Optical waveguide analysis using the fourier transform and its application to intersecting waveguides

In analyzing inhomogeneous waveguides, this paper derives an analytical method that is effective even for the radiation mode light. Also, the propagation characteristic of intersecting waveguides is studied by using this method. In this analysis, considering virtual waveguides that include the real waveguide completely, the propagating light is expressed by the Fourier transform with virtual modes set up in the virtual waveguides. Moreover, using the concept of the power flow equation, the Helmholtz equation is transformed into a difference equation of Fourier coefficients, where weak coupling and paraxial rays are assumed.

Applying this method to intersecting waveguides having inhomogeneous index gradients, we study the dependency of the propagation characteristics of the intersecting angle and the index gradient difference. From these results, light propagation in branching waveguides is found for low intersecting angles. This phenomenon is explained successfully by a model which combines TM₀ and TM₁ modes. Furthermore, the propagation characteristics of inhomogeneous waveguides are simulated and their dependency on the index gradient is studied.