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.     

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.     

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.     

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).     

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.      

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.     

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     

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.     

Holographic and photoelectric characterization of a novel photorefractive organic glass

We present a detailed study of the photoelectric as well as the holographic properties of a novel organic photorefractive glass based on triphenylamine. We studied the quantum efficiency Φ of the photogeneration of charges by means of photoinduced discharge measurements. The photoconductivity σ and the charge carrier mobility μ were obtained via dc photoconduction and pulsed time-of-flight experiments, respectively. The holographic characterization was performed by two-wave and degenerate four-wave mixing experiments allowing for the determination of properties such as diffraction efficiency η, modulation of the refractive index Δn, gain coefficient Γ, and phase-shift φ_p of the investigated system. The experimental data for Φ could be successfully described by the Onsager formalism with a thermalization radius of r₀=24 ? and a primary quantum yield of Φ₀=40%. We evaluated the E field and temperature-dependent measurements of μ using the B?ssler formalism yielding a width of the density of states of σ=0.13 eV and a disorder parameter Σ=3.6. On this basis the lifetime and the average drift length of the charge carriers could be estimated from the dc photoconduction experiments. From the photoelectric measurements we also calculated the holographic response time that matched very well to the measured response time and described the E-field dependence satisfactorily. The presented photorefractive system shows outstanding optical properties and stability with respect to degradation. We measured a gain coefficient of Γ=90 cm^-1, and a diffraction efficiency of η=27% at a response time of 30 ms for only 40-μm-thick samples. Orientational enhancement was observed and evaluated quantitatively. To our knowledge, this work presents the first determination of each of the above quantities all in one single organic photorefractive material. Received: 16 November 1998 / Revised version: 4 January 1999 / Published online: 31 March 1999     

Pattern formation in a passive incoherent ring resonator system based on nonlinear material with the self-focusing non-instantaneous Kerr response

We have analyzed the pattern formation in a nonlinear medium with self-focusing non-instantaneous Kerr response by employing the passive incoherent ring resonator system. In such a system, coherence time of the light is much shorter than the time of one round trip in the resonator. This delayed response of the nonlinearity can amplify the noise of certain spatial frequencies of the perturbed wave field and thus patterns can form when nonlinear gain (i.e., amplification of the noises) overcomes the loss (i.e., a well defined cavity threshold set by the coherence properties) in a single pass. The expression for the spatial spectral density of the perturbed wave field, which is the characteristic parameters of the pattern formation, have been derived in the case of lowest order approximation. It is found that for a specific value of the spatial frequency of the perturbed wave field, the intensity feedback of the cavity is much effective factor rather than the crystal thickness of the nonlinear media and amplitude of the incoming beam in the cavity for the enhancement of the spatial spectral density of the intensity pattern, which greatly improved the performance and applications of the pattern formation such as information processing, symmetry-breaking, and dynamics in non-equilibrium systems.     

Experimental evidence of a non-relationship between photorefractive inhibition and photoconductivity increase in LiNbO3:Mg

By means of measurements of both photoconductivity and two-wave mixing using cw 532 nm laser light, a direct relationship between optical damage resistance and photoconductivity coefficient for several congruent magnesium-doped lithium niobate crystals, with concentrations below and above the threshold of around 4.6 mol% MgO in melt, has not been observed. Specifically, when the polar axis is parallel to the photorefractive grating vector formed by two-interference beams, an increase of optical-damage resistance above the threshold is obtained. However, the photoconductivity coefficient is of the same magnitude of those samples below the threshold. On the other hand, when the optical axis is perpendicular to the grating vector, a decrease of the refractive index grating for crystals below the threshold could be observed, but even for this case the photoconductivity coefficient is unchanged, except for only one specimen with high magnesium level which exhibits simultaneously photorefractive response and high photoconductivity. These results suggest that the increase of photoconductivity is not very essential in the process of photorefractive inhibition; rather, the distribution of magnesium ions with respect to polar axis is an important parameter in the mechanism of optical-damage resistance.     

Influence of bismuth nitrate doping towards the characteristics of L-Alanine nonlinear optical crystals

In the present study, an amino acid derivatives, L-alanine (LA) and Bismuth nitrate-doped L-alanine (BNLA) crystals were grown by the slow evaporation technique. The crystal structure and quality of the grown crystal were examined by single-crystal X-ray diffraction (XRD) and powder XRD. The X-ray diffraction analysis of LA and BNLA crystals confirmed the orthorhombic crystal system without any internal structural grain boundaries. The optical properties of the LA and BNLA crystals have been determined using UV-Visible spectroscopy and Photoluminescence (PL). The second harmonic generation (SHG) efficiency of the crystal was measured using Kurtz powder technique. The dielectric constant measurement was performed at room temperature for different frequencies. Photoconductivity tests show that the LA and BNLA crystals have negative photoconductivity value. On testing of the retentivity or remanent magnetization, the BNLA crystal has increased values as compared to the pure LA crystals, in addition to the observation of changes in coercivity. Further, the observation of maximum intensity peak for the BNLA crystal at 346.9 nm pointed out that the crystal has blue fluorescence emission. The third-order nonlinear optical properties of the grown crystal were studied using Z-scan technique. The enhancement in nonlinear refractive index and third-order NLO susceptibility value shows that the grown BNLA crystals may be of good quality and less in defect than that of pure LA crystals.     

