radiation is highly monochromatic. (2) Directionality: In ordinary light, divergence of light takes place as it propagates through the medium. For laser radiation also, this divergence takes place as it propagates through the medium. The laser light of wavelength emerges through a laser source aperture diameter d, then it propagates as a parallel beam up to d 2 / (small value) and gets d d1 diverged. The angle of divergence of a laser beam is expressed as 2 s 2 s1 Where d1 d 2 are the diameters of the laser spots measured at distances s 1 and s 2 from the laser aperture. For laser light 103 radians. It is clear from the above value that the divergence is low and it is highly directional. Prepared by SHANKER RAO GATTU, (9949435575)
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(3) Coherence: Coherence is the property of a wave being in phase with itself and also with another wave over a period of time, and space or distance. Coherence is the predictability of the amplitude and phase at any point on the wave knowing the amplitude and phase at any point either on the same wave or on a neighbouring wave. Coherence is two types. Temporal coherence: If it is possible to predict the amplitude and phase at a point on the wave with respect to another point on the same wave, then the wave is in temporal coherence. i.e. if we know the phase and amplitude at any point is known, we can calculate the same for any other point on the same wave by using the wave equation. For laser radiation, as all the emitted photons (waves) are in phase, the result radiation has temporal coherence.
Spatial coherence: If it is possible to predict the amplitude and phase at a point on a wave with respect to another point on a second wave then the wave are said to be spacially coherence. The emitted photons (waves) in the laser radiation satisfies coherence. Thus, laser radiation is highly coherence. (4) Intensity: Let there be ‘n’ number of coherent photons of amplitude ‘a’ in the emitted laser radiation. These photons reinforce with each other and the amplitude of the resulting wave becomes na and hence the intensity is proportional to
n 2 a 2 . Thus, due to coherent additions of amplitude and negligible divergence the intensity or brightness increases enormously. Energy states of atoms: (i) Ground state; It is the lowest possible energy state of an atom which has the most stable state. Atoms can remain in this state for unlimited time. (ii) Excited state: These are the possible energy states of an atom which are higher than the ground state. Atoms remain in such energy states for short time called life time typically of the order of 10-8 s. (iii)Metastable state: These are excited states of an atom which relatively larger life times of the order of 10-3 s. As these energy states are neither as stable as ground state nor as unstable as the other excited states, they are known as metastable states.
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Absorption of radiation: Let us consider two energy levels 1 & 2 of an atom with energies E1 & E2. Let the atom is initially in lower state 1. Now the atom is exposed to light radiation of energy hν. Then the atom will excited to level 2. In this process, the absorption of energy from external field takes place. The provided photon energy hν must be equal to the energy difference of E1 & E2. Spontaneous emission: Let us consider the atom already in excited state E2. This state is not a stable state. So after a short interval of time 10-8 sec. the atom jumps back to ground state E1 by emitting a photon of frequency ν. This type of emission is called as spontaneous emission. “The emission which takes place without external incitement is called spontaneous emission.” Stimulated emission: Suppose an atom is already in the excited state of energy level E2, whose ground level energy is E1. At this moment if a photon of energy hν = E2 -E1 is incident on the excited atom, the incident photon stimulates the excited atom. Now transition takes place much sooner than 10-8 sec. “The process of speeding up the atomic transition from the excited state to lower state is called stimulated emission.” Spontaneous emission 1. Emission of light photon after 10 - 8 sec 2. Poly chromatic 3. No incident photon required. 4. Single photon emitted. 5. Incoherent radiation. 6. Less intensity. 7. Less directionality and more angular spread. 8. This was proposed by Bohr.
Stimulated emission 1. Emission of photon much sooner than10-8 sec 2.Monochrmatic 3. Incident photon is required it’s energy is E = E1 - E2 4. Two photons of same energy emitted. 5.Coherent radiation 6. High intensity. 7. High directionality and less angular spread. 8. It was proposed by Einstein.
