Diffraction efficiency and energy transfer in two-wave mixing experiments with Bi12SiO20 crystals

The diffraction efficiency and energy transfer are investigated in photorefractive Bi₁₂SiO₂₀ crystals (BSO). Dependence on fringe spacing, electric fields, light intensity and rise-time constants are reported. The optimum crystallographic orientation for each effect is determined for vertical polarization of the recording beams. It is shown that beam coupling is a very sensitive phenomenon in BSO crystals where charge transport lengths are equivalent to usual fringe spacings. Experimental results are interpreted on the basis of the nonlinear theory of self-diffraction developed by Kukhtarev et al. [10].     

High-sensitivity read-write volume holographic storage in reduced KNbO3 crystals

Reduced KNbO₃ is a photoconductive ferroelectric in which holograms can be recorded by the photorefractive effect. Read-write volume hologram storage and erase sensitivities ofS ⁻¹=100 J/cm² andS ⁻¹=84 J/cm² (S=d(Δn)/d(I₀t)‖_t=0) have been measured at zero applied electric field, where the charge transport is shown to be due to diffusion of photoexcited electrons. By applying an electric field along thec-axis, the migration length of the photoexcited electrons becomes comparable to the holographic grating spacing. This leads to storage sensitivities comparable to high-resolution photographic plates. Experimental data on storage and erase sensitivity as a function of the grating spacing, applied electric field, writing light intensity and temperature are reported and interpreted on the basis of the theoretical results of Young et al. and Amodei. Changes of the intensity ratio of the writing beams by self diffraction (beam coupling), reflections from surfaces and the residual dark conductivity are assumed to cause experimental results which deviate from the theoretical models. It is shown, that in reduced KNbO₃ and other ferroelectric photoconductors having photocarrier transport lengths much larger than the unit cell dimension, photovoltaic currents do not contribute significantly to the build-up of space-charges leading to the photorefractive effect.     

Properties of thermally fixed holograms in photorefractive LiNbO<Subscript>3</Subscript>:Zn:Fe crystals

We have investigated the properties of thermally fixed holograms in LiNbO₃ crystals doped with the optical damage inhibitor Zn as well as the photorefractive Fe dopants. Time decays of fixed holograms at different temperatures showed a single thermally activated process with an activation energy of ∼1.08 eV. We have also studied the effect of an external electric field on the diffraction efficiency of these holograms. Results analysis has provided a new method to determine the photovoltaic field of the samples as well as the effective concentration of photorefractive traps.     

Detection of small phase modulation using two-wave mixing in photorefractive crystals

Two-wave mixing of phase-modulated beams in photorefractive crystals under a dc electric field is studied both theoretically and experimentally. Based on the vectorial theory of light diffraction in crystals of cubic symmetry, we derived an analytical expression that describes the phase demodulation in crystals with an arbitrarily oriented electric field. The phase-demodulation technique was used for estimation of the space-charge field created in photorefractive crystals. It is shown that the space-charge-field grating created in GaP and Bi₁₂TiO₂₀ crystals is much smaller than that predicted from the one-level band-transport model of the photorefractive effect. Received: 12 December 2000 / Revised version: 8 February 2001 / Published online: 27 April 2001     

Investigation of the phase transitions of ferroelectric KIO3 and KNbO3 crystals by optical diffraction

Optical diffraction is reviewed as a technique for investigation of the phase transitions in crystals with a multidomain structure. It has been used to study the phase transitions in KIO₃ and KNbO₃ single crystals. Strong optical diffraction bands resulted from electric domains in KNbO₃ crystals and their change with temperature were observed when a laser beam passed through the crystals. The diffraction patterns observed changed abruptly at 427°C, 223°C, and -50°C respectively, at which KNbO₃ crystals undergo structural phase transitions. It is considered that the change of the diffraction patterns with temperature is due to change of the electric domains in the crystals.     

Photorefractive properties of (1-10) and (111)-cut sillenite crystals when external electric field is applied along the direction of the optimum diffraction efficiency

We study the influence of the application of an external electric field on the grating formed in (1-10) and (111)-cut photorefractive sillenite crystals. Optimum conditions for application of the bias field are examined, taking into account the shift of the grating orientation for maximum diffraction efficiency along the crystal depth. The contribution of the piezoelectric effect is considered both in the electro-optic tensor and space charge field calculations. An analysis on the diffractive properties under these optimum conditions shows an increase of 30% in maximum diffraction efficiency in Bi₁₂GeO₂₀, and experimental verification for this is provided. Received: 5 November 2001 / Revised version: 18 April 2002 / Published online: 8 August 2002     

