Strong and fast phase modulation for quantitative analysis of photorefractive gratings

A new approach for studying photorefractive gratings in two-wave mixing experiments by a phase modulation technique is presented. The introduction of a large-amplitude, high-frequency sinusoidal phase modulation in one of the input beams blurs the interference pattern and provides powerful harmonic signals for accurate measurements of the grating diffraction efficiency η and the output phase shift ϕ between the transmitted and diffracted waves. The blurring of the light fringes can be used to suppress the higher spatial harmonics of the grating, allowing a space-charge field with sinusoidal profile to be recorded. Although the presence of such a strong phase modulation affects the beam coupling in a rather complicated way, it is shown that for the special case of equal intensity input beams, the effect of the phase modulation on η and ϕ is reduced to a weakening of the coupling strength. The potentialities of the technique are illustrated in a study of refractive-index waves excited by running interference patterns in a Bi₁₂TiO₂₀ crystal. Expressions for the diffraction efficiency and the output phase shift are derived and used to match numerically calculated curves to the experimental data. The theoretical model is supported by the very good data fitting and allows the computation of important material parameters. PACS 42.40.Ht; 42.40.Kw; 42.70.Nq     

Two-wave mixing via reflection population gratings

Theoretical analysis of two-wave mixing (TWM) via reflection population grating, aiming to support current experimental investigations of dynamic gratings in Erbium (Er)-doped fibers, is presented. It is shown that for low recording intensities the stationary TWM via reflection saturated absorption gratings is well described in approximation of a spatially uniform grating amplitude. The analysis of the transient TWM is performed both for rectangular and for sinusoidal phase modulation of one of the recording waves and it is shown how the recorded grating amplitude and characteristic recording time can be obtained from the detected signals. It is pointed out that the majority of the existing experimental results on TWM in Er-doped fibers are qualitatively explained within the framework of the developed model.     

Coupling modulation in photorefractive materials by applying AC electric fields

In general, the application of an electric field to a photorefractive material with optical activity results in a change in the effective electro-optic coefficient, r_eff, which, in turn, alters the coupling between the two beams in a two-wave mixing experiment. When an alternating field is applied, this results in a modulation of both the phase and the coupling of the beams. Equations that have been developed to describe the change in the electro-optic coefficient as function of an applied dc field across an optically active crystal, have been used to demonstrate coupling modulation effects in BSO whilst applying large sinusoidal fields. Methods of overcoming these modulation effects are included.     

非相干背景光辐照对LiNbO3∶Fe与LiNbO3∶Fe∶In晶体中二波耦合的控制

理论分析和实验观测了非相干背景光辐照下掺杂LiNbO₃晶体中的二波耦合,发现非相干背景光能够在很大范围内灵活有效地控制信号光增益,抑制扇形效应,提高信噪比,缩短光栅的建立时间.入射光光强比一定时,适当地增大背景光光强可以使光栅响应时间减小一个数量级.尤其对于抽运光光强远大于信号光光强的情况下,上述作用更为明显. 关键词： 光折变 二波耦合 非相干背景光     

Ce∶KNSBN晶体两波耦合中的光扇效应

采用两波耦合非同时读出实验装置 ,测量了掺铈钾钠铌酸锶钡 (Ce∶KNSBN)晶体两波耦合过程中的信号光和抽运光非同时打开条件下两波耦合增益的时间变化规律 ,讨论了光扇的入射光强阈值及光扇效应对两波耦合动态过程的影响。结果表明 :6 32 .8nmHe Ne激光在Ce∶KNSBN晶体中写入体光栅时 ,光扇效应存在明显的写入光强阈值特性 ,当入射光强大于 30mW /cm2 时 ,才存在强烈的光扇效应。利用修正耦合波方程对Ce∶KNSBN晶体中的两波耦合动态过程、增益随着信号光和抽运光打开时间间隔Δt的变化进行了模拟计算 ,理论模拟结果与实验测量结果基本一致     

Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption

Experimental observation of phase (i.e. refractive index) component in the dynamic gratings recorded in erbium-doped optical fiber with saturation of optical absorption is reported. We utilized configuration of transient two-wave mixing with rectangular phase modulation of one of counterpropagating recording waves, where unshifted phase grating resulted in a transient energy exchange. The reported experiments were performed with heavily doped (≈5400 ppm erbium) fibers in a wide spectral range of Er³⁺ fundamental absorption at selected laser wavelengths 1492, 1526, 1549, and 1568 nm. Relative contribution of phase grating was especially large (up to ≈100% of the maximal amplitude component) at the opposite sides of the investigated spectral range and was significantly lower in its central part. The amplitude grating was found especially strong at short wavelength side of the spectrum (i.e. at 1492 nm), where the grating amplitude proved to be only two times lower than the theoretically predicted from consideration of two-level model.     

