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).     

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 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.     

Oscillation characteristics of a coupled unidirectional ring resonators with photorefractive crystals

For a coupled unidirectional photorefractive ring resonator (UPRR), the oscillation characteristics have been studied in details in terms of the photoconductive and dielectric constant of the photorefractive (PR) crystals under the assumption of the plane-wave approximation based on non-degenerate two-wave mixing in the photorefractive materials. It has been found that the steady oscillations are possible when the two resonators oscillate independently. Using the plane-wave approximation and steady state oscillation conditions, the effect of the frequency detuning, photoconductivity and dielectric constant of the PR crystals on the relative intensity and frequency of oscillation of the secondary resonator in the coupled UPRR have been studied. It has been found that the relative oscillation frequency of the secondary resonator could be enhanced by selecting PR crystal A of higher absorption strength relative to PR crystal B and the higher photoconductivity of the crystals B as compared to that of the crystal A. Due to the non-reciprocal energy transfer between the oscillating beams and the additional PR phase-shift in the PR crystals A and B, the magnitude of the relative oscillation frequency of the secondary resonator could be controlled by the absorption strength, dielectric constant and photoconductivity of the two crystals.     

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.     

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).     

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.     

Dynamic study of the gain in two beam coupling in photorefractive materials

Wave equations describing the non-linear two-beam coupling have been solved and expressions for the gain of the two beams in the photorefractive crystals have been derived. In case of the degenerate two-beam coupling, the gain depends upon the crystal thickness, coupling coefficient, absorption coefficient and the input intensity ratio. The effect of these parameters on the gain has been studied in details. In case of non-degenerate two-beam coupling the gain not only depends upon crystal thickness, coupling coefficient, absorption coefficient and the input intensity ratio but also on the response time of the photorefractive medium. This response time is the function of concentration ratio. The influence of oscillation frequency shift, concentration ratio on the gain for the non-degenerate two-beam coupling has also been studied.     

Crystal orientation dependence of the SNR for signal beam amplification in photorefractive BaTiO3

In signal beam amplification by two-beam coupling in BaTiO₃ photorefractive crystals, beam fanning in the direction of the amplified signal reduces the signal-to-noise ratio (SNR). The dependence of the SNR and the signal beam gain on the crystal orientation are analysed using a HeNe laser. It is found that orientating the crystal for maximum gain gives poor signal-to-noise ratio. A compromise has to be made between the SNR and high gain for optimum signal amplification.     

Photorefractive mode coupling between two unidirectional ring oscillators

We consider the coupling between two photorefractive unidirectional ring resonators. The first resonator is driven by an external laser beam via photorefractive two-wave mixing. The internal oscillating beam is then employed to drive the second ring resonator via the same mechanism. Closed form solutions for the oscillation intensities and frequencies are given, and their numerical results are presented and 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.     

Coherent beam amplification with a photorefractive liquid crystal

Coherent amplification of a signal beam by a strong pump beam is observed in thin films of fullerene-doped nematic liquid crystal. Exponential gain constants as high as 2890 cm(-1) with no phase cross talk are achieved at low applied dc bias voltage and pump beam intensity. The underlying mechanism is the electro-optically induced spatially reorientation of the liquid-crystal axis and the resultant phase-shifted index grating required for two-beam coupling.     

Instabilities in coupled photorefractive ring cavities and self-pumped phase conjugators

We investigate the temporal instabilities of mode intensities in two coupled unidirectional photorefractive ring resonators. The first resonator is driven by an external laser beam via photorefractive two-wave mixing. The internal oscillating beam is then employed to drive the second ring resonator. The second ring resonator provides a nonlinear loss mechanism for the coupled system. Complete spatial-temporal equations for describing the coupled system are derived and mean-field approximation is employed to simplify the transient analysis. The results of linear stability analysis indicate that the coupled system exhibits instability in the off-state and steady-state operation. The instability is explained in terms of competition between nonlinear gain and loss. The results are presented and discussed.Part II on Numerical Results will be published in a forthcoming issue of Applied Physics B     

Simple method for determining the gain coefficient of a photorefractive polymer film

We propose a simple method for measuring the gain coefficient of two-beam coupling for photorefractive polymer film. To measure the gain coefficient, we attached a phase grating onto the photorefractive polymer film and made an interference pattern between the transmitted and diffracted beams in the photorefractive film by using an illuminating single beam. The gain coefficient values measured at various external fields by our method showed good agreement with those measured by a standard two-beam coupling method. Compared to standard two-beam coupling, this method exhibited fairly improved stability of the output signal to external factors such as human sounds and airstreams.     

