为了实现一个表达式同时反映Y分支光波导在纵横两方向上的折射率分布, 通过对玻璃结构和离子交换过程进行分析, 采用逆向分离变量法提出了基于横向和纵向两个方向折射率分布函数乘积的横截面折射率分布函数, 并利用MATLAB软件对优化结果进行了编程模拟。利用Tl+-Na+离子交换法在BK7玻璃基底上制备了Y分支1×2型3维光波导, 利用雅明干涉法对光波导横截面的折射率分布进行了测量。结果表明, 利用改折射率分布函数模拟得到的Y分支光波导横截面折射率分布与雅明干涉法实验测得的结果吻合。该改进型折射率分布函数可以对Y分支光波导横截面折射率分布进行模拟, 能准确快捷地对Tl+-Na+离子交换Y分支3维光波导横截面折射率分布进行重建。

In order to describe the refractive index profiles of Y-branch waveguide in x and y direction with only one expression, after analyzing the construction of glass substrate and the ion exchange process, an expression based on the product of refractive index distribution functions on the horizontal direction and the vertical direction was put forward by means of inverse variable separation method. Then the refractive index profiles were simulated with MATLAB. A 1×2 Y-branch optical waveguide was fabricated on BK7 glass substrate by means of Tl+-Na+ ion-exchange method, and its refractive-index profiles was measured by means of interference method. The simulated profiles were in good agreement with experimental results. The results show that the refractive-index distribution of Y-branch optical waveguide in cross-section can be reconstructed by the improved function n(x, y) easily.