## A theoretical investigation of birefringences in cubic and uniaxial magnetic crystals.

##### Abstract

In this thesis a consistent multipole theory is used to describe light propagation in nonabsorbing magnetic cubic and uniaxial crystals to the order of electric octopoles and magnetic quadrupoles. The first chapter extends Maxwell's equations for a vacuum to their macroscopic form in
matter by including bound-source contributions as multipole expansions. From these the corresponding forms for D and H are obtained, which ensure origin-independence of Maxwell's equations. A multipole eigenyalue equation describing light propagation in a source-free homogeneous medium is then derived, which is the basic equation applied in this thesis.
In the second chapter it is shown how, from the multipolar form of the propagation equation for transverse waves, expressions can be derived for the various birefringences that may be exhibited in macroscopic platelets of the medium, as introduced by Jones in the formulation of his M-matrix.
The following chapter presents the derivation, by means of first-order perturbation theory, of the quantum mechanical expressions for the polarizability tensors which enter the eigenvalue wave equation. The origin independence of the expressions for the various observable quantities is then established. In the fourth chapter the independent components of the polarizability tensors are calculated for two selected crystal point groups, namely 622 and 432, by way of illustration. In chapter five the components calculated in the manner illustrated in the previous chapter are presented in tabular form. The Jones method outlined in chapter two is then applied to the crystal point group 6m2, again as an illustration of the method used to determine the optical effects displayed by this point group. Chapter five concludes with a table containing a listing of the predicted optical effects calculated in this way for all of the magnetic uniaxial and cubic point groups.
The thesis concludes with chapter six, in which a summary of the results of the work undertaken is given, together with a discussion of factors influencing measurements of the predicted optical effects.