Approximate solution of eigenmode problems for layered coupled waveguide arrays

The characteristic modes of coupled waveguide arrays with a simple layered structure are examined using the approximate coupled wave theory. It is shown that evanescent waves may arise from total internal reflection at a boundary between two semi-infinite arrays. The transmission and reflection coefficients for this process are derived. If a suitable, finite, array is sandwiched between two semi-infinite arrays so that total internal reflection occurs at both boundaries, "guided" characteristic modes may arise. These have most of their power confined between the boundaries. The theory is used to specify an array distribution suitable for use in a transverse-mode-locked array laser.