## U.S. Department of Defense

#### Date of this Version

2011

#### Abstract

This work presents a new explanation for the extinction paradox and shows that the canonical explanations are incorrect. This paradox refers to the large size limit of a particle’s extinction cross section. It is called a paradox because the geometrical optics approximation, which should be valid in this limit, predicts a cross section that is half of the true value. The new explanation is achieved by formulating the scattered wave in terms of an integral over the particle’s surface where the seemingly unrelated Ewald–Oseen theorem appears in the formulation. By expressing the cross section in terms of this surface integral, the Ewald–Oseen theorem is analytically connected to the cross section. Several illustrations are used to reveal the significance of this connection: The paradox is seen to be a consequence of the requirement that the incident wave be canceled within the particle by secondary radiation from its own internal field. Following this, the canonical explanations are examined to reveal serious problems. In the process, the same asymptotic extinction behavior is shown to occur for small highly refractive dielectric particles, and thus is not just a large particle size or small wave length effect as is often stated. The traditional explanations cannot account for this behavior while the new one actually predicts it. All in all, this work constitutes a fundamental reworking of 60 years of accepted understanding for the cause of the asymptotic behavior of the extinction cross section.

## Comments

Published in

Journal of Quantitative Spectroscopy & Radiative Transfer, 112, (2011), 1170–1181