Reflection and transmission of light for a layer of a naturally gyrotropic medium found in an external magnetic field

The propagation of electromagnetic waves through a layer of a naturally gyrotropic medium found in a magnetic field is studied. The problem is solved mathematically using 4×4 Berreman matrices. The Berreman Δ matrix and exact Jones reflection (R?) and transmission (T?) matrices are constructed. The reflectivity, the transmittance, the azimuth, and the ellipticity of polarization of the transmitted wave are calculated. Specific features of the irreversibility of waves are studied. It is shown that multiple reflections in a finite layer lead to a manifold increase in irreversibility, which makes possible the use of such systems as optical diodes working in reflection or as unidirectional reflectors. It is shown that three eigenmodes are excited in such media under certain conditions. The relation between the azimuths of transmitted and incident waves is found and specific features of the relation are analyzed.     

扭曲向列型LCD电光特性计算的理论研究

本文在叶伯琦(Pochi Yeh)扩展琼斯矩阵的基础上,推导出在斜入射情况下扭曲向列型液晶显示器(LCD)电光特性计算公式,并与Berreman的4×4矩阵、Lien的扩展琼斯矩阵进行了数值比较结果表明,运用本论文的计算公式得到的结果要比Lien的更接近于用Berreman 4×4矩阵得到的结果,并且本文推导得出的公式具有运算量小,直接和简洁等特点.     

Modal analysis of circular Bragg fibers with arbitrary index profiles

A finite-difference approach based upon the immersed interface method is used to analyze the mode structure of Bragg fibers with arbitrary index profiles. The method allows general propagation constants and eigenmodes to be calculated to a high degree of accuracy, while computation times are kept to a minimum by exploiting sparse matrix algebra. The method is well suited to handle complicated structures comprised of a large number of thin layers with high-index contrast and simultaneously determines multiple eigenmodes without modification.     

Use of Dirac matrices in polarization optics

Several matrix methods have been developed for studying polarization properties of light. Jones was the first to apply the matrix method to the study of polarization optics. In Jones matrix formalism the polarized wave field is represented by 2-element column matrix known as Jones Vector and the polarization device encountered by light is represented by a 2×2 matrix, known as the characteristic Jones matrix of the device. Mueller introduced a new matrix method where the wave field is represented by a 4-dimensional vector. The elements of the vector are the Stokes parameters of the beam. In Mueller matrix formalism the optical device is represented by a 4×4 real matrix known as ‘Mueller Matrix’ of the device. The use of coherency matrix also proves to the useful in the study of partially polarized light. Pauli spin matrices have been used to unify the different matrix treatments of polarization optical phenomena. The present article is an attempt to unify the analysis of polarization phenomena using Dirac matrices used by Dirac in quantum mechanics. We have however redefined the set of Dirac matrices in terms of the Kronecher product of Pauli spin matrices.     

单模光纤的磁光效应

本文利用琼斯(Janes)矩阵叙述了单模光纤磁光效应的理论,导出了既具有双折射又具有法拉第效应的琼斯矩阵形式,并利用Mueller矩阵导出电流传感器系统输出光强与法拉第旋转角之间的关系.     

Dielectric properties of ice and liquid water from first-principles calculations

We present a first-principles study of the static dielectric properties of ice and liquid water. The eigenmodes of the dielectric matrix E are analyzed in terms of maximally localized dielectric functions similar, in their definition, to maximally localized Wannier orbitals obtained from Bloch eigenstates of the electronic Hamiltonian. We show that the lowest eigenmodes of E (-1) are localized in real space and can be separated into groups related to the screening of lone pairs, intra-, and intermolecular bonds, respectively. The local properties of the dielectric matrix can be conveniently exploited to build approximate dielectric matrices for efficient, yet accurate calculations of quasiparticle energies.     

Jones phase microscopy of transparent and anisotropic samples

We developed an interferometric microscopy technique, referred to as Jones phase microscopy, capable of extracting the spatially resolved Jones polarization matrix associated with transparent and anisotropic samples. This is a generalization of quantitative phase imaging, which is recovered from one diagonal element of the measured matrix. The principle of the technique is demonstrated with measurements of a liquid crystal spatial light modulator and the potential for live cell imaging with experiments on live neurons in culture.     

