Note on optoelectronic propagation using spectral index technique

A variational principle first applied in optoelectronics to find the propagation constants of rib waveguides is here applied to a radiation problem in the form of a thin dielectric waveguide incident normally upon a uniform dielectric half-space. This is compared with a new analytic solution to the same problem. The results are very encouraging, being exact for the amplitude of the reflected wave, and within 4% for its phase. The far-field profile of the ongoing beam with its narrow, forward-scattered shape is shown as it expands. The method is applicable to mode conversion at a laser facet and to other optoelectronic problems.