Spectral properties of nonlinear surface polaritons of Mid-IR range in a "semiconductor–layered metamaterial" structure

Spectral properties of surface TM-waves (polaritons) are considered in the guiding structure based on a narrow-band semiconductor (n-InSb) and a nanocomposite medium (layered metamaterial) in the mid-infrared region ($5\div20 \mu m$). The nanocomposite medium has a weak gyrotropy and contains layers of bismuth-doped iron garnet (BLIG, Lu$_{3-x}$Bi$_x$Fe$_{5-y}$Ga$_y$O$_{12}$) and gallium-gadolinium garnet (GGG, Gd$_3$Ga$_5$O$_{12}$) layers magnetized to saturation. Solutions of the dispersion equations are investigated for the cases of linear and nonlinear response of the semiconductor. For an analytical description of the nonlinear response of the structure we use the «uniaxial» (longitudinal) and «biaxial» approximations. Dispersion spectra for the propagation constant, as well as field and energy characteristics of the surface polaritons are obtained and analyzed. Regions of the existence of soliton-like wave-fields of the surface polaritons are found for each of the description methods used. It is shown that the «uniaxial» model may be unsuitable for the calculation of the electromagnetic fields and energy flows in the structures based on cubic nonlinear media.