PATH-INTEGRAL ANALYSIS OF THE PROPAGATOR OF 2 COUPLED GRADED-INDEX WAVE-GUIDES

The method of path integration is used to study coupled graded-index w aveguides in the context of paraxial, scalar-wave optics. The cases of strong and intermediate strength coupling for waveguides of arbitrary and variable spacing are considered, and a variational estimate of th e propagator of such a waveguide structure is derived in closed form. The complete variational calculation is presented for the case of para llel waveguides only, and the propagator, lowest-order-mode field prof ile, the first two lowest-order-mode propagation constants, and the be at length of the structure are determined in closed form.