Feedback method of the noise suppression in wave-mixing amplifiers based on non-linear materials with photorefractive response in a reflection grating configuration

In the photorefractive wave-mixing system, fluctuation in the signal beam intensity of the photorefractive output with a reflection grating has been analyzed by employing pump feedback method. In this method, fluctuations of the photorefractive wave-mixing process not only induce the intensity fluctuation of the mixing waves but also induce phase fluctuation of the mixing waves. Thus, the phase of the pump and signal beams at the output surface fluctuates in time around a mean value. Using such a positive feedback method of a pump beams, the relative fluctuation in the photorefractive output signal beam intensity with respect to its mean intensity can be minimized significantly without reducing its mean intensity. The factors that control the fluctuation in the signal beam intensity, such as the phase fluctuation of the output pump beam, absorption strength of the material and the feedback reflectivity of the cavity mirrors, on the relative fluctuation of the output signal intensity in the photorefractive wave-mixing systems have been studied in detail. It has been found that the fluctuation of the output signal intensity relative to its mean intensity in the photorefractive wave-mixing system can be suppressed to larger extent by taking lower value of feedback reflectivity of the cavity mirrors which could exist at a higher value of absorption strength of the photorefractive materials.     

Coherent CW image amplifier and oscillator using two-wave interaction in a BaTiO3-crystal

A BaTiO₃ crystal was used to amplify an image illuminated by an Ar-laser. The amplification mechanism is two-wave mixing in an electrooptic crystal, usually called dynamic holography. We achieved gain factors of 4000 with pump powers of 150 mW and holographic resolution. As the interaction between signal and pump wave is not effected through excited states of the crystal, the amplification process is virtually noise free. This has to be traded in with slow response, 0.1-1 s. To demonstrate the high optical quality of the amplifier, it was incorporated in a ring resonator as gain medium. It was possible to excite pure discrete transversal modes of higher order. That reveals the high optical homogeneity of the crystal over the mode cross-section of > 1 mm. The coupling process of the pump with the two counter-propagating waves forming the standing resonator wave is not symmetric. Consequently a travelling wave develops in the resonator.     

Photorefractive amplification and generation of light beams in BaTiO3 controlled by the intensity of the pump light

3 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. Received: 23 January 1998     

Optical bistability and multistability in a photorefractive bidirectional ring oscillator

We consider optical bistability and multistability based on the theory of bidirectional oscillations induced by four-wave mixing (FWM) in a photorefractive (PR) phaseconjugate ring resonator model. Bistable and multistable effects of the intensity of oscillation have been established numerically using a successive bisection method that can predict repeated roots as well as discontinuities.Oscillation intensities are studied as a function of parameters such as the nonlinear coupling strength (gL), the ratio of pump beam intensities (R) and the product of reflection coefficients of three cavity mirrors (|r|). It is shown that for certain combinations of these parameters and assuming that gL exceeds its threshold value, the oscillation intensity becomes double-valued or multivalued corresponding to the number of oscillating modes in the cavity. The multiplicity of solutions as well as the possible regions of bistable/multistable branches are greatly affected by the sign of gL and also depend on whether R and |r| are greater than or less than unity.     

光折变晶体中高速调制光放大特性的研究

本文对光折变晶体中高速调制光的放大特性进行了理论分析,给出了在Ce:SBN晶体中进行的实验结果,并从物理概念上进行了讨论,指出光折变晶体中的双光束耦合可以用于时域编码通讯。     

Transverse effects in photorefractive two-wave mixing

In a biased photorefractive crystal, the process of two one-dimensional waves mixing, i.e., the dynamical evolution of both pump beam and signal beam, is traced by numerically solving the coupled-wave equation. Direct simulations show that the propagation and stability of the two beams are completely determined by the system parameters, such as the external bias field, the intensity and the beam waist of the pump beam. By adjusting these parameters, one can control the state of two Gaussian waves mixing. The numerical results are helpful for performing a two-wave mixing experiment.