Abstract

The beam propagation method ^1,2 has been extensively employed in recent years to model various guided wave structures. This method involves an operator solution of the Hemholtz equation (or of this equation in the Fresnel approximation) which has the advantageous property that it gives a unified treatment of guided and radiation modes in complex waveguide structures, where the index is also allowed to vary in the propagation direction . Hence, an incident exciting field can be traced through the structure, and important waveguide and device properties can be calculated. These include propagation constants and modal fields^3,4, loss ( e g due to bends) ⁵, crosstalk in switches⁶, switching voltage in electrooptic devices⁷, coupling efficiences as well as gain and attenuation in media, with gain or loss⁸. This makes the method ideally suited for simulation of integrated optics devices^9,10. However, the method is only applicable in cases with limited transverse spatial frequency bandwidth of index profiles and field (paraxiality requirements) as well as limited index steps ^11,12.

© 1989 Optical Society of America