International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. D. ch. 1.6, pp. 167-168
Section 1.6.5.2. The dielectric tensor and spatial dispersion
a
Department of Physics, University of Oxford, Parks Roads, Oxford OX1 3PU, England, and bDepartment of Earth Sciences, University of Oxford, Parks Roads, Oxford OX1 3PR, England |
The relevant polarization term to consider here is
The important part of this expression is the use of the field gradient, which implies a variation of the electric field across the unit cell of the crystal rather than the assumption that is everywhere constant. This variation in is known as spatial dispersion (Agranovich & Ginzburg, 1984).
Assume propagation of a plane wave given by through an optically active crystal. Substituting into the expression for the polarization gives This term can now be treated as a perturbation to the dielectric tensor to form the effective dielectric tensor : where has been written for the susceptibility in order to distinguish it from the use of elsewhere. Note that this can be expressed more generally as a power-series expansion in the vector (Agranovich & Ginzburg, 1984) to allow for a generalization to include all possible spatial dispersion effects: where the susceptibilities are in general themselves dependent on frequency.
References
Agranovich, V. M. & Ginzburg, V. C. (1984). Crystal optics with spatial dispersion, and excitons. Berlin: Springer.Google Scholar