On the unambiguous determination of effective optical properties of periodic metamaterials: a one-dimensional case study

N. A. Mortensen; M. Yan; O. Sigmund; O. Breinbjerg

doi:10.2971/jeos.2010.10010

Journal of the European Optical Society - Rapid publications, Vol 5 (2010)

On the unambiguous determination of effective optical properties of periodic metamaterials: a one-dimensional case study

N. A. Mortensen, M. Yan, O. Sigmund, O. Breinbjerg

Abstract

We show how branch ambiguities in the extraction of effective parameters is arising as a direct consequence of the underlying Bloch state physics. The mutual importance of the different branches in general depends on the experimental context, and we show how the Fourier spectrum of the field inside the metamaterial can be used to access this. Different numerical examples illustrate how a predominant branch may be identified for $\lambda\gg a$ while at higher frequency the power may be distributed over more branches. This is in particular true near band-edges and strong resonances. Extensions to two and three-dimensional metamaterial designs are discussed.

Full Text: PDF

Citation Details

Cite this article

References

V. G. Veselago, "Electrodynamics of substances with simulataneously negative values of e and m" Sov. Phys. Uspekhi 10, 509 (1968).

J. B. Pendry, and D. R. Smith, "Reversing light with negative refraction" Phys. Today 57, 37-43 (2004).

N. Engheta, and R. W. Ziolkowski, "A positive future for doublenegative metamaterials" IEEE T. Microw. Theory 53, 1535-1556 (2005).

V. M. Shalaev, "Optical negative-index metamaterials" Nat. Photonics 1, 41-48 (2007).

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refractive index at optical wavelengths" Science 315, 47-49 (2007).

D. R. Smith, and J. B. Pendry, "Homogenization of metamaterials by field averaging (invited paper)" J. Opt. Soc. Am. B 23, 391-403 (2006).

D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, "Direct calculation of permeability and permittivity for a left-handed metamaterial" Appl. Phys. Lett. 77, 2246-2248 (2000).

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials" Phys. Rev. E 71, 036617 (2005).

D. Felbacq, and G. Bouchitte, "Theory of mesoscopic magnetism in photonic crystals" Phys. Rev. Lett. 94, 183902 (2005).

J. M. Lerat, N. Mallejac, and O. Acher, "Determination of the effective parameters of a metamaterial by field summation method" J. Appl. Phys. 100, 084908 (2006).

N. A. Mortensen, S. S. Xiao, and D. Felbacq, "Mesoscopic magnetism in dielectric photonic crystal meta materials: topology and inhomogeneous broadening" J. Europ. Opt. Soc. Rap. Public. 1, 06019 (2006).

L. Peng, L. X. Ran, H. S. Chen, H. F. Zhang, J. A. Kong, and T. M. Grzegorczyk, "Experimental observation of left-handed behavior in an array of standard dielectric resonators" Phys. Rev. Lett. 98, 157403 (2007).

O. Acher, J. Lerat, and N. Malléjac, "Evaluation and illustration of the properties of metamaterials using field summation" Opt. Express 15, 1096-1106 (2007).

M. G. Silveirinha, "Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters" Phys. Rev. B 75, 115104 (2007).

A. I. Cabuz, D. Felbacq, and D. Cassagne, "Homogenization of negative-index composite metamaterials: a two-step approach" Phys. Rev. Lett. 98, 037403 (2007).

S. L. Sun, S. T. Chui, and L. Zhou, "Effective-medium properties of metamaterials: a quasimode theory" Phys. Rev. E 79, 066604 (2009).

D. Felbacq, B. Guizal, G. Bouchitte, and C. Bourel, "Resonant homogenization of a dielectric metamaterial" Microw. Opt. Techn. Let. 51, 2695-2701 (2009).

A. Andryieuski, R. Malureanu, and A. V. Lavrinenko, "Wave propagation retrieval method for metamaterials: unambiguous restoration of effective parameters" Phys. Rev. B 80, 193101 (2009).

C. Rockstuhl, C. Menzel, T. Paul, T. Pertsch, and F. Lederer, "Light propagation in a fishnet metamaterial" Phys. Rev. B 78, 155102 (2008).

C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, "Retrieving effective parameters for metamaterials at oblique incidence" Phys. Rev. B 77, 195328 (2008).

C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, and F. Lederer, "Validity of effective material parameters for optical fishnet metamaterials" Phys. Rev. B 81, 035320 (2010).

C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. P. Meyrath, and H. Giessen, "Transition from thin-film to bulk properties of metamaterials" Phys. Rev. B 77, 035126 (2008).

D. R. Smith, S. Schultz, P. Marko_s, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients" Phys. Rev. B 65, 195104 (2002).

Z. C. Ruan, M. Qiu, S. S. Xiao, S. L. He, and L. Thylén, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction" Phys. Rev. B 71, 045111 (2005).

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, "Nonlocal effects in effective-medium response of nanolayered metamaterials" Appl. Phys. Lett. 90, 191109 (2007).

R. E. Collin, Foundations for Microwave Engineering (2nd Edition, IEEE Press, New York, 2001).

C. Kittel, Introduction to Solid State Physics (8th Edition, John Wiley & Sons, New Jersey, 2005).

N. Le Thomas, R. Houdré, M. V. Kotlyar, D. O'Brien, and T. E. Krauss, "Exploring light propagating in photonic crystals with Fourier optics" J. Opt. Soc. Am. B 24, 2964-2971 (2007).

B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdré, "Fourier analysis of Bloch wave propagation in photonic crystals" J. Opt. Soc. Am. B 22, 1179-1190 (2005).