Optical properties of a stack of layers of a cholesteric liquid crystal and an isotropic medium

Optical properties of a stack consisting of layers of a cholesteric liquid crystal (CLC) and an isotropic medium are investigated. The problem is solved using the modified Ambartsumyan layer-summation method. Particular features of reflectance spectra of this system are studied. It is shown that, in contrast to a single CLC layer, this system exhibits multiple photonic band gaps. There are two types of photonic band gaps: selective and nonselective with respect to polarization of the incident light. It is shown that eigenpolarizations in the system generally coincide with quasi-orthogonal quasi-circular polarizations, except for regions that are selective with respect to polarization of the diffractive reflection. It is shown that, for an even number of layers, the system under consideration is nonreciprocal and can function as an optical diode. The influence of thickness of CLC sublayers, angle of incidence, local dielectric anisotropy of CLC layers, refractive indices and thicknesses of layers of an isotropic media on reflectance spectra and other optical characteristics of the system is investigated.     

Experimental investigation of one-sided optical transparency in cholesteric liquid crystal thin film

Influence of boundary conditions on optical properties of a layer of cholesteric liquid crystal (CLC) has been investigated. In particular, a sample was obtained which is transparent for circularly polarized light incident from one side and gives losses in the transmission spectrum (within nearly 100 nm wide wavelength range) if light is incident from the opposite side, i.e. exhibits optical diode behavior. Two selective reflection bands were detected in the reflection spectrum of the sample. Spectral position of both selective reflection bands and transmission spectrum are shown to be CLC temperature-controllable.     

Optical properties of a stack of right- and left-handed layers of a cholesteric liquid crystal

We have studied the optical properties of a stack that consists of right- and left-handed layers of a cholesteric liquid crystal (CLC). The problem has been solved using the modified Ambartsumyan layer-summation method. We have examined particular features of the reflection spectra of this system and have shown that, as distinct from a single CLC layer, this system has multiple photonic band gaps. Particular features of the spectra of the photonic density of states have been considered. We have shown that this system has unique polarization characteristics; thus, in particular, if the number of sublayers is even, the eigenpolarizations of the system are degenerate (both eigenpolarizations coincide) and, as distinct from ordinary gyrotropic media, the rotation of the plane of polarization can decrease with increasing thickness of the system, the sign of the rotation depends on the sign of the chirality of the first sublayer of the system, the system is very sensitive to the variation in the number of sublayers, etc. We have investigated how the sublayer thickness, the angle of incidence, the local dielectric anisotropy, and the pitch of helix of sublayers affect the reflection spectra and other optical characteristics of the system.     

NLC-CLC-NLC cell as an electrically tunable polarization plane rotator

A liquid crystal optical device made of an optically anisotropic heterostructure is considered. The device consists of a cholesteric liquid crystal (CLC) layer sandwiched by two phase-shifting anisotropic layers of a nematic liquid crystal (NLC). In this structure each of the NLC layers is a quarterwave plate. The problem is solved both by Ambartsumian’s method of layer addition and Muller’s matrix method. The peculiarities of reflection spectra, eigen polarizations, rotation of polarization plane and polarization ellipticity are studied. It is shown that this device can work as a light modulator or a system for obtaining linearly polarized light with electrically tunable rotation of the polarization plane (which is especially important for optical communication), as well as a device for obtaining the linearly polarized light from a non-polarized one.     

