Fizika Nizkikh Temperatur: Volume 47, Number 11 (November 2021), p. 1039-1044
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Transverse Anderson localization of evanescent waves propagating in randomly layered mediaO. V. Usatenko^{1}, S. S. Melnyk^{1}, and V. A. Yampol’skii^{1,2} ^{1}O. Ya. Usikov Institute for Radiophysics and Electronics of NAS of Ukraine, Kharkiv 61085, Ukraine ^{2}V. N. Karazin Kharkov National University, Kharkiv 61077, Ukraine Received June 15, 2021, published online September 24, 2021 Abstract We study theoretically the transverse Anderson localization of light in the simplest geometry, where the p-polarized wave propagates along the layers in the randomly stratified dielectric and evanesces exponentially in the direction across the layers. In this case, there exist two reasons for the localization of the wave in the direction transverse to its propagation: the usual evanescent wave confinement and the Anderson mechanism related to the randomness of the spatial distribution of permittivity. We solve the problem using the retarded-Green- function formalism in the Born approximation and show that, for fixed values of the wave frequency ω and wavenumber q, the random inhomogeneity results in the weakening of the wave localization. In the case of the surface plasmon-polaritons (SPPs) propagation, the Anderson mechanism changes the dispersion law for SPPs, moving the dispersion curves away from the light line. Therefore, the localization depth varies in different ways when increasing the disorder, depending on which of the values, wave vector q or frequency ω, is fixed. Namely, the localization depth increases for given q, but it decreases for given ω. Key words: inhomogeneous wave, depth of localization, Green's function, surface plasmon-polariton, dispersion law. |