Optical solitary wave solutions in quadratic nonlinear media

We study optical solitary wave solutions in one-dimensional quadratic nonlinear media with modulation of both the linear and nonlinear susceptibilities. Aiming at the coupled averaged equations that include induced quadratic and cubic nonlinearities derived recently, we obtain analytically bright and dark fundamental solitary wave solutions coupled by second harmonic waves that are plane waves. Furthermore, we investigate the stability of these solutions under the perturbations of both amplitude noises and phase noises by numerical simulations.