FINITE-DIFFERENCE SOLUTION OF INHOMOGENEOUS WAVE-GUIDE MODES USING A FAST DIRECT SOLVER ROUTINE

The objective is a computer program, based on a "fast direct solver", to solve for the dominant mode in a waveguide of arbitrary refractive index profile within a rectangular box. The 2-dimensional field problem is first reduced to a conventional eigenvalue problem in terms of the transverse magnetic field components. The two coupled scalar equations are solved using the software package "FISHPAK", which solves a scalar Helmholtz problem using finite differences with an M by N mesh in time proportional to MNlog2N. This "fast solver" is within two iteration loops,- the outer being a "Rayleigh quotient iteration", the inner solves the two coupled equations. Results emerge typically in between 2 and 30 total calls of FISHPAK.