An efficient finite‐difference frequency‐domain method including thin layers

Abstract

A method is presented to incorporate thin, lossy layers into a finite‐difference frequency‐domain model while retaining a coarse grid‐spacing. This approach significantly reduces computational effort. The new method is validated by a comparison with analytical solutions. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 43: 40–44, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20369

An efficient finite-difference frequency domain-method for waveguiding structures including thin curved layers

“…In addition, by using a cylindrical (as opposed to rectangular) mesh for the circular structures, it is often possible to reduce the number of grid points required to attain a given accuracy. To illustrate this, we compare the cylindrical compact FDFD method and the rectangular compact FDFD method [2,3] for determining the effective index (n eff ) of the fundamental HE 11 mode of the structure shown in Figure 6 with no thin layer present. Figure 8 shows the calculated n eff for increasing number of grid points along the x and y directions or the and directions.…”

“…To collapse the discrete equations to two dimensions, we allow ⌬ z 3 0, which is done by replacing all differences with respect to ⌬ z by Ѩ/Ѩ z, which can then be replaced by Ϫj␥ (refer to [3]). In compact 2D form, the z-component of the electric field is then …”

“…(13)-(18) reduce to the standard compact cylindrical FDFD equations. To construct the eigenvalue equation, (17) and (18) are substituted into (13)-(16) and the resulting coefficients are arranged into a matrix eigenvalue equation, as described in [2,3]. Note that at the origin the differ-ence equation for E z cannot be evaluated directly; instead, the integral method given in [6] is employed.…”

“…The finite-difference frequency-domain (FDFD) method is a wellknown method for the numerical solution of the propagation constants and electromagnetic fields of general guided-wave structures (see, for example [1][2][3]). Unlike the finite-difference timedomain (FDTD) method, the FDFD method solves for the waveguide modes and the associated propagation constants directly without time-consuming post-processing.…”

“…Various methods for this have been proposed, including the "compact" formulation presented in [2], which uses only four field components in the eigenvalue equation. In [3], we showed how the FDFD equations developed in [2] could be viewed as approximations of Maxwell's equations in integral form. In this way, thin layers could be taken into account using the contour-path (CP) method [4,5] while retaining a mesh size many times larger than the thickness of the thin layer.…”