Einstein coefficients: The probable rate of occurrence of the absorption transition from state 1 to state 2 depends on the properties of states 1 and 2 and is proportional to energy density u(υ) of the radiation frequency υ incident on the atom. Thus ρ12 ∞ u(υ) ρ12 =B12 u(υ) ----(1) The probability constant B12 is known as” Einstein’s coefficient of Absorption of radiation”
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The probability of spontaneous emission from state 2 to state 1 depends only on the properties of states 1 and 2. This is independent of energy density u(υ) of incident radiation Einstein denoted this probability per unit time by A21 (ρ21)sp=A21 --------- (2) The probability constant A21 is known as” Einstein’s coefficient of Spontaneous emission of radiation” The probability of stimulated emission transition from state 2 tostate 1 is proportional to the energy density u(υ) of the stimulation. i.e., (ρ21)st = B21 u(υ) ---------(3) The probability constant B21 is known as” Einstein’s coefficient of stimulated emission of radiation” The total probability for an atom in state 2 to drop to the lower state 1 is (ρ21) = A21 + B21 u(υ) ---------(4) Consider an assembly of atoms in thermal equilibrium at temperature T with radiation of frequency υ and energy density u(υ). Let N1 and N2 be the number of atoms in energy states 1 and 2 at any instant. The number of atoms in state 1 that absorb a photon and rise to state 2 per unit time is given by N1ρ12 = N1 B12 u(υ) ---------(5) The number of photons in state 2 that can cause emission process (spontaneous + stimulated) per unit time us given by N2ρ21 = N2 (A21 + B21 u(υ))-----(6) For equilibrium, the absorption and emission must occur equally, Hence, N1ρ12 = N2ρ21 N 1 B12 u(υ) = N2 (A21 + B21 u(υ)) u(υ) (N1B12 – N2 B21) = N2 A21 N 2 A 21 u(υ) = N1 B12 N 2 B21 A 21 A 21 N2 N2 = = . . N B B B21 B21 N 2 ( 1 12 1) N1 12 N 2 N 2 B21 B21 A 21 1 ----------(7) . u(υ) = B21 N1 B12 ( 1) N 2 B21 According to Boltzmann’s distribution law, the number of atoms N1 and N2 in energy states E1 and E2 in thermal equilibrium at temperature T is given by
E1
E2
N1 = No e kT and N2 = No e kT Where No is total number of atoms present k is Boltzmann’s constant
N2 = N1
N0e Noe
E2 kT E1 kT
=
e
E2 E1 kT
= e
h kT
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h
N2 = e kT N1 h
N1 = e kT ----------------- (8) N2 From eq (7) and eq (8) A 21 1 u(υ) = ---------------- (9) . h B21 B 12 (e kT 1) B21 According to Planck’s radiation formula 1 8h 3 u(υ) = . h ----------------- (10) 3 c kT e 1 By comparing eq (9) and eq (10) B A21 8h 3 = and 12 = 1 B12 = B21 3 c B21 B21 Hence, (1) As B12 = B21, the probability of stimulated emission is same as induced absorption. A (2) 21 ∞ ν3 i.e., the ratio of spontaneous emission and stimulated emission is B21 proportional to ν3 . This shows that the probability of spontaneous emission increases rapidly with energy difference between two states 1 (3) The function represents the ratio of rate of stimulated emission to hkT e 1 spontaneous emission rate. Population inversion (condition for laser action): Consider a two level energy system of energies E1 and E 2 . Let N 1 , N 2 are be the number of atoms per unit volume in an energy levels E1 and E 2 . The number of atoms per unit volume in an energy level is known as population of that energy level. That means N 1 and N 2 are the populations of E1 and E 2 . To get the laser emission N 2 N1 i.e. the population of the higher energy level ( E 2 ) should be greater than the population of the lower level energy level ( E1 ). In general, the population of a lower energy level will be greater than that of the higher energy level. The stage of making the population of the higher energy level to be greater than the population of the lower energy level is known as population inversion. The process of sending the atoms from lower energy level to higher energy level to get the population inversion is known as pumping.
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Consider a three energy level system with energies E1 , E 2 and E3 of populations N 1 , N 2 and
N 3 . In normal conditions E1 < E 2 < E3 , and N 3 < N 2 < N 1 . E1 is the lower energy state (ground state) with more life time of an atom. E3 is the highest energy state with less life time of an atom ( 108 s ) compared to that of E3 . E 2 is the intermediate energy state with more life time of an atom( 103 s ) compared to that of E3 . This intermediate energy state with more life time of an atom is known as meta stable state. This state provides necessary population inversion for the laser emission. When a suitable energy is supplied to the system, atoms get excited to E3 and transit to E 2 . Due to more life time of an atom, the atoms stay for a longer time in E 2 when compared to E3 . Due to accumulation of atoms in E 2 , a stage will be reached where N 2 N1 . Thus, population inversion is established between E1 and E 2 . Requisites of laser system: Any Laser system consisting of three important components.
