EFFECTS OF NONLINEARITY ON WAVE PROPAGATION IN FIBER BRAGG GRATINGS

In this paper, we show that the solution of linear coupled mode equations (LCME) is a good approximation to that of the nonlinear coupled mode equations (NLCME) for small times, provided that the nonlinearity is weak. We bound the difierence between the two solutions using energy estimates. We illustrate our flndings in numerical examples. This work is motivated by the need to examine the behavior of a flber Bragg grating when large amplitude light is propagated in the flber. We start with the assumption that the grating has been designed for operation in the linear regime, while the flber itself has a mild nonlinearity. A flber Bragg grating, in its simplest form, is a length of flber whose index of refraction is periodic in the direction of light propagation. It can be made by exposing a treated flber to ultra- violet radiation which changes the index of refraction. It has many uses, for instance, flltering and dispersion compensation (6). It works by coupling the forward- and backward-moving waves in the flber. The periodicity and the wavelength of light determines the coupling strength. While it is not the scope of this work to examine the rich phenomena that result from nonlinearity and periodicity, it should be mentioned that some work exploring such aspects as solitons, gap solitons, and light-stopping, exists (3,4,9). In this work, we start with the nonlinear coupled mode equations (NLCME), whose derivation can be found in (9). It has been pointed out that NLCME is related