Simultaneous Diffraction of Two Waves at a Transmission Volume Hologram

On the basis of the theory of coupled waves the simultaneous diffraction of two waves at a plane dielelectric transmission volume hologram is described. The intensities of the output beams strongly depend on the phase shift between the incident waves and the phase shift of the holographic grating with respect to the interference pattern of the read-out waves. This gives the possibility to transfer the energy from one beam into the other and can be used for the modulation and deflection of the reconstructed beams. The possibility of a separate determination of the different phase shifts by intensity or phase measurements is discussed.     

Diffraction efficiency of sequentially stored gratings in reflection volume holograms

On the basis of the theory of coupled waves the amplitudes of the first-order diffracted waves and the diffraction efficiency is calculated for sequentially superposed phase gratings stored in dielectric reflection holograms. The investigations are restricted to the case of a fixed reference wave during recording and Bragg-angle incidence.By analogy to the transmission volume grating the coupling effects which appear between incident beams and diffracted waves give the possibility of building up beam-couplers and -splitters with certain coupling parameters determined by the recording process. Moreover, reflection gratings allow a favourable combination between coupling and reflecting properties and avoid the diffraction efficiency oscillations that are characteristic of transmission gratings. The performance of the reconstruction process with several waves simultaneously allows the tuning of the intensities of diffracted waves with dependence on amplitude or phase differences between incident beams.     

超短脉冲激光光束被局域体全息光栅衍射的性质分析

利用二维耦合波理论,分析了超短脉冲激光光束被完全重叠型的局域体全息光栅衍射的时空变化性质,给出了衍射和透射脉冲激光光束沿光栅出射边界的强度时空分布。以LiNbO3晶体为例,数值研究了衍射光脉冲强度沿光栅出射边界的分布和脉冲波形的变化及光栅的总衍射效率受光栅二维尺寸、入射角度、光栅折射率调制度及入射脉冲的脉冲时域半峰全宽等条件的影响而变化的情况。与一维体全息光栅对超短脉冲激光光束衍射的性质,及此光栅对连续光衍射的性质作比较,给出了合理选择光栅参量及入射条件以在光栅出射边界上得到总衍射效率较大且分布较均匀的衍射光脉冲的方法。     

Amplification in photorefractive materials via a higher order wave

It is shown that power exchange is possible in photorefractive materials even though the grating produced by the two incident waves is in phase with their interference pattern. The reason is that the interaction of the principal waves will produced higher order waves and their presence will form further gratings which assist power transfer between the principle beams. Under favourable conditions significant amounts of power may be transferred.     

Simultaneous diffraction of two finite waves at non-uniform dynamic volume reflection gratings

Based on the two-dimensional coupled-wave theory, the simultaneous diffraction of two finite waves with non-constant amplitude distribution at a finite non-uniform dynamic volume reflection grating is described. A coupled differential equation is derived and solved numerically with the aid of a two-dimensional Runge-Kutta method. The results for the chosen example of a planar volume reflection grating both for pure phase and absorption gratings show the dependence of the fidelity and diffraction efficiency on the normalized parameter grating strength, on the phase shift with respect to the interference pattern of the read-out waves and on the absorption modulation. In contrast to the transmission grating, a high fidelity of the enhanced beam can be achieved for reflection gratings. The numerical results are compared with the solution of the one-dimensional theory.     

局域体全息光栅的衍射特性

基于三维耦合波理论，研究了两束有限宽度的任意偏振平面波干涉产生的局域体全息光栅的衍射问题。以单位均匀振幅的任意偏振平面波为例，给出了透射波和衍射波振幅的主分量和交叉分量的解析表达式，讨论了记录过程和再现过程中入射的参考光波的偏振角对透射波和衍射波振幅的影响。计算结果表明，记录过程中的偏振角越小，形成的光栅内的耦合越强，衍射效率越高，但光束质量越差；再现过程中不同的偏振角，由于入射波和衍射波的电矢量的不同方向的耦合强弱不同，透射波和衍射波振幅的主分量和交叉分量的振幅变化行为不同。     

