晶体的连续双折射双反射及其集成应用:1×N电光开关

根据惠更斯定理 ,给出了单轴晶体内双折射与全内双反射的光线方向和光波法线方向的普遍公式。并讨论了在晶体内沿多个面的连续双折射双反射 ,分析了前一界面输出量和后一界面输入量之间的联系 ,得到多次双折射双反射后的光线方向和光波法线方向。在此基础上 ,提出一种单块晶体集成的 1×N电光开关 ,即把多个电光调制器安置在全反射面之间。由于双折射效应 ,寻常光和非常光有不同的全内反射 ;给不同的电极对上加上半波电压改变输入光的偏振状态 ,再使光通过不同数目的反射面反射 ,最后输出光就有不同的角度。具有结构简单、插入损耗小、抗干扰性强等优点。给出了 1× 4光开关的实例。     

作图法分析光波在两个单轴晶体分界面上的双反射和双折射

通过几何作图法,分析了光轴取向任意时,光波在两个单轴晶体分界面上的双反射和双折射.考虑到入射光波、反射光波、折射光波在界面上相位相等和晶体折射率面的定义,采用斯涅尔作图法,直接在图上得到了两条反射光波和两条折射光波.根据晶体的光学各向异性,进一步讨论了各光波对应的光线方向和振动方向,并通过几何分析,给出了各反射光波、折射光波、反射光线和折射光线位置的一般表达式.斯涅尔作图法简单直观,可以直接获得光波的方向,结果具有普遍性.     

光波p分量在单轴晶体表面反射和折射的相位特性

根据单轴晶体的双折射和双反射性质,通过数值计算研究了光轴在入射面内并与晶体界面成任意角时光波p分量在单轴晶体表面反射和折射的相位特性.结果表明,光轴取向对相位变化有较大影响,光从光疏各向同性介质射入单轴晶体时,光轴方向改变反射光p分量的相位突变点,但对折射光p分量相位无影响.光从光密各向同性介质射入单轴晶体未发生全反射时,光轴方向同时影响p分量反射光和折射光的相位突变|发生全反射后,光轴方向影响反射光p分量的相位变化曲线.从单轴晶体出射到光疏各向同性介质未发生全反射时,光轴方向改变反射光p分量的相位跃变规律,折射光p分量在光轴方向和晶面成小角度时在布儒斯特角附近发生相位突变|发生全反射后,反射光p分量的相位变化曲线随光轴方向的改变发生较大变化.     

光波p分量在单轴晶体表面反射和折射的相位特性

根据单轴晶体的双折射和双反射性质,通过数值计算研究了光轴在入射面内并与晶体界面成任意角时光波p分量在单轴晶体表面反射和折射的相位特性.结果表明,光轴取向对相位变化有较大影响,光从光疏各向同性介质射入单轴晶体时,光轴方向改变反射光p分量的相位突变点,但对折射光p分量相位无影响.光从光密各向同性介质射入单轴晶体未发生全反射时,光轴方向同时影响p分量反射光和折射光的相位突变;发生全反射后,光轴方向影响反射光p分量的相位变化曲线.从单轴晶体出射到光疏各向同性介质未发生全反射时,光轴方向改变反射光p分量的相位跃变规律,折射光p分量在光轴方向和晶面成小角度时在布儒斯特角附近发生相位突变;发生全反射后,反射光p分量的相位变化曲线随光轴方向的改变发生较大变化.     

光在双轴晶体中的传播

单轴晶体中光的传播情况已为人们所熟知.它的物理图象简单清晰,也便于定量计算.双轴晶体中光的传播要复杂得多,且不便于定量计算.本文的分析表明,单色平面波在双轴晶体中传播时,相应的两光振动是处在这样两个平面内,即由波法线分别和两个晶体光轴所成平面的两个平分平面内.与单轴晶体相类似,我们定义这两个平分平面为两光的主平面,相应的两光线也分别处在这两个主平面内,其方向与波法线方向之间有明确的关系.在晶体界面上的双折射中,两光波法线都满足折射定律,两光线方向也可随之确定. 一、一般描述 若单色平面波在晶体中的波法线为S,两个…     

单轴晶体的光程差和Lyot型滤光器的视场

 建立了以光线入射方向和晶体光轴方向为基准的入射坐标系，利用波法线反曲面方程和电磁场在晶体折射界面处切向分量连续性的边界条件，得到了晶体中波法线方向、射线方向、波法线折射率和射线折射率的表达式。从非常光的射线方向和射线折射率出发，得到了在任意的晶体光轴方向和入射角条件下，光通过单轴晶体后寻常光、非常光的光程差表达式。对Lyot型滤光单元的透射率和视场进行了计算分析后发现，滤光单元的透射率随光线入射角的变化呈现一定的周期性，视场随光轴倾角的增大而减小。得出了透射率和视场随光轴倾角(光轴与晶体表面的夹角)和光线入射角(光线在晶体表面的入射角)的变化规律。讨论了通过改变晶体倾角实现滤光器调谐和补偿晶体厚度加工误差等技术问题。     

