Abstract
In the present paper, the generalization of the optical theorem to the case of a penetrable particle deposited near a transparent substrate that is excited by a multipole of an arbitrary order and polarization has been derived. In the derivation we employ classic Maxwell’s theory, Gauss’s theorem, and use a special representation for the multipole excitation. It has been shown that the extinction cross-section can be evaluated by the calculation of some specific derivatives from the scattered field at the position of the multipole location, in addition to some finite integrals which account for the multipole polarization and the presence of the substrate. Finally, the present paper considers some specific examples for the excitation of a particle by an electric quadrupole.
Highlights
The objective of the introduction is to trace the path of generalization of the optical theorem, starting from the classical result obtained initially for a scatterer located in free space that is excited by a plane wave; subsequently moving to the case of a scatterer in the presence of a transparent substrate; focusing on the excitation by dipoles and multipoles in free space; and, considering the generalized result we obtained for a penetrable obstacle located near a transparent substrate, that is excited by an electric multipole of an arbitrary order
The optical theorem introduces the fundamental concept of the extinction cross-section, which shows how much energy the scatterer takes from external excitation, regardless of whether it is a plane wave or a local source
The present paper considers a generalization of the optical theorem (OT) to the case of excitation of a local obstacle located near a lossless prism by an electric multipole of arbitrary order and polarization
Summary
Excitation of a Particle near aThe objective of the introduction is to trace the path of generalization of the optical theorem, starting from the classical result obtained initially for a scatterer located in free space that is excited by a plane wave; subsequently moving to the case of a scatterer in the presence of a transparent substrate; focusing on the excitation by dipoles and multipoles in free space; and, considering the generalized result we obtained for a penetrable obstacle located near a transparent substrate, that is excited by an electric multipole of an arbitrary order. The optical theorem (OT) is one of the famous theoretical results in the plane wave scattering theory of electromagnetic waves [1] It states that the sum of the scattering and absorption cross-sections (that is the extinction cross-section) is proportional to the scattered field amplitude in the propagation direction of the exciting plane wave. Many generalizations and implementations of the OT were suggested [5,6,7] In computational electromagnetics, this theorem is employed for the checking or verification of light scattering computer models, since, for a lossless particle, the total scattering crosssection must be equal to the imaginary part of the forward scattering amplitude [8]. The authors themselves have repeatedly used this method to test newly developed codes
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