Reconciliation of the forward scattering and wave theories of electric-field-gradient-induced birefringence

Abstract

Abstract We consider propagation of a linearly polarized, harmonic, plane electromagnetic wave incident on a dilute gas subject to a non-uniform electrostatic field. We work to electric quadrupole–magnetic dipole order. In general, the wave is distorted to include a perpendicular component induced by the electrostatic field gradient, and the resultant is not a plane wave. Although the induced component is small, its contribution to the polarization-dependent refractive index of the gas in Buckingham's quadrupole experiment is significant. We show that distortion of the incident wave accounts exactly for the present discrepancy between wave theory and forward scattering theory of electric-field-gradient-induced birefringence in a gas: both theories yield the result obtained originally by Buckingham and Longuet-Higgins. Acknowledgments The authors thank Professor A. D. Buckingham, CBE, FRS, for comments which have improved the manuscript. We also thank Professor C. Graham and Dr. E. B. Graham for many helpful discussions.