Effect of Nonlinear Loss and Gain in Multilayer PT-Symmetric Bragg Grating

The analysis of a nonlinear gain and loss in multilayer PT-symmetric Bragg grating structure is presented. The simple model shows wave propagation through nonlinear multilayer grating in an optical way (without the need to use complex methods). A new behavior of output intensity versus input intensity in such a structure has been obtained for the first time. At the beginning, the structure is examined without taking into account the gain and loss saturation. In this case, the characteristics of reflection and transmission coefficients, and eigenvalues of S matrix are obtained as a function of geometrical parameters of Bragg gratings. The characteristics reveal special points, discussed later, where the structure is PT-symmetric or has a broken symmetry phase. In the first case, the amplitudes of both waves, travelling in opposite directions, do not change, which corresponds to the unimodularity of the S matrix eigenvalues. In the other case, the increase of one amplitude forces the decrease of the other one, and the eigenvalues have reciprocal magnitudes. For these points, the systematic study including the gain and loss saturation effects is conducted. The obtained characteristics illustrate the influence of the saturation intensities on the output intensities, reflection and transmission coefficients, and eigenvalues of S matrix for the incident plane wave with a given intensity. The characteristics demonstrate strong nonreciprocal response and the bistable behavior of the structure. Moreover, for certain values of Bragg gratings geometrical parameters, the investigated structure transits from broken symmetry phase to a PT-symmetric one.