Analysis of optical directional couplers that include gain or loss and their application to semiconductor slab dielectric guides

The effect of gain or loss in one arm of a pair of parallel coupled optical guides has been investigated theoretically. The general transfer characteristics have been derived for the weakly coupled case in terms of the individual waveguide characteristics and the coupling coefficient. Examples of strongly coupled dielectric slab guides, appropriate for embodiment in the form of semiconductor heterostructures, have also been examined. Only small deviations from the weakly coupled behavior are found, even at maximum coupling when the core layers come into contact. In particular the interesting and useful condition where the two composite modes of the system become degenerate, with identical phase, attenuation, and field distribution characteristics, still occurs. Applications for integrated optics are discussed.