Propagation of eigenmodes and transfer amplitudes in optical waveguide structures

A method of transfer amplitudes suitable for modeling and simulation in integrated optical circuits is presented. The method is based on vectorial formulation of electrodynamics: distributions and propagation of electromagnetic fields in optical circuits are described by equivalent surface sources. This approach permits a division of complex optical waveguide structures into sets of primitive blocks and to separately calculate the transfer amplitude for each block. The transfer amplitude of the entire optical system is represented by a convolution of transfer amplitudes of its primitive blocks. Diffraction in slab regions is taken into account using known propagation functions. It is shown that the concept of a normalized transverse eigenfunction of the diffracted field is very useful in calculations of transfer amplitudes. The crucial role of transverse Bloch modes in propagation through multiwaveguide structures is emphasized. With this method, the eigenvalues and eigenfunctions of an arbitrary waveguide structure can be obtained with high accuracy. The general approach is illustrated with the transfer amplitude and efficiency calculations for a star coupler and a waveguide grating router.