Two-wave Mixing In Photorefractive Materials Research Articles

Improvement of oscillation characteristics of ring oscillator through photoconductivity and dielectric constant of photorefractive materials

The intensity of oscillation and the oscillation frequency shift are two most important parameters that characterize the performance of a photorefractive ring oscillator. In this paper, the effect of photoconductivity and dielectric constant of photorefractive (PR) materials on these parameters has been studied in case of non-degenerate two-wave mixing in PR materials. It has been found that for a given value of photoconductivity of PR material, the highly reflecting ( $$ R > 90\% $$ ) cavity mirrors are much effective parameter as compared to the other parameters (frequency detuning, absorption strength, energy beam coupling strength and dielectric constant) for the enhancement of the intensity of oscillation in the oscillator. Also, the magnitude of oscillation frequency of the photorefractive ring oscillator (PRO) can be increased by inserting PR crystal of lower dielectric constant ( $$ \varepsilon < 7.0 $$ ), higher photoconductivity ( $$ \sigma_{\text{p}} > 500\,{\text{pS/cm}} $$ ) and highly reflectivity ( $$ R > 90\% $$ ) cavity mirrors provided that the cavity-length detuning $$ \left( {\frac{\Delta \varGamma }{\pi } > 1.0} \right) $$ of the oscillator is higher. This means that the intensity and frequency of the PRO could be controlled by the dielectric constant and photoconductivity of a PR crystal which would greatly improve performance of a PRO and their applications based on these photorefractive ring oscillators such as wave front color conversion, optical limiting, optical computing and beam cleanup.

Study of photoconductive and dielectric dependence of gain and phase-shift in the coupled unidirectional ring resonators based on non-degenerate wave-mixing in photorefractive materials

Photoconductive and dielectric dependence of gain and phase-shift in the coupled unidirectional photorefractive ring resonators (UPRR) have been analyzed for the case of non-degenerate two-wave mixing in photorefractive materials by employing the plane-wave approximation method. The effect of photoconductivity and dielectric constant of the coupled photorefractive crystals (A and B) on the gain and phase-shift in the coupled UPRR have also been studied in details. It has been found that for a given value of the photoconductivity of crystal B, the gain in the primary resonator can be enhanced by selecting lower value of frequency detuning of the same resonator and PR crystal A of higher photoconductivity in the coupled UPRR. But reverse of the case is found for the enhancement of phase-shift. Such enhancement of the gain and phase-shift in the primary resonator are responsible for build-up and non-reciprocal energy transfer between the modes of the internal oscillations, which greatly improves the performance of the coupled UPRR.

Effect of photoconductivity and dielectric constant of the photorefractive materials on two-beam coupling gain and phase-shifts for a single unidirectional photorefractive ring resonator

Photoconductive dependence of two-beam coupling between the pump beam and the signal beam in photorefractive materials have been analyzed in case of non-degenerate wave mixing under the undepleted pump approximation method. During the two-wave mixing in photorefractive materials, steady state amplification of the signal beam and oscillation characteristics of a single unidirectional ring resonator has been studied. The domination of the two-beam coupling gain over the combined absorption and resonator losses such as Fresnel reflections from the crystal and imperfect mirrors builds up unidirectional oscillation. The buildup of such an oscillation leads to a saturation of the gain, which can be explained in terms of the photorefractive phase-shift. The existence of this phase-shift between the photorefractive index grating and the illumination intensity pattern, which is of characteristic of the photorefractive effect, leads to an energy transfer between the two beams. For a single unidirectional ring resonators, the effects of photoconductivity of the materials, two-beam energy coupling coefficient, dielectric constant, crystal thickness, and material's absorption coefficient on amplification of the two-beam coupling gain and photorefractive phase-shifts of the signal beam have also been studied in detail. It has been found that amplification of the signal beam and phase-shift can be enhanced by taking the photorefractive crystal having higher photoconductivity and lower dielectric constant, which improves performance of the resonators.

Dependence of gain and phase-shift on crystal parameters and pump intensity in unidirectional photorefractive ring resonators

The steady-state amplification of light beam during two-wave mixing in photorefractive materials has been analysed in the strong nonlinear regime. The oscillation conditions for unidirectional ring resonator have been studied. The signal beam can be amplified in the presence of material absorption, provided the gain due to the beam coupling is large enough to overcome the cavity losses. Such amplification is responsible for the oscillations. The gain bandwidth is only a few Hz. In spite of such an extremely narrow bandwidth, unidirectional oscillation can be observed easily at any cavity length in ring resonators by using photorefractive crystals as the medium and this can be explained in terms of the photorefractive phase-shift. The presence of such a phase-shift allows the possibility of the non-reciprocal steady-state transfer of energy between the two light beams. Dependence of gain bandwidth on coupling constant, absorption coefficient of the material’s cavity length (crystal length) and modulation ratio have also been studied.

