Condensed matrix method for implicit type scheme in imaginary distance beam propagation method

Abstract

The modes of a waveguide structure can be accurately determined using finite difference imaginary distance beam propagation method. In implicit type formulation of the problem, a matrix equation has to be solved. The matrix is sparse and large. The sparsity of the matrix can be used to form a condensed matrix of much lower dimension leaving aside the zero element blocks; this condensed matrix takes much smaller storage space and consequently saves a great deal of run-time. The algorithm for the solution of the matrix equation from such a condensed matrix is developed here. This method is comparable with other sparse matrix methods in terms of CPU usage.