What is extinction? Operational definition of the extinguished power for plane waves and collimated beams. (May 2020) - Markel, Vadim A.
Highlights: Extinguished energy can be measured directly as a physical energy flux for collimated incident beams and relatively small scatterers. A paradox related to extinction of narrowly-collimated beams is formulated and resolved. In the case of narrow collimated beams and small scatterers, the extinguished power is removed from the beam in agreement with the conventional interpretation. In the case of an infinite-front incident plane wave or a large scatterer with a sharply forward-peaked scattering function the operation definition of extinguished power in terms of energy fluxes is possible but problematic. Abstract: We discuss an operational scheme for measuring the power extinguished by a single particle in terms of physical energy fluxes. Illumination by an infinite plane wave and a collimated Gaussian beam is considered. For the case of a collimated beam, consideration of extinguished power presents an apparent paradox, which is resolved in this paper. It is then shown that the extinguished power is measurable as a flow of energy for a narrow, collimated incident beam and a small scatterer. In this case, the extinguished power is simply removed from the transmitted beam. If we relax the above assumptions, definition of the extinguished power in terms of measurable energy fluxes is still possible but becomes more nuanced.