A perturbation analysis for modes in diffused waveguides with a gaussian profile

Matrix method for determining propagation characteristics of optical waveguides

“…We first apply the method to a symmetric profile withn 2 (4) = n 2 + An .sech 2 (t) for which exact analytical solutions of (1) can be obtained and the propagation constants are given by simple algebraic expressions [7]. The values of the normalized parameters b = Q2/k$-n : )/An for bound modes as obtained by our calculations are tabulated in Table I for k,aG = 4,O and 7.0 along with the exact results;m = 0,2, 4, .…”

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

“…The deviation An effi m in the case of an unperturbed profile η|(1.04ξ) [8] are shown also in curve (c) Fig. 3.…”

“…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).…”

“…In [8] it has been developed the first order perturbation theory considering the Gaussian index profile as a perturbation on an Epstein function, denoted as n| (1.04 ξ) here. This version of the perturbation method was found to be the most accurate but in order to obtain the perturbed propagation constants, integrals of special functions should be numerically calculated.…”