Propagation of light through a forbidden zone in chiral media

The particular features of the propagation of light in uniaxial chiral liquid crystals with a large pitch of the spiral are considered. There exist forbidden zones in these systems for fairly large angles of incidence of an extraordinary ray. On the one hand, this results in an efficient reflection of the wave from the zone boundary, and, on the other hand, this causes the wave to decay inside the zone. A case of narrow forbidden zones is studied, and it is shown that optical effects that arise upon propagation of rays near turning points are equivalent to the tunnel and over-barrier reflection effects. The angular dependences of the intensities of rays that were refracted in a forbidden zone and transmitted through it are calculated. The percolation effect is experimentally studied in a mixture of a nematic liquid crystal with a chiral addition. The intensity of a transmitted extraordinary ray is studied as a function of the angle of incidence, which determines the width of the forbidden zone. Both the over-barrier reflection and the percolation effects are observed. The calculation results are shown to agree with experiment.     

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.     

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.     

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。     

Electrically controlled switching of light beams in the plane of liquid crystal layer

A simple experimental method and a set-up to control light beams in the plane of liquid crystal (LC) cell is developed. The main idea of the method is the reflection and the refraction of light beams propagating in a plane of LC layer from the boundary, which separates the regions of a liquid crystal cell with different director orientations and refractive indices. This boundary can be produced by electric field applied to the LC layer with a planar homogeneous orientation. The disclination lines that separate the extremely sharp changes of LC orientation can be also used for this purpose. The possibility of discrete deflection of light beam from the initial direction is shown. A computer simulation confirmed that the proposed experimental geometry was most suitable to control intensity of extraordinary rays propagating in the plane of liquid crystal layer.     

Complementary interference method for determining optical parameters of liquid crystals

ABSTRACT

Wedge cells of small apex angle, filled with liquid crystals, were used to determining optical characteristics as functions of temperature for three liquid crystalline mixtures recently produced and a reference nematic. The interference fringes appearing in polarised monochromatic light (of sodium yellow line) normally incident on the cell were exploited to measure the ordinary and extraordinary refractive indices in the reflection mode and birefringence in the transmission mode. The measurements were repeated using Abbe's refractometer for 6CHBT as the reference to verifying the precision. Additionally the order parameter was computed from birefringence as a function of temperature. The results confirm the usefulness of the method and provide the properties of two nematic liquid crystals of small and large birefringence and one smectic liquid crystal of medium birefringence, recently produced. The experimental systems served also to investigating phase transition between the liquid crystals and the isotropic liquid at near-clearing temperature.     

光轴方向任意的晶体连续双折射双反射

根据惠更斯定理,研究了单轴晶体光轴任意方向的双折射与全内双反射,给出了光线方向和光波法线方向的普遍公式.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,适当地选取晶体的界面参数,相当于选取光轴方向,可以使o光和e光的分离角Δoe更大.光轴方向任意的晶体连续双折射双反射对晶体器件的最优化设计非常有帮助.最后给出了改变斜入射2×2电光开关的出射面参数使Δoe优化的实例.     

Specific features of optical properties of helical liquid crystals with a large helix pitch

Light propagation in helical liquid crystals with the helix pitch considerably exceeding the light wavelength is studied. Using a multidimensional analog of the WKB method, the Green function of the electromagnetic field in such a medium is calculated. This function contains terms corresponding to ordinary and extraordinary waves. The behavior of the Green function in the far-field region is analyzed. It is shown that for the extraordinary ray there exists, on the surface of the wave vectors, a forbidden zone, which, due to periodic changes of the refractive index, corresponds to conditions of the beam turn with the formation of a flat wave channel. The extraordinary beam trajectory, both inside and outside the wave channel, determined by the ray vector, is not flat. The asymptotic behavior of the Green function inside and outside the wave channel is substantially different.     

Reflection spectrum of a cholesteric liquid crystal with structural defects

An expression is obtained for the reflection coefficient of circularly polarized light normally incident on the film of a cholesteric liquid crystal with a variable helix pitch. It is shown that, in the case of a single defect (local change in the helix pitch), the spectrum of light reflection from a cholesteric acquires a dip corresponding to the defect mode. New qualitative features appear in the reflection spectrum of a cholesteric with two defects as the distance between them varies.     

光在单轴晶体内表面上的反射

基于电磁波边界条件，从几何光学的角度，对单轴日 体内表面上光的反射规律进行了分析和讨论，给出了寻常光和非常光波法线和光线反射的公式，同时指出了上述结果与由费马原理导出的结果是一致的。     

Study on Optimum Incident Angles of Cross Polarized Four-Wave Mixing with a Photorefractive Crystal

We consider the optimum incident angles of cross polarized four-wave mixing with a photorefractive crystal. First, the phase matching angles are obtained for two operation modes: one in which the writing beams are ordinary rays and the reading beam is an extraordinary ray, we call this Mode 1. The other in which the writing beams are extraordinary rays and the reading beam is an ordinary ray, Mode 2. Next, practicable ranges of the incident angles are calculated considering of the total internal reflection of the phase conjugate beam in cases where the two writing beams illuminate the same surface of the BaTiO₃ crystal and where they illuminate the neighboring right-angled surfaces, respectively. Then, the coupling coefficient is determined as a function of the incident angle, and the optimum incident angles for effective beam interaction in Mode 1 and Mode 2 are estimated.     

