A perturbation analysis of modes in diffused optical waveguides with Gaussian index profile

Mode Spectra and Fields in Diffused Optical Waveguides with Gaussian Refractive Index Profiles: Comparison of Different Approaches

“…In [6] it was shown that sufficiently far from the cut-off (B>0.65) the well-known HermiteGaussian functions can be used. In [7] it was proposed to treat the case approximating the Gaussian profile by sticking a parabola with an exponent.…”

“…In [7] it was proposed to treat the case approximating the Gaussian profile by sticking a parabola with an exponent. Applied to this problem the first order perturbation technique becomes rather cumbersome [6] and is connected with integrals which can be solved numerically only. Field calculations in analytical form by such a technique for Gaussian refractive index profile can not be found in the literature.…”

“…So, the function η|(1.085ξ) = η|(ζ/(1ι/2)) = ηΙ(ζ/1ι*), hereafter called "modified Epstein", can be derived from for Gaussian profile by means of first order perturbation corrections starting from a parabolic profile Πρ (ξ), from [5] and [6], respectively [6,8]: n b = 2.20, Δη = n s -n b = 0.05, ζ 1/ε = 3μπι, λ 0 = 0,53 um. The exact Gaussian profile values n£f f>m lie on the abscissa (a).…”

“…Lotspeich [6] used the first three terms of the expansion of (2), taking, however, the quartic term with a suitable weight factor in order to obtain more accurate approximation of the Gaussian profile. He has found in such a way a formula for the first order perturbation correction on the zero-order parabolic solutions: B m = Bj), + 8 (1) B m .…”

“…Sometimes the simple parabolic approximation is good enough [5]. Several attempts have been made to apply first-order perturbation theory to the parabolic profile [5,6] to improve the results of the approximated calculations. More recently another method has been suggested approximating the Gaussian profile by a combination of a parabolic and an exponential function [7].…”