NanoSingapore 2006

NanoElectromagnetic Metamaterials Approaching Telecommunications Frequencies B. D. F. Casse, H. O. Moser,∗ M. Bahou, L. K. Jian, and P. D. Gu Singapore Synchrotron Light Source, National University of Singapore, 5 Research Link, Singapore 117603 (Dated: October 15, 2005) Abstract- Arrays of gold Rod-Split-Ring-Resonators with structural details down to sub 100 nm, and exhibiting electromagnetic metamaterial (EM3 ) behavior near telecommunications frequencies, have been produced by nanofabrication. Samples were characterized at the Singapore Synchrotron Light Source ISMI (Infrared Spectro/MIcroscopy) facility using Bruker Optics’ IFS 66v/S Fourier transform interferometer and Hyperion 2000 Microscope powered by synchrotron radiation. Oblique incidence transmission spectra were measured and revealed a spectral resonance around 190 THz. The present work extends the frequency range in which EM3 are available, thereby opening up opportunities for new applications in the telecommunications frequency regime. I.

INTRODUCTION

Electromagnetic metamaterials (EM3 ) refer to artificially engineered materials having simultaneously negative permittivity ε and permeability μ, which exhibit exotic properties such as a negative index of refraction and ˇ an inverse Doppler and Cerenkov effect. These materials were first envisioned and theoretically studied by Victor Veselago in 1968 [1]. He coined the word “left-handed materials” for such media due to the left-handed triad formed by the vectors E, H and k. Since no naturally occurring materials were known at that time, his work remained purely academic and lay dormant for a span of thirty years until Sir John Pendry and co-workers devised schemes for obtaining εeff < 0 [2] and μeff < 0 [3] by a combination of metallic wires and split-ring resonators. The first demonstration of EM3 started in the microwave regime [4] [5], i.e., in the Gigahertz range. Subsequently micro- and nanofabrication technologies were deployed to boost EM3 resonant frequencies up to four orders of magnitude [6] [7] [8] [9], with H.O. Moser et al. [10] being the first group to manufacture micro-electromagnetic metamaterials. An obvious goal of this development is to be able to produce metamaterials at telecommunications frequencies and up to the visible. We present nano-electromagnetic metamaterials, with a rod-split-ring-resonator (RSR) design, having overall structure size below 1 m with structural details down to sub 100 nm. The comparison of experimental results obtained at SSLS’ Infrared Spectro/MIcroscopy beamline (ISMI) with Pendry’s analytical formula and numerical simulations with Ansoft’s HFSS indicate that the nanofabricated composite materials behave as EM3 in the range 50–187 THz. II.

c r g c

d

a

w l

b

FIG. 1: Geometric parameter definition of the RSR (left). Periodic arrangement of the RSR adopted for nanofabrication (right).

εeff < 0 over a much wider range than μeff < 0, provided that a small ratio of radius to distance of the wires is used, the lower and upper limit of the frequency interval over which μeff < 0 was calculated from Pendry’s formula [3]  1 ν0 3dc20 < νmp =  (1) ν0 = 2 3 2π π r 1 − πr2 /ab where c0 is the speed of light in vacuo. Five geometric variants were used for the nanoelectromagnetic metamaterials. The sets of those geometric parameters and the limits of the interval in which the composites have EM3 behavior are shown in table I. For numerical simulations we use Ansoft’s HFSS which utilizes a 3D full-wave Finite Element Method (FEM) to compute the electromagnetic behavior of high-frequency and high-speed components.

DESIGN AND SIMULATION

The design used here closely follows the one in our recent work [10], i.e., a planar model of Pendry’s prototype [3] adapted for micro- and nanolithography. The geometric parameter definition of the nano-RSR and

∗ Electronic

their periodic arrangement is shown in figure 1. While

address: [email protected]

0-7803-9358-9/06/$20.00 © 2006 IEEE

III. A.

EXPERIMENTAL Nanofabrication

0.5-mm thick glass wafers coated with a 5 nm layer of indium tin oxide (ITO) were used as substrates for EM3 composites S2–S4. The ITO bears the role of preventing charging effects of the resist layer during the electron beam exposure. For EM3 composite S1, the substrate