基于琼斯矩阵的FIR晶体光滤波器设计方法

FIR晶体光滤波器由夹在两个偏振片之间的N个厚度相同的晶片构成,设计过程中需要根据要求的频率响应求出各个晶体波片的光轴方向和输出端偏振片的通光方向.提出了一种基于琼斯矩阵的反向递推设计方法.FIR晶体光滤波器的琼斯矩阵是各个晶片以及偏振片琼斯矩阵的乘积,利用这一关系可以建立简单的反向递推关系,并计算出与输出偏振分量对应的正交偏振分量,通过迭代运算确定所有元件的角度参数.实例设计的结果与使用其它方法得到的结果一致,设计过程简单.     

Polarization of the light output from a weakly birefringent solid state laser

The output from a zero-degree ruby laser is shown to be fully elliptically polarized. Using a matrix formalism the eigenmodes of a Perot-Fabry cavity containing a partial polarizer and a weakly anisotropic medium are shown to be elliptically polarized.     

Jones matrix formalism for quasioptical EPR

The Jones matrix formalism that has been used to analyze quasioptical millimeter-wave circuits is extended for specific application to high-frequency electron paramagnetic resonance (EPR). A survey of general expressions for Jones matrices of elements commonly used in quasioptical EPR spectrometers is given. The Jones matrix representations of quasioptical transmission and reflection cavities are derived, and their relationship to the equivalent circuit and transmission line representations used for conventional EPR cavities is demonstrated. The formalism is applied to selected quasioptical EPR spectrometer designs and experimental tests of the formalism are presented for two configurations of a quasioptical spectrometer operating at 220 GHz.     

Partial eigenvalue assignment for structural damage mitigation

In partial eigenvalue assignment, not all eigenvalues of the open loop system matrix are modified through a multiple input state or output feedback controller. This freedom available to assign selected eigenvalues of the closed loop system matrix has been widely used in design contexts such as to eliminate spillover effects in structural control problems. Similar approach is also required to modify damping and/or stiffness characteristics in selected eigenmodes of a damaged structure. When an external force acts on the damaged structure, partial eigenvalue assignment in this fashion will attempt to use minimal control effort and keep the structure active with safe operation. In this paper, a new approach to partial eigenvalue assignment and its application to structural damage mitigation are presented. A three mass spring-damper model with damage in one of the springs is illustrated with damping modifications at specific eigenmodes. The procedure is repeated for a second example, which is a cantilever beam modeled using two inputs and 10 state variables.     

Evolution of the mean instantaneous intensity in fibers affected by polarization mode dispersion

It is shown that the mean instantaneous intensity (MII) of a pulse propagating in an optical fiber affected by polarization mode dispersion is related to the frequency autocorrelation of the fiber's Jones matrix through a Fourier transform. A simple derivation of the diffusion equation satisfied by the MII and the autocorrelation function of a Jones matrix is described.     

Extended nature of coupled optical interface modes in Thue-Morse dielectric superlattices

We investigate coupled optical interface modes in Thue-Morse (TM) dielectric superlattices composed of two kinds of materials with frequency-dependent dielectric functions. Four basic transfer matrices are derived in the dielectric continuum approximation. By a standard matrix operation method, the trace map of the global transfer matrix in this configuration is obtained. Under Born-von Kármán boundary conditions, the frequency spectra are calculated and their branching rules together with the quartet property are elucidated. It is further proved rigorously that nearly all eigenmodes in this framework have extended nature. The quartet of the eigenmodes is illuminated analytically. The common features and pronounced differences compared with coupled optical interface modes in periodic and Fibonacci dielectric superlattices as well as with other collective elementary excitations in TM structures are also revealed. Received 24 September 2002 / Received in final form 11 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: gjin@nju.edu.cn     

Analysis of Fabry-Perot interference effects on the modulation properties of liquid crystal displays

