Determination of Field Configuration and Eigenvalues of Planar Optical Waveguides with Arbitrary Index Profiles

We extend the analytic transfer matrix (ATM) method to solve the field configuration of planar optical waveguides with arbitrary index profiles including several turning points. The results are compared with the predictions obtained from the finite element method and the Wentzel--Kramer--Brillouin approximation technique. It is shown that the ATM method not only can produce accurate eigenvalues, but also reach correct and meaningful field configuration for any type of optical planar waveguides.