(i)
Source of energy
(ii)
Active medium
(iii)
Optical cavity or resonator. (i)Source of energy: To get laser emission first we must have population inversion in the system. The source of energy supplies sufficient amount of energy to the active medium by which the atoms or molecules in it can be excited to the higher energy level as a result we get population inversion in an active medium. That means the source of energy supplies energy and pumps the atoms or molecules in the active medium to the excited states. (ii)Active medium: This medium where stimulated emission of radiation takes place. After receiving energy from the source the atoms or molecules get excited to higher energy levels. While transisting to lower energy level the emitted photons starts the stimulated emission process which results in laser emission. Depending upon the type of active medium, we have solid state, liquid state, gaseous state and semi conductor lasers. Prepared by SHANKER RAO GATTU, (9949435575)
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(iii)Optical cavity or resonator: The active medium is enclosed between a fully reflective mirror and partially reflective mirror. These mirrors constitute an optical cavity or resonator. The reflecting portion of the mirror reflects the incident radiation into the active medium. The reflected radiation enhance the stimulated emission process with in the active medium. As a result, we get high intensity, monochromatic and coherent laser light through the non reflecting portion of the mirror. CO2 LASER: Principle: The carbon dioxide laser makes use of transitions in the molecular vibrational and rotational energy levels. In addition to the electronic energy levels in atoms, the molecules posses vibrational and rotational energies which are quantized. The CO2 molecule has three modes of vibrations. In symmetric stretching mode, the two oxygen atoms either simultaneously move towards or away from the carbon atom. In asymmetric stretching mode one of the oxygen atom moves towards and other away from the carbon atom. In the bending mode, the three atoms vibrate perpendicular to the axis of the molecule in such a way that the carbon atom moves in the opposite direction to the oxygen atom which move in same direction at any instant of time. The difference in energies between these molecular levels is small compared to the atomic energy levels. Hence radiation emitted by transition in molecular energy levels lies in far infrared region of the spectrum. Construction: A mixture of Co2, He, and N2 is circulated in a glass tube which has two electrodes connected to a power supply. One end of the tube has a partially silvered and the other end has Brewester’s window. A completely silvered mirror is kept beyond the Brewester’s window. Working: The high voltage across the electrodes excites the gas molecules. The nitrogen molecules in the gas are excited to higher levels and transfer energy to CO 2 molecules by collisions. The CO2 molecules are excited to the meta stable state E5 where population inversion takes place with respect to the two lower lasing levels E3 and E4. Transition from E5 to E4 gives rise to 10.6 µm wavelength laser and the transition from E5 to E3 gives rise to 9.6 µm wavelength which are both in the far infra red region. He depopulates the lower energy levels in CO2 which facilitates population inversion.
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The carbon dioxide laser is a high power laser producing power as high as 10kW. It also has very high efficiency of the order of about 40%. Applications: Out put powers of several watts to several hundred watts are obtained from CO2 laser. Hence CO2 laser, because of its high output power, finds the application in industry for welding, drilling, cutting, etc. they are also used in open air communication systems and optical radar systems. SEMICONDUTOR LASER: Principle: When a p-n junction is formed across a p and n type semiconductor a depletion region will be created. When the junction is forward biased, the width of the depletion region decreases allowing more number of electrons from n type to cross the junction and recombine with hole in p type. Thus, recombination of electron-hole pairs across the junction emits the radiation. When electrons from the conduction band recombines with the hole in the valence band then the emitted energy is
E h E g
c
Eg h
hc Eg
Eg h
Construction: A rectangular block of GaAs semiconductor is converted into p and n type by proper doping of impurities into the block. The upper region acts as p type and the lower portion as n type. Between these two regions, we have a p-n junction. To achieve population inversion p and n regions are heavily doped with the impurities. The pn junctions serve as active medium. The two faces of the block, one fully polished and the other partially polished, act as an optical resonator. Working: A suitable forward bias voltage is applied to the diode so as to overcome the potential barrier. As a result the electrons are injected from the n region, and the holes are injected from the p region into the junction. A current begins to flowing, which there will be region near the interface which population inversion conditions are attained. The active region is Prepared by SHANKER RAO GATTU, (9949435575)
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very thin. At this stage, a photon released by a spontaneous emission may trigger stimulated emissions over a large number of recombinations leading to build up of laser radiation of high power. Advantages: 1. The efficiency of a GaAs laser is high and can be increased by decreasing the temperature of the junction. 2. The laser output can be modulated within the semiconductor itself. 