Investigation on the phase shifts of extinction and phase gratings in polymethyl methacrylate

The phase shifts of the extinction and refractive index gratings to the illumination pattern are revealed in doped polymethyl methacrylate （PMMA）. The dynamic process of these shifts is studied via two-wave coupling at 351 nm. It is shown that these shifts are from the strain and the shrinkage inside the sample and accompanied with the photo-repolymerization process during the building process of the holographic grating. Such shifts will cause obvious energy exchange between the two recording beams and enough attention should be paid to the nonlocal property of the holographic gratings of the material in the application.     

Visualization of a Phase Object by Two-Wave Coupling in a Photorefractive Bismuth Silicon Oxide Crystal

We propose a method to visualize a phase object using a locally-controllable image amplification scheme we developed earlier which is based on two-wave coupling in a bismuth silicon oxide (Bi₁₂SiO₂₀, or BSO) crystal. In this method the BSO crystal is used as a phase plate in the configuration of Zernike’s phase contrast imaging system. The principle of the phase-visualization with two-wave coupling is presented. An experimental result to verify the proposed method is shown.     

Perturbative analysis of cross-talk of two pieces of photorefractive phase gratings stored in one point by angle multiplexing

In this paper, we have applied a perturbative expanding method to the hopping model, and studied the cross-talk between two pieces of phase gratings stored in one point of photorefractive material by angle multiplexing. The coupling equations and their steady solution have been derived. It has been found that the fundamental harmonic of the first grating is coupled with the second-order harmonic of the second grating and the second-order harmonic of the first gating is coupled with the fundamental harmonic of the second grating. The positions of maximums of the plots about the normalised fundamental and second-order harmonics of the space-charge field vs. the normalised grating vector (k/k₀) are at k/k₀=1.414 and k/k₀=1.01 for Δk/k₀=0, respectively, which are at k/k₀=1 and for the case of storing single grating in one point. This kind of deviation has been confirmed by our two-wave coupling experiment with Ce:KNSBN crystal. At the same time, we have found the degree of deviation of the second-order harmonic of the space-charge field strongly depends on the difference of normalised grating vector (k/k₀)between the two pieces of gratings, but that of fundamental harmonic weakly depends on it. In addition, it has been found that the degrees of deviation of both harmonics do not depend on the modulation depth.     

Two-wave interaction on a photorefractive grating in cubic gyrotropic crystals in the case of strong coupling

The effect of nonunidirectional energy exchange on the intensity and polarization state of the signal wave is analyzed in the case of symmetric two-wave coupling on a transmission photorefractive grating produced by a diffusion mechanism in a gyrotropic cubic crystal belonging to the point group 23.     

Photorefractive effect in Fe-doped GaN

The photorefractive effect was observed in Fe-doped semi-insulating GaN. We measured the two-beam coupling constant and the grating formation time as a function of pump intensity at a wavelength of 458 nm in reflection geometry. The photorefractive gain coefficient was 0.39 cm⁻¹, and the grating formation time was 7 ms at a pump intensity of 1.0 W/cm². Besides the refractive index grating, the contribution of an absorption grating was also observed in a two-wave mixing experiment. The coupling constant of the absorption grating was negative and increased with the pump intensity. The origin of the absorption grating was attributed to light-intensity-dependent photochromism.     

