Klaus H. Ringhofer

Reflection holograms in sillenite crystals for double-exposure interferometry

Holographic recording in reflection geometry offers high lateral image resolution (necessary to analyze microscopically structured objects, e.g. biological cellular structures) and a compact and simple setup (Denisyuk holography). Our aim is to combine this high resolution three-dimensional imaging with holographic double-exposure interferometry to allow the analysis of a dynamic process on the microscopic scale. We derive analytic expressions for gain and diffraction efficiency valid for arbitrary optical activity (and thus not only for Bi 12 SiO 20 but also for Bi 12 TiO 20 crystals). The theoretical predictions agree convincingly both with the experimental data published in [J. Opt. Soc. Am. B 14 (1997) 1179] and with our experimental data.

Optimum thickness of cubic photorefractive piezocrystal for diffraction efficiency

The analytical dependencies of crystal thickness, for which the diffraction efficiency optimized on the polarization angle reaches the maximum values, on the orientation angle are derived. It is shown that optimum thickness of the crystal is inversely proportional to its specific rotation and plots of dependence of crystal optimum thickness on the orientation angle are set of an equidistant curves with period 180 degree(s) corresponding different local maxima. A distance between these curves is defined by the specific rotation of the crystal (alpha) . The optimum thickness for the first local maximum can not be less than (pi) /(2(alpha) ). The magnitudes of crystal thickness, optimal for the diffraction efficiency of the hologram and gain coincide for some intervals of the orientation angle (theta) between the gating vector and direction [001]. Analytical expression, permitting to determine the azimuths of polarization of a reading light, at which the diffraction efficiency will be optimized simultaneously on the polarization angle and the crystal thickness, is found.

Diffusion recording in photorefractive sillenite crystals: an analytical approach for engineering purposes

Simple formulae for the two-wave mixing (TWM) gain and diffraction efficiency obtained in the approximation of weak coupling and strong optical activity allow us to tune the experimental setup for interferometric applications. We prove that two invariant parameters, trace and determinant of the coupling tensor, are sufficient to optimize the experimental setup. Both practically important crystal cuts, (110) and (111), can be treated in a unified manner. Fundamental TWM properties (90°-jumps of the optimum polarization, apparent doubling of the local maxima of the diffraction efficiency in comparison with the gain, drastic changes between regimes of small and large polarization rotation, the crucial role of elastooptic properties) are systematized. The guidelines for the design of an optimum experimental setup for interferometric applications including anisotropic self-diffraction using sillenite crystals are presented. Quantitative agreement with previous experimental data is demonstrated.

Optimization of diffraction efficiency of transmission hologram in cubic photorefractive piezocrystal of (110)-cut in dc electric field

On the base of the analytical solution of the couple differential equations system in the photorefractive piezocrystal with transmission holographic grating the optimization of the diffraction efficiency is conducted by choice of the crystal orientation and linear polarization of the reading light. It has been theoretically established, that for bi12SiO20 piezocrystal with thickness 10 mm at different values of external electric field E0 the maximum diffraction efficiency (eta) M is reached for the following magnitudes of the (theta) and (Psi) respectively: without electric field (theta) =42 degree(s), (Psi) =35 degree(s), with electric field 5 kV/cm (theta) =51 degree(s), (Psi) =19 degree(s). Without taking into account the piezoelectric effect these orientation and polarization angles have the following values: without electric field (theta) =0 degree(s), (Psi) =107 degree(s), with electric field 5 kVcm (theta) =43 degree(s), (Psi) =31 degree(s). It is shown, that taking into account the piezoelectric effect increases the maximum diffraction efficiency (eta) M in 2.13 times at E0; in 2.47 times at E0=5 kV/cm; in 1.75 times at E0=1- kV/cm; in 1.43 times at E0=15 kV/cm.

Energy exchange optimization in (110)-cut BTO crystal by choice of interacting waves polarization

Abstract The relative intensity dependence of a signal wave on the orientation angle between holographic grating vector and crystallographic axis [0xa00xa01] is experimentally found for the first time for fixed thickness of (1xa01xa00)-cut BTO crystal in the case of two-wave mixing. Azimuth of polarization of interacting waves corresponding to maximum energy exchange is theoretically found for every value of the orientation angle. Comparison of theoretical and experimental orientation dependencies of gain for two special linear polarizations (in the incidence plane and perpendicularly to this one) and maximum gain is fulfilled as well.

Optimization of diffraction efficiency and gain for two-wave mixing in cubic (111)-cut photorefractive piezocrystals

The dependence of the diffraction efficiency of holograms and the effective gain of the signal wave on the polarization and orientation angles is investigated for two-wave mixing in transmission geometry in cubic (1 1 1)-cut photorefractive piezocrystals (classes 23 and 43m). It is shown theoretically that maximum diffraction efficiency and gain in BSO and GaAs depend on the orientation angle. It is confirmed experimentally for BSO crystal (class 23). It is obtained theoretically and experimentally that in 2.1 mm thick BSO crystals the piezoelectric effect leads to an increase of the diffraction efficiency by 70% and of the gain by 30% for certain values of the polarization and orientation angles.

Photorefractive novelty filters for transient phase evaluation

In our report we compare different ways of realizing an optical novelty filter with photorefractive barium titanate crystals. We present experiments on the basis of beam fanning, two-wave mixing and self-pumped phase conjugate geometries. The application of photorefractive novelty filters not only for phase visualization but also for the measurement of transient phase changes in a laser beam is demonstrated. The phase calculation from an interferogram is supplied or replaced by the novelty filters phase transfer function. The use of such techniques instead of conventional interferometry for transient phase evaluation results in a simplified measuring procedure.

Theoretical study of feedback-controlled photorefractive beam-coupling dynamics

Theoretically we investigate the operation of a novel nonlinear system, feedback controlled photorefractive beam coupling. It is shown that the feedback conditions used earlier ((pi) /2 phase shift between the diffracted and transmitted beam components) are satisfactory only during a relatively short initial stage of development. We have generalized these conditions by taking into account the inertia inherent any real feedback loop. The inertial feedback conditions ensure the permanent operation of the nonlinear system and lead to a variety of periodic and quasi-periodic regimes. We investigate the distinctive features of these regimes and transitions between them for moderately thick crystals.

The effect of bulk light absorption on running photorefractive holograms

The influence of bulk light absorption on running photorefractive holograms is investigated. By solving the coupled wave equations we prove that the beam intensities, but not the beam phases, can be calculated by averaging the coupling constant over the crystal thickness. We show the importance of the effect by calculating the dielectric relaxation time at the crystal front, and from that the quantum efficiency from a feedback-controlled experiment with a 2.05 mm thick BTO crystal. We propose to simulate the effect of bulk light absorption by a rude estimate of the average dielectric relaxation time which is related in a simple way to the dielectric relaxation time at the crystal front. In doing so an error of less than 10% is introduced.

Elastic contributions to electro-optics

In this talk I shall show you how the electro-optic effect is modified by elasticity and also give a few applications from the field of volume-holography in photo-refractive crystals. I shall also comment on a striking similarity between the electro-optic effect owing to elasticity and the magnetostatic field owing to a distribution of electric currents.