Complete determination of the conical Mueller matrix for one-dimensional rough metallic surfaces

We present results of the complete determination of the Mueller matrix for the light scattered by a one-dimensional random rough metallic surface under a conical or out-the-plane of incidence geometry. We present and apply a reduced method for its complete determination. This reduced method considers only 16 intensity-polarized measurements instead of the 36 intensity-polarized measurements recently reported. Effects related with the enhanced backscattering were observed.     

Active polarization imaging system to discriminate adaptively with diagonal Mueller matrix

A promising method to optimize the polarization state of two-channel active polarization imaging system is presented. In this method, it is seminal that the detecting function of the imaging system is regarded as a discriminant projection of the observed objects’ polarization features (elements of the Mueller matrix). The polarization state can be seen as a physical classifier which can be obtained by training samples. The image acquired with the system that has the designed optimal polarization state become discriminative results directly. The effectiveness of the proposed method and the discriminative ability of the optimal polarization state are demonstrated by the experimental results.     

Polarization characteristics of backscattering of turbid media based on Mueller matrix

Mueller matrix is one approach to characterizing optical polarization of the turbid media. We have simulated the two-dimensional images of Mueller matrix based on single-scattering approximation model and implemented experiments to verify the simulations. By comparing the experimental results to the theoretical simulations, we have obtained some conclusions. When the particle size is smaller than the wavelength, the linearly polarized light propagating through the turbid media of Rayleigh scatterers has better polarization-maintaining ability. Whereas when the particle size is larger than the wavelength, the circularly polarized light propagating through the turbid media of Mie scatterers has better polarization-maintaining ability. Moreover, the radial dependence of the element patterns becomes weak as the transport mean free path decreases. This study can help us understand to the fundamental principle of optical polarization.     

Polarization state and Mueller matrix measurements in terahertz-time domain spectroscopy

We derive the complete formulae governing the polarization state measurement in terahertz-time domain spectroscopy (THz-TDS) by using a rotatable THz polarizer. Four Stokes parameters can be uniquely obtained by spectrally-resolved measurement in THz-TDS. Further, we propose a new approach to measure the Mueller matrix of a pure birefringent material, using THz-TDS, by rotating the material under test. Based on the above techniques, we successfully measured the Mueller matrices of a quartz crystal in the frequency domain.     

Programming matrix optics into Mathematica

The various non-linear transformations incurred by the rays in an optical system can be modelled by matrix products up to any desired order of approximation. Mathematica software has been used to find the appropriate matrix coefficients for the straight path transformation and for the transformations induced by conical surfaces, both direction change and position offset. The same software package was programmed to model optical systems in seventh order. A Petzval lens was used to exemplify the modelling power of the program.     

Differentiating characteristic microstructural features of cancerous tissues using Mueller matrix microscope

Polarized light imaging can provide rich microstructural information of samples, and has been applied to the detections of various abnormal tissues. In this paper, we report a polarized light microscope based on Mueller matrix imaging by adding the polarization state generator and analyzer (PSG and PSA) to a commercial transmission optical microscope. The maximum errors for the absolute values of Mueller matrix elements are reduced to 0.01 after calibration. This Mueller matrix microscope has been used to examine human cervical and liver cancerous tissues with fibrosis. Images of the transformed Mueller matrix parameters provide quantitative assessment on the characteristic features of the pathological tissues. Contrast mechanism of the experimental results are backed up by Monte Carlo simulations based on the sphere–cylinder birefringence model, which reveal the relationship between the pathological features in the cancerous tissues at the cellular level and the polarization parameters. Both the experimental and simulated data indicate that the microscopic transformed Mueller matrix parameters can distinguish the breaking down of birefringent normal tissues for cervical cancer, or the formation of birefringent surrounding structures accompanying the inflammatory reaction for liver cancer. With its simple structure, fast measurement and high precision, polarized light microscope based on Mueller matrix shows a good diagnosis application prospect.     

