光折变光栅在超短脉冲光照射下衍射的研究

利用Kogelnik单色光在体光栅中衍射效率公式推导出超短脉冲光读出稳态光折变体光栅时的衍射光频谱表达式,并在此基础上导出了脉冲光读出时的总衍射光强及总光强衍射效率.研究发现衍射光的频谱分布、总光强及衍射效率与光栅周期Λ、光栅厚度d和读出光脉冲宽度Δτ有密切的关系.通过调整这些参量,光折变光栅可以对入射的超短脉冲光实现不同程度的滤波作用.该结论可用于超短脉冲的整形研究.     

Diffraction study of photorefractive hologram under ultrashort pulse readout

Based on the diffraction efficiency equation of Kogelnik, the diffraction effect of a cw photorefractive hologram under ultrashort pulse illumination is theoretically analyzed. We find that the recorded grating has the function of filter to the incident pulse beam. To fully reconstruct the incident pulse, the crystal width must be smaller and grating period must be larger. In this paper we also discuss the total diffraction efficiency of the hologram, and find that the total diffraction efficiency is functions of the crystal length, pulse duration and the grating period. The conclusion of our paper can be used in ultrashort pulse shaping application.     

光折变多重存储的栅自增强读出特性研究

研究了光折变重存储读出时折射率栅自增强特性与记录晶体厚度、记录时的光强比以及写入的折射率栅振幅之间的关系.结果表明记录晶体的厚度大于某一值,才有自增强效应;较小的参物光强比具有较大的自增强效果,能获得较大的读出衍射效率;自增强读出所能达到的最大衍射效率与写入的栅振幅大小无关,而读出时衍射效率增加的速率与写入的栅振幅成反比.     

透射型光折变体全息光栅对超短脉冲激光光束衍射的特性

在Kogelnik耦合波理论的基础上,考虑光栅记录介质的色散效应的影响,研究了光折变体全息光栅对不同偏振状态的超短脉冲激光光束衍射的性质,讨论了高斯型入射脉冲激光光束的谱宽与光栅的有效衍射谱宽之比不同时,衍射和透射光束的光谱宽度、时间宽度、波形和衍射效率的变化。结果表明,光栅的有效衍射谱宽受光栅参量及入射条件的影响,对衍射性质的影响很大,且在考虑光栅记录介质的色散效应时减小。当入射脉冲的偏振方向垂直于入射面时,光栅的有效衍射谱宽大于偏振方向平行于入射面的情形,衍射效率在入射脉冲宽度较大时小于偏振方向平行于入射面的情形;谱宽比较大时,衍射光束的时间分布曲线产生展宽和变形,且比偏振方向平行于入射面的情形展宽和变形得更加明显。     

光轴方向任意时光折变晶体中体全息光栅的衍射性质

利用坐标旋转方法和Kogelnik耦合波理论,建立了光轴方向任意时单轴晶体中体光栅布拉格衍射的耦合波方程,分析了Li NbO3晶体的光轴方向对光折变体全息光栅的各向同性和各向异性布拉格衍射性质的影响。模拟计算表明,在给定光栅的结构参量时,通过适当选择光轴方向角可以使得光折变体光栅的各向同性和各向异性布拉格衍射的衍射效率达到最大,给出了相应类型的衍射效率取得最大值时晶体光轴的大致方向。这些理论分析为光折变体全息光学器件的优化设计和进一步广泛应用提供了很好的理论参考依据。     

反射型体全息光栅对超短脉冲激光光束衍射的性质

在光栅记录介质色散效应的影响下,拓展Kogelnik的耦合波理论研究了反射型体全息光栅对偏振方向垂直和平行于入射面的超短脉冲激光光束衍射的性质。结果表明对于记录在LiNbO3光折变晶体中的体全息光栅,在色散效应、光栅参量和入射条件的共同影响下,光栅对偏振方向垂直于入射面的超短脉冲激光光束衍射的光谱带宽大于对偏振方向平行于入射面的超短脉冲激光光束衍射的光谱带宽,在不考虑光栅介质色散效应的影响时,它们都变大。进一步给出了衍射光的光谱带宽及光栅的衍射效率随入射脉冲的光谱带宽与光栅的光谱带宽比值的变化情况。     

偏振控制的Ce:KNSBN类光纤光折变光开关

在Ce:KNSBN光折变类光纤晶体中,用不同偏振的读出光控制衍射光强的大小从而实现光折变光开关的开－关功能.实验结果表明e光读出时的光栅衍射效率是o光读出的310倍,而且衍射效率比不随写入光光强比的变化而变化.与块状晶体做了比较,并用理论进行了分析,在光折变类光纤中的衍射效率比是块状晶体的10倍,光折变类光纤晶体有着更好的光开关性能.     

