Abstract
A relatively simple and efficient numerical method is developed for analyzing the scattering of light by a layered cylindrical structure of arbitrary cross section surrounded by a layered background. The method significantly extends an existing vertical mode expansion method (VMEM) for circular or elliptic cylindrical structures. The original VMEM and its extension give rise to effective two-dimensional formulations for the three-dimensional scattering problems of layered cylindrical structures. The extended VMEM developed in this paper uses boundary integral equations to handle the two-dimensional Helmholtz equations that appear in the vertical mode expansion process. The method is applied to analyze the transmission of light through subwavelength apertures in metallic films and the scattering of light by metallic nanoparticles.
Highlights
In many applications, it is necessary to analyze the scattering of light by three-dimensional (3D) objects that are one-dimensional (1D), i.e., layered, in different parts of the structure
The method is related to the earlier work of Boscolo and Midrio [19] and its further extensions [20, 21] for photonic crystal slabs, and it has been used to analyze light transmission through apertures in metallic films and scattering of light by metallic nanoparticles
Our approach is to use boundary integral equations (BIEs) to handle the 2D Helmholtz equations that appear in the vertical mode expansion process
Summary
It is necessary to analyze the scattering of light by three-dimensional (3D) objects that are one-dimensional (1D), i.e., layered, in different parts of the structure. We are interested in a single layered cylindrical object surrounded by an infinite layered background. Simple examples of such doubly-layered structures include a metallic film with a cylindrical hole and a cylindrical metallic nanoparticle on a substrate. A vertical mode expansion method (VMEM) was developed for analyzing circular or elliptic cylindrical objects in a layered background [17, 18]. For circular and elliptic objects, the polar and elliptic coordinates have been used in the horizontal plane perpendicular to the axis of the cylinder, and the solutions in each region are obtained by analytic or numerical separation of variables. We illustrate the new VMEM by numerical examples for plasmonics applications [22]
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