Abstract

The field correction method is a numerical method for calculation of scalar modes of waveguides with arbitrary index profiles, that can be adequately represented by a two-dimensional array. The method is based on the local minimization of a finite difference approximation of the scalar wave equation by locally modifying the field. The field, also stored in a two-dimensional array, is modified iteratively, point by point, until the effective index of the mode, calculated by integration over the total field, converges to the desired precision. The method thus generates the field and propagation constant of the mode. The boundary conditions determine which low order mode is calculated. Higher order modes are calculated by modifying a field which is orthogonal to that of the lower order modes. The accuracy of the method is limited by the spacing of the grid points which describes the index profile and the field. The method is reasonably fast, though the calculation time depends on the precision required and the index steps, and can easily be implemented on a personal computer. Examples of mode calculations for fused couplers and rib waveguides are presented and component design is discussed.

© 1993 Optical Society of America