长周期保偏光纤光栅的偏振特性研究

用高频CO2激光脉冲写入法在熊猫保偏光纤上写入长周期光纤光栅,并对其偏振特性进行了全面的试验研究.试验结果表明,在输入椭圆偏振光偏振角度0到2π的变化范围内,高频CO2激光脉冲写入法在熊猫保偏光纤上写入的长周期光纤光栅谐振峰幅值会随着入射椭圆偏振光偏振角度的改变发生以π为周期的周期性变化,并且相邻两谐振峰幅值变化趋势相反,相位差为π.在相同偏振角度下将两谐振峰幅值相减,其差值呈近似于锯齿波的周期性变化,周期也为π.在没有发生模式干扰的情况下,谐振峰波长几乎没有发生漂移.基于模式耦合理论,文中还对所观察到的试验现象进行了定性的理论解释.     

Scattering by rough surfaces in a conical configuration: experimental Mueller matrix

A simple method for measuring the Mueller matrix associated with rough surfaces in a conical configuration is presented. I present result of experimental measurements of the Mueller matrix for the angular distribution of the light scattered by a one-dimensional gold-coated randomly rough surface in a conical configuration. Effects related to the phenomenon of enhanced backscattering are reported.     

混浊介质中后向单次漫散射米勒矩阵特征

采用斯托克斯(Stokes)矢量形式,推导出当无限窄的连续光束垂直入射到混浊介质表面时,后向单次漫散射米勒(Mueller)矩阵的解析表达式。基于米氏(Mie)散射模式,详细分析了单次散射米勒矩阵元素的分布模式,以及与介质粒子数密度,粒子尺寸参量之间的关系。研究表明:单次散射米勒矩阵的方位变化随粒子数密度的增加,逐渐消失,而矩阵元素m22,m33,m23,m32随粒子数密度的变化,具有更显著的方位变化特征。矩阵元素m22,m33在方位角=45°时的值随尺寸参量的变化有一定的规律性,当尺寸参量小于某一特征参量时,其值呈下降趋势,反之则呈波动上升趋势。当介质粒子数密度以及粒子尺寸参量改变时,米勒矩阵元素强度的径向分布模式不变,即在任何方位,强度随径向距离都近似成指数规律衰减,方位变化呈周期性。     

Non-singular Mueller matrices characterizing passive systems

We extended previous results and explained why it is necessary to work with SO(6,1)_e (sub-group of matrices with unit determinant and positive left upper corner element) in order to define a parametric form of an arbitrary non-singular Mueller matrix. The previously proposed solution in Devlaminck and Terrier [Definition of a parametric form of nonsingular Mueller matrices. J. Opt. Soc. Am. A 25 (2008) 2636-2643], was just a subset of this one. The issue of transmittance conditions for the matrices generated by this formalism is considered and conditions related to the elements of the polar decomposition are derived and give sufficient conditions to guarantee the transmittance conditions for the product matrix.     

Mueller matrix for characterization of one-dimensional rough perfectly reflecting surfaces in a conical configuration

Theoretical results of the use of a Mueller matrix to characterize a one-dimensional rough perfectly reflecting, single-scattering surface in a conical configuration are presented. The conical Mueller matrix (CMM) is derived from the known Mueller matrix of this kind of surface in the plane of incidence [the plane Mueller matrix (PMM)]. The key argument is that, as the PMM is considered to be a Mueller-Jones matrix, an appropriate rotation of the complex amplitude matrix provides the conic Mueller matrix.     

Least-squares analysis of the Mueller matrix

In a single-mode fiber excited by light with a fixed polarization state, the output polarizations obtained at two different optical frequencies are related by a Mueller matrix. We examine least-squares procedures for estimating this matrix from repeated measurements of the output Stokes vector for a random set of input polarization states. We then apply these methods to the determination of polarization mode dispersion and polarization-dependent loss in an optical fiber. We find that a relatively simple formalism leads to results that are comparable with those of far more involved techniques.     

Product decompositions of depolarizing Mueller matrices with negative determinants

We show that the product decomposition of a depolarizing Mueller matrix (S.-Y. Lu, R.A. Chipman, J. Opt. Soc. Am. A 13 (1996) 1106) as well as the recently proposed reverse decomposition (R. Ossikovski, A. De Martino, Opt. Lett. 32 (2007) 689) need to be extended in order to account for Mueller matrices with negative determinants. The necessity of such an extension of the formalism is illustrated on experimentally determined Mueller matrices. The procedure of the modified decomposition formalism is explicitly described.     

