Electromagnetic Scattering of Finite and Infinite 3D Lattices in Polarizable Backgrounds

Abstract

Abstract. A novel method is elaborated for the electromagnetic scattering from periodical arrays of scatterers embedded in a polarizable background. A dyadic periodic Green's function is introduced to calculate the scattered electric field in a lattice of dielectric or metallic objects. The method exhibits strong advantages: discretization and computation of the field are restricted to the volume of the scatterers in the unit cell, open and periodic boundary conditions for the electric field are included in the Green's tensor, and finally both near and far-fields physics are directly revealed, without any additional computational effort. Promising applications include the design of periodic structures such as frequency-selective surfaces, photonic crystals and metamaterials.Keywords: Electromagnetic Scattering, Dyadic Green Function, Periodic Structures PACS: 42.70. Qs,78.67.Bf,02.70.Pt Recent developments in the fabrication of periodic structures with tailored optical periodic structures call for specific modeUng tools. Most real structures are threedimensional but still very few techniques are able to simulate them without considerable computational efforts [1,2]. There is therefore a need to seek for a general method supporting full 3D vectorial calculations, enabling the investigation of both near and far-fields physics. Our approach is based on the volume integral equation for scattering in free space and at surfaces [3].We first develop the Bloch modes calculations in lattices using the Green's tensor formalism. The method exhibits strong advantages, especially about the restriction of the discretization and the minimal computational efforts required to reveal both near and far-field physics. Then two examples of calculations are reported to illustrate some physical effects that can be simulated: grating effects, propagation in multi-dimensional finite and infinite size lattices. Promising appUcations include the design of periodic structures such as frequency-selective surfaces, photonic crystals, and metamaterials. DYADIC GREEN'S FUNCTION FOR PERIODIC STRUCTURESThe scalar Green's function has been previously reported for energy bands calculations using Schrodinger's equation in a periodic potential [4]. Our objective is to deduct its dyadic form in electromagnetism for a lattice of point sources. Consider a scattering system described by a dielectric function e(r) embedded in an infinite homogeneous background medium EB. Nonmagnetic materials and harmonic fields with an exp(-/a)f) dependance are assumed. When this system is illuminated by an incident field E°(r) propagating in the background medium, the total electric field (incident plus scattered field) is a solution of the vectorial wave equation:where feg = ap-/c^ is the vacuum wave number The permittivity e(r) is assumed to have a spatial periodicity: e(r + l) = e(r), where 1 = wai +ma2 + pa3 {m,n,p integers) is a translation vector of the lattice and ai, a2, as are the translation primitive vectors. The volume of the unit cell is called Q.. If t...

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