Source: https://www.osapublishing.org/oe/abstract.cfm?uri=oe-20-14-15100
Timestamp: 2019-04-19 15:05:24+00:00

Document:
We study the anisotropic properties of multilayer fishnet optical metamaterials and describe topological transitions between the elliptic and hyperbolic dispersion regimes. In contrast to other hyperbolic media, multilayer fishnet metamaterials may have negative components not only in the effective permittivity tensor but also in the effective permeability tensor, thus allowing the realization of magnetic hyperbolic and generalized indefinite media.
D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 075103 (2006).
A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74, 075103 (2006).
M. A. Noginov, Yu. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94, 151105 (2009).
A. Fang, T. Koschny, and C. M. Soukoulis, “Optical anisotropic metamaterials: Negative refraction and focusing,” Phys. Rev. B 79, 245127 (2009).
L. M. Custodio, C. T. Sousa, J. Ventura, J. M. Teixeira, P. V. S. Marques, and J. P. Araujo, “Birefringence swap at the transition to hyperbolic dispersion in metamaterilas,” Phys. Rev. B 85, 165408 (2012).
H. N. S. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological Transitions in Metamaterials,” Science 336, 205–209 (2012).
E. Narimanov and I. Smolyaninov, “Beyond Stefan-Boltzmann law: thermal hyper-conductivity,” arXiv:1109.5444v1.
M. Beruete, M. Navarro-Cia, and M. Sorolla, “High numerical aperture and low-loss negative refraction based on the fishnet rich anisotropy,” Photonics Nanostruct. Fundam. Appl. 10(3), 263–270 (2012).
M. Beruete, M. Navarro-Cia, and M. Sorolla, “Strong lateral displacement in polarization anisotropic extraordinary transmission metamaterial,” New J. Phys. 12, 063037 (2010).
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).
J. Zhou, T. Koschny, M. Kafesaki, and C. Soukoulis, “Negative refractive index response of weakly and strongly coupled optical metamaterials,” Phys. Rev. B. 80, 035109 (2009).
A. Minovich, D. N. Neshev, D. A. Powell, I. V. Shadrivov, M. Lapine, I. McKerracher, H. T. Hattori, H. H. Tan, C. Jagadish, and Yu. S. Kivshar, “Tilted response of fishnet metamaterials at near-infrared optical wavelengths,” Phys. Rev. B 81, 115109 (2010).
C. Garcia-Meca, J. Hurtado, J. Marti, A. Martinez, W. Dickson, and A. V. Zayats, “Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths,” Phys. Rev. Lett. 106, 083104 (2011).
Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1959).
A. V. Chebykin, A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Yu. S. Kivshar, and P. A. Belov, “Nonlocal effective medium model for multilayered metal-dielectric metamaterials,” Phys. Rev. B 84, 115438 (2011).
A. A. Orlov, P. M. Voroshilov, P. A. Belov, and Yu. S. Kivshar, “Engineered optical nonlocality in nanostructured metamaterials,” Phys. Rev. B 84, 045424 (2011).
Fig. 1 (a) A unit cell with a=500 nm, b=351 nm, c=100 nm, d=45 nm, e=30 nm. (b) Single functional layer fishnet metamaterial. (c) Ten functional layer fishnet metamaterial. (d–f) Transmission, n and FOM for the single-layer fishnet (dashed curves) and 22-layer fishnet (solid curves). (g–i) Transmission, Real part of n and FOM for the fishnets versus wavelength and number of functional layers.
Fig. 2 Propagation of the electromagnetic wave through the multilayer fishnet metamaterial in y − z cross-section. (a) Normal incidence at wavelength 1.25 μm (see Media 1). (b) Oblique incidence at 45° angle, 1.20 μm wavelength (see Media 2). Color arrows show the direction of the phase velocity.
Fig. 3 (a,e) TE and TM polarization of incident wave. (b,f) Transmission of the ten-layer fishnet versus wavelength and angle of incidence for TE and TM. (c,f) Isofrequency surfaces for wavelengths 1.03 μm (red curves), 1.09 μm (green curve) and 1.17 μm (blue curve) for TE and TM polarizations. (d,h) Real part of neff for normal incidence (red), 30° angle of incidence (green) and 60° angle of incidence (blue) for TE and TM. Solid curves correspond to the absolute values of neff, dashed curves correspond to the neff with sign chosen as proposed in [13, 14].
(3) a = − Re [ k z k 0 ] 2 + Im [ k z k 0 ] 2 − sin ( ϕ ) 2 ; b = − Re [ k z k 0 ] 2 Im [ k z k 0 ] 2 .
(4) TE : k y 2 ε x μ z + k z 2 ε x μ y = ω 2 c 2 ; TM : k x 2 ε z μ y + k z 2 ε x μ y = ω 2 c 2 .
(5) ε ^ = ( ε x ( ω , k x ) 0 0 0 ε y 0 0 0 ε z ( ω ) ) ; μ ^ = ( μ x 0 0 0 μ y ( ω ) 0 0 0 1 ) .

References: V. 
 V. 
 V. 
 V. 
 V. 
 V. 
 V.