超短脉冲激光光束在一维反射型体全息光栅中的衍射

基于Kogelnik的耦合波理论,研究了在色散效应的影响下,超短脉冲激光光束在反射型体全息光栅中衍射的性质.研究给出了衍射光及透射光在频谱域及时间域的振幅及强度分布、光栅的光谱宽度及衍射效率随光栅参量及入射条件的变化.数值研究的结果表明,在光栅记录介质色散效应的影响下,衍射光束的光谱宽度减小,脉冲展宽,衍射效率降低.通过适当的选取光栅参量及入射条件,可以控制衍射和透射光束的频谱和时间强度分布,得到满意的衍射和透射光束的带宽和波形,从而可以将其应用于脉冲整形等技术中.     

Diffraction properties of ultrashort pulsed beams with arbitrary temporal profiles by a volume holographic grating

In this paper, the diffraction properties of an ultrashort optical pulse with arbitrary profiles in time diffracted by a volume holographic grating are investigated using the modified Kogelnik coupled-wave theory. Simple analytical expressions for the spectrum and spatial profiles of the transmitted and diffracted beams are obtained. The dependences of the diffraction bandwidth, the Bragg selectivity bandwidth and the total diffraction efficiency of the volume grating on the temporal profiles of the input ultrashort pulse are investigated. For three different temporal profiles, numerical results of diffraction properties are given. It is shown that the temporal shapes of the input pulsed beams have been found to be an important factor in the analyses of the propagation characteristics.     

Enhancement of the diffraction efficiency of the hologram recorded in photorefractive media under the action of external electric field

Diffraction efficiency as a function of the applied electric field for the non-linear regime has been calculated by solving numerically the beam coupling equations. The refractive index variation used in the beam coupling equations was calculated directly from the material rate equations via the total space charge field. The diffraction efficiency of the holograms recorded in photorefractive media is not only a function of the applied external electric field but also a function of crystal thickness, diffusion field, reduced fringe contrast modulation ratio and absorption coefficient of the materials. The effects of these parameters on the efficiency of the holograms have been studied in details. In the absence of the external applied field, it is found that the diffraction efficiency of the holograms could be maximized for a thinner photorefractive crystal having lower absorption coefficient and higher value of diffusion field, which could exist at a much lower value of reduced fringe contrast modulation ratio of the index grating. More efficient holograms can be recorded in the presence of the externally applied electric field as compared to the case of no external field.     

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.     

Diffraction properties of ultrashort pulsed beams with arbitrary temporal profiles by a reflection volume holographic grating

The diffraction properties of reflection volume holographic gratings are studied when the gratings are illuminated by an ultrashort beam with arbitrary temporal profiles. The modified Kogelnik's theory of coupled waves is used. Simple analytical expressions for spectral and temporal distribution of the transmitted and diffracted are obtained. The dependences of the diffraction bandwidth, the Bragg selectivity bandwidth and the total diffraction efficiency of the reflection volume grating on the temporal profiles of the input ultrashort pulse are investigated. Study shows that the bandwidth of the reflection volume holographic gratings varies with the grating parameters more slowly than the transmitting volume holographic gratings. For three different temporal profiles, numerical results about diffraction properties of the reflection volume holographic gratings are given and compared with the transmitting volume holographic gratings.     

Anisotropic Bragg diffraction of finite-sized volume holographic grating in photorefractive crystals

Anisotropic diffraction of uniform plane wave by finite-sized volume holographic grating in photorefractive crystals is considered. It is found that the anisotropic diffraction can take place when some special conditions are satisfied. The diffracted image is obtained in experiment for the anisotropic Bragg diffraction in Fe:LiNbO₃ crystals. A coupled wave analysis is presented to study the properties of anisotropic diffraction. An analytical integral solution for the amplitudes of the diffracted beams is submitted. A trade off between high diffraction efficiency and the deterioration of reconstruction fidelity is analyzed. Numerical evaluations also show that the finite-sized anisotropic volume grating exhibits strong angular and wavelength selectivity. All the results are useful for the optimizing design of VHOE based on finite-sized volume grating structures.     

棱镜-光栅-棱镜分光模块整体化设计及衍射特性分析

PGP模块是超光谱成像仪中重要分光器件。为了能够在制作前有效预测PGP整个系统的衍射效率分布及其衍射特性,提出了PGP整体化设计方法。从体位相全息光栅设计角度出发,结合棱镜与光栅各项参数的制约关系,编制了计算PGP整体衍射效率的分析软件,综合考察了棱镜与光栅各项参数对PGP模块衍射特性的影响,讨论了光栅布拉格波长的漂移特性,据此设计了一种用于成像光谱仪的宽波段高衍射效率PGP分光模块。模拟结果表明：棱镜1材料的色散系数越小,PGP的光谱带宽越窄;光栅布拉格波长的漂移增大了PGP模块和光栅的光谱带宽,带宽增大使光栅的角度选择性随之增大,拓宽了棱镜1材料的选择要求;棱镜1顶角、光栅的胶层厚度和相对介电常数调制度等参数是影响PGP衍射效率分布的重要因素,制作时需要精确控制。利用此方法设计的PGP分光模块在400～1 000 nm波段范围内衍射效率不低于50%,并给出具体设计参数,这对PGP制作具有一定的参考价值。     

