Włodzimierz Kucharczyk

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.

Application of the Jones calculus for Gaussian beams in uniaxial crystals

Following our recent approach in which the Jones matrix calculus was applied to a modulated double-refracted and partially interfering light beam propagating in a homogeneous electro-optic crystal [J. Opt. Soc. Am. A21, 132 (2004)], we generalize the method for any distribution of the light intensity. Special attention is paid to Gaussian, flat-topped Gaussian, and quasi-Gaussian beams for which the intensity of the light emerging from the optical system is found analytically. Application of the method to an optical system with an electro-optic crystal is described.

Systematic approach for finding configurations for measuring quadratic electro-optic coefficients in noncentrosymmetric crystals.

A new approach for finding configurations for measuring quadratic electro-optic effect in noncentrosymmetric crystals without any background of a linear electro-optic response is presented. This approach utilizes a generalized form of Fresnels wave vectors equation. The method allows the modulation of the fast and slow waves in the crystal to be considered separately. An example is given for the lithium niobate crystal.

Effect of divergence of light wave and alignment of crystal on the response of electro-optic modulators

In this work we report on numerical investigations of the effect of the light beam divergence or imperfect crystal alignment on the response of electrooptic modulators. Resulting non linearities are discussed both in terms of nonlinear distortion of modulators and as related to errors in measurements of quadratic electrooptic coefficients. Our calculations based on the Jones calculus have been performed for uniaxial crystals including KDP, and its isomorphs, and LiNbO3. The results obtained confirm that either the response of the modulators or results of electrooptic measurements can be significantly affected by the light divergence or imperfections in the crystals alignment.

Bond polarizability approach to nonlinear phenomena in crystals

Applications of the bond polarizability model to various nonlinear phenomena in crystals are shown. Special attention is paid to second harmonic generation, nonlinear refractive index and hyper-Raman scattering.

Calculations of third-order electronic susceptibility of alkali halides

Hyper-Raman scattering by the zone-center optical phonons in some alkali halides is investigated. In our calculations we relate the electrooptic part of the hyper-Raman tensor to the third-order optical susceptibility and the electric field associated with the LO phonons. The result obtained for those alkali halides for which the third-order optical susceptibility has not been measured yet, show that the electrooptic and lattice contributions to the hyper-Raman scattering are comparable. In all crystals considered, we found the cubic anisotropy of the electrooptic part of the hyper-Raman tensor to be not strongly exhibited.