Efficient Computation of TM- and TE-Polarized Leaky Modes in Multilayered Circular Waveguides

Abstract

Abstract-In combination with the Perfectly Matched Layer (PML)-paradigm, eigenmode expansion techniques have become increasingly important in the analysis and design of cylindrical and planar waveguides for photonics applications. To achieve high accuracy, these techniques rely on the determination of many modes of the modal spectrum of the waveguide under consideration. In this paper we focus on the efficient computation of Transverse Magnetic (TM) and Transverse Electric (TE) polarized leaky modes for multilayered cylindrical waveguides. First, quasi-static estimates are derived for the propagation constants of these modes. Second, these estimates are used as a starting point in an advanced Newton iteration scheme after they have been subjected to an adaptive linear error correction. To prove the validity of the computation technique it is applied to technologically important cases: vertical-cavity surface-emitting lasers (VCSELs) and a monomode fiber.

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.…”

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

“…5, and the relative errors are given in Table. 2. The solutions of the two relations (19) and (22) are very close, and the relative errors are so small that they can be ignored for large propagation constants.…”

“…Suppose the index profile in the core is a continuous function; the approximation by thin films could be used [18][19][20][21][22]. However, it is also proved that the transfer matrix for each film exhibits the exponential scaling, which would lead to the numerical instabilities, while the number of films is large.…”

“…(14) and (16). The relations (19) and (20) are exact, but very difficult to solve, and therefore the asymptotic method is needed. The asymptotic formulations for leaky and Berenger modes are derived as follows.…”

Perfectly Matched Layer based modelling of layered media: Overview and perspective

“…It is well-known that for mode matching techniques to be accurate, a large number of modes needs to be retained. Therefore, a lot of research has been and still is devoted to the efficient computation of many modes of (multi)layered planar and circular dielectric waveguides [14]- [17].…”