渐变折射率光波导精确色散方程的解析表示及实验验证

The characteristics of the propagating modes in optical waveguides with arbitrary refractive index profile are obtained by solving Maxwell's equations subject to the appropriate boundary conditions. However, exact analytic solutions are difficult to obtain except for several special profiles. The most popular approximate technique in this field is WKB method owing to its simplicity and the clear physical explanation. On the other hand, WKB method is appropriate for the slow index changing profiles. According to analytic transfer matrix (ATM) method, an analytic dispersion equation with clear physical meaning has been proposed in this program. Not only it keeps the simplicity of the WKB method, but also it includes the contribution of the sub-waves, which is always neglected by the WKB method. Furthermore, we conclude that the phase shift at a turning point is , but not as in the WKB method. Due to the above substantial improvements, the ATM equation we developed is exact. Based on the exact ATM equation, an inversed ATM method is proposed to replace the IWKB method. It has been proved to be universally reliable not only in slowly changing profiles but also the profiles changing rapidly in which IWKB method would find difficult.

利用转移矩阵理论建立渐变折射率光波导的解折色散方程，该方程不仅具有简单的相位积分的形式，而且可给出数值方法才能达到的精确度。我们的方法可解决WKB近似转折点处场的⑸⒑妥鄣愦Φ南嘁屏酱竽烟猓⒖赏乒愕桨氲禾辶孔于搴投嘣臃肿拥脑际缱犹攘煊颉Ｔ诖嘶∩希馔ü齏KB近似无法处理的光漂白聚合物波导进行实验证实。