It is shown that when an electromagnetic wave with some degree of amplitude rolloff in the transverse direction is scattered by a spherical particle, the optical theorem is not valid. For such shaped beams the extinction cross section may be written as an infinite series in powers of the reciprocal of the beam width. The imaginary part of the forward-scattering amplitude is shown to be the first term in this series. Two approximations to the extinction cross section are presented for the special case of Gaussian-beam scattering. The first one is based on the dominance of diffraction in the forward direction for w0 ≳ a, where w0 is the beam half-width and a is the target particle radius. The second approximation, valid for w0 ≲ a, is based on transmission-compensating field interference.
© 1995 Optical Society of America
Original Manuscript: April 10, 1995
Revised Manuscript: June 30, 1995
Manuscript Accepted: July 5, 1995
Published: December 1, 1995
James A. Lock, Joseph T. Hodges, and Gérard Gouesbet, "Failure of the optical theorem for Gaussian-beam scattering by a spherical particle," J. Opt. Soc. Am. A 12, 2708-2715 (1995)