迭代法重建平板光波导折射率分布

提出了一种用于重建渐变折射率平板光波导折射率分布的方法，这种方法通过数值法求解亥姆霍兹方程．从光波导的低阶模开始采用迭代法顺次对各个模式对应的“转折点”位置进行校正．并多次重复迭代以消除“转折点”外折射率分布的变化对相应模式“转折点”位置的影响。借助WKB近似原理说明了这种方法迭代过程中“转折点”坐标的收敛性。对折射率按照指数规律变化的平板光波导的折射率分布重建结果证明这种方法具有较高的精度。分析表明：这种方法克服了WKB法固有的缺陷，即忽略模式“转折点”外折射率分布对相应模式传输常鞋的影响和“转折点”处相移的不确定性，因而比逆WKB法具有更好的自洽性和精确性。

Reconstruction of Refractive Index Profile of Diffused Planner Waveguide by Iteration Method

An iteration method is presented to reconstruct planar waveguide refractive index profile from mode indices spectra. In the current method, a numerical process is employed to solve the Helmholtz equation, the “turning point” positions of all the propagation modes are adjusted in sequence from the lowest to the highest by iteration, and repetitions of the iteration are performed to eliminate the effect of refractive index profile variation beyond each “turning point” on the corresponding “turning point” position. The convergence of “turning point” position over iteration in this process is briefly illustrated by means of the WKB principle. A demonstrative reconstruction is made for a planar waveguide with exponential refractive index profile, and results show that the current method can be used to reconstruct planar waveguide refractive index profile with high accuracy. Analysis indicates: this iteration method is expected to be superior in both self-consistence and accuracy to the inverse WKB method.