An analytical approximation to measure the extinction cross-section using: Localized Waves

Abstract

We present a general expression for the optical theorem in terms of Localized Waves. This representation is well-known and commonly used to generate Frozen waves, Xwaves, and other propagation invariant beams. We analyze several examples using different input beam sources on a circular detector to measure the extinction cross-section.

Failures of the classical optical theorem under arbitrary-shaped beam incidence in electromagnetism, acoustics, and quantum mechanics: motivation and a review

“…The case of invariant beams (another name for "nondiffracting" beams) was analyzed by Rondon-Ojeda and Soto-Eguibar [70] using an angular spectrum representation, ASR (which could be converted to an analysis in terms of BSCs, as observed in [51]) with applications to Rayleigh scattering and to Bessel beam scattering, as shown by Rondon and Lee [71], for a similar complementary discussion. Another paper by Rondon [72] proposed a general expression for the optical theorem in terms of localized waves (which have frozen waves as a special case), e.g., [73][74][75][76] and references therein. They used ASR to write a physical condition related to the optical theorem.…”