In this paper, we present the analysis of Fabry-Perot interferences in a twisted nematic liquid crystal display (LCD), and its influence on the modulation properties of the device. We develop a theoretical analysis based on the Jones matrix formalism and compare the results with the experimental response of a commercial display. The developed theory considers multiple reflections to derive a new Jones matrix for the display, which accounts for both polarization and Fabry-Perot interference effects. The validity of this treatment is limited to normal incidence illumination, but it is much simpler than other 4 × 4 matrix treatments developed for a general oblique incidence. It is shown that the existence of multiple reflections can be added to previously existing simplified models for the display, resulting in a modified Jones matrix with two new parameters: the Fresnel reflection coefficient r and the voltage independent phase Φ. In addition, a calibration procedure is proposed where the calculation of these two new parameters related with the multiple reflections, can be uncoupled from the calculation of the rest of the parameters, related with the modulation properties. We remark the good agreement between the theoretical results and the experimental measurements.     

用琼斯矩阵法分析别汉棱镜像面偏振态分布

 基于反射定律的矢量式易于追迹复杂系统中光线的三维空间传播方向,计算了别汉棱镜每一面反射光线的方向,利用琼斯矢量法建立每一反射平面的琼斯矩阵以及面与面之间的传输矩阵,得到了一束线偏振平行光通过别汉棱镜后像面上的偏振状态分布,即经由2个屋脊面出射的光束是2个方位角不同的椭圆偏振光,这2个方位角的大小与入射线偏振光的振动方向有关。采用斯托克斯参量测量法,对别汉棱镜像面上偏振状态的分布进行了实验检测,得到了与理论分析一致的结果,指出别汉棱镜的偏振效应将会导致出射光束偏振状态的不均匀分布。     

喇曼感生克尔效应光谱的琼斯矩阵分析

介绍喇曼感生克尔效应光谱(RIKES)的琼斯(Jones)矩阵分析方法.探测光束的传输强度不仅由所经过的每一个光学器件的琼斯矩阵所决定,而且还受到强的泵波在非线性介质样品中感生依赖于强度的二向色性和双折射(克尔效应)对琼斯矩阵的影响.同时计及样品和光学器件由强泵波作用下感生应力和其他外部产生的线双折射对喇曼感生克尔效应光谱观察的不利影响,导出测量系统的功率传输函数的完整表达式和喇曼感生克尔效应光谱的实现观察条件,最后简述以甲笨(C_7H_8)液体为试样的喇曼感生克尔效应光谱实验结果分析.     

Generalization of a scattering theorem for plane-stratified gyrotropic media

A previously derived eigenmode scattering theorem for plane-stratified gyrotropic media established that the scattering matricesS andS′, defined, respectively, in terms of a given and a conjugate set of eigenmode amplitudes, are mutually transposed, i.e. , the theorem being valid specifically for the incoming and outgoing eigenmodes ofgyrotropic bounding media. In this paper the theorem is extended to include linearly and circularly polarized base-modes in theisotropic media which may bound the multilayered, gyrotropic structure. Transformation of the eigenmode scattering matrix leads to a generalization of the scattering theorem to include base modes which are not necessarily eigenmodes of the medium. In the important special case in which the ambient magnetic field is parallel to the plane of the stratification, the scattering matrix is shown to have a special symmetry whose form depends on the base modes chosen (eigenmodes, linear modes or circular modes).     

保偏光纤双折射主轴的旋转对消光比的影响

本文利用无穷切片模型和Jones矩阵理论,给出了主轴连续旋转的保偏光纤的等效矩阵,并讨论了主轴旋转对消光比的影响.     

关于圆偏振器

讨论了圆偏振器的结构、功能和Jones矩阵表示法,纠正了传统光学教材关于圆起偏器Jones矩阵表达式的错误描述．     

A simple and effective model for Jones matrix to evaluate the transmission performance of Savart polariscope

Starting from the wave normal tracing treatment in the Savart polariscope that relates the Jones matrix to its transmission performance,this paper establishes a simple and effective model for the Jones matrix at an arbitrary inci-dence in the spatial domain.Analytical expressions of all the matrix components are determined with the consideration of all the main impact factors.This model needs only a few parameters hence it is convenient to be employed to evaluate the propagation performance of any birefringent optical system.The simulated results obtained with it demonstrate that this model gives a precise representation of the characteristic of light propagation in the Savart polariscope.This would provide useful suggestions for the design,calibration,and performance improvement of any other birefringent polarisation element and optical system.