斯托克斯空间用邦加球表示光偏振态的再研究

从斯托克斯子空间引入邦加球 ,在邦加球上表示光的任意偏振态 ,给出了表达式     

全偏振光通过延迟器件后的布卡尔球表示

以全偏振光的矢量描述和布卡尔球表示为理论基础 ,用斯托克斯矢量表示全偏振光 ,用Muller矩阵表示延迟器件 ,推导了全偏振光通过一个快轴与X/Y轴重合而相位差为δ1 的延迟器后的斯托克斯矢量表示 ,并由此计算了全偏振光通过该器件后的球坐标。由全偏振光通过延迟器件前后的球坐标表示的特点 ,可得到一束全偏振光通过此延迟器件后在布卡尔球上的位置 ,并可证明完全是由初相位差 δ0 和延迟器的相位差 δ1 决定的。给出了实例 ,并验证了此结论。     

Adiabatic geometric phase in the nonlinear coherent coupler

We introduce the concept of geometric phase to the nonlinear coherent coupler. With considering the adiabatic change of the distance-dependent phase mismatch, we calculate the adiabatic geometric phase related to the supermode of the coupler analytically. We find that the phase depends on the input light intensity explicitly. In particular, in the low and high intensity limits, the phase equals half of the area on the Poincare sphere enclosed by the evolution loop of the system. At the critical intensity where different supermodes merge, the phase diverges, which can be considered as the signal of a continuous phase transition.     

Bifurcations in biparametric quadratic potentials

Numerous dynamical systems are represented by quadratic Hamiltonians with the phase space on the S (2) sphere. For a class of these Hamiltonians depending on two parameters, we analyze the occurrence of bifurcations and we obtain the bifurcation lines in the parameter plane. As the parameters evolve, the appearance-disappearance of homoclinic orbits in the phase portrait is governed by three types of bifurcations, the pitchfork, the teardrop and the oyster bifurcations. We find that the teardrop bifurcation is associated with a non-elementary fixed point whose Poincare index is zero. (c) 1995 American Institute of Physics.     

Generalization of the Poincare sphere to process 2D displacement signals

Traditionally the multiple phase method has been considered as an essential tool for phase information recovery. The in-quadrature phase method that theoretically is an alternative pathway to achieve the same goal failed in actual applications. The authors in a previous paper dealing with 1D signals have shown that properly implemented the in-quadrature method yields phase values with the same accuracy than the multiple phase method. The present paper extends the methodology developed in 1D to 2D. This extension is not a straight forward process and requires the introduction of a number of additional concepts and developments. The concept of monogenic function provides the necessary tools required for the extension process. The monogenic function has a graphic representation through the Poincare sphere familiar in the field of Photoelasticity and through the developments introduced in this paper connected to the analysis of displacement fringe patterns. The paper is illustrated with examples of application that show that multiple phases method and the in-quadrature are two aspects of the same basic theoretical model.     

电控径向双折射滤波器的横向超分辨与轴向扩展焦深

提出利用电控径向双折射光瞳滤波器实现横向超分辨性能参量的调制与轴向扩展焦深。该光瞳滤波器由两个平行偏光镜,一个电光晶体与一个径向对称双折射晶体组成。分析了电光晶体与径向双折射元件对光偏振态的空间调制作用,通过控制电光晶体的相位延迟实现径向中心处初始偏振态的控制,与径向双折射元件横向偏振态调制结合,实现了庞加莱球上偏振态演变路径与阶段的控制,从而对焦点附近偏振态进行空间调制以实现光强的重新分布。研究结果表明,外加电场调制可以实现横向上超分辨性能的调控以及轴向上焦深的扩展,并可得到相应的电光相位延迟范围。     

利用琼斯矩阵分析全偏振光通过旋光器件的邦加球表示

用琼斯矩阵表示旋光器件．用琼斯矢量表示偏振光．计算椭圆偏振光通过旋光器件后的琼斯矢量，分析椭圆偏振光通过旋光器件的邦加球表示。结果表明．用此法得到的结论与已有结论一致。     

Optical-mechanical analogy in problems of polarization optics

Within the framework of optical-mechanical analogy, the problem of propagation of polarized light (both linear and circular) is studied for a medium with the inhomogeneity of dielectrical permittivity and gyrotropy. The analysis is carried out both with use of a system of coupled equations and the Poincare sphere.     

