A.V. Sadovnikov, A.G. Rozhnev

The Bragg grating systems is widely used in the optical communications systems, as a notch filters, in the optical multiplexers and demultiplexers with an optical circulator and as a fiber Bragg grating sensors. The nonlinear waveguides and the periodical nonlinear structures exhibit attractive properties that make them suitable for novel devices development with the wavelength tuneable characteristics. In this paper, the model of Bragg grating consisting of periodical layers with the Kerr nonlinearity is considered. The values of the cut-off frequencies are approximately estimated with the effective refractive index method. The obtained values of the cut-off frequencies are in good correspondence to the theoretical results The dynamic of electromagnetic wave propagation in the nonlinear Bragg grating is numerically studied. For the calculations of the transmission spectra and spatio-temporal dynamics we utilize the FDTD (Finite Difference Time Domain) numerical simulation method. To simulate the wave propagation in an unbounded medium the PML (Perfectly Matched Layer) absorbing boundary conditions was used. The possibility of the propagation of the signal which frequency lie within the band gap was demonstrated: the CW signal with the small amplitude and frequency which lie within the band gap exponentially decay along the system, but it was demonstrated that increasing the input signal amplitude one can obtain the signal propagation along the system. Moreover the signal profile inside the Bragg grating is specifically modulated.