光在光轴取向任意条件下的晶体表面透射率

为了分析一束光在晶体表面的能量损失以及两束折射光的能量比,给出了一种求解反射率和透射率的方法。讨论了光从各向同性介质入射到单轴晶体表面时的折射和反射,注意到了e光线与e光波方向的不同,e光折射率与e光波法线折射率的不同,得出了在界面处应该满足的边界方程。在晶体光轴取向任意的条件下,给出了表明各光束间能量关系的折射率和反射率的理论表达式,为晶体器件特性的研究提供了有力的理论工具。数值模拟表明:得到的结果满足能量守恒;反射到各向同性介质中的光的电场(或磁场)与原入射光的电场(或磁场)不再平行;光轴的取向和入射角的大小对折射的o光、e光的能量比有很大的影响。     

去除光学器件弹光双折射的方法

在电光、磁光调制器和传感器等光学器件的制作和使用过程中,经常会产生影响器件性能的弹光双折射.根据折射率椭球分析法,通过系统分析各晶系晶体的弹光效应,提出了若干去除光学器件中静态弹光双折射的方法.主要结论包括:对于正交晶系的双轴晶体,当光波沿着晶体任意一个主轴方向传播时,如果作用于晶体另外两个主轴方向的应力能够满足某一与晶体自身参数有关的倍数关系且不存在剪切应力,则可以去除这两个应力引起的弹光双折射;对利用所有单轴晶体,ˉ43m,432,m3m点群的立方晶体和匀质光学玻璃制作的光学器件,如果能够保持晶体沿着x1,x2轴方向的正应力相等且不存在剪切应力,或只对晶体施加x3方向的正应力,也可以避免沿着晶体主光轴x3方向传播光波的弹光双折射.上述去除弹光双折射的方法对光学器件的设计、制作和使用具有重要参考价值.     

光在双轴晶体表面的反射与折射

介绍了光在双轴晶体表面反射、折射问题的求解方法.用该方法可以方便精确地计算晶体任意取向下光从任意方向入射时折射光的折射率、偏振态、波矢方向、能流方向. 推导了反射光、折射光的振幅和能量的计算公式. 并以KTP晶体为例，给出了数值计算的结果. 关键词： 双轴晶体 双折射 菲涅耳公式 布儒斯特角     

光在两单轴晶体间界面的反射和透射

根据位相匹配条件和应该满足的边界方程,在光轴取向任意的条件下,得到了光在两单轴晶体界面的反射和折射的理论表达式,给出了更普遍的公式计算光能量损失以及两束折射光的能量比。数值模拟表明所得结果满足能量守恒,光轴的取向和入射角大小对晶体中折射的o光、e光的能量比有重大影响,但是对反射率影响很小。只要知道了晶体的有关参数及入射条件,利用所给表达式可以计算各光束光能量比,为晶体器件特性研究提供了有力的工具。由于对光轴取向和入射角度没有任何限制,公式具有普遍性。     

The coefficients of reflection and refraction on interface of the crystals in the Savart polariscope

According to the boundary conditions of the electromagnetic field, the coefficients of reflection and refraction on the interface of crystal in the Savart polariscope are obtained for ordinary ray (o-ray) and extraordinary ray (e-ray).The coefficients of reflection and refraction are different from an isotropic medium and have more complicated forms than isotropic medium.     

Fast electro-optical response of a cell with a homeoplanar layer of a nematic liquid crystal

The refraction of light, i.e., the turn of an extraordinary ray in the liquid crystal layer similar to total internal reflection at an interface between two media, has been studied in a cell with the homeoplanar orientation of the director. The rise, τ_on, and decay, τ_off, times of optical responses have been obtained for various angles of incidence of light on a liquid crystal layer subjected to an electric field. The times τ_on and τ_off of optical responses for the angles of incidence much larger than the angle of total internal reflection are 1–2 ms, which is three orders of magnitude smaller than the relaxation time of an optical response in the case of normal incidence of the ray.     

Amphoteric refraction exhibited by anisotropic crystals

Amphoteric refraction of light ray at the interface between isotropic materials and anisotropic materials is analyzed. Depending on the incident angle, the refractive light ray can either refract positively or negatively. This amphoteric refraction phenomenon can be quite prevalent when the difference of the two principal refractive indices is large. The reflectance under various incident angles has also been calculated, and an experimental demonstration with a calcite crystal in air is presented.     