Study on the instantaneous characteristics of diffracted and transmitted light of static photorefractive grating illuminated by ultra-short pulse laser

Based on Kogelnik's coupled wave theory, the time-domain diffraction and transmission of static PR gratings are theoretically studied when they are illuminated by ultra-short pulse laser. Study shows that the waveforms of the diffracted and transmitted pulses depend on the readout pulse duration, grating spacing, crystal thickness and refractive index modulation. By changing the values of these parameters, the diffracted and transmitted waveforms can be controlled. Also we find there is a displacement of diffracted and transmitted pulse along the time-axis when compared to readout pulse. Conclusions of our study could be used in many areas, such as pulse shaping and signal processing.     

Beam splitting, combining, and cross coupling through multiple superimposed volume-index gratings

We investigate the diffraction properties of multiple-superimposed index gratings from a vector synthetic viewpoint using coupled wave analysis with Bragg and non-Bragg readout. The vector synthetic gratings consist of two volume-index gratings with different grating wave vectors, which can be obtained in photorefractive materials, in optical fibers or in Bragg cells with two driving acoustic waves. This structure can realize beam splitting, beam combining, and beam cross coupling, etc. Analytic expressions for the diffraction efficiency as well as the amplitude of the waves involved are obtained. The results are presented and discussed.     

Filter characteristics of a chirped volume holographic grating

We compare and analyze the filter properties of transmission-type volume holographic gratings, especially the dispersion characteristics for uniform and chirped gratings. It is theoretically and experimentally shown that the dispersion characteristics can be controlled by introducing one-dimensional chirping to the volume grating in a photorefractive crystal. The filter response including output power and dispersion comes from a combined effect of the spatial spectra of the grating structure, input beam, and output-coupling fiber mode. Filter responses can be designed by controlling these parameters for optical communication applications.     

Analysis of lateral-spread photorefractive planar lenses

The photorefractive planar lens for converting a vertical incident plane wave to a lateral-spread spherical wave and vice versa, is suggested. Using the two-beam coupled-wave theory, the coupled wave equations are derived and their half-analytical solutions are also given in terms of an infinite series. The diffraction properties (beam profiles, diffraction efficiency) of the local volume grating in the lens are presented. And the focusing property of the lens is discussed and compared with that of an ideal convergent spherical wave. It is demonstrated that the suggested photorefractive planar lens shows a good focusing effect.     

Design of high-efficiency diffraction gratings based on total internal reflection for pulse compressor

We present designs of high-efficiency compression grating based on total internal reflection (TIR) for picosecond pulse laser at 1053 nm. The setup is devised by directly etching gratings into the bottom side of a prism so that light can successfully enter (or exit) the compression grating. Dependence of the −1 order diffraction efficiencies on the constructive parameters is analyzed for TE- and TM-polarized incident light at Littrow angle by using Fourier modal method in order to obtain optimal grating structure. The electric field enhancement within the high-efficiency TIR gratings is regarded as another criterion to optimize the structure of the TIR gratings. With the criterion of high diffraction efficiency, low electric field enhancement and sufficient manufacturing latitude, TIR compression gratings with optimized constructive parameters are obtained for TE- and TM-polarized incident light, respectively. The grating for TE-polarized light exhibits diffraction efficiencies higher than 0.95 within 23 nm bandwidth and relatively low square of electric field enhancement ratio of 5.7. Regardless of the internal electric field enhancement, the grating for TM-polarized light provides diffraction efficiencies higher than 0.95 within 42 nm bandwidth. With compact structure, such TIR compression gratings made solely of fused silica should be of great interest for application to chirped pulse amplification (CPA) systems.     

Effects of applied DC/AC fields in electrical fixing process with SBN:60

We present experimental investigations of electrical fixing techniques in Ce:SBN:60. The effect of crystal fatigue on the diffraction efficiency of electrically fixed photorefractive gratings is studied. We observed that applying an ac field to the crystal eliminated crystal fatigue and improved diffraction efficiency. A controllable diffraction efficiency of a photorefractive grating is presented. A reproducible diffraction efficiency of up to 75% is obtained using a write-reveal grating technique with high-voltage pulses of opposite polarity. We also show that the diffraction efficiency can be controlled by varying the intensity of the writing beams incident to the crystal during the recording process. A method of determining the hysteresis loop using the domain-fixing technique is proposed. The dependence of the diffraction efficiency on the direction of the applied electric field while writing the hologram is studied. Our experiments show that, during writing, when the electric field is applied opposite to the c axis the grating can be successfully revealed with both positive and negative dc voltages. However, when the grating is written with a field parallel to the c axis, the grating can be revealed only with a field applied in the opposite direction. Received: 28 October 2002 / Revised version: 28 February 2003 / Published online: 14 May 2003 RID="*" ID="*"Corresponding author. Fax: +1-812/872-6167, E-mail: azad.siahmakoun@rose-hulman.edu