Nonlinear Verdet law in magnetophotonic crystals: Interrelation between Faraday and Borrmann effects

Abstract

The magneto-optical Faraday effect is studied in one-dimensional magnetophotonic crystals ͑MPCs͒. Mechanisms of a strong enhancement of the Faraday rotation at the edges of the photonic band gap are considered. High difference of refractive indexes of bismuth-substituted yttrium iron garnet ͑Bi:YIG͒ and SiO 2 layers provides a strong spatial localization of the optical field in Bi:YIG layers, which leads to manifold Faraday rotation enhancement at the photonic band edges. The Faraday rotation angle in the finite MPCs appears to be a nonlinear function of the total thickness of magnetic material in the stack that can be interpreted as the nonlinear Verdet law. Relation between the enhancement of the Faraday rotation and localization of optical field in magnetic layers is treated as a Borrmann-type effect. This relation shows that the Faraday rotation can be considered as a measure of the density of photonic states trapped within Bi:YIG layers.

Inverse Borrmann effect in photonic crystals

“…In the first case, for the frequencies at the bottom of the BG, the energy concentration in a high permittivity layer is greater than that for frequencies at the top of the BG. The direct Borrmann effect was confirmed in recent experiments [4]. In the case of the inverse Borrmann effect, the spatial distribution of energy is inverted and the electric field for frequencies at the bottom of the BG is mainly localized in the low permittivity layers.…”

“…3, it was theoretically shown that the spatial distribution of the electric field in a MPC strongly depends on both the field frequency and the material parameters of magnetic and non-magnetic layers. As a result, a possibility of a substantial enhancement of the Faraday effect as well as nonlinear magneto-optical effects in MPCs was predicted [3][4][5] and experimentally verified. 4 The dependence of optical and magneto-optical properties of PCs on the spatial distribution of electromagnetic waves inside PCs can be considered as an optical analog of the Borrmann effect, which manifests itself in anomalous absorption/transmission of x-rays in near-perfect crystals.…”

“…As a result, a possibility of a substantial enhancement of the Faraday effect as well as nonlinear magneto-optical effects in MPCs was predicted [3][4][5] and experimentally verified. 4 The dependence of optical and magneto-optical properties of PCs on the spatial distribution of electromagnetic waves inside PCs can be considered as an optical analog of the Borrmann effect, which manifests itself in anomalous absorption/transmission of x-rays in near-perfect crystals. 6 In this paper, we present a detailed analysis of the optical Borrmann effect in one-dimensional (1D) PCs.…”

Transmittance Magneto-Optical Responses of One-Dimensional Magnetophotonic Heterostructures

“…For both substructures, the magnitude of FR has local maxima at the PBG edges that corresponded to the maxima in the transmittance spectra. The maximum angle of the FR for each substructure is at the long-wavelength edge of the PBG, which is a clear manifestation of the optical Borrmann eect in the articially stratied media [23]. Figure 2c shows the transmittance spectrum of the heterostructure SH.…”

Magnetic Properties of Magnetoplasmonic Crystals Based on Commercial Digital Discs

“…Sensitivity of MO sensors can be enhanced by creating them on the base of the magnetophotonic crystals which allows one to enhance magneto-optical Faraday or Kerr eects at the edge of the photonic band gap or at the micro cavity mode [4]. Magnetoplasmonic nanostructures represent a special class of plasmonic nanostructures fabricated from magnetic metals (for example, from nickel, cobalt and iron or from composites of magnetic materials) and noble metals [58].…”