Theoretical Study in the Realization of Real-Time Parallel Optical Logic Operations Using Two-Wave Mixing in Photorefractive Materials

Theoretical Study in the Realization of Real-Time Parallel Optical Logic Operations Using Two-Wave Mixing in Photorefractive Materials

Effects of strong modulation on beam-coupling gain in photorefractive materials: application to B 12 SiO 20

The steady-state beam-coupling gain during two-wave mixing in photorefractive materials has been analyzed in the strong nonlinear regime (high modulation depths). Numerical simulations have been carried out for B12SiO20, for which detailed information on photorefractive parameters is already available. First the amplitude and the phase mismatch (with regard to the light) of the recorded index grating and consequently the coupling gain coefficient were obtained under an applied field E0=5 kV/cm. Then the evolution of the intensities of the two interfering beams during propagation was determined for several light-modulation depths. The energy exchange was considerably enhanced with regard to the linear regime. The light and index fringe profiles at large modulation m were also obtained. The bending for both kinds of fringe differed appreciably from that previously calculated with a linear approach to the material equations.

Resonant two-wave mixing in photorefractive materials with the aid of dc and ac fields

A recently predicted resonant effect for the enhancement of two-wave mixing in photorefractive materials is investigated. The resonance occurs when the frequency of the applied ac field agrees with the eigenfrequency of the excited space-charge wave. Experimentally a clear resonance is found, as predicted by the theory, for high dc electric fields, but the resonance is smeared out for lower fields. A modified theory, taking into account the second temporal harmonic of the space-charge wave, shows good agreement with the experimental results.

High-frequency resonances in photorefractive crystals

Two-wave mixing in photorefractive materials is investigated for the case of applied dc electric fields and large detuning frequencies and for high-frequency alternating electric fields. The appearance of high-frequency resonances is demonstrated.

Dynamics of multiple two-wave mixing and fanning in photorefractive materials

We investigate the dynamics of multiple two-wave mixing in photorefractive materials. This is the first time to our knowledge that a study of the dynamics of many pairs of two-wave mixing interactions has taken place. A basic case with three waves undergoing multiple two-wave mixing is studied numerically. A numerical study is also performed in which many waves are used to model the time development of the fanning effect. Comparison of this numerical model with a basic experiment involving fanning in the presence of a two-wave mixing interaction is given. A qualitative agreement is exhibited. In addition, it is found that effectively reducing the coupling constant of a two-wave mixing interaction by the addition of an incoherent background beam can, under certain circumstances, significantly reduce the fanning without lowering the signal level.

Dynamic range compression of images by two-wave mixing in photorefractive materials

We propose and demonstrate a method for the dynamic-range compression of images using two-wave mixing in photorefractive materials. This method, in which an image is carried on the signal beam, permits a certain amount of control over the shape of the input and output curves by the variation of the pump intensity, the coupling constant, and the time at which the output image is examined. We also discuss the possible option of adding a feedback loop from the output image so that the range compression can be adapted to suit the intensity profile in the input image.

Two-wave mixing of time-varying non-plane-wave optical fields in photorefractive materials

A theoretical analysis is presented of two-wave mixing in photorefractive materials in which the complex amplitude of a weak signal beam has slowly varying but otherwise arbitrary spatial dependence and arbitrary time variation. The set of coupled partial differential equations that couple the dynamics of the optical fields to the photorefractive medium is solved analytically to give the complex amplitude of the transmitted signal in the undepleted pump regime. The results are compared with known results for the transient two-wave mixing of plane waves.

Analytical Solutions from the Non-truncated Kukhtarev Expansion for Two-wave Mixing in Photorefractive Materials

Abstract The series expansion put forward by Kukhtarev and co-workers to deal with two-wave mixing in photorefractive materials is re-examined. We show that a truncated approximation is only appropriate for a crystal thickness well below a certain critical value. On the other hand, the series can be summed under conditions where one of the beams is undepleted. This provides the same analytical time-dependent solutions as those reported by Heaton and Solymar and by Croning-Golomb, which followed different approaches.

A simple analytic solution for transient two-wave mixing in photorefractive materials

We present a very simple solution to the coupled partial differential equations which describe the time dependence of hologram formation in photorefractive materials. The equations are solved in the strong pump beam regime and the simple expression is compared with numerical solutions over a range of typical experimental conditions.

Coherent optical detection through two-wave mixing in photorefractive materials

Photorefractively induced index-of-refraction phase gratings are shown to combine coherently the optical fields of a strong pump and a suitably amplitude- or phase-modulated signal beam in such a way that an apparent amplification of the modulating waveform appears as intensity modulation of the transmitted signal and pump beam intensities. The source of the signal gain is shown to be the square-law (intensity) detection of the coherently combined pump and modulated signal beams, just as in coherent optical communication systems in which a strong local-oscillator field is coherently added with a weak optical signal field by a beam splitter.