Effect of Grating Spacing on Response Time and Sensitivity in Photorefractive Materials at Large Modulation Depth

Photorefractive response time and photorefractive sensitivity are two important parameters characterizing photorefractive materials. We study theoretically the effect of the grating spacing on these parameters at large modulation depth in the absence and presence of an applied electric field for some of the most promising photorefractive materials, namely, LiNbO₃, KNSBN, SPS, BGO, and GaAs. We find that the response time increases with increasing grating spacing for LiNbO₃ and KNSBN, whereas the response time decreases with increasing grating spacing for SPS, BGO, and GaAs. The photorefractive sensitivity is mainly affected by the mobility–lifetime product in the presence of an applied electric field.     

Light diffraction on acoustophotorefractive holographic gratings

The intermediate regime of light diffraction on acoustophotorefractive holographic gratings written in cubic photorefractive crystals according to the synchronous-detection mechanism is studied. It is shown that the diffraction efficiency in sillenite-type gyrotropic crystals only slightly depends on the incident light polarization and the external electric field. The highest diffraction efficiency in nongyrotropic crystals was achieved for p-polarized writing and reading light and at a considerable external electric field strength.     

Cooperative nonradiative cross-relaxation in crystals of La(1−x)CexF3 solid solutions

The phenomenon of concentration quenching of the luminescence from donor ions in crystals of La_1?x Ce_xF₃ solid solutions was studied. A cooperative nonradiative energy transfer from a single excited neodymium ion to a cooperative acceptor representing a couple of cerium ions, as well as from a single erbium ion to three cerium atoms (also forming a cooperative acceptor center), was observed.     

“Running” holograms in photorefractive Bi12SiO20 crystals

It is shown that under uniform illumination and application of an external electric field, a phase volume hologram in a photorefractive crystal exists in the form of relaxing running wave. Effective recording of such a running hologram is possible only by an interference pattern moving synchronously with the recorded grating. The physical nature of this phenomenon, the possible enhancement of the hologram diffraction efficiency upon recording of a running pattern and the main factors limiting its value are discussed for the case of photorefractive Bi₁₂SiO₂₀ crystals.     

Z-scan measurements of photorefractive nonlinearities for a SBN: Ce crystal

 In this paper, we derived the Z-scan formula for a photorefractive crystal sample under an external applied electric field. The far-field diffraction pattern of a Gaussian beam wavefront through a photorefractive crystal is calculated by considering spatial-phase perturbation induced by the space-charge field. The photorefractive drift nonlinearities and correspondingly, the electro-optic coefficients r ₃₃, r ₁₃, (r ₂₃) and the characteristic ratio n ³ _e r ₃₃/n ³ _o r ₁₃ for a cerium-doped Sr_0.61Ba_0.39Nb₂O₆ crystal are determined from the Z-scan experiments. Z-scan with enhanced sensitivity is also realized by measuring the normalized transmittance at the off-axis position in the far field. A deviation between the off-axis Z-scan experimental results and the theoretical prediction is discussed too. Received: 22 July 1996/Revised version: 7 October 1996     

Feedback controlled periodic states for different kinds of photorefractive nonlinear response

We investigate analytically and numerically the influence of the type of the photorefractive nonlinear response on the periodic states (attractors) which occur during feedback controlled 2W-coupling and correspond to almost 100% diffraction efficiency of the dynamic index grating. In addition to the case of the local response typical, for example, for LiNbO₃ crystals we consider the cases of nonlocal (diffusive) response (BaTiO₃, SBN) and resonant response (DC-biased BSO, BTO, and BGO crystals). It is shown that the conditions for the transition to the periodic states and their apparent characteristics are strongly different for the two limiting cases above. Received 16 July 2002 / Received in final form 29 October 2002 Published online 4 March 2003     

OBSERVATION OF PHOTOREFRACTIVE EFFECT OF KNbO3 CRYSTAL AT μW ILLUMINATION

The photorefractive effects of the as-grown and proton-implanted KNbO₃ crystals were studied by two-wave mixing at 62.2μW/cm² illumination. At this pump power level, the as-grown crystal showed little photorefractive effect, while the proton-implanted crystal showed an obvious effect. Furthermore, there seemed to exist two photorefractive gratings with response times of 22.54 and 1596.30s, at 62.2μW/cm² pump power level, in the proton-implanted sample. This phenomenon has been attributed to the influence of proton-implantation.     