Anatomy of a polarization switch of a vertical-cavity semiconductor laser

Using a streak camera we have measured the three Stokes polarization parameters during a polarization switch of a vertical-cavity semiconductor laser. The switch occurs along a corkscrew path on the Poincare sphere and takes on average a few nanoseconds; this value agrees with a theoretical treatment based upon the Fokker-Planck equation.     

光纤中光的偏振态的几种表示方法

阐述了光纤中影响光的偏振态的几个因素。用椭圆表示法和邦加（Poincare)球图形表示法对光的任意偏振态进行了描述，并用平面的史密斯圆图来等效邦加球。编制了QUICK BASIC计算机程序，绘制了史密斯圆图的等α线、等δ线和等β线，程序能快速显示任意偏振态的椭圆表示和史密斯圆图表示，讨论了史密斯圆图的特性和应用。     

Mueller Matrix Analysis of PDL Components

A detailed Mueller-Stokes analysis of an arbitrary elliptical dichroic polarizer is presented. Explicit expressions for the Jones matrix, the Stokes parameters, and the Mueller matrix for a distributed and localized dichroic polarizer acting as a polarization-dependent loss (PDL) element are derived. Application to wavelength-dependent PDL elements is discussed. The Poincare sphere representation and the application of the Mueller matrices for the study of randomly oriented concatenated PDL elements and PDL vector measurement are addressed.     

设计和实现三维空间任意庞加莱截平面电路

庞加莱截面法是简化分析复杂动力系统运动状态的有效方法.为实现在线方便观测复杂系统的状态,本文设计并实现了三维任意庞加莱截平面电子电路.文章首先详细分析和研究了设计三维任意庞加莱截平面电路的关键性问题,然后分类设计和实现了物理电路.由于蔡氏电路具有丰富的动力学行为,因此以典型的蔡氏电路作为实验待测动力系统,对设计的截平面电路进行了大量的物理实验,测出了蔡氏电路各种状态下的截平面图,以及同一种混沌状态下选取不同截面的测试实验.实验中采用了两种双踪示波器(模拟示波器和数字示波器)在线实测了庞加莱截平面映射和状态图.与此同时,利用Matlab进行了计算机仿真辅助实验.所有实验结果表明设计的庞加莱截平面电路具有实用性和有效性.     

线双折射传感光栅中的传输光偏振态分析

 深入研究了线双折射光栅中透射光偏振特性的演变过程。采用耦合模理论和琼斯矩阵分析了传输距离、双折射大小、入射起偏态等因素对透射光偏振特性的影响,并利用邦加球中描绘了偏振态的演变趋势。结果表明：光栅中的线双折射和传输距离会改变传输光的偏振态,偏振态的波长相关曲线会随传输距离和线双折射的增大而不断扩展,入射起偏态的不同并不改变偏振态的拓展趋势。同时,第一斯托克斯参量与偏振相关损耗在峰值波长点上存在对应关系,两者幅值均与线双折射呈单调递增关系,可应用于传感测量。     

Realization of Arbitrary Inverse Unitary Transformation of Single Mode Fibre by Using Three Wave Plates

We report a method to realize the arbitrary inverse unitary transformation imposed by a single-mode fibre on photon＇s polarization by the succession of two quarter-wave plates and a half-wave plate. The process of realization is analysed on a Poincar6 sphere due to the fact that unitary transformation does not change the angle formed by polarization state vector. The method is meaningful in quantum communication experiment such as quantum teleportation, in which an unknown arbitrary quantum state should be kept to be unchanged in the case of using a single-mode fibre for time delay.[第一段]     

高双折射光纤中非线性耦合模偏振态稳定性分析

通过高双折射光纤中非线性耦合模传输方程,首先,利用斯托克斯参量,用庞加莱球研究分析了耦合模传输的稳定性及偏振态的演变,结果表明高双折射光纤中耦合模的传输不产生分歧现象,传输具有稳定性;其次,描述了拉曼效应对各种状态下偏振态演变规律的影响,给出了斯托克斯参量S₁,S₂与S₃的解析解及拉曼效应对偏振态的演变周期的影响.     

