K. H. Ringhofer

Space-charge waves in photorefractive crystals and their parametric excitation

It is shown that weakly damped space-charge waves exist in photorefractive crystals with a sufficiently large lifetime–mobility product. The dispersion law, the damping constant, and the quality factor of these waves and their dependence on the crystal parameters and on the experimental conditions are found. The instability of the fundamental grating against excitation of these waves is investigated; the fundamental grating is excited either by a moving interference pattern or by a standing interference pattern plus an oscillating external electric field. The dependence of the threshold and the characteristic exponent of the instability on the wave vectors of the exciting waves and on the experimental parameters is found for the three-dimensional case. It turns out that the strongest instabilities correspond to the cases of optimal enhancement of photoinduced gratings. The theory is compared with the experimental data for BSO crystals.

Low frequency peculiarities of the photorefractive response in sillenites

We investigate experimentally and theoretically the dependence of the amplitude of the spatial fundamental grating, created by a pair of coherent light beams while using the running grating technique [M.P. Petrov, S.I. Stepanov and A.V. Khomenko, Photorefractive Crystals in Coherent Optical Systems, Springer Series in Optical Sciences (Springer, 1991); P. Refregier, L. Solymar, H. Rajbenbach and J.P. Huignard, J. Appl. Phys. 58 (1985) 45], as a function of detuning frequency and beam ratio s in photorefractive Bi12SiO20. It is shown that for s > 0.05, in addition to the main peak in the frequency dependence of the amplitude, there is an additional peak of lower frequency which, as a rule, dominates the main peak. The position of the main peak depends on s. The experimental results are in good agreement with the theoretical analysis and the general ideas about excitation and nonlinear interaction of weakly damped space-charge waves.

Optical activity in photorefractive Bi12TiO20

The influence of optical activity on two-wave mixing (TWM) in photorefractive BTO and BSO crystals in the absence of an applied field is studied both theoretically and experimentally. For the conventinal orientations of the grating vector, K [001] and K[001], the piezoelectric and photoelastic effects are either zero or negligible. This makes an analytical treatment of the TWM problem possible. We obtain an analytical solution for the coupled wave equations of TWM valid for arbitrary optical activity. This result is of special importance for BTO crystals. In these crystals under the condition of maximum energy transfer (|K|rD=1, where rD is the Debye radius) neither the approximation of small optical activity nor the one of dominating optical activity is applicable and our analytical solution becomes essential. Our experimental setup uses beams with a trapezoidal overlap that allows us to study the thickness-dependence of the gain in a single measurement. Experimental and theoretical results for a BTO crystal are compared with those for a BSO crystal and are explained in the framework of the model used.

Space-charge waves in photorefractive ferroelectrics

The conditions for the existence and the main characteristics of weakly damped space-charge waves are investigated for photorefractive ferroelectrics. These conditions are opposite those derived previously for sillenites and may be fulfilled in such crystals as LiNbO3, BaTiO3, and SrBaNb2O6. The waves exist for sufficiently large values of the applied or photovoltaic field and have a linear dispersion law. The resonance excitation of space-charge waves by a moving light pattern is investigated. Possible manifestations of the instability of the photorefractive grating against parametric excitation of eigenmodes are considered.

Instability of spatial gratings induced by ac fields in photorefractive crystals

It is shown that spatial gratings in photorefractive crystals, induced by the standing interference pattern of two coherent waves and an external alternating electric field, may be unstable against the excitation of weakly damped eigenmodes. The dependence of the exponential rate of growth of the instability on experimental parameters and crystal characteristics is investigated. The instability influences the amplification of the photorefractive sensitivity by an ac field. A comparison is made between theoretical results and experimental data.

Optimum orientation of volume phase gratings in sillenite crystals: is it always [111]?

We study the simultaneous influence of optical activity, piezoelectric effect, and elasto-optic effect on two-wave mixing (TWM) under diffusion recording in photorefractive Bi12TiO20 and Bi12SiO20 crystals and find numerically the maximum of the TWM gain as a function of the orientation of the grating vector. Contrary to widespread belief, the grating orientation K∥[111] is the optimum orientation only if optical activity is negligibly small. Nonzero optical activity results in a strong dependence of the optimum grating orientation on the crystal thickness. The strongest deviation of the optimum from the [111] direction is achieved for ϱd=180°, where ϱ is the rotatory power and d is the crystal thickness. Our theory explains well prior results for crystals of moderate thickness and predicts new effects for thick (e.g., fiberlike) crystals.

Investigation of photorefractive subharmonics in the absence of wave mixing

Using a new optical configuration free from the influence of photorefractive optical nonlinearity, we investigate the main characteristics of the spatial subharmonic K/2 excited in a Bi12SiO20 crystal by a light-intensity pattern with wave vector K and frequency O. It is shown that in a large region of intensity and applied electric field the optimum value O of the frequency corresponds to the conditions of parametric excitation of the weakly damped eigenmodes of the medium: the space-charge waves. The threshold and above-threshold characteristics of the subharmonic regime are in good agreement with the theory.

Verification of the standard model of the photorefractive nonlinearity in BSO crystals

On the basis of the standard model for the photorefractive nonlinearity we investigate whether a systematic description of the dependence of two-beam energy exchange on beam polarization and grating vector K is possible. Our result is that there is good agreement between theory and experiment with respect to the polarization properties and semi-quantitative agreement with respect to the K-dependence of the energy exchange.

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 (111)-cut photorefractive piezocrystals (classes 23 and 43 m). It is shown theoretically and experimentally that in 2.1 mm thick BSO crystals (class 23) 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. Without the piezoelectric effect the diffraction efficiency does not depend on polarization and orientation angles in both optically active (BSO) and optically inactive (GaAs) crystals, whereas the effective gain depends on polarization and orientation angles while its maximum value remains constant. It is found that for thickness of BSO crystal 8.2 mm the diffraction efficiency and the effective gain do not depend on polarization of reading light. For the first time the experimental dependence of maximum diffraction efficiency of hologram in (111)-cut BSO crystal on the orientation angle θ is found. The results of the experiment confirm correctness of chosen physical model of the diffraction.

Giant momentary readout produced by switching electric fields during two-wave mixing in sillenites

We show theoretically and experimentally that switching an applied square-wave field produces strong and short pulses of the outgoing signal during two-wave mixing in sillenite crystals. These pulses originate from the strong effect of the field on the optical eigenmodes and can be used in new optical schemes based on time-separated recording and readout processes.