复合周期的介质-液晶光子晶体研究

本文研究了掺入各向同性周期性介质层缺陷的一维复合周期胆甾型液晶光子晶体的禁带特性.发现同一般的胆甾型液晶不同,复合介质-液晶周期结构对左旋偏振入射光和右旋入射光都会出现共同禁带.当各向同性介质层占一个周期的厚度比例越小,左旋偏振光的禁带效应逐渐消失,而右旋偏振光的禁带则逐渐合并变大;且各向同性介质的折射率越大,则两种偏振光的禁带效应越明显,更容易出现共同禁带;通过调整厚度比,可以在可见光范围内出现对应红、绿、蓝色波长的禁带,从而可以用于液晶显示的反射式彩色滤光片. 关键词： 胆甾型液晶 光子晶体 禁带 缺陷     

Optical defect modes in chiral liquid crystals

An analytic approach to the theory of optical defect modes in chiral liquid crystals (CLCs) is developed. The analytic study is facilitated by the choice of the problem parameters. Specifically, an isotropic layer (with the dielectric susceptibility equal to the average CLC dielectric susceptibility) sandwiched between two CLC layers is studied. The chosen model allows eliminating the polarization mixing and reducing the corresponding equations to the equations for light of diffracting polarization only. The dispersion equation relating the defect mode (DM) frequency to the isotropic layer thickness and an analytic expression for the field distribution in the DM structure are obtained and the corresponding dependences are plotted for some values of the DM structure parameters. Analytic expressions for the transmission and reflection coefficients of the DM structure (CLC-defect layer-CLC) are presented and analyzed for nonabsorbing, absorbing, and amplifying CLCs. The anomalously strong light absorption effect at the DM frequency is revealed. The limit case of infinitely thick CLC layers is considered in detail. It is shown that for distributed feedback lasing in a defect structure, adjusting the lasing frequency to the DM frequency results in a significant decrease in the lasing threshold. The DM dispersion equations are solved numerically for typical values of the relevant parameters. Our approach helps clarify the physics of the optical DMs in CLCs and completely agrees with the corresponding results of the previous numerical investigations.     

Optical properties of a stack of cholesteric liquid crystal and isotropic medium layers

Some new optical properties of a stack consisting of cholesteric liquid crystal (CLC) and isotropic medium layers are studied. The problem is solved by the modified Ambartsumyan method for the summation of layers. Bragg conditions for the photonic band gaps of the proposed system are presented. It is shown that the choice of proper sublayer parameters can be used to control the band structure of the system. In the general case, the effect of full suppression of absorption, which is observed in a finite homogeneous CLC layer, is not detected in the presence of anisotropic absorption in CLC sublayers. It is shown that this effect can be generated in the system under study if certain conditions are imposed on the isotropic sublayer thickness. Under these conditions, the maximum photonic density of states (PDS) increases significantly at the boundaries of the corresponding band. The influence of a change in the CLC sublayer thickness and the system thickness on PDS is investigated.     

Light transmission through a stack of right- and left-hand cholesteric liquid crystal layers with indefinite dielectric and magnetic permittivities. I. Reflection peculiarities

Optical properties of a stack of layers of right- and left-hand cholesteric liquid crystal (CLC) with locally indefinite dielectric and magnetic permittivities are investigated. The problem is solved by the modified Ambartsumian??s layer addition method. The peculiarities of reflection spectra of this system are studied and it is shown that, in contrast to a single layer of CLC, this system has multiple photonic band gaps (PBG). It is shown that the indefinite character of the dielectric and magnetic permittivities essentially affects the PBG map of the system. These multiple PBG can find wide application, in particular, in technologies of production of displays.     

Photonic density and nonreciprocal optical properties in chiral liquid crystals

Nonreciprocal optical properties of anisotropic (nano-film) heterostructures made of a cholesteric and nematic liquid crystal (CLC-NLC) layers are studied. Namely, a NLC-CLC (and CLC-NLC) structures are considered in which the NLC layer is a quarter-wave plate. The problem is exactly solvable by Ambartsumians’ modified layer addition and Mullers’ transfer-matrix methods. The peculiarities of the polarization dependent properties, such as the photonic density of states, reflection spectra, the polarization plane rotation and ellipticity spectra are investigated. It is shown that such a system canwork as a light modulator, an element for obtaining linearly polarized light with an electrically tunable polarization plane rotation, or a transformer of non-polarized source into linearly polarized light. The analysis of the optical properties in investigated structures can be used for design of perspective optical diodes, microlasers and multifunctional elements on chiral liquid crystals with electrically tunable polarization plane rotation and field controlled light polarization.     

