Electromagnetic Metamaterials

The term “metamaterials” was first coined by Rodger Walser: Macroscopic composites having a manmade, three-dimensional, periodic cellular architecture designed to produce an optimized combination, not available in nature, of two or more responses to specific excitation [1]. Exciting (and sometimes controversial) applications have emerged like negative index of refraction super-lenses [2] and electromagnetic cloaks [3]. But how practical are these devices? Potential complications include very narrow bandwidths, large loss, bi-anisotropy, and validity of the effective medium approximation.
Understanding metamaterial resonances

Split-ring resonators (SRRs) have been used extensively in metamaterial structures. One way to understand the resonance is to apply a capacitive-inductance (LC) model. In the optical regime, application of LC models is complicated by the less-than-idea resolution afforded by current fabrication techniques and by skin effects of materials used.



Simulated E field (left) showing the capacitor-like response of the SRR at resonance and simulated current (right) showing how current “seeps in” from the surface of the SRR due to the relatively large ratio of the SRR dimensions compared to the skin depth.  Any model for the inductance of the SRR must take this penetration into account.  
To learn more: T. D. Corrigan, P. W. Kolb, A. B. Sushkov, H. D. Drew, D. C. Schmadel, and R. J. Phaneuf, “Optical plasmonic resonances in split-ring resonator structures: an improved LC model,” Optics Express 16(24), 19850–19864 (2008).
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Bi-anisotropy and spatial dispersion
Don’t be fooled! Resonances that appear to be excited by a magnetic field may actually be better attributed to the electric field; this “mixing” of the magnetic and electric responses is known as bi-anisotropy. The resonant frequency is prone to shifting with changing angle of incidence, indicating that effective material parameters will not be true constants but depend on the “k vector” of incident light; this dependence is known as spatial dispersion.

Simulated transmission through rod pairs in and U-shapes in (b) for the polarization shown in the inset. Differences in the phase of the electric field along the resonator arms at oblique incidence can excite the resonances labeled R1 and U1. Shifts in the resonant frequency with increasing incident angle can be a signature of spatial dispersion.


“Bianisotropy and spatial dispersion in highly anisotropic near-infrared resonator arrays,” P. W. Kolb, T. D. Corrigan, H. D. Drew, A. B. Sushkov, R. J. Phaneuf, A. Khanikaev, S. Hossein Mousavi, and G. Shvets, 18(23), 24025-24036 (2010).

[1]    Rodger M Walser, "Electromagnetic Metamaterials," Proceedings of SPIE, vol. 4467, pp. 1-15, 2001.
[2]    Victor G. Veselago, "The electrodynamics of substances with simultaneously negative values of m and e," Soviet Physics Uspekhi, 10, 509-514 (1968).
J. B. Pendry, "Negative Refraction Makes a Perfect Lens," Physical Review Letters, 85, 3966-3969 (2000).
D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Compostie Medium with Simultaneous Negative Permeability and Permittivity," Physical Review Letters, 84, 4184-4187 (2000).
[3]    D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science, 314, 977-980 (2006).