Mode analysis and prism coupling for multilayered optical waveguides

Recursion relationships are developed which generate the characteristic mode equations for both free and prism-loaded optical waveguides composed of N arbitrary dielectric layers. The solutions of these equations allow the computation of the effective mode-propagation coefficients and, in the case of prism loading, leakage rates and coupling efficiencies for arbitrary gap shape and coupling strength. As an illustration four specific prism/waveguide couplers with linearly tapered gaps are numerically analyzed. Two of these are single-layer waveguides (N = 1), and the other two are multilayered waveguides (N = 19) with n(i) chosen to simulate exponential index gradients. Results obtained from the present theory in the weak coupling limit are shown to agree with those obtained in previous work.