3. We can have a continuous or pulsed output and the output is tunable. APPLICATIONS OF LASERS: (i)Welding: The two metal plates to be welded are held in contact at their edges and a high power is focused on the line of contact. The metal at the line of contact melts and solidifies on cooling which causes the two plates to stick together. As the laser can be focused to a very sharp point, the heated effect area is very small. Hence laser welding does not cause distortion of the plates. Also, it is a contact less procedure. Hence there is no possibility of introducing impurities. Laser welding is commonly used in automobile, ship building and aircraft manufacturing industries CO2 and Nd-YAG lasers are used for this purpose. (ii)Cutting: Cutting of the metal sheets is achieved using high power lasers like CO2 and Nd-YAG lasers. The laser is focused on the metal sheet and a jet of oxygen is blown on the spot. A significant part of the energy required for cutting is supplied by burning of the metal in oxygen. The oxygen jet also blows away the vapourised metal and also cools the adjacent edges. Higher cutting speeds have been achieved with lasers compared to other conventional methods. Laser cutting produces higher quality of the cut edges. (iii)Drilling: Holes can be drilled in to materials using high power pulsed lasers of 10-4 to 10-3s duration. The laser pulse evaporates the material which leaves a hole in its place Nd-YAG laser is commonly used for this purpose. Laser drilling has a very high degree of precision and holes can be drilled having diameters of the order of a few microns. As there are no mechanical vibrations, holes can be drilled very close to the edges without damaging the metal plates. (iv)Measurement of atmospheric pollution levels: Pollution in the atmosphere is due to suspended particulate matter like dust, smoke, fly-ash, aerosols etc. and non particulate matter like carbon monoxide, sulphur dioxide etc. Conventional method for measurement of pollution levels require collection of sample and then its chemical analysis. This is a time consuming process and does not give real time data. Using lasers, we can get real time data by transmitting the laser beam in atmosphere and then observing either the reflected or transmitted beam. LIDAR (Light detection and ranging) is used to measure concentration of suspended particulate matter in the atmosphere. A pulse of laser is transmitted in to the Prepared by SHANKER RAO GATTU, (9949435575)
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atmosphere and the back scattered light is recorded using photo diodes. This gives information regarding concentration of suspended particulate matter. Absorption of certain wavelengths by some gases is used to study their presence in the atmosphere by transmitting a laser beam through the atmosphere and recording the transmitted intensity. The presence of different gaseous pollutants is best studied by means of Raman back scattering. The back scattering laser contains the transmitted wavelength as well as longer and shorter wavelengths than the transmitted wavelength. The change in wavelength from the original transmitted wavelength is known as Raman shift and is specific for particular gas. Hence these gases can be detected.
Holography Holography is remarkable application of laser in which interference, the wave phenomenon of light is employed. A photography records a two dimensional image of an object using ordinary light and is sensitive only to variations in intensity. When cut into pieces the information in a photograph is lost. Holography is a technique of recording the whole information, i.e. intensity and phase of an object. In Greek ‘holo’ means whole and ‘graphy’ means recording or writing. In holography, the three dimensional image of an object is recorded using laser and is sensitive to both intensity and phase variations. When cut into pieces, each piece consists of the whole information. In 1948, Dennis Gabor proposed a method to record both amplitude and phase of a wave by a technique called wave front construction. This technique is called holography. Holography is actually a recording of interference pattern formed between two beams of coherent light coming from the same source. In this process both the amplitude and phase components of light wave are recorded on a light sensitive medium such as a photographic plate. The recording is known as a hologram. Principle of Holography: Holography is two step process. First step is the recording of hologram where the object is transformed into a photographic record and the second step is the reconstruction in which the hologram is transformed into image. Recording of the hologram: A broad laser beam is divided into two beams, namely a reference beam and an object beam by a splitter. The reference beam goes directly to the photographic plate. The second beam of light is directed onto the object to be photographed. Each point of the object scatters the incident light and acts as the source of spherical waves. Part of the light, scattered by the object, travels towards the photographic plate. At the photographic plate the innumerable spherical waves from the object combine with the plane light wave from the reference beam. The sets of light waves are coherent because they are from the same laser. They interfere and form interference fringes on the plane of the photographic plate. These interference fringes are a series of zone plate like rings, but these rings are also superimposed, making Prepared by SHANKER RAO GATTU, (9949435575)
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a complex pattern of lines and swirls. The developed negative of these interference fringe patterns is a hologram. Thus, the hologram does not contain a distinct image of the object but carries a record of both the intensity and the relative phase of the light waves at each point. Reconstruction of the image: For reconstruction of the image, the hologram is illuminated by a parallel beam of light from the laser. Most of the light passes straight through, but the complex of fine fringes acts as a elaborate diffraction grating. Light is diffracted at a fairly wide angle and forms a virtual image and a real image. The virtual image appears at the location formerly occupied by the object and is sometimes called as the true image. The real image formed in front of the hologram. Since the light rays pass through the point where the real image is, it can be photographed. The virtual image of the hologram is only viewing. Observer can move to different positions and look around the image to the same extent that he would be able to, where he looking directly at the real object. This type of hologram is known as transmission hologram since the image is seen by looking through it. The three dimensional image is seen suspended in midair at a point which corresponds to the position of the real object which was photographed. Applications of holography: (i) Holography finds wide applications in the field og non-destructing testing. An object which has to be checked for any flaws is viewed through its hologram. (ii) Images can be projected in space using holographic lens in which a hologram functions as a lens. (iii)Vibrations of an object can be measured using time averaged holographic interferometry. (iv) It is used for high density optical storage.
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