Calculation of light distribution in optical devices by a global solution of an inhomogeneous scalar wave equation

A numerical scheme is suggested for solving the scalar wave equation for optical devices characterized by a z-dependent refractive index. The homogeneous wave equation is converted into a single-column inhomogeneous linear system by applying imaginary (absorbing) boundary potentials at the device boundaries. The imposed absorbing boundary conditions enable discrete representation of the device on a compact grid. Our scheme is based on applying an efficient sparse preconditioner to the linear system, which enables its global solution (i.e., simultaneously for all z values) by fast iterative methods, such as the quasi-minimal residual algorithm. A single solution of the inhomogeneous equation with the imaginary boundary operators allows the calculation of mode-specific as well as region-specific light-intensity coupling probabilities for initial mode of interest. Numerical examples illustrate the usefulness of the suggested scheme to the optimization of optical devices.