New Perspective on the Optical Theorem of Classical Electrodynamics

TL;DR

This paper offers a new proof of the optical theorem in classical electrodynamics, linking forward scattering amplitude to absorption and scattering without requiring detailed knowledge of internal oscillations.

Contribution

It provides a general proof connecting the optical theorem to induced oscillations within scatterers, avoiding assumptions about their mathematical form.

Findings

Establishes a direct relation between extinction cross-section and forward scattering amplitude.

Reveals the energy exchange mechanism between incident waves and scatterers.

Clarifies the physical basis of the optical theorem in classical electrodynamics.

Abstract

A general proof of the optical theorem (also known as the optical cross-section theorem) is presented that reveals the intimate connection between the forward scattering amplitude and the absorption-plus-scattering of the incident wave within the scatterer. The oscillating electric charges and currents as well as the electric and magnetic dipoles of the scatterer, driven by an incident plane-wave, extract energy from the incident beam at a certain rate. The same oscillators radiate electro-magnetic energy into the far field, thus giving rise to well-defined scattering amplitudes along various directions. The essence of the proof presented here is that the extinction cross-section of an object can be related to its forward scattering amplitude using the induced oscillations within the object but without an actual knowledge of the mathematical form assumed by these oscillations.