Phase mismatch effects on the dynamics of a semilinear photorefractive oscillator with reflection-type gratings

This paper describes the effect of pump waves misalignement on the performance of the semilinear photorefractive coherent oscillator with the reflection gratings. The oscillation intensity and its modulation frequency are calculated numerically for different misalignement angles, coupling strengths and pump intensity ratios. It is shown that a small angular detuning of the pump wave, less than one milliradian, extends the range of pump ratios and the range of coupling strengths for which a non-degenerate oscillation occurs. The results of experiments with the BaTiO₃-based semilinear oscillator are in qualitative agreement with the calculated data.     

Phase diagrams for semilinear photorefractive coherent oscillator

The sequence of optical phase transitions is considered for a photorefractive coherent oscillator with a conventional mirror and a four-wave mixing phase conjugate mirror. Analogous to phase transitions in solids, the phase diagrams are constructed and defined qualitatively as different states of a whole system (light-induced scattering below the threshold of oscillation, single-frequency oscillation, two-frequency oscillation, and multimode mirrorless oscillation). The attempt of experimental mapping of a phase diagram is presented for a coherent oscillator with Co-doped BaTiO₃. PACS 42.65.Hw; 05.45.-a; 42.65.Pc; 42.65.Sf.     

Frequency degenerate oscillation in semilinear photorefractive oscillator with reflection gratings

The oscillation intensity of a semilinear photorefractive oscillator with reflection gratings is calculated for different cavity losses, different pump intensity ratios and different crystal orientations. Distinct from an oscillator with transmission gratings, this oscillator always has a soft excitation in the vicinity of the threshold. The theoretical results are in reasonable agreement with that of experimental studies with BaTiO₃:Co as a photorefractive crystal.This revised version was published online in March 2005. In the previous version, the published online date was missing     

Reflection-type photorefractive gratings in tin hypotiodiphosphate

Reflection photorefractive gratings recorded by nearly counterpropagating light waves in the near infrared are studied in tin hypothiodiphosphate. The ratios are established for certain electrooptic tensor components responsible for reflection grating recording, and the Debye screening length is evaluated. Reflection holograms of binary objects are recorded. Received: 26 June 2001 / Revised version: 3 September 2001 / Published online: 29 November 2001     

Threshold behavior of semi-linear photorefractive oscillator

A general analysis of the threshold behavior for the photorefractive semi-linear oscillator is performed within the linear approximation on the basis of the classical wave-coupling model. This analysis shows that the well known particular results on the frequency degenerate oscillation are valid only within a restricted range of the external parameters. The theory specifies the conditions for onset and properties of the frequency non-degenerate oscillations, including the necessary values of the coupling strength, pump intensity ratio, the increments of the instability, and the frequency splits. Important generalizations of the basic model are considered.     

Amplification of holographic gratings in photorefractive crystals

In this work, we have theoretically and experimentally investigated the process of image amplification in photorefractive crystals as a result of the self-diffraction phenomenon. We have found that the amplification process is of the threshold type and is observed only for an angle of convergence of the light rays greater than a threshold value. The gain coefficient is rather high. For the LiNbO₃ crystal, at a wavelength of 0.63 µm the gain coefficient reached 15 dB; at a wavelength of 0.44 µm, the gain was greater than 50 dB.Tomsk State Academy for Control Systems and Radioelectronics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 22–26, June, 1994.     

Instability of moving gratings in photorefractive crystals

It is shown that a moving intensity grating in a photorefractive crystal with a sufficiently large lifetimemobility product can give rise to an instability against excitation of weakly damped space-charge waves. Increments and threshold of the instability are investigated for the threedimensional case. Subharmonics and other nonlinear scenarios of saturation are discussed.     

Strong beam coupling in mesogenic materials with photorefractive Bragg gratings

Strong beam coupling was observed in mesogenic materials consisting of low- and high-molar-mass liquidcrystal mixtures with high concentration ratios of the latter type of liquid crystal. The beam-coupling effects originate in orientational photorefractive Bragg gratings, and a weak signal beam with an intensity of 1 mW is amplif ied to 8 mW by energy exchange with a strong pump beam after the passage of a 50-mum-thick film under a low operating voltage of 1-4 V/ mum. There is a superior net two-beam coupling gain of more than 600 cm(-1) with the low operating voltage and high resolution.     