传输同步辐射X射线的锥形单毛细管的物理特性

根据北京同步辐射装置生物大分子实验站(2W1A)的条件和应用,从理论上研究了锥形单毛细管传输同步辐射X射线的物理特性.计算了锥管传输效率随锥管长度、X射线能量的变化规律;计算了锥管出口处的光强分布,强度增益随工作距离的变化规律.结果表明:与传输发散X射线相比,锥形单毛细管传输平行X射线的物理特性有明显的不同.     

Cross-spectral density matrix of the far field generated by a blackbody source

An expression is derived for the cross-spectral density matrix, valid in the paraxial region of the far field, generated by a planar blackbody source. With the help of it we determine the spectral degrees of polarization and of cross-polarization of the far field.     

Generalizations of the Virasoro algebra and matrix Sturm–Liouville operators

We study the series of Lie algebras generalizing the Virasoro algebra introduced in [V. Yu, Ovsienko, C. Roger, Functional Anal. Appl. 30 (4) (1996)]. We show that the coadjoint representation of each of these Lie algebras has a natural geometrical interpretation by matrix differential operators generalizing the Sturm–Liouville operators.     

Optical Mueller matrices in terms of geometric algebra

Connection between optical Mueller matrices and geometrical (Clifford) algebra multivectors is established. It is shown that starting from 3-dimensional (3D) Cl_3,0 algebra and using isomorphism between Cl_3,0 and even Cl_3,1⁺ subalgebra one can generate canonical Mueller matrices and their combinations that describe an optical system. It appears that representation of polarization devices in terms of geometric algebra is very compact and, in contrast to Mueller matrix approach, there is no need for speculative physical restrictions. If needed, properties of media can be logically introduced into Maxwell equation in a form of Clifford algebra via constitutive relations. Since representation of polarization by Cl_3,1 algebra is Lorentz invariant it allows to include relativistic effects of moving bodies on light polarization as well. In this paper only simple examples of connection between Mueller matrices and geometric algebra multivectors is presented.     

手性介质中后向散射米勒矩阵特性及其在血糖无创检测中的应用初探

利用斯托克斯-米勒矩阵表述分析偏振光在手性介质中的传输规律,利用瑞利近似下的单次散射模型和基于米氏散射理论的多次散射的蒙特卡罗方法,探讨葡萄糖对后向散射偏振光传输特性的影响,计算了不同葡萄糖浓度下的后向散射米勒矩阵. 结果表明在含有葡萄糖的手性介质中后向散射米勒矩阵的若干矩阵元表现出微弱的旋光效应,旋光度随葡萄糖浓度增大而增大. 为了检测低浓度下微小的旋光变化,定义了函数对含-不含葡萄糖的米勒矩阵元图像进行处理,提取由葡萄糖引入的图像差异. 结合无创血糖检测应用要求,分析了葡萄糖生理浓度下的矩阵元图像,获 关键词： 医用光学与生物技术 偏振光 斯托克斯-米勒表述 蒙特卡罗模拟     

锥形梯度折射率激光准直系统的矩阵光学研究

把梯度折射率激光准直系统视为一个整体,采用矩阵光学的方法,研究了高斯光束经锥形梯度折射率激光准直系统的传输特性.讨论了多级密接锥形梯度折射率激光准直系统的设计原理.     

随机非球形粒子全极化散射的时间相关Mueller矩阵解

从与时间相关的矢量辐射传输方程推导一阶Mueller矩阵解,用来模拟Gauss型平面脉冲波入射下,一层随机、非均匀取向非球形粒子的全极化双站散射.数值计算了同极化和去极化脉冲响应,与入射脉冲进行了比较,说明了随机介质的物理参数,如粒子的取向和占空比、入射角、极化以及层厚等对脉冲响应的影响 关键词： 平面脉冲波 非球形粒子 Mueller矩阵