Gratings In Photorefractive Crystals Research Articles

Space-charge gratings in photorefractive crystals controlled by an external variable electric field

Specific features of space-charge gratings excited in photorefractive crystals in the presence of an external variable electric field that exhibits power-law time dependence are studied. It is demonstrated that the process under study substantially depends on a parameter of an increase in the external electric field over a time interval that corresponds to the generation of space-charge gratings in the absence of the field. At a relatively small parameter, the charge can be increased in accordance with variations in the field, charge oscillations with increasing amplitude can be induced, and identical excitation of the gratings can be maintained. At a relatively large parameter, the charge of the gratings is proportional to the time of external action, so that the charge can be controlled using external variable electric field.

Anisotropic Bragg diffraction of finite-sized volume holographic grating in photorefractive crystals

Anisotropic diffraction of uniform plane wave by finite-sized volume holographic grating in photorefractive crystals is considered. It is found that the anisotropic diffraction can take place when some special conditions are satisfied. The diffracted image is obtained in experiment for the anisotropic Bragg diffraction in Fe:LiNbO 3 crystals. A coupled wave analysis is presented to study the properties of anisotropic diffraction. An analytical integral solution for the amplitudes of the diffracted beams is submitted. A trade off between high diffraction efficiency and the deterioration of reconstruction fidelity is analyzed. Numerical evaluations also show that the finite-sized anisotropic volume grating exhibits strong angular and wavelength selectivity. All the results are useful for the optimizing design of VHOE based on finite-sized volume grating structures.

Effect of recording conditions on the anisotropic diffraction of volume holographic gratings

The anisotropic Bragg diffraction of the volume holographic gratings in photorefractive crystals are investigated based on the model of anisotropic coupled-wave theory. The effect of the initial intensity ratio and the recording angles of the two recording waves on the anisotropic Bragg diffraction properties is discussed. It is shown that both the ratio of the initial intensity and the incident angles of the recording waves are selective action for the anisotropic Bragg diffraction efficiency of the volume holographic gratings, while these two recording conditions are not selective action for the isotropic Bragg diffraction. Furthermore, the Bragg phase matching condition of anisotropic diffraction is analyzed when the recording angles change.

Description of readout processes during strong beam coupling.

We show, using the symmetry properties of the coupled-wave equations for the transmission and reflection geometries, that any readout characteristic of dynamic spatially nonuniform index gratings in photorefractive crystals can be explicitly expressed through the characteristics of the recording light beams. This approach is applied to describe the impact of beam coupling on the diffraction efficiency of dynamic gratings and on the output intensities of the light beams at instantaneous input phase changes (light grating translation). Further implications of this general approach are discussed.

Holographic surface gratings in iron-doped lithium niobate

Surface gratings associated with holographic volume gratings in photorefractive crystals of iron-doped lithium niobate have been studied using diffraction of a reflected probe beam and high-resolution phase-shifted interferometric profilometry. Both techniques show that the surface gratings exist in the form of periodical corrugations of the same period as that of the volume grating. The maximum amplitude of the periodical surface relief measured by both techniques is close to 6.5 nm. We also demonstrated that the periodical electric forces on the surface were capable of assembling polystyrene microspheres along the fringes of the grating. Large amplitude of the periodic electric field (1.6×104 V/cm) is associated with the photogalvanic effect.

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.

Recording of second-harmonic index gratings in photorefractive (K_05Na_05)_02(Sr_075Ba_025)_09Nb_2O_6 crystals

We propose and demonstrate a novel method for recording second-harmonic volume index gratings in photorefractive crystals. The fundamental component of the index grating is eliminated by means of a ?-phase shifted double-exposure process that uses the Mach–Zehnder interferometric technique. Experimental results for K0.5Na0.50.2Sr0.75Ba0.250.9Nb2O6 crystals are presented and discussed.

Excitation of higher harmonic gratings in AC-field biased photorefractive crystals

We analyze the nonlinear excitation of holographic gratings in a photorefractive crystal being subject to an alternating electric field and a stationary light interference pattern. The influence of the higher harmonics on the fundamental grating is illustrated for the case where a crystal of Bi 12SiO 20 is the recording medium. We analyze both the steady state and the transient consequences of the higher harmonic excitation.

Two-dimensional Perturbative Analysis of Slant Grating in Photorefractive Crystals in an External Electric Field

A slant grating was recorded with two laser beams incident on photorefractive crystal in an external dc electric field. Two-dimensional perturbative analytical solution for the first two-order space-charge field for steady-state photorefractive slant grating recording has been obtained. It is shown that the inclusion of the longitudinal component of the space-charge field during photorefractive two-wave coupling can predict reduction of the fundamental harmonic and enhancement or reduction of the second-order harmonic for various applied field strength and various grating slant angles. The dependence of the first two-order harmonics on the slant angle and on the applied field strength is examined.

