Theory of modulational instability in a parametric band gap system

Summary form only given. We study the modulational instability (MI) of continuous electromagnetic waves in Bragg gratings with quadratic nonlinearity. There are three major reasons for this. The first is that the absence of MI is a necessary condition for the stable co-propagation of second- and sub-harmonic fields, and hence for the stability of dark simultons. Secondly, MI in the closely related system consisting of a grating with a Kerr nonlinearity has proven interesting, and has the potential application of a tunable pulse generator; however, the effect of a quadratic nonlinearity can be much larger than that of a Kerr nonlinearity, and the threshold in the system we consider can thus be much lower. Thirdly, this system may provide a useful way of generating second-harmonic radiation in an integrated optics environment; the modulational instability provides some understanding of the complex relationships between the four different fields that are present.