Vectorial coupled-mode solitons in one-dimensional photonic crystals

We study the dynamics of vectorial coupled-mode solitons in one-dimensional photonic crystals with quadratic and cubic nonlinearities.Starting from Maxwell's equations,the vectorial,ths vectorial coupled-mode equations for the envelopes of two fundamental-frequency optical mode and one low-frequency mode components due to optical rectification are derived by means of the method of multiple scales.A set of coupled soliton solutions of the vectorial coupled-mode equations is provided.The results show that a modulation of the fundamental-frequency optical modes occurs due to the optical rectification field resulting from the quadratic nonlinearity.The optical rectification field disappears when the frequency of the fundamental-frequency optical fields approaches the adge of the photonic bands.