选取任意庞加莱截面的新方法

针对用庞加莱截面分析非线性系统时较难选择合适截面的问题,提出了一种投影时域法.该方法可以在时域上直观地判断所选平面是否合适并实时准确地调整平面的方向与位置.文中给出了投影时域法的完整定义并从理论上详细分析了该方法的原理;同时研究了在时域上判断所选平面是否是合适的庞加莱截面的条件以及如何调整所选平面的方向与位置;最后,利用投影时域法对三种典型的三维或四维非线性系统进行了仿真实验,实验结果证明了该方法的有效性和实用性.     

用琼斯算法求解椭圆光正反射问题需采用的数学处理方法

采用琼斯算法并结合Poincare球的图示研究了单色椭圆偏振光经理想平面镜正反射的特性,然后将获得的结论推广到圆偏振光及线偏振光经平面镜正反射的情形,再用偏振态几何参量表示法对结论加以验证,并提出便于记住结论的镜像法,以期对椭圆偏振光正反射问题的琼斯算法及获得结果的物理含义给出比较直观的诠释。同时指出采用琼斯算法求解偏振光学问题时需采用的特殊数学处理方法及产生这一现象的原因。     

Quantum chaos for the radially vibrating spherical billiard

The spherical quantum billiard with a time-varying radius, a(t), is considered. It is proved that only superposition states with components of common rotational symmetry give rise to chaos. Examples of both nonchaotic and chaotic states are described. In both cases, a Hamiltonian is derived in which a and P are canonical coordinate and momentum, respectively. For the chaotic case, working in Bloch variables (x,y,z), equations describing the motion are derived. A potential function is introduced which gives bounded motion of a(t). Poincare maps of (a,P) at x=0 and the Bloch sphere projected onto the (x,y) plane at P=0 both reveal chaotic characteristics. (c) 2000 American Institute of Physics.     

Polarized light

Following the recent work of Chandleret al on quasi probability distributions for spin-1/2 particles, we show that polarized light can be interpreted in terms of trivariate probability distributions in two different ways by choosing the variates to correspond to (i) the co-ordinates on the Poincare sphere, (ii) the components of the spin operator of the photon. In either case, it is shown that the Margenau-Hill procedure leads to probability mass functions while the Wigner-Weyl approach leads to probability density functions and the well-known Stokes parameters are also realised as appropriate averages with respect to these distribution functions.     

Modeling and simulation of polarization errors in Sagnac fiber optic current sensor

Sagnac fiber optic current sensor (S-FOCS) is a kind of optical interferometer based on Sagnac structure, optical polarization states of sensing light wave in Sagnac fiber optic current sensor are limited. However, several factors induce optical polarization error, and non-ideal polarized light waves cause the interference signal crosstalk in sensor, including polarizer, quarter-wave retarder, splice angular, birefringence and so on. With these errors, linearly polarized light wave in PM fiber and circularly polarized light wave in sensing fiber become elliptically polarized light wave, then, nonreciprocal phase shift induced by magnetic field of the current is interrupted by wrong polarization state. To clarify characteristics of optical polarization error in fiber optic current sensor, we analyze the evolution process of random optical polarization state, linear optical polarization state and circular optical polarization state in Sagnac fiber optic current sensor by using Poincare sphere, then, build optical polarization error models by using Jones matrix. Based on models of polarization state in Sagnac fiber optic current sensor, we investigate the influence of several main error factors on optical polarization error characteristics theoretically, including extinction ratio in polarizer, phase delay in quarter-wave retarder, splice angular between quarter-wave retarder and polarization maintaining fiber. Finally, we simulate and quantify nonreciprocal phase shift to be detected in fiber optic current sensor related with optical polarization errors. In the end, we demonstrate S-FOCS in test. The results show that transfer matrix errors are induced by inaccurate polarization properties during polarization state conversion, then, the stability and accuracy of the S-FOCS are affected, and it is important to control the polarization properties at each step of the polarization state conversion precisely.