Peculiarities of light propagation in chiral liquid crystal cells in an external electric field

We investigate the propagation of the extraordinary ray in a cell with a chiral liquid crystal at oblique incidence. For a 180° twist cell, we study the dependence of the minimum incidence angle at which the light does not yet pass through the cell on the applied voltage. The orientational structure of a liquid crystal in an external electric field has been calculated by directly minimizing the free energy. This has allowed the ray trajectories and the limiting refraction angles to be determined. The results of our calculations are consistent with the experiment. We show that allowance for the electric field nonuniformity in a chiral system is important for agreement between theory and experiment.     

From selective to wide-band light reflection: a simple thermal diffusion in a glassy cholesteric liquid crystal

Due to their helicoidal structure, cholesteric liquid crystals exhibit remarkable optical properties. Selective light reflection occurs when the pitch (repeat distance) is of the order of the wavelength of incident light propagating along the helix axis. The wavelength bandwidth, due to the optical anisotropy, is typically limited to 50 nm which is insufficient for some applications (full-colors displays, for example). By introducing a pitch gradient in the helix during a novel two-step process in a cholesteric glass, we show that reflection may occur over a wavelength bandwidth greater than 300 nm. First, the reflection bandwidth is adjusted by thermal annealing. Then, the optical properties are permanently stored by quenching the viscous material to a glass at room temperature. The two steps, pitch gradient establishment and film hardening, are independently controlled. The present process exhibits some reversibility and properties intrinsic to the glassy state are gained: laser-writing high resolution full-color images on solid films for image recording or high-density optical data-storage are indeed conceivable. Received 17 December 1998     

Bloch oscillations for circularly polarized light

All previous investigations on the Bloch oscillations of waves focus on scalar waves. Here we demonstrate, for the first time, the existence of Bloch oscillations of vector fields for circularly polarized light (CPL) propagating through a designed liquid crystal structure. To obtain the Wannier-Stark ladder of the CPL, we have designed a cholesteric liquid crystal structure with spatially varying pitch. The Bloch oscillations of the CPL have been observed in such a structure by exact numerical simulations. We have also shown that such a phenomenon can be easily detected in time-resolved reflection experiments.     

单轴晶体光轴任意取向时非寻常光的折射规律

在单轴晶体光轴任意取向的情形下 ,应用惠更斯原理导出了非寻常光折射方向的普遍计算公式 ,并给出了确定非寻常光线折射面和折射角的具体解。结合几种熟知的特殊情形进行了简要讨论 ,揭示了文中所得到的折射规律较之斯涅尔定律更具有普遍性 ,从而为光学系统中各类单轴晶体光学元件的应用提供了一个理论依据     

Infrared cylindrical cloak in nanosphere dispersed liquid crystal metamaterial

We present a design of an infrared cylindrical cloak using nanosphere dispersed nematic liquid crystal (NLC) metamaterial following the approach of Smith's group [Science 314, 977 (2006)]. Cloaking conditions require spatial distribution of liquid crystal birefringence with constant extraordinary index of refraction and radially dependent ordinary index of refraction. An approximate analytical formula for the latter is derived. Finite element (FE) simulations confirm the cloaking effect. Owing to the tunable birefringence of the liquid crystal component, such cloaking material offers the interesting possibilities of real-time control of invisibility. The possibility of experimental realization is briefly discussed.     

晶体转动时非常光的轨迹

本文就光入射到单轴晶体的情况,求得了非常光线方向的普遍公式,并按冰洲石的相应数据画出了三视图,使得晶体转动时,非常光的轨迹明显可见。所得结果为测定晶片光学常数的新方法提供了可能性。     

单轴晶体中光轴任意取向时寻常光与非常光间的离散

晶体器件（特别是非线性光学器件）的性能与晶体内o光与e光的离散有很大的关系。详细讨论了光在晶体表面折射时，对于任意光轴取向、任意入射角情况，如何确定o光与e光的离散。借助于转动晶体的方法，形象地描绘出e光相对o光的离散曲线。当入射角较大时，离散曲线的形状 随光轴取向变化很大：从简单的圆或椭圆到复杂的双闭合曲线。理论计算与实验结果很好地吻合。     

Catastrophes and nonlinear dynamics in the standard geometry of optically induced reorientation of nematic liquid crystals

Discontinuities and hysteresis have been observed when controlling the orientation state of a nematic liquid crystal (NLC) with a single laser beam in standard geometry: the light beam of extraordinary polarization interacts with a homogeneously oriented NLC. In a certain range of control parameters (light intensity and incidence angle), the system exhibits a new phenomenon of nonlinear dynamics.