Transform technique for planar optical waveguides

A new method for obtaining total field solutions and propagation constants for planar optical waveguiding structures by using a transform technique is presented. The method reduces the two-dimensional Helmholtz equation into a system of linear algebraic equations that can be solved on a computer. The method takes into account arbitrary input excitation and is applicable to arbitrary refractive-index variations in the transverse direction. We illustrate the method by applying it to directional couplers and straight waveguides with graded-index profiles-parabolic and exponential profiles. The results are in good agreement with analytical results