Modulational Instability In Fiber Bragg Gratings With Nonlinearity Management

Soon after the emergence of fiber amplifier technology, fiber grating is another amazing breakthrough, which is the ideal apparatus used for fiber communication, fiber laser and fiber sensor. Usually regarded as the potent of production of soliton, modulation instability is a very normal phenomenon existing in nonlinearity system. This paper researches on the modulation instability of fiber grating in nonlinearity management. The research result will be greatly beneficial for the development of the soliton theory and all-optical device based on fiber grating. The main research results are listed below:Firstly, we study MI in fiber Bragg grating with nonlinearity management that proposed recently. We begin with the coupled-mode theory, and then we obtained the new dispersion relation of modulation instability in nonlinearity management fiber Bragg grating.Secondly, from the new dispersion relation we get the gain spectrum for modulation instability in nonlinearity management fiber Bragg grating, and we compared it with normal nonlinear fiber grating. It is found that in the anomalous dispersion regime, the variance of Kerr nonlinearity alters the spectral width and amplitude of the gain spectrum, the gain amplitude of two distinct sidelobes originally on either side of zero wave number region diminishes to zero as the variance of Kerr nonlinearity increases, and a new single peak around zero wave number is formulated gradually after a region of zero gain; while in the normal dispersion regime, besides the original two gain regions, a new gain region is occurred around zero wave number region, and its gain amplitude increases as the nonlinearity management coefficient augments.Thirdly, we analyzed the reason why nonlinearity management cause the changing of gain spectrum of modulation instability. We found that it is the effect of odd-order term of f which describe the total energy collocation between forward wave and backward wave that causes the difference of modulation instability between normal dispersion region and abnormal dispersion region. In addition, caused by the occurrence of new first order terms ofωand q , the gain spectrum of modulation instability displays a significant asymmetry for high powers.