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

Abstract

The classical optical theorem states that for a wave propagating in a lossless medium and incident on a finite scatterer, the extinction cross section is proportional to the real part of the scattering amplitude in the forward direction. When developing a light scattering theory known as the generalized Lorenz–Mie theory, it has been a surprise to observe that in 1982, the optical theorem failed when the scatterer was illuminated by an arbitrary-shaped beam. The extremely simple reason for that failure has been understood only in 2014 and published in 2016. This represents a more than three-decade-long story, which is called a “wow” story for reasons that will be mentioned in this paper. The opportunity of this story which pertains to both the history and philosophy of sciences is considered to provide a review of the optical theorem under arbitrary-shaped beam incidence in electromagnetism, acoustics, and quantum mechanics.