Effect of photoconductivity and oscillation frequency shift on the signal beam intensity in two beam coupling in photorefractive materials

A general theory of the two-beam coupling between a pump beam and a signal beam in photorefractive materials is presented. The coupled wave equations describing the non-linear two beam coupling are derived, based on Maxwell's wave equation. The coupled equation for the intensities of the two beams in the photorefractive crystals with the absorbing properties have been derived analytically. The intensity of the signal beam increases with the increasing crystal thickness, reaches a maximum and then decreases. The influence of energy beam coupling coefficient, oscillation frequency shift, crystal thickness, absorption coefficient and the input beam intensity ratio on the signal beam intensity have been studied in details. The effect of the photoconductivity of the materials on the intensities of the two beams in both the co-directional as well as contra-directional two beam coupling cases have been studied.     

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.     

Critical enhancement of photorefractive beam coupling

We show that a hybridization of the optical and material nonlinearities takes place near the threshold of the subharmonic generation in photorefractive crystals. It results in a critical (with a singularity) enhancement of the rate of spatial amplification of light waves and leads to a variety of new optical critical phenomena.     

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.     

Theoretical analysis of the effects of frequency detuning dependence of photorefractive two- beam coupling coefficient on gain and phase-shifts of the signal beam for a coupled unidirectional photorefractive ring resonators

Dependence of two-beam coupling gain and phase-shift of the signal beams on the frequency detuning for a coupled unidirectional ring resonators based on non-degenerate two-wave mixing in the photorefractive crystals have been investigated in details. The effects of various parameters characterizing the photorefractive medium such as frequency detuning, absorption strength, two-beam energy coupling strength and pump intensity of the external laser beams, on the two-beam coupling gain and phase-shift of the signal beams for a coupled UPRR have also been studied in details. It has been found that the photorefractive gain of the signal beam in the primary cavity of the coupled UPRR can be enhanced to the higher order by taking the lower value of the frequency detuning of the primary cavity which could exist at much lower value of the absorption strength of the crystal B. This higher value of photorefractive gains in the cavities are responsible for the strong coupling between the modes of the oscillations of the coupled UPRR.     

Method for determining the two-beam coupling gain coefficients of photorefractive crystals

A new method is proposed for determining the two-beam coupling gain coefficients of photorefractive crystals with both o- and e-polarized lights. This method enables one to determine simultaneously and precisely the gain coefficients of a crystal for o- and e-polarized lights while the fanning effect is diminished. Experimental demonstrations are presented.     

Powerful, diffraction-limited semiconductor laser using photorefractive beam coupling

We use semiconductor laser amplifiers and a photorefractive crystal to generate a high-power, diffraction-limited laser beam at 860 nm. Using a single flared amplifier, we obtain 1.09 W in a diffraction-limited beam from 2.2 W of pump power. Using an array of flared amplifiers, we also demonstrate efficient beam coupling, showing that this technique is easily extended to semiconductor amplifier arrays.     

Oscillation dependence of two-wave mixing gain for unidirectional ring resonator in photorefractive materials

Dependence of the coupling strength of two-wave mixing gain in photorefractive materials for the single unidirectional ring resonator on oscillation conditions has been analyzed in the strong nonlinear regime. In this regime, difference between the frequency of the pump beam and oscillating beam is proportional to the cavity-length detuning, which can be explained in terms of the photorefractive phase-shift. This phase-shift results due to slightly non-degenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for the steady-state oscillation. The presence of such a phase-shift allows the possibility of the nonreciprocal steady-state energy transfer between the pump and oscillating beams. If the gain due to the beam coupling is large enough to overcome the cavity losses then the signal beam is amplified in the presence of material absorption. Such amplification is responsible for the oscillations. For the single unidirectional ring resonator, the effects of cavity-length detuning, energy coupling coefficient, crystal thickness of the material, reflectivity of the cavity mirrors and material's absorption coefficient on the frequency and intensity of oscillations have also been studied in detail. It has been found that for the smaller value of absorption coefficient (α) of the photorefractive crystal, the unidirectional ring resonator can oscillate at almost any cavity-length detuning (ΔΓ) whereas for the larger value of α oscillation occurs only when the cavity-length detuning is limited to small region (around ΔΓ=0). But reverse of the case is found for energy coupling coefficient (γ₀).     

Study of transient photorefractive beam coupling in high- and low-molar-mass liquid crystal mixtures

We observed transient signals of Bragg grating formation in high-performance photorefractive high- and low-molar-mass liquid crystal mixtures (HL-LCMs). These transient signals including oscillation-like behavior can be explained by a complex time constant in the case of a finite applied dc field. The time constant for the space-charge field to reach its steady state and the oscillation frequency are estimated. Received: 30 October 1998 / Revised version: 14 December 1998 / Published online: 24 February 1999     

Review of photorefractive materials: an application to laser beam cleanup

Nonlinear photorefractive materials are well suited to record dynamic volume holograms using the wave mixing of coherent laser beams. The photo-induced index modulation is due to a space charge field which modulates the crystal refractive index. The basic phenomena and beam interactions are reviewed for different types of materials operating in the visible and near infrared. In particular, we outline their ability to amplify a low intensity signal beam due to the intensity transfer of a spatially multimode pump beam. We apply this interaction to the cleanup of a multimode large core fiber amplifier. This class of nonlinear materials contribute to extending the performances of laser sources for advanced applications of photonics. To cite this article: L. Lombard et al., C. R. Physique 8 (2007).     

