Photorefractive Four-wave Mixing Research Articles

Photorefractive four-wave mixing cannot be treated perturbatively. Revisiting the undepleted-pump approximation

We theoretically consider photorefractive degenerate four-wave mixing oscillators and show that, for this particular system, the linear stability analysis technique leads to incorrect results. The reason for this astonishing failure lies in the unphysical predictions of the undepleted-pump approximation, which appear naturally during the linearization process of the full model. As a consequence, photorefractive four-wave mixing does not seem to permit a perturbative treatment that allows the derivation of mean-field models, and one is forced to use the full model in order to make sensible predictions.

Adaptive defect and pattern detection in amplitude and phase structures via photorefractive four-wave mixing.

This work comprises the theoretical and numerical validations of experimental work on pattern and defect detection of periodic amplitude and phase structures using four-wave mixing in photorefractive materials. The four-wave mixing optical processor uses intensity filtering in the Fourier domain. Specifically, the nonlinear transfer function describing four-wave mixing is modeled, and the theory for detection of amplitude and phase defects and dislocations are developed. Furthermore, numerical simulations are performed for these cases. The results show that this technique successfully detects the slightest defects clearly even with no prior enhancement. This technique should prove to be useful in quality control systems, production-line defect inspection, and e-beam lithography.

Slowing down of light pulses using photorefractive four-wave mixing: Nontrivial behavior with increasing coupling strength

The slowing down of light pulses with backward-wave four-wave mixing is analyzed for photorefractive crystals with different coupling strengths. The conditions are found for which the delay of a phase-conjugate pulse decreases when the coupling strength increases and can even become negative, switching the pulse deceleration to acceleration. It is shown that for relatively low coupling strength the backward-wave four-wave mixing ensures a longer delay as compared to the two-beam-coupling technique. For coupling strengths tending to zero, the delay of long pulses approaches the response time of the medium. The conclusions of the theoretical analysis are confirmed experimentally with backward-wave four-wave mixing in barium titanate.

Slow light with photorefractive four-wave mixing

A slowing down of light pulses using backward-wave four-wave mixing is achieved in photorefractive crystals with different coupling strength. The delay and width of the output pulse are studied as a function of the input pulse width and pump intensity ratio for the amplified transmitted beam and for the phase-conjugated beam. The delay characteristics are compared with those of the two-beam coupling. It is demonstrated that the four-wave mixing process ensures a larger slowing down of short pulses (pulses with width shorter than the photorefractive response time) as compared to the photorefractive two-beam coupling scheme and guarantees the elimination of forerunners. The delay of long pulses in the four-wave mixing configuration is almost the same as the one that can be reached with two-beam coupling. The effect of absorption on the nonlinear shape transformation of the output pulses is discussed qualitatively.

Nonlinear pulse deceleration using photorefractive four-wave mixing

We investigate the possibilities of the backward four-wave coupling based on the nonlocal photorefractive response for the nonlinear deceleration of light pulses. The presence of an additional external variable parameter—the pump intensity ratio—allows to improve the output characteristics of the decelerated pulses compared to those typical of the two-wave coupling. In particular, large delay times of the output pulses can be achieved without their strong amplification. This positive distinctive feature of the pulse deceleration occurs far from threshold of the mirrorless optical oscillation.

Optical manipulation of multiple stable states in photorefractive four-wave mixing

We propose an approach to manipulate the convergence in multiple solutions of phase conjugate reflectivity in photorefractive four-wave mixing. Although a method forcibly adding a π-phase shift to an incident beam has been already proposed to control the reflectivity, some restrictions have been required in the boundary conditions for the successful operation. Here, we control the reflectivity with the boundary conditions in which the phase shift operation is ineffective by itself. In our method, the phase shift operation is combined with the procedure of turning an incident beam on and off. With a numerical analysis of four-wave mixing, we show that our new approach brings drastic change in the spatial distribution of the index grating and leads the phase conjugate reflectivity which was not manipulated previously.

