s‐polarization Brewster's angle of stratified metal–dielectric metamaterial in optical regime

Abstract

1 Introduction A metamaterial is an artificial composite with an exotic electromagnetic response that is not readily found in nature. It consists of a unit with a size smaller than the wavelength of the incident electromagnetic wave while much larger than the atomic scale. Such a composite can be regarded as an effective new material, the properties of which can be designed artificially by its structure.In 1967, Veselago considered wave propagation in a material with negative permittivity and negative permeability (double negative material) [1]. He noticed that light can propagate in such a medium but in a strange way: The wave vector and the Poynting vector are opposite in sign. It is referred to as a left-handed material because electric, magnetic and wave vectors form a left-handed triad. At the interface between an ordinary material and such an extraordinary medium, the light refracts in a "wrong" direction in order to conserve the tangential component of wave vectors and energy flow at the interface. Thus the refractive index of this material is understood to be negative in this case.In 1999, Pendry pointed out that it is possible to realize negative permeability by use of artificial composites [2]. In 2000, Smith demonstrated that the double negative material at microwave regime with the use of split-ring resonators (SRR) and a metal wire array [3].So far in metamaterial research, SRRs and their derivatives have been mainly used in order to modify permeability. The magnetic-field component of the incident light induces an electric current inside the ring, and then the induced magnetic field negates the incident magnetic field, which changes the magnetic permeability. The cut in the ring works as a capacitor that accumulates charge carried by the current. The inductance of the ring and the capacitance determines the resonance frequency of SRR.It can be shown that the material with nonunity permeability exhibits an optical response that does not occur in ordinary materials. For instance, in ordinary transparent materials such as quartz, the reflectivity for p-polarization vanishes at a certain incident angle (Brewster's angle). But as can be seen from the Fresnel equations below, Brewster's angle of s-polarization can also exist, if permeability is not unity:We demonstrate that the optical reflectivity for s-polarized light vanishes at a certain angle in a stratified metal -dielectric metamaterial numerically and experimentally. The metamaterial consists of a unit cell where a Ag layer of 30 nm thickness is sandwiched by Al 2 O 3 layers of 60 nm thickness. In order to understand the phenomenon in terms of effective permittivity and permeability, we extended a field-sampling method. The permeability is found to be significantly different from unity, which is the origin of Brewster's angle for s-polarization. The microscopic field distribution is readily coarse grained with the effective optical parameters. The present result is a manifestation of the magnetic response in the optical regime. where r s , r p ar...

Diversity of optical indices in stratified metal dielectric metamaterials

“…This is because SMDMs often show nonlocal responses. 12,13 Therefore, the validity of effective media approximation is restricted at relatively narrow incident angles. To obtain adequate descriptions for deep oblique incidence or a wide range of incident angles, it is inevitable to include nonlocality or to give effective parameters such as ε eff and μ eff k-dependence (k: wave vector).…”

“…9 Moreover, several interesting results on finitely thick SMDMs have been reported to date: Negative refraction behaviors of Gaussian beam under p polarization, 10,11 nonlocal responses, 12 and Brewster effect under s polarization. 13 When light travels in the xz plane of Fig. 1, p and s polarizations satisfy H ŷ and E ŷ, respectively.…”

No-Reflection Phenomena for Chiral Media

“…However, since we can fabricate magnetic media in high frequency regions with a metamaterial technique (Pendry et al, 1999;Holloway et al, 2003;Zhang et al, 2005), the Brewster condition for TE waves can be satisfied (Doyle, 1980;Futterman, 1995;Fu et al, 2005). In fact, the TE Brewster effect has been experimentally observed in the microwave region (Tamayama et al, 2006) and also in the optical region (Watanabe et al, 2008). In addition to permittivity and permeability, chirality parameter and non-reciprocity parameter can be controlled using metamaterials.…”

Transverse-electric Brewster effect enabled by nonmagnetic two-dimensional materials

“…Recently, the advent of metamaterials [9] provides a new way to create nonunity effective relative permeability in all-dielectric systems. This led to the TE Brewster effect being experimentally reported in bulk metamaterials [10,11], and the Brewster effect being studied in magnetic [12,13], anisotropic [7,[14][15][16][17][18][19], chiral [2,20], and bianisotropic [21] media. Moreover, although the Brewster effect is regarded as a phenomenon occurring at a homogeneous interface between two different bulk media, its concept has been extended to the thin metasurface through artificially tailoring the interface to be nonhomogeneous [19,22,23].…”

“…Moreover, although the Brewster effect is regarded as a phenomenon occurring at a homogeneous interface between two different bulk media, its concept has been extended to the thin metasurface through artificially tailoring the interface to be nonhomogeneous [19,22,23]. Note that in order to realize the TE Brewster effect, the unit cells in the metamaterials and metasurfaces are all designed to have * kaminer@mit.edu † hansomchen@zju.edu.cn strong magnetic responses [10,11,22,23]. It is still a longstanding challenge to achieve the TE Brewster effect at a homogeneous interface in all-dielectric systems without magnetic responses.…”