Realizable differential matrices for depolarizing media

The evolution of a Stokes vector through depolarizing media is considered. A general form for the differential matrix is found that is appropriate in the presence of depolarization and it is parameterized in a manner that ensures that it yields, upon integration, a valid Mueller matrix for any choice of parameters. The form expands the more limited form for a nondepolarizing matrix given by Azzam [J. Opt. Soc. Am. 68, 1756 (1978)] and which was extended recently by others to include depolarization. A Mueller matrix decomposition is proposed that is based upon the new parameterization.     

Lorentz beams as a basis for a new class of rectangularly symmetric optical fields

In this work we present a new and wide class of scalar, rectangular symmetrical optical fields, the free-space propagation of which can be given in a closed-form in the paraxial approximation. In particular it is shown how such fields can be expressed as a finite linear combination of the recently introduced Lorentz beams [O. El Gawhary, S. Severini, J. Opt. A: Pure Appl. Opt., 8 (2006) 409.] that, in this way, act as a basis for the newly introduced class. Because of their mathematical form, we call such fields super-Lorentzian beams. Some common features of the class are pointed out and the concept of order of the beam introduced. Moreover, by using these results, we demonstrate the existence of a new family of mutually orthogonal paraxial fields with a related new class of orthogonal polynomials.     

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.     

New arbitrated quantum signature of classical messages against collective amplitude damping noise

Recently, Chong et al. [Opt. Comm. 284, (2011) 893-895] pointed out that a dishonest party in Yang and Wen's arbitrated quantum signature scheme [Opt. Comm. 283, (2010) 3198-3201] is able to reveal the other party's secret key without being detected by using the Trojan-horse attacks. However, the solution to avoid the attack still remains open. This work further points out that in Yang and Wen's scheme, the arbitrator is unable to arbitrate the dispute between two users. Consequently, a user can deny that he/she has signed or verified a signature without performing a Trojan-horse attack. A solution is proposed to solve this problem as well as the open problem mentioned earlier.     

Comment on “Focusing of high polarization order axially-symmetric polarized beams” [Chin.Opt.Lett.7,938 (2009)]

Some mathematical and conceptual errors contained in a recent letter [Chin.Opt.Lett.7,938 （2009）] are pointed out.     

高斯光束通过多光阑B=0成像系统传输的解析公式研究

采用将硬边光阑窗口函数展开为有限个复高斯函数之和的方法和A0CD矩阵分解的技巧，推导 出了高斯光束通过多光阑B=0光学成像系统解析的传输公式，并用典型数值计算例加以说明. 最后，指出了所用方法的优点. 关键词： 硬边光阑 复高斯函数 传输方程 矩阵分解     

Enhanced Multiparty Controlled QSDC Using GHZ State

Recently, Gao et al. [Opt. Commun. 283 (2010) 192] pointed out that Wang et al.'s multiparty controlled quantum secure directcommunication (CQSDC) protocol [Opt. Commun. 266 (2006)732] has the information leakage problem and proposed an improvedprotocol. However, in the improved protocol, due to the introductionof an additional random sampling to avoid the weakness, the qubitefficiency is decreased. By introducing the base changing techniqueto the random sampling in Wang et al.'s protocol, this study overcomesthe information leakage problem and provides a better qubit efficiency.     

Eavesdropping on the improved three-party quantum secret sharing protocol

Lin et al. [Song Lin, Fei Gao, Qiao-yan Wen, Fu-chen Zhu, Opt. Commun. 281 (2008) 4553] pointed out that the multiparty quantum secret sharing protocol [Zhan-jun Zhang, Gan Gao, Xin Wang, Lian-fang Han, Shou-hua Shi, Opt. Commun. 269 (2007) 418] is not secure and proposed an improved three-party quantum secret sharing protocol. In this paper, we study the security of the improved three-party quantum secret sharing protocol and find that it is still not secure. Finally, a further improved three-party quantum secret sharing protocol is proposed.     

阶矩阵及其在传统预处理方法中的应用

本文应用矩阵元素阶和阶矩阵概念,讨论了ICCG和MICCG这两种传统的预处理方法在实用中的一些问题。为什么ICCG(s,t)在s+t固定时取(s,t)=(1,1),(1,2),(1,3),(2,4),(3,5),…有较高的收敛速度?为什么MICCG(m)当m>3时迭代次数不变?ICCG和MICCG的填入方式如何系统化?MICCG是否总比ICCG收敛速度高?本文拟作一个初步的讨论。通过LU分解的阶矩阵,本文给出了按阶递增的填入原则,将ICCG和MICCG系统化为P阶ICCG和P阶MICCG,并讨论了MICCG原有填入方式存在的问题。应用误差阵的阶矩阵,本文讨沦了MICCG迭代参数选取中存在的问题,给出了合理的参数选取方法。通过不同算例,本文还比较了ICCG和MICCG的计算效率。     

平面光学元件最小焦距的双星点定焦测量法的精度分析

分析用双星点定焦法测量平面光学元件最小焦距时影响测量精度的因素，指出测量中应注意的问题。     

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.     