Transient gain enhancement in photorefractive crystals with two types of movable charge carrier

Considerable improvement of a transient two-beam coupling gain is reported for Sn(2)P(2)S(6), a photorefractive crystal that possesses two types of movable charge carrier. A gain enhancement occurs if the phase difference of the interacting beams is abruptly changed to pi. Enhancement is also achieved with periodic phase variations of zero and pi between two discrete states at modulation frequencies lower than the smallest of two reciprocal characteristic times of the space-charge formation.     

Dependence of space charge field and gain coefficient on the applied electric field in photorefractive materials

Intensity dependent space charge field and gain coefficient in the photorefractive medium due to the two interfering beams have been calculated by solving the material rate equations in presence of externally applied dc electric field. The gain coefficient has been studied with respect to variations in the input intensity, modulation depth, concentration ratio and normalized diffusion field in the absence and presence of the externally applied dc electric field. Space charge field has also been computed by varying the intensity ratio in the presence and absence of the externally applied dc electric field. It has been found that the rate of change of the space charge field with the normalized dc field decreases with the increasing intensity ratio for different values of the normalized diffusion field. It has also been found that the externally applied dc electric field has appreciable effect only when it is larger than the diffusion field.     

Slowing down of light in photorefractive crystals with beam intensity coupling reduced to zero

A considerable deceleration of light pulses in crystals with nearly compensated space-charge field proves that the strong dispersion of dynamic photorefractive gratings in the vicinity of Bragg resonance is of primary importance for light slowing down.     

Dynamic light beam deflection caused by space charge waves in photorefractive crystals

During holographic recording in photorefractive crystals (BSO, BGO, and BTO) by an oscillating interference pattern we observe a strong dynamic deflection of the laser beams reflected from the crystal’s surface. The theoretical treatment shows that this new effect is associated with a nonlinear interaction of space charge gratings resulting in a quasi-homogeneous oscillating space charge field which provides deformations of the crystal via the piezoelectric effect. Received: 3 August 1999 / Accepted 5 August 1999 / Published online: 8 September 1999     

双光束耦合增益振荡的理论研究

本文从双光束增益振荡的动态方程组出发,给出一般情况下双光束光折变振荡稳态时的普遍结果,解释了文献[1,2]中理论不完全符合实验规律的原因,表明文献[1,2]中的理论只适合于光折变效应为纯扩散机制的特殊情况。     

External electric field induced modulation instability of an electromagnetic beam in two-photon photorefractive materials

The modulation instability of a broad electromagnetic beam in a biased two-photon photovoltaic photorefractive material, due to two-photon-photorefractive effect has been investigated. The one-dimensional modulation instability growth rate has been estimated under the linear stability framework. The behavior of the gain spectrum is different in low and high power regions. It has been predicted that, with the application of external electric field, it is possible to initiate and control growth of the instability in those media, where modulation instability was hitherto prohibited. The influence of different system parameters on the instability growth rate has been examined.     

Competition between subharmonic and signal beams for photorefractive gain in BSO with two pump beams

It is shown that two pump beams incident upon a bismuth silicon oxide crystal give rise to a subharmonic beam bisecting the pump beam. Simultaneously a signal beam injected between the pump beams may be strongly amplified at the expense of the pump beams. It is shown that the amplified signal beam grows with a faster time constant than the subharmonic beam and that there is competition for gain in the steady state regime.     

Theoretical study on coupling effects of modulation depth between two photorefractive phase gratings with an external applied field

1　Ｉｎｔｒｏｄｕｃｔｉｏｎ　　Ｗｈｅｎｔｗｏｐｈｏｔｏｒｅｆｒａｃｔｉｖｅｐｈａｓｅｇｒａｔｉｎｇｓａｒｅｓｉｍｕｌｔａｎｅｏｕｓｌｙｒｅｃｏｒｄｅｄｉｎｏｎｅｐｏｉｎｔ,ｔｈｅｖａｒｉｏｕｓｃｏｕｐｌｉｎｇｅｆｆｅｃｔｓｂｅｔｗｅｅｎｔｈｅｔｗｏｇｒａｔｉｎｇｗｉｌｌｐｒｅｓｅｎｔ,ｂｅｃａｕｓｅｏｆｔｈｅｎｏｎ ｌｉｎｅａｒｒｅｓｐｏｎｓｅｏｆｍａｔｅｒｉａｌｓ .Ｒｅｃｅｎｔｌｙ ,ｍａｎｙｒｅｓｅａｒｃｈｅｒｓｈａｖｅｓｔｕｄｉｅｄｔｈｅｉｎｔｅｒａｃｔｉｏｎｂｅｔｗｅｅｎｔｈｅｔｗｏｇｒａｔ…