Specific features of the circular dichroism of a chiral photonic crystal with a defect layer inside in the presence of a gain

The specific features of the circular dichroism (CD) spectra of a cholesteric liquid crystal (CLC) layer with a defect layer inside in the presence of gain have been investigated. The features of the dependence of CD on the parameter characterizing the gain on the defect mode are analyzed for two cases: (i) gain is present in the defect layer and is absent in the CLC sublayers and (ii) gain is absent in the defect layer but is present in the CLC sublayers. It is shown that these dependences significantly differ in the two aforementioned cases. The dependences of the reflection, transmission, and absorption on the defect mode on the gain parameter have been investigated for incident light with both circular polarizations.

     

Localized modes in optics of photonic liquid crystals with local anisotropy of absorption

The localized optical modes in spiral photonic liquid crystals are theoretically studied for the certainty at the example of chiral liquid crystals (CLCs) for the case of CLC with an anisotropic local absorption. The model adopted here (absence of dielectric interfaces in the structures under investigation) makes it possible to get rid of mixing of polarizations on the surfaces of the CLC layer and of the defect structure and to reduce the corresponding equations to only the equations for light with polarization diffracting in the CLC. The dispersion equations determining connection of the edge mode (EM) and defect mode (DM) frequencies with the CLC layer parameters (anisotropy of local absorption, CLC order parameter) and other parameters of the DMS are obtained. Analytic expressions for the transmission and reflection coefficients of CLC layer and DMS for the case of CLC with an anisotropic local absorption are presented and analyzed. It is shown that the CLC layers with locally anisotropic absorption reduce the EM and DM lifetimes (and increase the lasing threshold) in the way different from the case of CLC with an isotropic local absorption. Due to the Borrmann effect revealing of which is different at the opposite stop-band edges in the case of CLC layers with an anisotropic local absorption the EM life-times for the EM frequencies at the opposite stop-bands edges may be significantly different. The options of experimental observations of the theoretically revealed phenomena are briefly discussed.     

Nonlinear reflection of elliptically polarized light

Nonlinear reflection of elliptically polarized light waves from the interface of two isotropic transparent media, is investigated for the first time. Nonlinear Fresnel formulae are obtained. It is shown, that when linear refractive indices are equalized, selfdeformation of the polarization ellipse in nonlinear reflection depends only on incident light ellipticity, not upon its intensity and the angle of incidence.     

Polarization plane's weak rotation amplifiers and polarization azimuth stabilizers

A simple and effective method to measure an electromagnetic wave polarization plane's weak rotations in various media is proposed. The specific features of the polarization plane's rotation amplification for the light reflection and transmission through the absorbing and amplifying isotropic layers are calculated. The amplification effects on an anisotropic and cholesteric liquid crystal (CLC) layers are also considered. In conclusion the question of probable choice of the amplifier's noise/signal ratio is discussed.     

Anisotropy of light propagation in thin opal films

Thin opal films are prepared by crystallization in a moving meniscus, and their optical transmission spectra are recorded in polarized light and studied. It is shown that the anisotropy of light propagation in the films is unambiguously related to the photonic band structure of opal and depends on the angle of incidence, the orientation of the incidence plane with respect to the opal lattice, and the wavelength and polarization of the incident light. Azimuthal diagrams of transmitted polarized light are constructed in the range of photonic band gaps of three orders for oblique incidence of a light beam. The anisotropy is found to vary with the light wave-length independently in perpendicular polarizations. A model of the band structure of opal wherein opal is represented as an fcc lattice of close-packed spheres adequately describes the optical transmission of opal films only in the range of the first-order photonic band gap.     