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TABLE I: THz specifications of a Rod-Split-Ring structure. Samples S1 S2 S3 S4 a For

a

r/nm 300 150 120 90

c/nm 200 90 90 90

d/nm 100 80 80 40

a/ m 2.00 1.07 1.01 0.79

b/ m 1.70 0.90 0.84 0.66

ν0 /THz 50.66 128.16 179.11 194.99

νmp /THz 52.91 133.14 184.09 199.93

all structures g = 50 nm, w = c, l = (r + 2c + d) × 2

used was silicon. PMMA 950k was spin coated onto the substrate to achieve a thickness of 200–250 nm. The for 2 sample was then softbaked in an oven at 160 hours. The design files with parameters shown in table I were created in the software Design CAD. The pattern transfer into the PMMA resist was achieved by electron beam lithography using the Sirion NPGS-SEM system from FEI company. For the writing, a beam of 30 kV was used with an exposure dose of around 100–150 C/cm2 and 200-250 C/cm2 for the silicon and glass substrate, respectively. A 5×5 array was exposed whereby one array contained 100 × 100 nanostructures. The PMMA was developed using a mixture of MIBK (methyl isobutylketone) and IPA (isopropanol) in a ratio 3:1 by volume for 70 seconds, followed by a dip in IPA for 30 seconds and a final rinse in deionized water for another 30 seconds. A 30 nm film of gold was then deposited onto the photoresist template, as shown in figure 2(left), by magnetron sputtering using the NSP 12-1 machine from Nanofilm Technologies International. Lift-off of the PMMA resist was achieved by immersing the sample in acetone for 1 hour. The end product is 500 × 500 m of 30 nm thick gold RSR on 0.5-mm thick glass substrate as shown in figure 2(right).

at the point where μeff (ω) < 0, then this situation corresponds to evanescent waves in the medium, i.e., a stop band where there is no propagation of electromagnetic waves. Similarly in a plasma medium where εeff (ω) < 0, we would have a stop band. In a transmission experiment, this would translate into a reduction in intensity of the incoming radiation. For the gold bars or wire arrays, this stop band is over a much wider range of frequencies compared to the SRRs, which can be deduced from the Drude model [12] εeff = 1 −

ωp2 ω 2 + iγω

(3)

where ωp is the plasma frequency and γ is some damping factor. Transmission experiments on the nanoEM3 composites were performed with Bruker’s Hyperion 2000 Microscope at the ISMI beamline at the Singapore Synchrotron Light Source. The Hyperion microscope was set to reflection-transmission mode for the experiment, meaning transmission through the sample, followed by a reflection on the silver mirror and a second transmission through the sample before reaching the detector. The schematic of the experimental setup is shown in figure 3. The incident angle of the beam on the samples was 23 to the normal, as set by the Schwarzschild objective. Schwarzschild objective

From source

To detector

FIG. 2: 30 nm gold film on the photoresist template (left). Array of gold RSR on glass substrate (right). Scale bar 2 m. o

23 23

B.

Spectroscopic Measurements

EM

Pendry’s formula for the effective permeability of a split ring resonator leads to a dispersion curve where at some spectral range μeff < 0. If we look into the dispersion relation of a frequency dispersive medium [11] k=ω



μ(ω)ε(ω)

(2)

o

3

Glass substrate Silver mirror

FIG. 3: Schematic diagram of the experimental setup.

A typical curve of the nanocomposites EM3 is given in

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transmission and is unlikely to either short-circuit the composite material or manifest any resonances.

100 90

Transmission [%]

figure 4. We can observe an attenuation in transmission between 4000 and 5000 cm−1 wavenumbers in the curve of the SRR (figure 5, left) alone, which corresponds to the region of negative μeff . Now combining the SRRs with the wire arrays (RSR), a bandpass emerges (characterized by an increase in transmission) around the same frequency range indicating that both εeff and μeff are negative.

100 RSR ( Wire arrays + SRRs) SRRs Short-circuited RSR

90 80

No substrate Bare glass substrate Glass substrate with ITO 3 EM S4

80 70 60

187 THz

50 Transmission [%]

70 40

60 50

30 8000

7500

7000

40

6000 6500 5500 -1 Wavenumber [cm ]

5000

4500

4000

30

FIG. 6: Transmission spectra of an RSR approaching telecommunications frequency, bare 0.5-mm thick glass substrate and glass substrate with 5 nm thick layer of ITO.

20 10 0 7500

7000

6500

6000 5500 5000 -1 Wavenumber [cm ]

4500

4000

3500

FIG. 4: Transmission Spectra of nano- SRR and RSR and short-circuited SRR.

Figure 7 shows a comparison of the measured results with values obtained from Pendry’s analytical formula and from HFSS simulations by plotting the inner radius r versus the position of the maxima of the resonance peaks for all the EM3 samples in table I.