Optical manipulation of multiple stable states in photorefractive four-wave mixing

Abstract We propose an approach to manipulate the convergence in multiple solutions of phase conjugate reflectivity in photorefractive four-wave mixing. Although a method forcibly adding a π-phase shift to an incident beam has been already proposed to control the reflectivity, some restrictions have been required in the boundary conditions for the successful operation. Here, we control the reflectivity with the boundary conditions in which the phase shift operation is ineffective by itself. In our method, the phase shift operation is combined with the procedure of turning an incident beam on and off. With a numerical analysis of four-wave mixing, we show that our new approach brings drastic change in the spatial distribution of the index grating and leads the phase conjugate reflectivity which was not manipulated previously.

Demonstration of fast switching of photorefractive four-wave mixing via Pockels effect

We demonstrate experimentally fast switching of the diffracted output from an orthogonally polarized pump (OPP) four-wave mixing (FWM) in a BaTiO 3 crystal. The switching mechanism is based on the phase mismatch in the FWM process induced by an applied electric field via Pockels effect, and, therefore, the switching speed is of the order of the Pockels effect. In our experiment, we obtain a switching time of the order of 10 ms, which is limited by the photodetector we used. The required voltage to switch off the diffracted output completely is about 225 V.

OPTICAL INVERSE FILTER FOR HOLOGRAPHIC FILTERING BY PHOTOREFRACTIVE FOUR-WAVE MIXING WITH INCOHERENT ERASURE

We analyzed the phase conjugate reflectivity by photorefractive four-wave mixing exposed to incoherent erasure, and found that the incoherent erasure brings inversion relation in amplitude of the phase conjugate beam with the intensity of the erasure even in a large coupling photorefractive material. Since such inversion relation appears in real-time, this function contributes to put forward holographic filtering to real-time processing. For the sake of confirmation of the analysis, we performed an experiment with employing a 45^{\circ} -cut \hbox{BaTiO}_3 crystal which is known as a crystal providing one of the largest photorefractive beam coupling.

Two-way two-dimensional pattern transferring upon requesting with BaTiO3 crystal

We propose a setup which is capable of transferring two-dimensional (2D) pictures from one plane to another in either way upon the requesting of the plane which wishes to obtain information from the other one. Since this picture transferring is purely optical, it is free of electromagnetic interference. The setup consists of a high-gain photorefractive BaTiO 3 crystal, and the crystal is set in a configuration of a Cat conjugator. The working principle of the setup relies on the mechanism of photorefractive self-pump phase conjugation and four-wave mixing.

Effect of the relative phase of grating components on the temporal behavior of photorefractive four-wave mixing

We show that the relative phase of the grating components has a large effect on the temporal behavior of four-wave mixing. When the two main components of the grating are in phase, the temporal behavior, especially during grating erasure, is totally different from that when the two components are out of phase. We give experimental results of orthogonally polarized four-wave mixing for two different BaTiO3 crystals that are in good agreement with our theoretical calculations. In our calculations we use a simplified numerical method to solve the coupled-wave equations, and the temporal analysis is based on a model with multiple charge recombination.

Coherent optical signal transferring on request by use of a BaTiO_3 crystal

We demonstrate experimentally a setup with which a two-dimensional picture can be transmitted from one plane to another at a signal request of the latter plane and the original picture continues to propagate unhindered along its original direction to the next stage. The setup makes use of photorefractive four-wave mixing and the self-pumped phase conjugation for its operation. Some means for increasing the contrast of the final transmitted image have been discussed.

Concept of Photorefractive Connection Module by Photorefractive Four-Wave Mixing with Extraordinary Writing Beams and an Ordinary Reading Beam

We propose a new optical network device photorefractive connection module (PRCM) which operates as optical switch, amplifier and signal distributor controlled by parallel optical signals. Simple optical control bus systems can be realized by cascade connection of PRCMs. PRCM branches off a desired channel from the spatial multiplexed optical bus line by appropriate setting of the control beam pattern. PRCM uses cross polarized four wave mixing (CPFWM) with extraordinary polarized writing beams and an ordinary polarized reading beam to achieve a high connection gain to the next PRCM stage. We analyze the phase matching angle of CPFWM in which the optical paths of two pump beams are slightly different. The phase conjugate reflectivity indicating a branching ratio of optical signal is derived and calculated in consideration of the phase mismatching Δk. The optimum pump ratio and the grating vector orientation for the largest phase conjugate reflectivity and signal amplification factor are discussed for optical design of PRCM. Since the measured signal beam power after passing through the BaTiO3 crystal is three or four times higher than its incident power, PRCM has a sufficient connection gain for optical bus and interconnection systems.

