A general method for calculating the solution of the scalar wave equation for the field propagating through integrated optical devices is presented. The method is capable of a three-dimensional description and of treating problems with reflected waves. It consists of dividing the device into a series of sections of axially uniform waveguides. The modes in each section are found by expansion of the field in a two-dimensional Fourier series and solving the associated matrix eigenvalue problem. Propagation is then described by relating the mode amplitudes of each section to the previous one. The amplitudes are related by a matrix that is the product of the eigenvector matrices of the two sections. The method is illustrated by the analysis of an adiabatic mode transformer, the coupling of light from a semiconductor laser through free space to a waveguide, and the propagation through an adiabatic 3 dB coupler and Y branch.
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