Laser ranging based on electro-optic switch

Based on electro-optic switch effect in crystal, a novel laser ranging method is proposed. CW-laser emitted by laser transmitter propagates forward to the measured target, after being reflected by the target, and then goes back to the transmitter. Close to the transmitter, a special mono-block LiNbO₃ crystal is added into the round-trip light beams. High-voltage pulses with the sharp enough changes in rising edges are loaded on the crystal. Based on electro-optic effect, double refraction and internal double reflection effect in crystal, the crystal cuts off the round-trip light beams, and reflects a light pulse cut out by the crystal to a detector aside from the original beam path. The pulse width T is the period that laser propagates forward and back between the crystal and the target. The feasibility of the new idea is proved by our experiments and a brand-new way for the laser ranging is provided.     

Analysis of Internal Conical Refraction Using Ray Tracing Formulas for the Biaxial Crystal

Internal or external conical refractions are strange optical phenomena appearing in biaxial crystal. In this paper the analysis of internal conical refraction is derived using the ray tracing formulas for the biaxial crystals, after explaining the theory of the ray tracing for the biaxial or uniaxial crystals. The double rings of conical refraction are also investigated; these are affected by the polarization state or angular intensity distributions of the incident light beam causing conical refraction.     

A novel ray refraction matrix for curved interface

A problem in fundamental 2 × 2 ray matrix for refraction at curved interface proposed by A. E. Siegman was found out and a novel one was derived in this paper. An experiment is introduced in detail to verify the reasonability of the novel ray matrix. Using the novel 2 × 2 ray matrix, augmented 5 × 5 ray matrix of refraction at misaligned curved interface between media of different refractive indices was deduced. With the refraction matrix, it is easy to characterize the effect of an astigmatic thick lens. The augmented ray matrix approach was applied to model and estimate the performance of an optical alignment system. Utilizing these matrices, one can readily design and evaluate optical systems, where contain astigmatic elements such as tilted spherical or cylindrical lenses, mirrors and so on. These results are also useful for cavity design, alignment, ray tracing and beam position control in 3D optical systems.     

单块晶体2×2光开关

利用晶体的双折射和全内双反射现象以及晶体的电光效应 ,设计了一种单块晶体集成的 2× 2光开关 ,将一个电光调制器和两个光束分束器集成到一块铌酸锂晶体上 ,实现了光束合束、偏振态调制和光束分束三种功能。根据这种光开关的工作原理 ,给出两种开关结构 ,一种是易于级联的垂直入射结构 ,另一种是有较低操作电压的倾斜入射结构 ,并对倾斜入射结构的光开关进行了制作和测试。实验结果表明 :这种集成结构的 2× 2光开关操作电压低 ,串扰小 ,能量损耗小 ,抗干扰 ,稳定可靠 ,适用于各种光学互连网络。     

单块晶体集成的N×N纵横开关网络及其控制算法

设计了一种单块晶体集成的n×n纵横开关(Crossbar)网络。通过综合考虑晶体的双折射和全内双反射现象,以及晶体的电光效应,将构成n×n纵横开关网络的所有单元器件都集成到一块具有电光效应的双折射晶体上。同时,给出了该网络的控制算法,通过对开关工作状态的控制,可以实现任意输入输出通道之间的无阻塞连接。这种单块晶体集成的纵横开关网络具有能量损耗低、无阻塞、易安装、抗干扰等优点,适合于全光网络发展的需要。     

Synchrotron radiation refraction topography for characterization of lightweight materials

The employment of synchrotron radiation for refraction topography of materials has considerable advantages over standard x‐ray sources. The much higher beam intensity and the parallel and monochromatic radiation provide faster measurements and better angular and spatial resolution. X‐ray refraction techniques image the inner surface and interface concentration of micro‐structured materials. This effect of x‐ray optics is additional to small‐angle scattering by diffraction, when the scattering objects reach micrometre dimensions. We have developed x‐ray refraction techniques within the last decade in order to meet the growing demands for improved non‐destructive characterization of high‐performance composites, ceramics and other low‐density materials. Sub‐micron particle dimensions, the pore size of ceramics, the crack density distribution and single fibre debonding within damaged composites can be measured and visualized by computer‐generated interface topographs. For this purpose investigations are now being performed at the new hard x‐ray beamline of the Federal Institute for Materials Research and Testing (BAM) at BESSY, Berlin. This BAMline provides monochromatic radiation of photon energies from 5 to 60 keV from a double multilayer and/or a double‐crystal monochromator. A separate instrument is dedicated to the further development and application of synchrotron radiation refraction (SRR) topography. Different from conventional small‐angle scattering cameras with collimating slits and pinholes, scattering angles down to a few seconds of arc are selected by a single‐crystal analyser, similar to a Bonse–Hart diffractometer. A 20 µm spatial resolution of the scattering micro‐structures is achieved by a CCD camera with a fluorescent converter. First SRR topographs of aircraft composites [carbon fibre‐reinforced plastics (CFRP), carbon fibre‐reinforced ceramics (C/C), metal matrix ceramics (MMC)] will be reported. Copyright © 2004 John Wiley & Sons, Ltd.