统一非对称光波导横向耦合模理论分析

Analysis of unified unsymmetric lateral coupled-mode theory of optical waveguide

光波导横向耦合模理论包含正交耦合模理论和非正交耦合模理论两大类,为了追求形式上的完美,两类理论没有统一的解析解,并且都没有对非匹配耦合系统中耦合功率的非对称性进行深入研究.本文一方面由Helmholtz方程出发推导出了一种新型的非正交耦合模方程,并对两类理论中的耦合模方程进行了统一处理和求解,得到了一种统一的解析解;另一方面根据所得到的统一的解析解对非匹配耦合系统中耦合功率的非对称性进行了详细研究,计算结果表明非匹配耦合系统中的最大互耦合功率和最小自耦合功率均可用统一的解析解进行近似计算.

Lateral coupled-mode theory of optical waveguide includes orthogonal coupled-mode theory and nonorthogonal coupled-mode theory. However, the two kinds of coupled-mode theories do not have unified analytical solutions. And they both do not deal with the asymmetric coupling power of unmatched-coupled waveguides deeply. On the one hand, a new kind of nonorthogonal coupled-mode equation is derived from the Helmholtz wave equation in this paper. And both of the orthogonal coupled-mode equations and the nonorthogonal coupled-mode equations are processed and solved uniformly. As a result, a unified solution is obtained. On the other hand, the asymmetric coupling power of unmatched-coupled waveguides is studied in detail, based on the obtained solution. The calculated results show that both of the maximum mutual-coupling power and the minimum self-coupling power can be approximated by the unified solution.