Roger E. Raab

Interferometric investigation of the quadratic electro-optic effect in KDP

Abstract A Michelson interferometer was used to study the quadratic electro-optic effect in KDP. The values for three individual coefficients, determined for the first time by interferometric means, are g 1111 =−4.0, g 3311 =−0.6, and g 2211 =0.2 (in units of 10 −20 m 2 V −2 ). The lattice contribution, which forms the dominant part of g 1111 and g 3311 , is discussed in terms of the bond polarizability model. The results provide further evidence that the third-order bond polarizability is of comparable magnitude for crystals of different structure and composition.

Analysis of accuracy of measurement of quadratic electro-optic coefficients in uniaxial crystals: a case study of KDP

Taking KDP as an example of a uniaxial crystal, we analyze contributions to its quadratic electro-optic response with a view to explaining differences in published values of certain quadratic coefficients. In an eigenvalue theory of light propagation we show that the linear electro-optic coefficient contributes to the quadratic response, even under ideal laboratory conditions. In addition, the effect of imperfect crystal cutting and alignment is investigated by means of computer calculations based on the Jones calculus. It is found that, for relatively small inaccuracies, the calculated values of the quadratic coefficient g(xyxy) are approximately two orders of magnitude greater when measured with a static field than with a dynamic one. This finding could explain the observed spread in some results for KDP-type crystals.

The quadratic electrooptic effect and estimation of antipolarization in ADP

Abstract The quadratic electrooptic coefficients g 1111 and g 2211 have been measured interferometrically in ADP at room temperature. In addition, ‖g 1111-g 2211‖ was determined by a dynamic polarimetric technique at the same temperature. Both experiments yield values for g 1111-g 2211 at 21 C and λ = 0.633 μm with an average of (−5.9±0.5)×10−20 m2/V2. An estimate is made, using this value, of the spontaneous antipolarization appearing in the antiferroelectric phase of ADP. This antipolarization is found to be comparable in magnitude with the spontaneous polarizations observed in ferroelectrics belonging to the KDP family of crystals.

Application of the Jones calculus for a modulated double-refracted light beam propagating in a homogeneous and nondepolarizing electro-optic uniaxial crystal

The Jones matrix calculus is applied to an electro-optic crystal with uniaxial symmetry when the light beam is incident nearly normally on the crystal face. The approach allows one to treat refracted waves and rays that diverge in the crystal and are modulated by an external low-frequency field. The effect of partial interference of overlapping refracted beams is allowed for and calculated for the case of uniform intensity of the beam over its cross section. The method is employed to analyze optical systems containing an imprecisely cut and aligned electro-optic crystal plate.

Effect of beam divergence from the optic axis in an electro-optic experiment to measure an induced Jones birefringence

Certain optical properties can be described in terms of two linear birefringences existing in separate Jones platelets of a medium. One of these, known as Jones birefringence, although occurring naturally in some crystals is too small to be measurable. However, the two birefringences can be induced by an electric field in 4 and 6 crystals for propagation along the optic axis. For an even slightly divergent light beam, natural birefringence may affect accuracy of measurement. Calculations show that in an experiment with a static field the error depends critically on beam divergence, whereas with a modulated field this is not so.

Algebraic determination of the principal refractive indices and axes in the electro-optic effect

A systematic algebraic approach is presented as a preferred alternative to an iterative numerical method for deriving expressions for the principal refractive indices and dielectric axes of a nonmagnetic crystal in a uniform electric field. This approach is applicable for an arbitrary field and for any symmetry point group. The results, to the chosen order in the field, are expressed algebraically in terms of measurable crystal tensors. Illustrations are given of the linear electro-optic effect for the point groups 4?3m, 3m, 4?2m, and 1 and of the quadratic effect in 4?2m. The latter serves to highlight a shortcoming in the numerical approach. Comparisons are drawn with numerical results published previously.

Physical implications of the use of primitive and traceless electric quadrupole moments

Theories of certain electromagnetic effects, such as chiral phenomena in fluids and crystals and gyrotropic birefringence in antiferromagnetic crystals, require the inclusion of electric quadrupole contributions for a full description of the effect. In a number of these theories the electric quadrupole moment is defined to be traceless, as indeed is the general practice for such moments in nuclear physics. It is shown that, when the traceless quadrupole moment is used in the derivation of the wave equation that describes light propagation through an optically active uniaxial medium, this equation and properties derived from it, in particular refractive index, depend in general on the arbitrary origin used to specify the quadrupole moment. This is physically unacceptable for an observable property of a substance. By contrast, this defect does not occur if the definition of the primitive quadrupole moment is adopted, namely Σqr α r β.

Covariant D and H fields for reflection from a magnetic anisotropic chiral medium

Difficulties have previously been noted in the use of the D and H fields in the Maxwell boundary conditions when these are applied to theories of reflection effects involving chiral media. Such difficulties may be avoided by adopting covariant forms of D and H. These are derived in the electric quadrupole–magnetic dipole approximation for a magnetic anisotropic chiral medium exposed to a plane monochromatic electromagnetic wave.

Eigenvector approach to the evaluation of the Jones N matrices of nonabsorbing crystalline media

An eigenvector equation within the electric octopole–magnetic quadrupole approximation is derived, from which it is possible in principle to establish the eigenvectors and the refractive indices of polarized light forms sustained by an anisotropic crystal for any chosen direction of phase propagation. It is shown that, for propagation along the crystal axes when the rays do not separate, a decomposition technique based on eigenvectors and the Jones resolution of a medium into independent differential plates substantially simplifies solution of the general problem. Precise expressions are obtained for the Jones parameters n, (ny − nx), (n−45 − n45), and (nR − nL) in terms of multipole-property tensors of the crystal. The effects of crystal symmetry on these expressions are summarized.

Use of Pulsed Magnetic Fields to Measure the Faraday Effect in Gases

Pulsed magnetic fields of approximately 40 kOe produced by the discharge of a 44-μF, 9.5-kV condenser bank through wire-wound solenoids, have been used to measure the Verdet constant of acetylene, carbon dioxide, chloromethane, chloroethane, dichlorodifluoromethane, and chlorodifluoromethane at six wavelengths between 5783 and 4089 A. An accuracy of approximately 1% has been attained with gas pressures between 600 and 2080 torr at temperatures between 22° and 30°C. The apparatus and experimental techniques are described.