TY - JOUR

T1 - Volume integral equation for electromagnetic scattering: Rigorous derivation and analysis for a set of multilayered particles with piecewise-smooth boundaries in a passive host medium

AU - Yurkin, Maxim A.

AU - Mishchenko, Michael I.

N1 - Publisher Copyright: © 2018 American Physical Society.

PY - 2018/4/12

Y1 - 2018/4/12

N2 - We present a general derivation of the frequency-domain volume integral equation (VIE) for the electric field inside a nonmagnetic scattering object from the differential Maxwell equations, transmission boundary conditions, radiation condition at infinity, and locally-finite-energy condition. The derivation applies to an arbitrary spatially finite group of particles made of isotropic materials and embedded in a passive host medium, including those with edges, corners, and intersecting internal interfaces. This is a substantially more general type of scatterer than in all previous derivations. We explicitly treat the strong singularity of the integral kernel, but keep the entire discussion accessible to the applied scattering community. We also consider the known results on the existence and uniqueness of VIE solution and conjecture a general sufficient condition for that. Finally, we discuss an alternative way of deriving the VIE for an arbitrary object by means of a continuous transformation of the everywhere smooth refractive-index function into a discontinuous one. Overall, the paper examines and pushes forward the state-of-the-art understanding of various analytical aspects of the VIE.

AB - We present a general derivation of the frequency-domain volume integral equation (VIE) for the electric field inside a nonmagnetic scattering object from the differential Maxwell equations, transmission boundary conditions, radiation condition at infinity, and locally-finite-energy condition. The derivation applies to an arbitrary spatially finite group of particles made of isotropic materials and embedded in a passive host medium, including those with edges, corners, and intersecting internal interfaces. This is a substantially more general type of scatterer than in all previous derivations. We explicitly treat the strong singularity of the integral kernel, but keep the entire discussion accessible to the applied scattering community. We also consider the known results on the existence and uniqueness of VIE solution and conjecture a general sufficient condition for that. Finally, we discuss an alternative way of deriving the VIE for an arbitrary object by means of a continuous transformation of the everywhere smooth refractive-index function into a discontinuous one. Overall, the paper examines and pushes forward the state-of-the-art understanding of various analytical aspects of the VIE.

KW - DISCRETE DIPOLE APPROXIMATION

KW - WEAKLY ABSORBING SPHERES

KW - LIGHT-SCATTERING

KW - RESONANCES

KW - OPERATOR

KW - FORMULATION

KW - SPECTRUM

KW - OBJECT

KW - BODY

UR - http://www.scopus.com/inward/record.url?scp=85045319145&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.97.043824

DO - 10.1103/PhysRevA.97.043824

M3 - Article

AN - SCOPUS:85045319145

VL - 97

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 4

M1 - 043824

ER -