A new approach is proposed for determining the optical properties of metamaterials with a complex unit cell geometry. It is based on the concept of an effective dielectric constant εeff (ω) and magnetic permeability μeff (ω) as a sum of Lorentzian functions, each of which is responsible for a certain dipole or multipole resonance of the structure. It is found that for "fishnet" metamaterials the spectral dependences εeff (ω) and magnetic permeability μeff (ω) are determined by a small number of resonances. This approach is used to calculate the effective dielectric constant and magnetic permeability of metamaterials with ordered and disordered unit cells. The spectra obtained by this analytical model are in good agreement with numerical simulations.
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L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd edn., Pergamon, Oxford (1984).
R. S. Penciu, M. Kafesaki, Th. Koschny, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B, 81, 235111 (2010).
E. N. Economou, Th. Koschny, and C. M. Soukoulis, Phys. Rev. B, 77, 092401 (2008).
Y. A. Urzhumov and G. Shvets, Sol. State Commun., 146, 208–220 (2008).
H. Zheng, R. Vallee, R. M. Almeida, T. Rivers, and S. Ravaine, Meta 2014 Conf., May 20–23, 2014, Singapore (2014).
Y. A. Urzhumov, G. Shvets, J. Fan, F. Capasso, D. Brandl, and P. Nordlander, Opt. Express, 15, 14129–14145 (2007).
V. Ponsinet, P. Barois, S. M. Gali, P. Richetti, J. B. Salmon, A. Vallecchi, M. Albani, A. Le Beulze, S. Gomez-Grana, E. Duguet, S. Mornet, and M. Treguer-Delapierre, Phys. Rev. B, 92, 220414 (2015).
M. Fruhnert, S. Mühlig, F. Lederer, and C. Rockstuhl, Phys. Rev. B, 89, 075408 (2014).
A. M Nicolson and G. F. Ross, IEEE Trans. Instrum. Measur., 19, 377–382 (1970).
P. O. Nilsson, Appl. Opt., 7, 435–442 (1968).
E. Nichelatti, J. Opt. A: Pure Appl. Opt., 4, 400–403 (2002).
S. Y. El-Zaiat, Optik, 124, 157–161 (2013).
G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, Opt. Lett., 32, 53–55 (2007).
S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Opt. Express, 14, 6778–6787 (2006).
W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications, Springer, New York (2010), pp. 112–113.
S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, Phys. Rev. Lett., 95, 137404 (2005).
S. Kozik, S. Ravaine, V. Belyi, and N. Kazak, Metamaterials’2015, Proc. 9th Int. Congress on Advanced Electromagnetic Materials in Microwaves and Optics, September 7–12, 2015, Minsk (2015), pp. 520–522.
A. K. Sarychev, G. Shvets, and V. M. Shalaev, Phys. Rev. E, 73, 036609 (2006).
G. Shvets and Y. A. Urzhumov, J. Opt. A: Pure Appl. Opt., 7, S23–S31 (2005).
R. Rojas and F. Claro, Phys. Rev., 34, 3730–3736 (1986).
D. J. Bergman, J. Phys. C: Sol. State Phys., 12, 4947–4960 (1979).
R. Braco, J. Phys. C: Sol. State Phys., 11, 3345–3355 (1978).
A. R. Day and M. F. Thorpe, J. Phys.: Condens. Matter, 11, 2551–2568 (1999).
G. A. Niklasson, T. K. Boströmb, and E. Tuncer, Proc. SPIE, 8168, 81680S-3 (2011).
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Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 83, No. 6, pp. 924–933, November–December, 2016.
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Kozik, S.E., Smirnov, A.G. Spectral Dependence of the Refractive Index of Magneto-Optical Metamaterials. J Appl Spectrosc 83, 975–983 (2017). https://doi.org/10.1007/s10812-017-0393-7
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DOI: https://doi.org/10.1007/s10812-017-0393-7