Positive and negative feedback effects of four-wave mixing in photorefractive crystals with two active centres

Based on a two-level model of optical transitions, the problem of positive and negative feedback effects during simultaneous reading and writing of dynamic holograms in photorefractive crystals has been solved analytically. The diffraction efficiency and the gain coefficient are shown to be nonlinear functions of the readout beam intensity and are nonreciprocal with respect to the readout from the two input ports. The readout beam intensity value that affects a previously recorded grating is shown to depend on microscopic parameters such as the cross-section of photoionization, the recombination coefficient and the concentration of photorefractive centres. An analysis of the amplitude of the overall shared grating has shown that with increasing readout beam intensity the holographic grating thickness decreases. In this case, under negative feedback the grating amplitude decreases, while with positive feedback it increases. The possibility is shown of achieving (under positive feedback) a maximum value of diffraction efficiency and complete energy transfer in a finite thickness of the photorefractive crystal, in contrast to the infinite thickness required in the standard two-beam coupling case.     

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.     

High photorefractive sensitivity at 860 nm in reduced rhodium-doped KNbO(3)

We show that high-temperature reduction in a CO-CO(2) atmosphere increases the photorefractive sensitivity of KNbO(3):Rh at 860nm by 4 orders of magnitude compared with that of the as-grown crystal. The effective trap density is increased by a factor of 3, and the photoconductivity by a factor of 30, and the photorefractive response at a grating spacing of 0.15 mu;m is accelerated by a factor of 400. The grating buildup time at a grating spacing of 0.7 microm and an intensity of 1Wcm(-2) is 0.5 s, a value comparable with that of as-grown KNbO(3):Fe at visible wavelengths. The optical and photorefractive parameters of Rh-doped KNbO(3) subjected to reduction treatment are characterized for wavelengths of 0.48-1.064 microm .     

First photoconductivity measurement following photoionization of rare-earth dopant in a dielectric powder

Transient response of the dielectric permittivity of dielectric powder of LSO:Ce³⁺ under pulsed laser excitation were recorded by the 8-mm microwave resonator technique at room temperature. The signal in absorption mode is the signature of Ce³⁺ photoionization and photoconductivity effect in the rare-earth-doped dielectric grains. The signal in dispersion mode results from surface defects around each grain leading to electronic traps. This opens new perspectives for photoconductivity measurements on rare-earth-doped insulating nanopowders.     

掺Ce,Fe系列LiNbO3晶体光折变效应光存储特性

研究了系列Ce：Fe掺杂以及不同后处理态(生长态、还原态和氧化态)铌酸锂晶体的透过率光谱和光折变全息存储特性。实验结果表明单掺Ce铌酸锂晶体具有较好的图像存储质量和较宽的透过率光谱范围,二波耦合增益相对较低;高掺杂铌酸锂样品的透过率光谱范围较窄,光折变二波耦合增益较低。晶体的后处理对铌酸锂样品的光折变特性影响明显,双掺Ce:Fe还原态铌酸锂晶体具有较高的二波耦合增益;氧化态样品具有较大的透过率光谱范围;还原态样品具有较大的光折变二波耦合增益特性。实验结果还表明在同种样品中难于同时获得大的二波耦合增益和图像存储质量。     

Optical bistability by two laser beams in photorefractive crystals

For a nonlinear medium, a given incident laser beam may produce different transmitted light waves. This phenomenon (the so-called optical bistability) corresponds to multiple solutions of the boundary value problems of the nonlinear Helmholtz equation. Optical bistability can be useful in the design of optical switches. Devices that display this behavior could potentially play a major role in the development of optical communication systems and computing. In this article we present experimental results concerning the optical bistability in photorefractive BaTiO₃:Fe crystal. Two laser beams were used to interact with the photorefractive crystal which resulted in the bistability of the intensity of transmitted wave. This was achieved without the application of any optical resonator. High contrast optical bistability is found experimentally in the pump-ratio dependence of the output intensity.     

外电场对SBN：Cr晶体二波耦合特性的影响及应用

对固液同成分SBN：Cr(Sr0.61Ba0.39Nb2O.6：Cr)晶体在外加直流电场作用下的光折变二波耦合特性及其应用进行了实验研究，分析了晶体的二波耦合强度增益 系数随外电场变化的趋势，并给出了实验测量结果.发现在适当的外电场作用下，晶体的光折变二波耦合增益和响 应速度可以得到一定程度的提高.进一步的研究表明，这种电场响应特性有助于改善SBN：Cr晶体的某些应用性能.利用该晶体通过光折变二波耦合非线性放大原理实现光学图像边沿增强时，通过给晶体沿轴向施加适当的外电场，可进一步提高图像边沿增强效果；在基于光 折变边沿增强预处理的联合变换相关器中，适当的外加电场可进一步改善联合变换相关器的相关识别性能. 关键词： SBN：Cr晶体 光折变二波耦合 边沿增强 联合变换相关器