Observation of the Goos-Hänchen Effect in a Phase-Conjugate Mirror

The Goos-H\anchen shift between a supercritically incident beam and its reflection in a total-internal-reflection mirror comprising a material interface is well established. We experimentally demonstrate that the Goos-H\anchen effect can also occur between the probe beam and the phase-conjugate beam in a phase-conjugate mirror. Controlled lateral displacements of up to $218\ensuremath{\mu}\mathrm{m}$ were measured using photorefractive four-wave mixing with a frequency-detuned Gaussian probe beam.

Steady state and dynamic gratings in photorefractive four-wave mixing

The structure and dynamics of the four-wave mixing transmission grating in a photorefractive crystal were investigated. The steady-state grating’s amplitude distribution looks like a motionless soliton. When the value of coupling strength is more than 2, there are three solutions for the steady-state grating: two stable and one unstable. The dynamics of all these gratings are described by the sine-Gordon equation. The four-wave mixing grating’s structure and location in space are determined by the input beams’ ratio, phase difference, or both.

Photorefractive amplification and generation of light beams in BaTiO 3 controlled by the intensity of the pump light

by photorefractive forward four-wave mixing. The intensity of a signal beam is amplified by a factor up to 3000. We show that heating of the crystal by absorption of the pump light influences the gain because of the thermo-optic effect. Thus both, amplification and generation can be controlled by the intensities of the pump beams.

Cross-polarized photorefractive four-wave mixing with extraordinary writing beams and an ordinary reading beam

In parallel-polarized photorefractive four-wave mixing the phase-matching condition can be achieved automatically if the pump beams are allowed to propagate in directions opposite to each other. However, in cross-polarized photorefractive four-wave mixing, the incident angles of the beams should be adjusted to maintain the phase-matching condition. We analyze the phase-matching properties of cross-polarized four-wave mixing with extraordinary writing beams and an ordinary reading beam and obtain the phase-conjugate reflectivity in consideration of phase mismatching. We also perform an experiment in which a phase-conjugate beam is generated in cross-polarized four-wave mixing and confirm the analyses.

Reflectivity of photorefractive cross-polarized four-wave mixing in consideration of pump depletion

We analyze the phase-conjugate reflectivity and the amplification property of cross-polarized four-wave mixing with a photorefractive BaTiO3 crystal in consideration of the pump-beam depletion. The coupled-wave equations of cross-polarized four-wave mixing with ordinary writing beams and an extraordinary reading beam are derived and solved with the grating-integral method. The results of calculations of the reflectivity and the amplification factors will be compared with the result under the undepleted-pumps approximation. In addition, to achieve high conversion efficiency, the optimum conditions for the intensity ratio and the angle configurations of the probe and pump beams are also discussed.

One-way image transmission through a thick dynamic distorter without a reference beam

We demonstrated a method to perform one-way image transmission through a dynamic distorter without a reference beam. In this method, a photorefractive four-wave mixing configuration was used to pick up the reconstructed image from the image-bearing signal beam, which acted as an erase beam. The fluctuation period of the dynamic distorter must be much shorter than the response time of the nonlinear material. Reconstructed images with high-fidelity have been obtained. Because use of a reference beam is unnecessary this method is simpler and more effective.

A selection equilibrium theory for "stimulated photorefractive backscattering and four-wave mixing" self-pumped phase conjugation

A selection equilibrium theory for "stimulated photorefractive backscattering and four-wave mixing" self-pumped phase conjugation