Abstract
The generalization of a two-dimensional spatial spectral volume integral equation to a three-dimensional spatial spectral integral equation formulation for electromagnetic scattering from dielectric objects in a stratified dielectric medium is explained. In the spectral domain, the Green function, contrast current density, and scattered electric field are represented on a complex integration manifold that evades the poles and branch cuts that are present in the Green function. In the spatial domain, the field-material interactions are reformulated by a normal-vector field approach, which obeys the Li factorization rules. Numerical evidence is shown that the computation time of this method scales as O(N log N) on the number of unknowns. The accuracy of the method for three numerical examples is compared to a finite element method reference.
Highlights
Efficient solvers for electromagnetic scattering in stratified media are important in e.g. metrology (Raymond 2001, Chapter 18), metamaterials (Nanfang et al 2011; Jahani and Jacob 2016), and integrated optics (Wang et al 2012)
In Dilz and Beurden (2017) an algorithm for two-dimensional electromagnetic scattering with TE polarization in a multilayered medium is presented, where both contrast-current density and scattered field are represented on a path in the complex plane of the spectral domain
The second example for which we provide computational data consists of a dielectric cylinder embedded in a multilayered medium as is described in Fig. 5b.√In Fig. 9, the electric field is shown at z = 10 nm for X = Y = 100 nm, = = 2∕3 and mx, my ∈ {−4, ... , 4} and nx, ny ∈ {−7, ... , 7}, which equals one basis function per 5.1 nm
Summary
Efficient solvers for electromagnetic scattering in stratified media are important in e.g. metrology (Raymond 2001, Chapter 18), metamaterials (Nanfang et al 2011; Jahani and Jacob 2016), and integrated optics (Wang et al 2012). Little computation time or memory is used for computing the scattered electromagnetic field throughout the entire layered stack, since the electric field on a domain slightly larger than the scattering object suffices It is possible, using Sommerfeld (1909) or Fourier integrals, to transform the Green function completely to the spatial domain and use it in an integral equation method (Chew 1995, Chapter 8; Felsen and Marcuvitz 1973, Chapter 5; Kong 1975, Chapter 4; Wait 1970, Chapter 2). In Dilz and Beurden (2017) an algorithm for two-dimensional electromagnetic scattering with TE polarization in a multilayered medium is presented, where both contrast-current density and scattered field are represented on a path in the complex plane of the spectral domain It is this path that allows for the use of Gohberg and Koltracht (1985) fast, flexible and recursive Green-function convolution in the stratification direction. The applicability of the present algorithm is highlighted by three numerical examples, with numerical evidence that the computation time scales as O(N log N) with the number of unknowns and comparison against a finite-element reference calculation
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