Photorefractive gratings generated by band-gap excitation: Application to KNbO3

A simple model was developed to account for the generation of thin space–charge gratings induced by band-gap illumination in photorefractive crystals. It includes the high-intensity regime where the contribution of free carriers to the space–charge field cannot be neglected. The model was specifically applied to explain the occurrence of two mutually π-phase-shifted gratings below the surface of KNbO₃ as well as diffraction features that have been previously observed experimentally. Received: 11 October 2000 / Revised version: 22 January 2001 / Published online: 20 April 2001     

Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals

The amplification of the input signal beam in two-wave mixing experiments with photorefractive Bi₁₂SiO₂₀ crystals is achieved when an additional phase shift is established between the photoinduced index modulation (phase volume hologram) and the incident fringe pattern. This stationary phase shift is introduced by either moving the crystal or the interference fringes at a constant speed. The transferred intensity is measured versus the applied electric field, fringe spacing and crystal velocity. The crystallographic orientation and the relative displacement with respect to the applied electric field polarity determine the amplitude of the energy transfer. For the first time in this crystal, signal beam amplification is reached for an applied field E₀ > 8 kV cm^?1 and a crystal or fringe displacement speed around 5 μm s^?1 at the green line (λ = 514 nm) of an argon laser.     

Control of sensitivity to hologram storage in LiNbO3 using an accessory photovoltaic crystal

Enhancement of sensitivity to hologram storage in a LiNbO₃ crystal is reported by using an accessory photovoltaic LiNbO₃ crystal, highly iron doped and reduced. With an illumination of 600 mW/cm² at λ=0.48 μm of the photovoltaic crystal the photogenerated electric field is about 10 kV/cm. This field is applied to a storage crystal having a higher resistivity and improves substantially the photorefractive sensitivity and saturation of the diffraction efficiency.     

Polymeric photorefractive surface waves

We theoretically studied photorefractive surface waves supported by polymers with orientationally enhanced photorefractive effect. We find that the orientational enhancement and the dependency of the quantum efficiency of generating mobile holes on the electric field make the diffusion nonlinearity in photorefractive polymers dependent not on only the variation of light intensity but also on external electric field, which is very different from the external electric field independent diffusion nonlinearity in inorganic photorefractive crystals. Consequently the profile, frequency and especially the penetration depth of polymeric photorefractive surface waves strongly depend on external electric field, which makes it more controllable than that in photorefractive inorganic crystals. The stability of polymeric photorefractive surface waves, the effects of birefringence component and electro-optic component of orientationally enhanced photorefractive nonlinearity on the formation of x or y-polarized polymeric photorefractive surface waves are also discussed.     

Determination of the Space-Charge Field Amplitude by the Phase Modulation Method

Results of experimental and theoretical investigations into the conversion of the phase modulation of light into its intensity modulation in photorefractive crystals are presented. Based on the vector diffraction theory, an analytical expression describing a phase demodulation in crystals in an external electric field applied in an arbitrary direction is derived. The phase demodulation is used to determine the space-charge field amplitude in cubic crystals. It is demonstrated that the space-charge magnitude measured in GaP and Bi₁₂TiO₂₀ crystals is less than that predicted by the Kukhtarev single-level model.     

Dynamic effects in photorefractive crystals at simultaneous read–write of holographic gratings

A two-level model of a simultaneous read–write of holographic gratings in photorefractive crystals has been developed for the nonstationary case at the applied electric field and unequality of recording beam intensities. The recurrent relationships both for the internal field amplitudes and for the amplitudes of the optical waves involved in interactions have been obtained. The use of a truncated power series expansion has allowed to obtain the expressions for diffraction efficiency and intensities of optical waves in nonstationary case. The obtained results were used for the analysis of simultaneous read–write dynamics in Bi₁₂SiO₂₀ crystals.     

Speed and diffraction efficiency in feedback-controlled running holograms for photorefractive crystal characterization

We report the measurement of the diffusion length, the Debye screening length and the quantum efficiency of photoelectron generation in strongly light absorbing photorefractive Bi₁₂TiO₂₀ crystals, using fringe-locked running hologram experiments. The effective applied electric field inside the sample is also computed and self-diffraction is considered. The novelty here, as compared to formerly reported experiments, is that the diffraction efficiency is now measured simultaneously with the hologram speed v. From these data the above referred to photorefractive and experimental parameters are obtained without the need for additional experiments. The method is used to analyze two photorefractive Bi₁₂TiO₂₀ crystal samples, in different experimental conditions, using the 514.5 nm wavelength. The computed parameters are in good agreement with the available information about these samples. Received: 23 November 2000 / Published online: 21 March 2001