Spatial structure of holographic gratings in photorefractive crystals with a nonlocal response

The structure and spatial positions of dynamic gratings responsible of steady-state four-wave mixing are determined for nonlinear media with a nonlocal response. It is shown that an analytic solution found for a double phase-conjugate mirror is fundamental and that it can be used to obtain solutions for such a mirror when two pump beams are present.

Subharmonic Generation by Phase Modulated Light Beams and AC Field

Generation of spatial subharmonic gratings in photorefractive crystal under an external AC field and a phase modulated interference pattern is investigated. This method of grating formation can lower the threshold contrast mth for the subharmonic generation.

Nonstationary gain processes of holographic gratings by two-wave interaction in photorefractive crystals

The transformation processes of holograph gratings in photorefractive crystals from two-wave interaction with detuning have been studied. For weak interactions an analytic solution has been obtained. Analysis of the gain, both for a purely nonlocal response, and for phase-shifted responses has been performed. Gain thresholds have been determined in terms of their dependence on materials parameters and the conditions of interaction. It is shown that the main effects in the gain process are a rotation of the grating vector towards its Bragg orientation and the appearance of a strong nonuniformity in the grating in proportion to the gain. As a result, for significant increases in the thresholds, the growth of the diffraction field of a non-Bragg-matched grating is larger than for diffraction of a Bragg-matched grating.

Holographic fixing, readout, and storage dynamics in photorefractive materials

Holographic gratings in photorefractive crystals that are based on charge redistribution inevitably decay as a result of ionic and electronic conduction. Under certain and restricted conditions these decay times can be acceptably long. Relevant decay rates and transient hologram field expressions are derived with special reference to LiNbO(3). Some experimental data are presented.

Photorefractive optical fuzzy-logic processor based on grating degeneracy

A novel optical fuzzy-logic processor using light-induced gratings in photorefractive crystals is proposed and demonstrated. By exploiting grating degeneracy, one can easily implement parallel fuzzy-logic functions in disjunctive normal form.

Spatial subharmonic instabilities in photorefractive crystals

The parametric generation of spatial subharmonic gratings in photorefractive crystals is studied based on an evolution equation for the space charge field. It is shown that a K n subharmonic instability can be resonantly excited when b = q/(1 + q 2 n 2) is satisfied with b and q the detuning parameter and the external de field, respectively. The spectral widths near the resonances for K 2 , K 3 and K 4 subharmonic instabilities are also given. The theoretical results are compared with previous experiments.

Generation of spatial subharmonic gratings in the absence of photorefractive beam coupling.

Using a new experimental geometry, we have proved for the first time that the generation of spatial subharmonic gratings in photorefractive crystals is not dependent on optical nonlinearity. We present results which confirm that the subharmonic gratings result from a parametric excitation of ultra low-frequency eigenmodes of a crystal by a time modulated fundamental grating.

Dynamics of a composite grating in photorefractive crystals for memory application

The dynamics of a composite grating that consists of an original grating and a newly superimposed grating are investigated for memory applications by solution of coupled-wave equations and photorefractive-material equations with the following initial conditions: the original grating has an arbitrary refractive index modulation, an arbitrary phase shift exists between the original and the superimposed grating, and there is an externally applied dc electric field. The effect of beam coupling, including fringe bending on the composite grating, is investigated by numerical simulation. Simplified analytical solutions that neglect beam coupling are derived, showing good agreement with experimental results. The investigation also shows that a selective erasure process in the presence of an external electric field is made possible by provision of an appropriate constant phase shift. Analytical solutions of the composite-grating dynamics are used to analyze both scheduled and incremental recording dynamics with an external electric field. It is shown that scheduled recording results in a nonuniform relative phase distribution among multiplexed gratings. In contrast, the incremental recording converges to a uniform relative phase distribution and indicates that selective erasure may be easily implemented for fast memory update.

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.

Polarization-encoded optical logic operations in photorefractive media

We propose and demonstrate optical logic operations using polarization encoding and wave mixing in photorefractive crystals. In our approach two orthogonal polarization states of light beams are used to represent respective logic values of 1 and 0. All 16 two-input logic operations can be easily achieved by use of the recording and readout of photoinduced volume gratings in photorefractive crystals. An optical full adder is also proposed and demonstrated.

Parametric generation of a spatial subharmonic grating in photorefractive crystals: theory

The instability of a spatial subharmonic grating during photorefractive hologram recording is investigated theoretically. It is shown that such instability arises in crystals if the electron drift length in the external field exceeds the fundamental grating period. Cases with dc and ac external fields are considered. The influence of diffusion and trap charge saturation is examined.