Ideal Soliton Environment Using Parametric Band Gaps

Simultaneous solitary wave solutions for laser propagation in nonlinear parametric media with up to ( $3+1$) dimensions are proved to exist. The combination of the large dispersion of a Bragg grating and the strong nonlinearity of ${\chi }^{\left(2\right)}$ optical material results in stable behavior with short interaction distances and low power requirements. The solutions are obtained by using the effective mass approximation to reduce the coupled propagation equations to those describing a dispersive parametric nonlinear waveguide, and are verified by solving the complete set of coupled band-gap equations numerically.