Analysis of planar optical waveguides using scattering data

Inverse scattering theory for optical waveguides and devices: Synthesis from rational and nonrational reflection coefficients

“…Realistic permittivity profiles have finite widths that are truncated at the core-cladding interfaces. For truncated permittivity profiles modeling optical waveguides and devices, the transverse reflection coefficient r(k) is no longer a rational function and has a more complicated, nonrational form [Mills and Tamil, 1992]. Analytical, closed-form reconstructions of permittivity profiles are not possible for nonrational reflection coefficients and so numerical methods must be used.…”

Spectral Inverse Scattering Theory for Dielectric Media: Application to Optical Devices

“…inverse scattering theories for designing optical waveguides [6][7][8][9], we make use of the fact that at a fixed frequency Maxwell's equations governing the light propagation in a waveguide can be transformed to Schr6dinger's equation with an energy-independent potential. In this equivalent quantum mechanical inverse problem, the bound states energies are associated with the prescribed propagation constants, and the potential is related to the refractive index of the designed waveguide.…”

“…In section 3, we review the Kay's inverse 3 scattering theory [7] and Gelfand, Levitan and Marchenko equation [1][2]. The inverse scattering theory is then applied to planar waveguides for the case of TM modes in the In order to verify the results obtained by inverse scattering theory we have developed I an efficient finite difference method to find the propagation constants of guided TE and TM modes and is presented in section 6.…”

“…based on the solution of the Gelfand-Levitan integral equation, has recently been applied to the design of monomode waveguides(51, [7]. In general, this technique is cumbersome when several bound states are present.…”

“…In previous work we completed an extensive analysis of these potentials from the standpoint of scattering theory, including the effects of truncations of the potentials to model core-cover interfaces, considering both single-and multimode waveguides [7]. In the present paper, we extend our analysis to include the effects of truncations upon the coupling coefficient.…”