Leaky modes of optical waveguides with varied refractive index for microchip optical interconnect applications – Asymptotic solutions

In two-dimensional optical waveguides with the varied refractive index, approximate analytic solutions of the leaky modes are derived by using an asymptotic analysis for both transverse electric (TE) and transverse magnetic (TM) modes. Numerical simulations show that the asymptotic solutions of the leaky modes are quite close to the exact ones. The results are useful in the eigenmode method, where the leaky modes appear if a perfectly matched layer (PML) is used to terminate the transverse directions of optical waveguides.