具有二阶和三阶非线性一维光子晶体中的耦合模孤子

Coupled solitons in one-dimensional photonic crystals with quadratic and cubic nonlinearities

研究同时具有二阶和三阶非线性的一维光子晶体中的耦合孤子动力学 .从Maxwell方程出发 ,利用多重尺度法 ,导出了光学整流场与两个基频电场包络的非线性耦合模方程组 ,给出了耦合模方程组的孤子解 .结果表明 ,由于二阶非线性导致的光学整流场对基频电场有调制作用 ,使得两个基频电场分量可以呈现为亮孤子 亮孤子、暗孤子 暗孤子及亮孤子 -暗孤子对 ;当两个基频电场的振动频率趋于光子晶体频带的带边频率时 。

The dynamics of the coupled solitons in one-dimensional photonic crystals with quadratic and cubic nonlinearities is studied. Starting from the Maxwell equation, the coupled-mode equations for the envelopes of two fundamental frequency mode and one low-frequency mode components due to the optical rectification are derived by multiple scales method. A set of coupled soliton solutions of the coupled-mode equations is provided. The results show that there exists a modulation of the fundamental frequency modes by the optical rectification field resulting from the quadratic nonlinearity, which makes the fundamental frequency mode components appear as soliton pairs of bright-bright, brigh-dark and dark-dark types. The optical rectification field will disappear when the frequencies of the fundamental frequency fields approach to the frequency of the photonic band boundary.