As a further evidence of EM3 behavior, the composite material was fabricated with the azimuthal gap g of the split rings closed, the short-circuited sample (figure 5, right), thus removing a decisive structure element of the SRR.

1000

MIR

NIR

VISIBLE 3

radius, r [nm]

NanoEM Experimental values HFSS simulation values EM3 S4 (scaled)

S1

ν0(r)

S2

S3

100

S4

10

FIG. 5: Split Ring Resonators (left, scale bar 2 m)). Shortcircuited EM3 structures (right, scale bar 1 m)).

The closed rings structure did not show any electromagnetic response in the relevant frequency range as expected. The EM3 sample, S4, that is approaching telecommunications frequency (194 THz  1.55 m) is shown in figure 6. The transmission curve for a bare glass substrate and that of glass with 5 nm of ITO film is also shown. The glass and glass+ITO curves indicate that 5 nm of ITO has negligible effects on the overall

100 ν res [THz]

1000

FIG. 7: Inner radius r of samples versus frequencies of the maxima of the spectral response curves for measured (Hyperion Microscope) and numerically simulated (HFSS) values. The solid curve ν0 (r) represents the log of Pendry’s r−3/2 dependence formula. When the sample S4 is scaled to the same value of d as the other samples, its resonant frequency also comes close to the curve (◦).

The curve ν0 (r) corresponds to the log of Pendry’s r−3/2 dependence formula. The overall agreement of numerical, analytical and measured values is very good. In the

330

case of sample S4, the frequency is lower as the value of the annular gap between the inner and outer ring, d is smaller by a factor of 2 which increases capacitance and decreases the resonance frequency. Scaling the latter to the same value of d as the other samples brings its resonant frequency close to the Pendry curve.

ducing electromagnetic metamaterials for the near infrared and beyond. From the nanofabrication point of view there is still potential to further reduce sizes such as to come close to the visible. Acknowledgments

IV.

CONCLUSION

We have produced composite materials by electron beam lithography which exhibit EM3 behavior in the mid and near infrared (MIR and NIR) up to 190 THz (∼1.6 m) which is close to telecommunications frequencies and wavelengths such as 1.55 m. We have shown that Pendry’s planar model is a viable option for pro-

[1] V. G. Veselago. The electrodynamics of substances with simultaneously negative values of ε and μ. Sov. Phys. Usp., 10:509, 1968. [2] J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs. Extremely low frequency plasmons in metallic mesostructures. Phys. Rev Lett., 76:4773, 1996. [3] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microwave Theory Tech., 47:2075, 1999. [4] D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. NematNasser, and S. Schultz. Composite medium with simultaneously negative permeability and permittivity. Phys. Rev Lett., 84:4184, 2000. [5] R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz. Microwave transmission through a twodimensional, isotropic, left-handed metamaterial. Appl. Phys. Lett, 78(4):489, 2001. [6] T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang. Terahertz magnetic response from artificial materials. Science, 303:1494, 2004. [7] Stefan Linden, Christian Enkrich, Martin Wegener, Jian-

The authors would like to thank Prof. Lim Hock and Gan Yeow Beng from the Temasek Laboratories, NUS, for valuable discussions. The work was performed at the Singapore Synchrotron Light Source (SSLS) under A*STAR/MOE RP3979908M, A*STAR 0121050038, and NUS Core Support C-380-003-003-001 grants.

[8]

[9]

[10]

[11] [12]

331

feng Zhou, Thomas Koschny, and Costas M. Soukoulis. Magnetic response of metamaterials at 100 terahertz. Science, 306:1351, 2004. B. D. F. Casse, H. O. Moser, O. Wilhelmi, and B. T. Saw. Micro- and nano-fabrication of electromagnetic metamaterials for the terahertz range. In Proceedings of the ICMAT 2005 Symposium R (Electromagnetic Materials), pages 18–25, Singapore, 2005. World Scientific. H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw. Electromagnetic metamaterials over the whole thz range — achievements and perspectives. In Proceedings of the ICMAT 2005 Symposium R (Electromagnetic Materials), pages 55–58, Singapore, 2005. World Scientific. H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw. Terahertz response of a microfabricated rod-splitring-resonator electromagnetic metamaterial. Phys. Rev. Lett., 94(6):063901, 2005. Jin Au Kong. Electromagnetic Wave Theory. John Wiley & Sons, Inc., New York, 1990. D. Pines and D. Bohm. A collective description of electron interactions: ii. collective vs individual particle aspects of the interactions. Phys. Rev., 85:338, 1952.