Bidirectional vectorial light amplification in cubic crystals with unshifted photorefractive gratings

We present a new method of light amplification based on vectorial two-wave mixing in cubic crystal via an unshifted photorefractive grating. The energy transfer between interacting waves is achieved in an experimental configuration that provides the amplitudes of modulation of refractive indices of opposite signs, Dn(1)=-Dn(2), for two orthogonal polarization modes of the interacting waves. The configuration demonstrates bidirectional amplification; i.e., the weak wave is always amplified, independent of its direction with respect to the strong pump beam. We present the results of numerical analysis along with the experimental results for a Bi(12)TiO(20) crystal with a dc applied electric field.     

Holographic gratings in photorefractive materials: A review

In this paper, the fundamental characteristics of the photorefractive effect, both in bulk crystals and waveguides, as well as some of the most important photorefractive materials, their properties, and applications, are reviewed. In the last section, we report some experimental considerations on diffracted power from holograms written in pure LiNbO₃ and Fe:LiNbO₃ crystals and waveguides.     

Multivalued phase conjugate reflectivity in the reflection-type photorefractive four-wave mixing; strong coupling regime

Optical multistability based on the theory of four-wave mixing (FWM) is considered for the case of reflection geometry in photorefractive crystals. The resultant nonlinear algebraic equation obtained from the initial nonlinear coupled differential equations, is solved numerically by using a successive bisection method which can predict repeated zeros (roots) as well as discontinuities (jumps). We show that apart from the effects of photorefractive phase shift, the strong nonlinear coupling itself is sufficient to bring about multivalued branching behaviour of the phase conjugate reflectivity (PCR). As the coupling strength increases, the solutions become richer and more complex. We find that for certain values of pump and probe ratios and owing to the nature of strong nonlinear coupling the appearance of multiple solutions has a close connection with the phenomenon of bistability and self-oscillation.     

High-resolution photorefractive gratings in nematic liquid crystals sandwiched with photoconductive polymer film

Photorefractive gratings with high grating resolution were observed in the 20 μm thick low-molar-mass nematic liquid crystal (NLC) cell with a separate photoconductive (PC) poly(N-vinylcarbazole) layer. An orientational grating with a grating spacing of 1.9 μm was produced. It is believed that a space–charge field with small fringe spacing forms in the PC layer and its evanescent component penetrates into the NLC layer. The penetrated evanescent field drives the NLC to reorient, and consequently the orientational grating forms. The model indicates that the modulated field exists in several hundred nanometers near the surface, and thus the orientational grating is not full of the NLC film, which is consistent with the observed phenomena of the multiple diffractions. Besides, asymmetric two-beam coupling of 11.2% was achieved for the grating with a grating spacing of 1.9 μm, and a net gain coefficient of larger than 62 cm⁻¹ was obtained.     

Nonstationary amplification of holographic gratings in birefringent photorefractive crystals

A theoretical model of nonstationary self-amplification of weak holographic gratings in birefringent photorefractive crystals with two-and one-frequency readout is presented. The model takes account of the multiwave and vector character of the interactions and the simultaneous occurrence of intra-and intermode recording and diffraction processes with different phase detunings and complex coupling constants, which take account of the local and nonlocal response mechanisms of the medium. Analytical solutions are obtained for the intercoupled recording and diffraction equations. The results of numerical calculations of the kinetics of the spatial amplitude-phase profile and gain of the holographic grating and the selective amplification properties with intra-and intermode interaction geometries are presented. Zh. Tekh. Fiz. 67, 68–77 (April 1997)     

Frequency detuning dependence of oscillation condition for a semilinear photorefractive optical resonator in a photorefractive material with reflection gratings

Frequency detuning dependence of four-beam coupling in a photorefractive crystal pumped with two counter-propagating waves for a semilinear coherent optical resonator on the oscillation conditions has been analyzed in the case of non-degenerate-wave mixing under the slowly varying amplitude approximation method. Self oscillation can be achieved when the gain arising from the four-beam coupling is large enough to overcome the cavity loss. The effects of frequency detuning (i.e., non-degeneracy), dielectric constant and photoconductivity of the photorefractive materials on the performance of the semilinear photorefractive coherent resonator with the reflection grating configuration have also been studied in detail. The phase-conjugate reflectivity of the pumped crystal and oscillation intensity has been calculated for different input pump beam intensity ratio, intensity reflectivity of the conventional mirrors, degenerate energy coupling strength of the interacting beams. It has been found that for the higher value of the photoconductivity σ_p(>2.0 pS/cm) of photorefractive crystal, the semilinear resonator can oscillate at almost any frequency detuning (Ω) of the oscillation beam with respect to the fixed frequency of the pump waves whereas for the lower value of photoconductivity σ_p(<0.1 pS/cm) oscillation occurs only when the frequency detuning is limited to small region around Ω = 0. But reverse of the case is found for dielectric constant (?), pump intensity ratio (p) and conventional mirror reflectivity (R).     

