Failure of the Optical Theorem for Gaussian-Beam Scattering by a Spherical Particle

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 based on the dominance of diffraction in the forward direction for w(0) greater than or similar to a, where w(0) is the beam half-width and a is the target particle radius. The second approximation, valid for w(0) less than or similar to a, is based on transmission-compensating field interference. (C) 1995 Optical Society of America.