A bidirectional beam propagation method for periodic waveguides

For waveguiding structures with multiple longitudinal reflecting interfaces, a bidirectional beam propagation method has been developed using a scattering operator formulation and rational approximations to the square root and the propagation operators. For periodic waveguides, it is possible to significantly speed up the method when scattering operators for a waveguide with s/sub 1/+s/sub 2/ periods are obtained directly from those operators associated with waveguides having s/sub 1/ and s/sub 2/ periods. The required computing time is then proportional to the logarithm of the total number of periods.