Generalization of the Optical Theorem to an Arbitrary Multipole Excitation of a Particle near a Transparent Substrate

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.

Keywords

• optical theorem
• arbitrary order of multipole
• Maxwell’s theory
• Gauss’s theorem
• transparent substrate
• extinction cross-section