Forward scattering theory of electric-field-gradient-induced birefringence

Abstract

We attempt to resolve the discrepancy between the Buckingham—Longuet-Higgins (BLH) and Imrie—Raab (IR) theories of linear birefringence induced in a gas of dipolar molecules by an electric field gradient. To this end we present a new calculation of the effect, based on forward scattering of a light beam incident on a thin lamina of gas molecules. We work to electric quadrupole—magnetic dipole order. The beam undergoes a time delay which is proportional to the thickness of the lamina and the electric field gradient, and can therefore be interpreted in terms of a contribution to the refractive index of the gas due to the field gradient. The birefringence is obtained by considering appropriate polarizations of the incident beam. To avoid the occurrence of a divergent quantity, such as appears in the BLH theory, it is essential to take account of the finite beam width. Calculations are performed using both primitive (traced) and traceless molecular quadrupole moments; as required on basic grounds, these results are equivalent. They are also identical to the BLH result. By contrast, the IR result is physically unacceptable because it is not invariant with respect to the use of traced and traceless moments. The source of error in the IR theory remains unclear.