An exact treatment of the Kerr-effect relaxation in a strong unidirectional electric field

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Abstract
The transient Kerr‐effect relaxation is treated taking contributions from both permanent and induced dipoles into account with a view to obtaining exact expressions for the electric birefringence following the sudden application of a unidirectional electric field based on the rotational Smoluchowkski equation for a symmetrical body. As a special case (i) where the contribution from the induced dipole is ignored, the Laplace transform of the electric birefringence is obtained exactly in terms of a continued fraction. At the same time, the electric birefringence at a very high field is expressed in terms of a hypergeometric function as an explicit function of the time. Also, in the case (iii) where the contribution from the permanent dipole is neglected, we obtain an exact expression for the Laplace transform of the electric birefringence in terms of a continued fraction. In both cases (i) and (ii), effective relaxation times are expressed theoretically as an explicit function of the applied electric field. Further, the static birefringence for cases (i) and (ii) are calculated by means of continued fractions.