Bragg resonance in multilayer structure with compound nonlinear layer

Abstract

Transmission of plane monochromatic waves through the Bragg layered resonators have been considered. Iterative numeric solutions for complex amplitudes of reflected and transmitted waves are found by modified method of transmission matrices. Influences of Kerr nonlinearity of permittivity of some layers on resonance properties have been investigated. Hysteresis behavior is observed for case of combination of high quality factor and nonlinearity.The emergence of powerful radiation sources in microwave, submillimeter, and optical frequency ranges stimulated intensive theoretical research and provided an opportunity to the experimental study of nonlinear phenomena.There are a lot of effects caused by nonlinearities: focusing, defocusing, wave interaction, bistability and multistability, the generation of spatial structures, optical turbulence, etc. One of the most important technical applications of nonlinear material properties is to create a logical device, memory and information processing devices based on the phenomenon of hysteresis [1][2][3][4].It is known that bistability (multistability) is characteristic property of nonlinear systems with feedback. The system can take two (or more) stable states at one and the same input power [5]. For the existence of multistable input-output characteristics in given intervals of the input variable, the values of feedback and nonlinearity must be in a specific ratio [6].The simplest model of nonlinearity is the Kerr nonlinearity. Such a model quite well agrees with a lot of experimental results [1, 6], but does not take into account the generation of higher frequency harmonics. It assumes the permittivity dependence on the square modulus of the electric field with a proportionality coefficient  . The nonlinearity coefficient has a broad range of variation. For example, the sodium vapor has coefficient of nonlinearity kW cm / 10 2 8   , the semiconductors have coefficient of nonlinearity kW cm / 10 10 2 2 5     , liquid crystals are characterized by "gigantic" nonlinearity kW cm / 1 . 0 2  . And in all cases, the physical mechanisms of nonlinearity are different, and the increasing of the value of  is accompanied by increasing inertial response of the nonlinear system [1,8].Using the Bragg reflectors for strong frequency-selective feedback in Fabry -Perot resonator allows us to observe multistability with less thickness of the nonlinear medium [8]. In most cases, the exact solution of problem of electromagnetic field distribution on the boundary of the layered Bragg structure with Kerr nonlinear layers can not be found, and we have to use approximate numerical methods [9].This approximate numerical method takes into account changing the field amplitude on the thickness of the nonlinear layer. The sufficient accuracy of proposed method can be achieved by increasing the number of sublayers decomposition of the nonlinear resonance layers. The presence of several nonlinearities in the resonant layer of Bragg structure leads to a complex hysteretic behavior of the freq...