SOLITARY WAVES IN BRAGG GRATINGS WITH A QUADRATIC NONLINEARITY

We study the formation of solitary waves in quadratic nonlinear materi als where the dispersion is provided by linear mode coupling mediated by a Bragg grating. We show that solitary wave solutions can be analyt ically found provided that the coupling of the second-harmonic waves c onsiderably exceeds that of the fundamental ones. Furthermore, we nume rically determine solitary wave solutions for the general case. These solutions prove to be close to the analytical ones. A nontrivial prope rty of Bragg grating solitary waves is that they do not fill the compl ete parameter space where exponentially decaying functions are allowed to exist. Instead, we find internal boundaries inside this parameter space where the soliton intensify diverges. Moreover, double-hump solu tions are found where a numerical propagation procedure shows that som e of them are fairly robust.