A Novel Technique for Measuring Defocus with Phase Shift Gratings on a Photomask

A focus monitor reticle having a novel grating structure is proposed. If a grating pattern has a property of being able to generate asymmetry between positive and negative diffraction orders, a defocus of the grating pattern can be translated to an easily measured pattern shift perpendicular to the optical axis. A possible grating for this purpose is composed of three components: opaque line, naked line and #x03C0;/2-phase-shifted groove. In particular, with their width ratio equivalent to 2/1/1, one of the two first-order beams disappears entirely. Consequently, tilted standing waves are formed by two-beam interference between zeroth-order and the other first-order on the image plane. This paper describes a new technique for measuring a defocus with a phase shift grating object. Good agreement between experimental sensitivities and theoretical expectation verifies that the technique achieves high accuracy of several nanometers or better. Applications of the technique show indicative ability in field curvature and astigmatism of the state-of-the-art scanner.     

π相移光纤光栅对超声波致非均匀应变场的传感特性

π相移光纤光栅用于水中超声传感时,超声波沿光纤轴向入射和垂直光纤入射时的传感波形及幅度显著不同。针对这一现象,本文建立了基于光学传递矩阵的光纤光栅声传感理论模型,计算了超声波分别沿轴向和沿垂直方向入射时π相移光纤光栅中的非均匀应变场分布,进而分析了光谱偏移,揭示了两种入射角度下π相移光纤光栅的传感特性与声传播导致的应变场分布相关,并通过实验进行了验证。结果表明,两种入射角度产生的不同的非均匀应变场分布对π相移光纤光栅的传感特性影响明显。超声波垂直入射时的传感波形和幅度均优于轴向入射,且π相移处对传感有显著作用。当入射位置远离π相移处时,垂直入射的响应也明显降低。本研究可为π相移光纤光栅超声传感的机理分析提供参考。     

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     

An Iteratively-Designed Binary Phase Grating for Flattop Beam Generation

A binary phase grating capable of shaping an incident Gaussian beam to a flattop beam in a Fourier domain is designed iteratively. It is essential in grating design to consider the phases of diffracted waves by the grating, in addition to their amplitude uniformity and diffraction efficiency. The optimized grating phase produces the in-phase diffracted waves that interfere constructively to form a uniform amplitude and phase profile. The dependence of the shaped profile on the illuminating amplitude distribution, the grating misalignment, and the lens focusing error is investigated by computer simulation and optical experiment.     

Lateral displacement of a Gaussian beam reflected from absorbing media

Lateral displacements of well-focused beams reflected from absorbing media are demonstrated in this paper. The incident beam is modeled as a tapered wave with a Gaussian spectrum. The field solutions are obtained on both sides of the interface by solving analytically from Maxwell's equations and by matching the boundary conditions at the interface. Numerical simulations are presented and the field values as well as the time-averaged power densities are computed. The influences of the polarization, the angle of incidence and the beam width on the displacement are discussed. The origin of the displacement lies in the absorption of the media, for which there is a phase shift between the incident and reflected waves. Because of this phase shift, the center of the reflected beam does not coincide with that of the incident one, similar to the Goos-Hänchen shift.     

Generation of femtosecond dual pulses by a transverse standing wave in a volume holographic grating

Based on Kogelnik's coupled-wave theory, it is found that when a femtosecond pulse is incident on a transmitted volume holographic grating, two transverse standing waves along the grating vector direction will be generated inside the volume holographic grating(VHG). Due to field localization of two standing waves, they have two different velocities along the propagation depth. On the output plane of the VHG, femtosecond dual pulses are generated in both the diffracted and transmitted directions. Results show that the pulse interval is determined by the refractive index modulation and thickness of the grating, while the waveform of the dual pulses is independent of the grating parameters.     

Bragg diffraction of light by rectangular phase gratings

Bragg diffraction of light by rectangular phase gratings is considered, utilizing two-dimensional coupled-wave theory. Diffraction characteristics for two important cases of incident plane waves and Gaussian-profile beams are presented. It is shown that the diffraction properties depend on the following normalized parameters: the grating strength and a geometry parameter, the beam width and a displacement. Values of these parameters for the realization of both nearly transmitting and nearly reflecting regimes of diffraction are determined. The results obtained are used for the choice of the design parameters of integrated optic Bragg-type devices.     

