Dispersion relations of the modes for open nonhomogeneous waveguides terminated by perfectly matched layers

Abstract

The perfectly matched layer (PML) is a widely used tool to truncate the infinite domain in modal analysis for optical waveguides. Since the PML mimics the unbounded domain, propagation modes and leaky modes of the original unbounded waveguide can be derived. However, the presence of PML will introduce a series of new modes, which depend on the parameters of PML, and they are named as Berenger modes. For twodimensional step-index waveguides, the eigenmode problem is usually transformed into an algebraic equation by the transfer matrix method (TMM). When the waveguide is nonhomogeneous, in which the refractive index in the core is varied, TMM is not available. In this paper, we use the differential TMM to derive the dispersion relation. We also deduced the asymptotic formulas for leaky modes and Berenger modes separately, which are accurate for large modes.

Analysis of Guided and Leaky Tm0n and Te0n Modes in Circular Dielectric Waveguide

“…In addition, Kim et al also defined and explained the regimes of these modes based on their physical meanings [15][16][17][18]. To solve the eigenvalue problems more efficiently, asymptotic formulas have been derived before using the numerical solvers for planar and circular multilayered structures [19][20][21][22][23]. The waveguides open to air or closed with perfect matching layer (PML) were considered, and Lambert W function [24,25] has been leveraged frequently to simplify the asymptotic expressions.…”

Relation construction of transverse magnetic modes and its application for nonhomogeneous waveguides terminated by perfectly matched layers

“…Rogier et al [24] found the propagation constants of leaky modes of planar and circular dielectric waveguides terminated by a PML. In another work [25], we derived a dispersion relation for a nonhomogeneous waveguide with two PMLs for the TE case. However, for the TM case, the relation of the modes was not given in [25] because of the mathematical complexity.…”

“…In another work [25], we derived a dispersion relation for a nonhomogeneous waveguide with two PMLs for the TE case. However, for the TM case, the relation of the modes was not given in [25] because of the mathematical complexity.…”

“…In Section 2, by use of the PML technique, the unbounded domain is terminated, then the differential transfer matrix method (DTMM) [26][27][28] is applied to derive two nonlinear dispersion relations. For a slowly varied waveguide, two higher approximate dispersion relations are given, where the approaches of the matrix U are better than the one in [25], then some analytical and asymptotic solutions of leaky modes are deduced. They may serve as better initial guess values for the Newton iterative method.…”