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.     

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.     

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).     

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.      

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).     

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.     

温度对中心对称光折变稳态暗孤子演化的影响

为了得到温度对中心对称光折变晶体中空间暗孤子影响的结果,数值研究了中心对称光折变暗孤子动态演化的温度特性。结果表明,孤子强度包络演化强烈地依赖于晶体的温度和介电常数的温度特性。在290-320K的温度变化范围内,暗孤子的宽度随温度的增加而变大,孤子的峰值强度随温度的增加而变小。在300K的温度下,中心对称光折变介质中可以形成稳定的暗空间孤子,当温度从300K升高或降低时,孤子将克服较小的扰动而保持稳定的传播。通过调整温度可以改变孤子的空间形态。     

线性电介质和中心对称光折变晶体界面表面波的研究

报道了中心对称光折变晶体与线性电介质界面表面波的形成及能量变化. 通过调节传播常数和波导参数的方法,可以得到非局域、振荡、局域三种类型的表面波. 波导参数和传播常数之差大于阈值时,线性电介质和中心对称光折变晶体界面可以形成局域表面波. 波导参数为正值时,局域表面波主要聚集在中心对称光折变晶体内,随着传播常数的增大,波能量随之单调递增,表面波可以稳定传播. 在给定的条件下,调节决定非线性作用强度的可变参量可以控制局域表面波模的阶数和传播波形. 关键词： 非线性光学 中心对称光折变晶体 表面波     

双光子光折变介质中非相干耦合亮-暗屏蔽光伏孤子对

对有外加电场的双光子光伏光折变晶体中两束偏振方向和波长都相同的互不相干光束的耦合进行研究,给出产生亮-暗双光子光折变屏蔽光伏孤子对需满足的条件.以Cu:KNSBN晶体作为研究对象,选取α=117.3,β=83.79,η=1.5×10-4,σ=104,δ=0.005,r=10时,给出双光子光折变晶体中的非相干耦合亮-暗屏蔽光伏孤子对2个孤子分量光强的空间分布,证明有外加电场的双光子光伏光折变晶体中存在非相干耦合亮-暗屏蔽光伏孤子对,指出孤子对是由偏振态和波长都相同的两束互不相干光形成的,当外加电场方向和晶体中光伏电场的方向与晶体光轴方向相同时,双光子光折变晶体中可支持亮孤子峰值光强稍大于暗孤子最大光强的非相干耦合亮-暗孤子对,当外加电场方向和晶体中光伏电场的方向与晶体光轴方向相反时,双光子光折变晶体中可支持亮孤子峰值光强稍小于暗孤子最大光强的非相干耦合亮-暗孤子对.     

无缺陷PbWO4晶体光学性质的模拟计算

利用完全势缀加平面波局域密度泛函近似研究PbWO4（PWO）晶体的光学性质.计算了完整的PWO晶体的电子结构、复数折射率、介电函数、光电导谱和吸收光谱.介电函数的虚部、吸收光谱、折射率等的峰值位置存在一一对应关系,这与电子从价带到导带的跃迁吸收有关.完整的PWO晶体在可见光范围内没有吸收,所以完整的PWO晶体是无色透明的晶体.     

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.     

Stoichiometric Mg:LiNbO(3) as an effective material for nonlinear optics

Photorefractive damage, optical absorption, photoconductivities, and photogalvanic currents of stoichiometric LiNbO(3) single crystals with different Mg doping levels have been investigated. Nominally pure stoichiometric LiNbO(3) shows lower photorefractive damage resistance than congruent crystal; however, stoichiometric crystals doped with MgO of more than 1.8 mol. % exhibit no measurable photorefractive damage at 532 nm to intensities of as much as 8 MW/cm(2) . This remarkable damage resistance can be attributed not only to increased photoconductivity but also to decreased photogalvanic current. Stoichiometric Mg:LiNbO(3) also demonstrates the shortest absorption edge, 302 nm, and a single-domain nature with low scattering losses.     

Optical bistability in radiation reflection from the boundary of a photorefractive crystal with the drift-diffusion nonlinearity mechanism

A rigorous solution is given in the plane-wave approximation for the boundary problem of light reflection from the interface between an isotropic medium and a photorefractive crystal with drift-diffusion nonlinearity. The possibility of realizing hysteresis reflection or optical bistability in the system under certain conditions is shown. Analytical expressions are obtained that describe the hysteresis behavior of reflectivity as a function of the angle of incidence or the strength of a constant external electric field applied to the crystal. The results of the study are of interest for the development of devices controlling laser radiation.     

对全入射角负折射二维光子晶体结构和电磁参量的研究

利用二维光子晶体的等频线分析原理和平面波展开方法,得到了使二维光子晶体产生全入射角负折射(All-Angle Negative Refraction,AANR)现象时,入射电磁波的频率取值范围.同时,分析了AANR频率范围随着结构参量(晶格类型、介质棒半径与晶格周期的比值)和电磁参量(介质柱介电常量、本底介电常量、入射电磁波偏振方向)变化的行为.结果表明:固定组成光子晶体的一种介质的介电常量,另一介质的介电常量只有达到一定阈值,才有可能使光子晶体出现AANR现象.在给定两种介质介电常量的条件下,存在使AANR频率范围最大化的结构参量和电磁参量.     

无偏压的串联光折变晶体回路中高斯光束传播特性调节

根据串联光折变晶体回路中独立空间孤子对理论,研究了明暗孤子对之间的相互依赖特性.假设一束暗孤子波和一束高斯光束分别入射到回路中两块晶体上,利用数值计算方法讨论了改变其中暗孤子光束的强度对高斯光束在另外一个晶体中传播特性的影响.结果表明,调节暗孤子的强度能够影响高斯光束的传播特性,可以决定高斯光束在晶体中是否能够演化为稳定传播的明孤子波 关键词： 非线性光学 光折变效应 光折变空间孤子对 高斯光束     

INCOHERENTLY COUPLED SCREENING-PHOTOVOLTAIC SOLITON FAMILIES IN BIASED PHOTOVOLTAIC PHOTOREFRACTIVE CRYSTALS

It is shown that the existence of incoherently coupled screening-photovoltaic soliton families is possible in biased photovoltaic photorefractive crystals under steady-state conditions. These screening-photovoltaic soliton families can be established provided the multiple incident beams have the same polarization and wavelength, and are mutually incoherent. Such soliton families reduce to screening-photovoltaic soliton pairs when they contain only two components. Relevant examples are presented where the photovoltaic photorefractive crystal is of the lithium niobate type.     

双光子光折变介质中的非相干耦合空间孤子对

对双光子光折变晶体中两束偏振方向和波长都相同的互不相干光束的耦合进行了研究, 预言了非相干耦合暗-暗、亮-亮及亮-暗双光子空间孤子对的存在. 关键词： 双光子光折变效应 光折变材料 空间孤子     

体全息存储系统中光折变晶体动态范围的理论研究

基于晶体中线性偏振波的耦合波理论以及光折变效应的能带传输模型，求出了体全息存储系统中光折变晶体动态范围的解析表达式。以ＬｉＮｂＯ３：Ｆｅ和ＢａＴｉＯ３晶体为例，讨论了读写光束与晶体作用的几何结构形式，晶体掺杂量大小及其氧化还原状态等因素对动态范围的影响。研究发现，对两种晶体来说，掺杂浓度越大，氧化程度越深，则可获得的动态范围越大。     

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