Abstract

In recent years substantial progress has been made by many workers in accurately modeling integrated optics devices using beam propagation techniques. The BPM is based on the symmetric factorization of a unitary evolution operator for the paraxial or Schrödinger wave equation into unitary parts representing free space propagation and phase changes induced by a space-dependent refractive index. the accuracy of the BPM is due in part to the stability guaranteed by the unitary form of the factored evolution operator as well as the accuracy with which the free space propagation operator can be represented using FFT techniques. The BPM, however, has important shortcomings including the following: it is restricted to second order in the propagation step due to commutation error, it cannot be applied to coordinate systems other than Cartesian, and it is restricted to slowly varying refractive index inhomogeneities. The latter restriction limits the accuracy of the BPM for some applications to semi-conductor ridge waveguide structures, for example.

© 1991 Optical Society of America