Multiline coherent oscillation in photorefractive crystals with two species of movable carriers

The coherent oscillation, because of nearly degenerate four-wave mixing in photorefractive crystals with two types of movable charge carriers, occurs at two spectral lines symmetrically shifted with respect to the pump frequency. Consequently the output oscillation exhibits the high contrast intensity modulation. The frequency separation of two oscillation modes (and modulation frequency of the output intensity) depend on the incident light intensity and spatial frequency of the developing grating. A model is presented explaining this type of oscillation by the two-maxima shape of the gain spectrum in crystals with sufficiently different relaxation times of two space-charge gratings, one formed by movable electrons and the other one by movable holes. The experimental data for coherent oscillator with tin hypothiodiphosphate (Sn₂P₂S₆) are in reasonable quantitative agreement with the calculations. Received: 12 November 1998 / Revised version: 11 January 1999 / Published online: 7 April 1999     

Holography,coherent light amplification and optical phase conjugation with photorefractive materials

This paper presents a review of photorefractive effects in electro-optic materials and their applications. Materials properties giving rise to increased photo-sensitivities are discussed and compared with experimental data for a series of newer materials. The formation of volume holograms in these crystals, and accompanying optical effects such as beam coupling and phase conjugation, are discussed. Theoretical results derived from charge transport parameters are compared with our original data obtained in “dynamic holography” experiments with Bi₁₂GeO₂₀, Bi₁₂SiO ₂₀ and KNbO₃:Fe²⁺. The optimum parameters for applications such as volume hologram storage, coherent light amplification, optical phase conjugation etc. have been determined, and possible applications are discussed.     

调相光栅的正交相干相位检测

本文提出了一种解调调相光栅相位的新方法.将一幅相位调制光栅图输入计算机,通过正交相干相位解调算法处理,能够高精度、快速地获得光栅的相位分布.本文详细论述了正交相干相位解调原理,并给出实验系统和处理结果,最后与其他类似的相位解调方法进行了比较.     

Information cloning of harmonic oscillator coherent states

We show that in the case of unknown harmonic oscillator coherent states it is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state. By making use of this perfect information cloning it would be possible to estimate the original state through measurements and make arbitrary number of copies of the estimator. We define the notion of a measurement fidelity and calculate it for our case as well as for the Gaussian cloners.     

Photon-added coherent states for the Morse oscillator

In the paper we have constructed and investigated some properties of the Perelomov's “generalized coherent states” and photon-added coherent states for the Morse one-dimensional Hamiltonian (MO-PACSs), using the SU(2) group generators. We have found the integration measure in the resolution of unity and we have calculated some expectation values in the MO-PACSs representation. Using these states, the diagonal P-representation of the density operator is constructed as a new result for Morse potential. In addition, we have calculated some thermal expectation values for the quantum canonical diatomic gas of the Morse oscillators.     

Off-Bragg-angle light diffraction and structure of dynamic interband photorefractive gratings

Steady-state and time-resolved off-Bragg-angle diffraction experiments are used to determine the structure and the dynamics of photorefractive gratings induced by interband photoexcitation. In potassium niobate, we identify in such gratings basically a two-layer structure. Close to the surface, we find a space-charge electric field generated by a charge modulation stored directly in the bands. This grating component is typically 50 μm thick, the amplitude of the refractive index modulation is larger than 10^-4, and the response time is a few μs for resonant intensities of 100 mW cm^-2. This component is also robust under non-resonant illumination. Deeper in the crystal, a second holographic layer extends over a few hundreds of μm, its amplitude is smaller, and its slower response time is in the ms range. The mutual phase shift between the grating components is also determined. Received: 23 November 1998 / Revised version: 14 January 1999 / Published online: 12 April 1999