Coupling of a planar waveguide and a dielectric disk [laser resonator]

The complete analytic solution to the problem of coupling between a slab waveguide and a ring has been derived. The two-configuration problem is reduced to two simultaneous single-configuration problems by the method of equivalence. These are independently solved to yield the exact solution in terms of modal content. The results are illustrated with a numerical example and corroborated independently by a variational approach.