Patent ID: 8407036

Claim:
A method for modeling one or more electromagnetic field modes of a waveguide, the method comprising: calculating, using a processor, a first matrix using a refractive index profile of the waveguide, the first matrix comprising a plurality of elements and having a first bandwidth, the plurality of elements of the first matrix stored in computer memory and representing an action of Maxwell's equations on a transverse magnetic field within the waveguide; rearranging the plurality of elements of the first matrix stored in computer memory to form a second matrix having a second bandwidth smaller than the first bandwidth; shifting the second matrix and inverting the shifted second matrix to form a third matrix; calculating one or more eigenvalues or eigenvectors of the third matrix corresponding to one or more modes of the waveguide; and calculating one or more propagation losses corresponding to the one or more modes of the waveguide using boundary conditions which comprise surrounding a simulation domain of the method by an absorbing material.