强外加电场与大调制度下光折变动力学光栅形成研究

强外加电场与大调制度在光折变效应的研究中已经得到了广泛应用。采用PDECOL算法,严格求解光折变带输运方程,得到外加电场时不同调制度下光折变晶体中随时间变化的空间电荷场、载流子浓度,并讨论了外加电场对它们的影响。通过将物质方程与耦合波方程联立数值求解,可得到光折变光栅形成过程中两波耦合增益系数以及光束条纹相位的变化。模拟结果表明,在强外加电场作用下,两束记录光之间的光强与相位耦合都得到了增强,而原有的解析式忽视了强外加电场与大调制度对空间电荷场相位耦合的影响,此时不再适用。同时发现折射率光栅与记录光束条纹均发生弯曲,并不再保持平行。     

Theoretical analysis of novel fiber grating pair

A novel fiber grating pair that consists of a conventional long-period fiber grating and a fiber Bragg cladding grating (FBCG) is proposed. The FBCG is a new type of fiber grating in which refractive index modulation is formed in the cladding. Through the coupled-mode theory, we accurately calculate the coupling coefficients between modes supported in the fibers. And some other mode coupling features in the fiber cladding gratings are analyzed in detail. The calculation of the modes involved in this paper is based on a model of three-layer step-index fiber geometry. Then, we have investigated the sensitivity characteristics for variation of the modulation strengths of the fiber Bragg cladding gratings’ resonance peaks and the long-period cladding gratings’ (LPCGs) dual resonant peaks. Finally, the modulation strength sensitivity of the grating pair’s three resonant peaks is demonstrated, and the results indicate that these grating pairs may find potential applications in optical fiber sensing.     

Effect of proton exchange and annealing on diffraction efficiency of Fe:LiNbO3 crystals

Influence of proton exchange and annealing on the photorefractive properties of Fe:LiNbO₃ crystals has been investigated using two-wave coupling phenomena. The two-wave coupling phenomena results in microscopic interference pattern inside the sample which subsequently helps in the formation of refractive index grating. The diffraction efficiency of the crystal increases after proton exchange, whereas the reverse is observed on annealed samples. The former is attributed to an increase of extraordinary refractive index of the crystal, while the latter to the oxidization of Fe²⁺ to Fe³⁺.     

重构多信道光纤光栅的改进离散层析算法

对重构多信道光纤光栅的离散层析算法进行了优化.在各信道加入相移的基础上,运用非线性最小二乘法对耦合系数进行高斯曲线拟合,降低了折射率调制深度的最大值且可以将剧烈变化的折射率调制深度平滑化.仿真表明,较之改进前的折射率调制最大值（0.001 3）,利用新算法在折射率调制最大值为0.000 5时成功设计了一个8信道光纤光栅,极大地降低了对光纤光敏性的要求.同时,折射率调制曲线的平滑化降低了光栅的实际刻写难度.     

LiNbO3:Fe晶体中调制双光束耦合衍射效率的测定

通过对LiNbO₃:Fe晶体中双光束耦合中的任一束光强进行低频调制,其衍射效率比无调制时提高两倍多(由30％提高到76％)。用运动光栅理论解释了这一实验结果。 关键词：     

KNbO3:Fe晶体的最佳二波耦合

本文在分析光折变晶体KNbO3:Fe的最佳二波耦合条件的基础上,通过计算和实验研究了晶体KNbO3:Fe的二波耦合增益系数Γ与两光束的夹角2θ、光栅矢量的取向β及不同电光系数r51或r42的关系,获得了在特定掺杂浓度N～1016cm-3条件下KNbO3:Fe晶体的最佳二波耦合条件为:θm～4°-8°并且βm～45°.     

Contribution of Absorptive and Refractive Gratings to Mixed Holograms Using Xanthene-Dye-Doped Films

The contribution of absorptive and refractive gratings to a mixed hologram is investigated by means of two-wave coupling technique by moving a hologram. Polyvinyl alcohol films doped with xanthene-dyes such as erythrosin B,eosin Y, uranin and fluorescein which absorb an argon-ion laser light of 488 nm and 515 nm are used as hologram recording materials in our experiment. A simple model of the two-level one-step photo-bleaching well explains the growth of an absorptive grating and the refractive index and also the working wavelength dependence of growth of the refractive grating in the xanthene-dye-doped films.     

Using optical PT-symmetry for switching applications

This work introduces a new class of PT-symmetry grating assisted devices for switching or modulation applications. Their operation is based on a four-wave interaction, thus marking a step forward in the development of PT-symmetry devices which currently are essentially based on two-wave interactions. A remarkable feature of the new structure is that all its properties also hold in the case of imperfect PT-symmetry operation, corresponding to the important practical case of fixed losses.     

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

We used the perturbation expanding method to the hopping model and studied coupling effects of the modulation depth between two photorefractive phase gratings stored in one point with an external applied DC electric field . It has been found that the modulation depth of one of the two gratings seriously affects the spatial-charge field of the other grating.