Thickness conditions for characterizing the periodic nanostructures with the retrieved electromagnetic parameters

D. Song; Z. Tang; L. Zhao; Z. Sui; S. Wen; D. Fan

doi:10.2971/jeos.2013.13028

Journal of the European Optical Society - Rapid publications, Vol 8 (2013)

Thickness conditions for characterizing the periodic nanostructures with the retrieved electromagnetic parameters

D. Song, Z. Tang, L. Zhao, Z. Sui, S. Wen, D. Fan

Abstract

By analyzing the convergence of the retrieved effective electromagnetic parameters, we presented that one wavelength of the propagating wave in the nanostructure is the minimum thickness requirement for effectively characterizing a finite thickness nanostructure. This thickness condition has been separately validated in a photonic crystal with negative refraction and in a typical fishnet metamaterial which has been investigated theoretically and experimentally before.

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References

A. Alù, ”Restoring the physical meaning of metamaterial constitutive parameters,” Phys. Rev. B 83, 081102(R) (2011).

R. Biswas, Z. Y. Li, and K. M. Ho, ”Impedance of photonic crystals and photonic crystal waveguides,” Appl. Phys. Lett. 84, 1254 (2004).

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

B. Momeni, A. A. Eftekhar, and A. Adibi, ”Effective impedance model for analysis of reflection at the interfaces of photonic crystals,” Opt. Lett. 32, 778–780 (2007).

B. Momeni, M. Badieirostami, and A. Adibi, ”Accurate and efficient techniques for the analysis of reflection at the interfaces of threedimensional photonic crystals,” J. Opt. Soc. Am. B 24, 2957–2963 (2007).

Z. L. Lu, and D. W. Prather, ”Calculation of effective permittivity, permeability, and surface impedance of negative-refraction photonic crystals,” Opt. Express 15, 8340–8345 (2007).

V. Yannopapas, and A. Moroz, ”Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys.: Condens. Matter 17, 3717 (2005).

Y. Wu, J. Li, Z.-Q. Zhang, and C. T. Chan, ”Effective medium theory for magnetodielectric composites: Beyond the long-wavelength limit,” Phys. Rev. B 74, 085111 (2006).

V. Yannopapas, ”Negative refraction in random photonic alloys of polaritonic and plasmonic microspheres,” Phys. Rev. B 75, 035112 (2007).

X. Huang, Y. Lai, Z. H. Hang, H. Zheng, and C. T. Chan, ”Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10, 582–586 (2011).

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).

S. O’Brien, and J. B. Pendry, ”Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys.: Condens. Matter 14, 4035 (2002).

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, Jr., and J. A. Kong, ”Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608 (2004).

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

C. R. Simovski, ”Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices,” Metamaterials 1, 62–80 (2007).

C. R. Simovski and S. A. Tretyakov, ”Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B 75, 195111 (2007).

C. Croënne, N. Fabre, D. P. Gaillot, O. Vanbésien, and D. Lippens, ”Bloch impedance in negative index photonic crystals,” Phys. Rev. B 77, 125333 (2008).

C. R. Simovski, ”Material parameters of metamaterials,” Opt. Spectrosc. 107, 726–753 (2009).

C. Tserkezis and N. Stefanou, ”Retrieving local effective constitutive parameters for anisotropic photonic crystals,” Phys. Rev. B 81, 115112 (2010).

X.-X. Liu, D. A. Powell, and A. Alù, ”Correcting the Fabry-Perot artifacts in metamaterial retrieval procedures,” Phys. Rev. B 84, 235106 (2011).

J. F. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, ”Size dependence and convergence of the retrieval parameters of metamaterials,” Photonics Nanostruct. Fundam. Appl. 6, 96–101 (2008).

J. F. Zhou, T. Koschny, M. Kafesaki, and C. M. Soukoulis, ”Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B 80, 035109 (2009).

W. C. Chen, A. Totachawattana, K. Fan, J. L. Ponsetto, A. C. Strikwerda, X. Zhang, R. D. Averitt, and W. J. Padilla, ”Single-layer terahertz metamaterials with bulk optical constants,” Phys. Rev. B 85, 035112 (2012).

S. Engelbrecht, A. M. Shuvaev, Ch. Kant, K. Unterrainer, and A. Pimenov, ”Experimental determination of effective parameters in a layered metamaterial,” Phys. Rev. B 85, 235437 (2012).

G. Dolling, M. Wegener, and S. Linden, ”Realization of a threefunctional- layer negative-index photonic metamaterial,” Opt. Lett. 32, 551–553f (2007).

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, ”Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. 7, 31–37 (2008).

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, S. R. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, et al., ”Magnetic response of split-ring resonators in the far-infrared frequency regime,” Opt. Lett. 30, 1348–1350 (2005).

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, ”Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376–379 (2008).

N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, and O. Vanbésien, ”Optical Near-Field Microscopy of Light Focusing through a Photonic Crystal Flat Lens,” Phys. Rev. Lett. 101, 073901 (2008).

W. ´Smigaj and B. Gralak, ”Validity of the effective-medium approximation of photonic crystals,” Phys. Rev. B 77, 235445 (2008).

A. Andryieuski, S. Ha, A. A. Sukhorukov, Y. S. Kivshar, and A. V. Lavrinenko, ”Bloch-mode analysis for retrieving effective parameters of metamaterials,” Phys. Rev. B 86, 035127 (2012).

W. B. Weir, ”Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62, 33–36 (1974).

Dong Jun Technology, EastFDTD v3.0, (Dongjun Information Technology Co., Shanghai, 2011).

C. Fietz, Y. Urzhumov, and G. Shvets, ”Complex k band diagrams of 3D metamaterial/photonic crystals,” Opt. Express 19, 19027–19041 (2011).

J. A. Reyes-Avendaño, U. Algredo-Badillo, P. Halevi, and F. Pérez- Rodríguez, ”From photonic crystals to metamaterials: the bianisotropic response,” New J. Phys. 13, 073041 (2011).

P. Y. Chen, C. G. Poulton, A. A. Asatryan, M. J. Steel, L. C. Botten, C. M. de Sterke, and R. C. McPhedran, ”Folded bands in metamaterial photonic crystals,” New J. Phys. 13, 053007 (2011).