Polarization and amplitude optical multistability in a nonlinear ring cavity

The stimulation of a ring cavity filled with an isotropic medium with third order nonlinearity by plane monochromatic arbitrary polarized light is studied. An evolution of the stationary transmission with the change of the polarization of the incident light from circular to linear is discussed. For the linear polarized incident light additional branches of high transmission corresponding to elliptically polarized transmitted light and degenerating with respect to the rotation of the polarization vector are found. The stability of the stationary solutions is discussed. The possibility of the transmitted light polarization and intensity control by changing the polarization ellipticity degree of the incident light is shown.     

微粗糙基底上多层涂层光散射偏振建模与特性研究

为满足多层涂层目标的偏振探测需求,基于一阶矢量扰动理论,结合偏振传输矩阵,建立微粗糙基底上多层涂层的光散射偏振双向反射分布函数模型,研究多因素影响下两种典型涂层目标,单层减反射涂层和多层高反射涂层的光散射偏振特性,结果表明单层减反射涂层目标的偏振度受观测位置影响,峰值左侧的偏振度较之裸基底增大,右侧反之,探测不同观测角下的偏振度可区分无涂层和涂层目标。不同观测角和入射波长下,多层高反射涂层目标的偏振度与涂层层数和涂层光学厚度显著相关,层数增加,多层涂层在镜反射附近具有去偏作用。仿真结果符合测量数据,验证了多涂层目标散射偏振模型的正确性与合理性,为实现多涂层目标偏振探测和反射隐身技术提供理论依据。     

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.     

Bragg diffraction of light by ultrasonic shear waves in a plane-parallel layer

We have studied anisotropic Bragg diffraction of light by ultrasonic shear waves in an optically isotropic plane-parallel layer. We have established the analytical dependences of the relative intensities and polarization azimuths of reflected and transmitted diffracted waves on the intensity of the ultrasound, the layer thickness, the angle of incidence, and the polarization azimuth of the incident light. We show that rotation of the plane of polarization of the diffracted wave is determined by the different Fresnel reflection of the s and p polarized components of the incident light in the plane-parallel layer. We have determined that in mismatched acousto-optic structures, deep amplitude modulation of transmitted and reflected light is possible which is an order of magnitude greater than the usual modulation in matched structures.     

Common electronic band gaps and similar optical properties of ZnO nanotubes

Electronic and optical properties of single-walled zinc oxide （ZnO） nanotubes are investigated from the firstprinciples calculations. Electronic structure calculations show that ZnO nanotubes are all direct band gap semiconducting nanotubes and the band gaps are relatively insensitive to the diameter and chirality of tubes. The origin of the common electronic band gaps of ZnO nanotubes is explained in terms of band-folding from the two-dimensional band structure of graphite-like sheet. Moreover, the optical properties such as dielectric function and energy loss function spectra of different ZnO nanotubes are very similar, relatively independent of diameter and chirality of tubes. The calculated dielectric function and loss function spectra show a moderate optical anisotropy with respect to light polarization.     

Optical properties of magnetic photonic crystals with an arbitrary magnetization orientation

We have studied the peculiarities of diffraction of light in magnetic photonic crystals at large values of magnetooptical activity parameter and modulation depth. We have considered the case of an arbitrary angle between the directions of the external static magnetic field and the normal to the layer. The problem has been solved by the modified Ambartsumyan layer summation method. It has been shown that the given system is nonreciprocal with respect to not only circular, but linear polarizations also. In this case, a new type of nonreciprocity is observed (namely, the relation R(α) ≠ R(–α) holds, where R is the reflection coefficient and α is the angle of incidence). It has been demonstrated that in the case of oblique incidence, there appears a new photonic forbidden band that is not selective relative to the polarization of incident light. We have detected strong dependences of reflectance, absorbance, transmittance nonreciprocity, and other characteristics on the angle between the direction of the external static magnetic field and the normal to the layer boundary. Such a system can be used as a controllable polarization filter and a mirror, as well as a source of circular (elliptic) polarization, a controllable optical diode, and so on.