Cutoff frequencies in diffusion-type power-law profile waveguides

The cutoff frequencies V/sub c0/ of strongly asymmetric planar waveguides with diffusion-type power-law refractive-index profiles g(X)=X/sup p/ are found to be the solutions of J/sub -/spl nu//(2/spl nu/V/sub c0/)=0 with /spl nu/=1/(p+2). To a high degree of accuracy, the cutoff frequencies can be approximated by linear functions of the profile parameter p. The effect of the cover, as well as that of the refractive-index gradient in the case of TM modes, can accurately be taken into account by simple perturbation corrections.