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 waveguides 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 the propagator of such a waveguide structure is derived in closed form. The complete variational calculation is presented for the case of parallel waveguides only, and the propagator, lowest-order-mode field profile, the first two lowest-order-mode propagation constants, and the beat length of the structure are determined in closed form.