Topological Structure of Knotted Vortex Lines in Liquid Crystals

In this paper, a novel decomposition expression for the U（1） gauge field in liquid crystals （LCs） is derived. Using this decomposition expression and the b-mapping topological current theory, we investigate the topological structure of the vortex lines in LCs in detail. A topological invariant, i.e., the Chern-Simons （CS） action for the knotted vortex lines is presented, and the CS action is shown to be the total sum of all the self-linking and linking numbers of the knot family. Moreover, it is pointed out that the CS action is preserved in the branch processes of the knotted vortex lines.     

Constrained matched filtering for extended dynamic range and improved noise rejection for Shack-Hartmann wavefront sensing

We recently introduced matched filtering in the context of astronomical Shack-Hartmann wavefront sensing with elongated sodium laser beacons [Appl. Opt. 45, 6568 (2006)]. Detailed wave optics Monte Carlo simulations implementing this technique for the Thirty Meter Telescope dual conjugate adaptive optics system have, however, revealed frequent bursts of degraded closed loop residual wavefront error [Proc. SPIE 6272, 627236 (2006)]. The origin of this problem is shown to be related to laser guide star jitter on the sky that kicks the filter out of its linear dynamic range, which leads to bursts of nonlinearities that are reconstructed into higher-order wavefront aberrations, particularly coma and trifoil for radially elongated subaperture spots. An elegant reformulation of the algorithm is proposed to extend its dynamic range using a set of linear constraints while preserving its improved noise rejection and Monte Carlo performance results are reported that confirm the benefits of the method.     

The “radiance law” in radiation transfer processes

The conservation law of radiance as a suitable tool for investigation of radiation transfer processes between two systems is treated. Original proofs of this law are given and its deep thermodynamical foundation is pointed out. Finally, applications to general problems of power coupling and particularly to the radiation transfer from incoherent sources (LED) into multimode optical fibres are carried out.     

Directionality of partially coherent annular flat-topped beams propagating through atmospheric turbulence

The closed-form expression for the angular spread of partially coherent annular flat-topped beams propagating through atmospheric turbulence is derived by using the integral transform technique. In comparison with previous work, the results obtained in this paper are more general. It is shown that, except for equivalent Gaussian Schell-model (GSM) beams as pointed out in Ref. [T. Shirai, A. Dogariu, E. Wolf, Opt. Lett. 28 (2003) 610], there also exist equivalent annular and non-annular beams which may generate the same directionality as the corresponding fully coherent Gaussian beam both in free space and in turbulence. The theoretical results are illustrated by numerical examples and interpreted physically.     

An indirect approach for quantum-mechanical eigenproblems: duality transforms

We suggest an indirect approach for solving eigenproblems in quantum mechanics. Unlike the usual method, this method is not a technique for solving differential equations. There exists a duality among potentials in quantum mechanics. The first example is the Newton–Hooke duality revealed by Newton in Principia. Potentials that are dual to each other form a duality family consisting of infinite numbers of family members. If one potential in a duality family is solved, the solutions of all other potentials in the family can be obtained by duality transforms. Instead of directly solving the eigenequation of a given potential, we turn to solve one of its dual potentials which is easier to solve. The solution of the given potential can then be obtained from the solution of this dual potential by a duality transform. The approach is as follows: first to construct the duality family of the given potential, then to find a dual potential which is easier to solve in the family and solve it, and finally to obtain the solution of the given potential by the duality transform. In this paper, as examples, we solve exact solutions for general polynomial potentials.     

On an optimal robust digital image watermarking based on SVD using differential evolution algorithm

It is shown that the optimal robust digital image watermarking based on singular value decomposition using differential evolution algorithm proposed by Veysel Aslantas [Opt. Commun. 282(5):769-777 (2009)] has a serious fundamental flaw and should not be used for proof of ownership application.     

Analytical solutions for the slow neutron capture process of heavy element nucleosynthesis

In this paper, the network equation for the slow neutron capture process (s-process) of heavy element nucleosynthesis is investigated. Dividing the s-process network reaction chains into two standard forms and using the technique of matrix decomposition, a group of analytical solutions for the network equation are obtained. With the analytical solutions, a calculation for heavy element abundance of the solar system is carried out and the results are in good agreement with the astrophysical measurements.