Effect of polarization on efficiency of volume Bragg grating filter

<正>Diffraction efficiency of volume Bragg grating,whose period is in the same order as the incident wavelength, is related to the polarization direction of the incident linear polarized beam.When two linearly polarized recording beams with the same polarization direction are used for recording volume Bragg gratings in a photopolymer with diffusion amplification,the azimuth of polarization of the reconstruction beam influences the diffraction efficiency of the grating.When the probe beam is linearly polarized and oriented orthogonally to the grating vectors,the±1-order diffraction beams are also linearly polarized with polarization direction parallel to that of the probe beam.According to the results,a two-dimensional nonspatial optical filter consisting of the volume Bragg gratings would achieve significantly higher efficiency.     

Study on holographic grating diffraction for Laguerre--Gaussian beam generation

Laguerre-Gaussian beams, as a special model with spiral phase structure, have been intensively investigated. Holographic grating method is a convenient method of generating Laguerre-Gaussian beams and measuring their orbital angular momenta. But due to some inevitable adverse factors such as lateral displacement, angular deflection and elliptical incident profile of incident beam, the practical effectiveness should be reevaluated. This paper is devoted to the study on the influences of the abovementioned three adverse factors on the holographic grating method. The characteristics of the mode decomposition of diffractive order and the relative powers of the orbital angular momentum eigen-states are also given.     

线偏光闪耀反射光栅衍射特性研究

通过数值方法对线偏光在Littrow装置中的理想导体闪耀光栅的偏振特性进行研究.用时域有限差分程序计算出任意偏振方向线偏光经过闪耀光栅衍射后的电磁场分布,提取衍射波的S偏振和P偏振分量,讨论了与光栅闪耀角和入射光波偏振角的关系.分析了在1530～1570nm光谱范围内,入射光波为线偏振波和园偏振波时,衍射光波的偏振色散特性与光栅闪耀角的关系,并给出了存在偏振色散的光栅闪耀角范围.这些分析和结果对工程设计具有一定的指导意义.     

Ce:KNSBN晶体衍射特性研究

在非同时读出条件下测量了Ce:KNSNB晶体两波耦合体光栅衍射效率随写入光强比、写入光偏振态和写入光夹角的变化关系,并与同时读出条件下衍射效率变化规律的测量结果进行了比较,发现二者基本一致.利用耦合波理论对实验结果进行了理论分析和拟合,拟合结果和实验数据较好的吻合.     

基于光学全息的任意矢量光的生成方法

基于光学全息的角度复用特性, 根据空间光调制器对光场的相位和振幅调制原理, 通过加载产生任意矢量光所需要的相位分布, 设计了一种生成任意矢量光的方法. 该方法首先利用光学全息技术记录空间光调制器加载的相位, 从而制作一个全息光栅; 再现过程中, 两束具有相同入射角度的参考光照射全息光栅, 使得两束再现光相干叠加, 进而获得可调控的任意矢量光. 该方法能够避免复杂偏振态的出现, 并且具有生成光路简单、方便操作、生成矢量光的偏振纯度高等优势. 通过计算机模拟生成了任意矢量光, 获得了很好的效果.     

Control of the energy exchange upon double two-wave mixing in photorefractive crystals

The problem of double two-wave mixing in photorefractive crystals is analytically solved in the framework of the two-level model of optical transitions. Relationships are derived for calculating the intensities of all four interacting waves and the amplitude of the holographic grating. It is demonstrated that the magnitude and direction of energy exchange between the interacting beams can be controlled by a purely optical method, namely, by varying the intensity ratio and the initial phase shift between the interference patterns.     

可实现存储光栅快速增强的新型全息存储结构

提出一种新型全息数据存储结构，该结构包含两块存储的内容完全相同的光折变晶体，无需相位共轭器，仅利用两束时域快速调制的平面参光波便可实现对存储全息图的迅速增强。文章讨论了调制速率，读出光强比，晶体非线性耦合强度及初始光栅强度对增强速度及可获得的饱和衍射效率的影响。