Some experimental and theoretical studies in crystal optics.
The contents of this thesis are divided into two separate parts, both of which are concerned with optical phenomena for light propagation through source-free nonmagnetic media. Considered in the first part are various theoretical investigations pertaining to nonmagnetic crystals. While the second part focuses specifically on the experimental investigation of the quadratic electro-optic effect in some crystals of the KDP family. The opening theoretical chapters of this thesis are based aln10st entirely on four publications which are the result of work completed in this PhD study. These papers~ in the order that they appear in the following chapters, are: Systematic Eigenvalue Approach to Crystal Optics: An Analytic Alternative to the Geometric Ellipsoid model (Gunning and Raab 1998a); Algebraic Determination of the Principal Refractive Indices and Axes in the Electrooptic Effect (Gunning and Raab 1998b); Physical Implications of the Use of Primitive and Traceless Electric Quadrupole moments (Gunning and Raab 1997a); and Electric-Field-Induced Optical Activity in Nonmagnetic Crystals (Gunning and Raab 1997b). In later chapters two separate experimental projects on the quadratic electro-optic effect in KDP-type crystals are described. Some of the results of these investigations have yet to be published, while others, for both the interferometric and polarimetric experiments, appear in the papers: The Quadratic Electrooptic Coefficient gxxxxgyyxx of DKDP Crystals (Gunning et al. 1998a); The Quadratic Electrooptic Effect and Estimation of Antipolarization in ADP (Gunning et al. 1998b); and Studies of the Quadratic Electrooptic Effect in KDP-type Crystals (Gunning et al. 1999). The first chapter introduces a multipole eigenvalue theory of light propagation through a nonmagnetic anisotropic dielectric. This theory, in the appropriate multipole order, explains a range of optical phenomena, including circular birefringence and the linear birefringences of Jones and Lorentz, not otherwise fully explained by the widely-used Fresnel ellipsoid or related indicatrix ellipsoid. By means of this model the birefringences, optic axes, and eigenpolarizations of light propagating through a transparent medium are fully accounted for. The theory presented here concentrates on the electric-dipole description, which is the formal basis of the ellipsoid models, and the description of the birefringences, optic axes, and eigenpolarizations is algebraic, rather than geometric, and in terms of measurable crystal property tensors. Chapter 2 follows the multipole approach of Chapter 1 with a systematic algebraic means to derive expressions for the principal refractive indices and dielectric axes of a source-free nonmagnetic crystal in a uniform electric field. This is seen as a preferred alternative to the more common iterative numerical approaches to the problem. Results obtained in this chapter, to the chosen order in the field, are again expressed algebraically in terms of crystal property tensors. A number of illustrations of the approach are given for the linear electro-optic effect in crystals of the symmetry point groups 43m, 3m, 42m, and 1. Also, to demonstrate the inadequacies of the numeric method, the quadratic effect in 42m is investigated. Throughout these examples, comparisons are drawn with published numerical results. Chapters 3 and 4 start to allow for higher-order multipole moments, in contrast to the opening two chapters which are limited to the electric-dipole description. Specifically, electromagnetic effects to the order of electric quadrupole and magnetic dipole are considered. Since these effects, such as chiral phenomena in fluids and crystals and gyrotropic birefringence in antiferromagnetic crystals, require for their full description the inclusion of electric quadrupoles, the nature of the electric-quadrupole moment is considered in Chapter 3. In many theories this moment is defined to be traceless, but this chapter shows that when this definition is used in the derivation of a wave equation to describe light propagation through an optically active uniaxial medium, this equation as well as properties derived from it, in particular the refractive index of the eigenpolarizations, are in general dependent on the origin used to define the Inoment. This is physically unacceptable for the theoretical expression of an observed effect. It is shown that if the primitive definition of the quadrupole monent is used in this theory instead, this difficulty does not arise. Also to the order of electric quadrupole and magnetic dipole, Chapter 4 presents a macroscopic theory of electric-field-induced optical activity in source-free nonmagnetic crystals. In this approach a wave equation, to this multipole order and including distortions linear in an applied electric field, is derived which allows for the description of the linear electric-field-induced circular birefringence. It also identifies other coexisting birefringences, both natural and fieldinduced which are described in this multipole order. All these birefringences are expressed in terms of measurable crystal property tensors. In this chapter, nonmagnetic crystal classes are identified which exhibit this field-induced optical activity for particular light-propagation and applied-field configurations for light waves with purely transverse fields. These crystals, symmetry considerations, and other coexisting natural and field-induced birefringence are presented in Table 4.1. The first chapter of Part 2 of this thesis introduces the quadratic electro-optic effect in KDP-type crystals and provides motivation for the present experimental inquiry of the effect. Tabulated are previous experimental results for components of the quadratic electro-optic coefficients of crystals of KDP, ADP, and DKDP investigated in this work. Also introduced is the electrostrictive effect in these crystals, since it plays a part in the experimental determination of quadratic electro-optic coefficients of these crystals, and values for coefficients of this effect are listed. A multipole theory, based on that in Chapters 1 and 2 to the order of electric dipole and allowing for perturbations quadratic in a low-frequency applied electric field, is presented which describes fully the observed quadratic electro-optic effect in these crystals for the lightpropagation and applied-field geometries of interest. The analytic results derived for the observed induced refractive index changes for the polarization eigenvectors for a particular propagation path through the medium are expressed in terms of the quadratic electro-optic coefficients gxxxx,gyyxx, and gxxxx, One of the two methods proposed in this work for the measurement of coefficients of the quadratic electro-optic effect in specimens of KDP-type crystals is the interferometric technique. Chapter 6 serves to introduce this approach and to provide the theoretical basis for it, within the context of determining small induced phase changes. After a number of experimental factors are highlighted the method proposed for this work is explained. Specifically, this approach utilizes a Michelson arrangement, invoking active stabilization against low-frequency noise influences, and the coefficients are measured by phase-compensation means. This apparatus and its various components is then fully described in Chapter 7, including the method for its operation. The results of this interferometric research appear in Chapter 8 for the various light-propagation and applied-field geometries used, and values are presented for the individual coefficients gxxxx, gyyx.x, and gxxx.x in KDP and ADP, and also the electrostrictive coefficients Yxxyy and Yxxxxin the same crystals. An explanation of the second approach to measure quadratic electro-optic coefficients in this work, the dynamic polarimetric technique, is given in Chapter 9. Two proposed means to investigate the KDP-type crystals by this approach are described and explained theoretically, and the layout of the apparatus and its various components is highlighted. Results of this polarimetric investigtion for two light-propagation directions are given in Chapter 10 for investigations on KDP, ADP, and DKDP single crystals. These give values for the difference in quadratic electrooptic coefficients |gxxxx - gyyxx| and |-n03gxxxx| 3gxxx.x - n/g==xJ Finally, in concluding this thesis a summary of the quadratic electro-optic and electrostrictive results determined by the interferometric and polarimetric techniques is given and comparison of these results is drawn with those published previously. Considered briefly are some further conclusions that may be derived from these values for the nature of the electro-optic effect in KDP, ADP, and DKDP.