Vectorial Pauli algebraic approach in polarization optics. I. Device and state operators

This paper inscribes on the line of the efforts (sketched in the Introduction) in elaborating theoretical approaches alternative to the traditional Jones and Mueller matrix calculi in polarization optics. The more abstract, compact and elevated forms of linear algebra are not fully exploited yet in the polarization optics. A vectorial and pure operatorial Pauli algebraic approach to the interaction between the polarized light and the polarization optical systems is given. This is the most compact, adequate and elegant calculus corresponding to the well-known geometric handling of the polarization states and their interaction with the polarization devices on the Poincaré sphere. In this first paper, we deduce the Pauli algebraic vectorial forms of the operators corresponding to the orthogonal and nonorthogonal polarization devices and to all the states of light polarization. In the next paper we shall give the vectorial Pauli algebraic analysis of the interaction between the whole hierarchy of these devices and the various forms of polarized light.     

Spin polarization of two-dimensional electron system in different Laughlin states and around filling factor

The spin configuration of the ground state of a two-dimensional electron system is investigated for different FQHE states from an analysis of circular polarization of time-resolved luminescence. The method clearly distinguishes between fully spin polarized, partially spin polarized and spin unpolarized FQHE ground states. We demonstrate that FQHE states which are spin unpolarized or partially polarized at low magnetic fields become fully spin polarized at high fields. Temperature dependence of the spin polarization reveals a nonmonotonic behavior at . At and the electron system is found to be fully spin polarized. This result does not indicate the existence of any skyrmionic excitations in high magnetic field limit. However, at the observed spin depolarization of electron system at and becomes broader for lower magnetic fields, so that full spin polarization remains only in a small vicinity of . Such a behavior could be considered as a precursor of skirmionic depolarization, which would dominate for smaller ratios between Zeeman and Coulomb energies.We demonstrate that the spin polarization of 2D-electron system at and can be strongly affected by hyperfine interaction between electrons and optically spin-oriented nuclears. This result is due to the fact that hyperfine interaction can both enhance and suppress effective Zeeman splitting in fixed external magnetic field.     

Operatorial form of the theory of polarization optical devices: I. Spectral theory of the basic devices

While the theory of operators in quantum mechanics is expressed nowadays in a pure operatorial form (wrapped mostly in Dirac's symbolic language), in optics the polarization device operators and their action are analyzed yet in the old matrix (Jones or Muller) formalism. The theory of polarization device operators has not taken systematically advantage of the very general, fundamental and deep results of the spectral theory of operators, on the basis of which it can be structured in an elegant deductive and physically expressive form. In this paper we apply the spectral theorem to the polarization device operators, we calculate their expansions in a pure operatorial Dirac-dyadic form and give some examples which illustrate the advantages from the physical insight viewpoint of such an approach. We are concerning here only with the basic polarization devices, to which correspond normal operators.     

Photoelectron spin polarization via the relativistic augmented-plane-wave method

A method for calculating the spin polarization of photoelectrons excited by circularly polarized light in solids is proposed. The matrix elements of the electron-photon interaction Hamiltonian are obtained with the relativistic augmented-plane-wave method by Loucks. The degree of the spin polarization can be calculated using these matrix elements which represent optical transitions taking into account the spin states.     

Three-dimensional polarization control in microscopy

We propose an approach to optical microscopy that enables full control over the three-dimensional polarization vector at the focal spot of a high-numerical-aperture lens. The input field to the lens is linearly polarized and no polarization optics are needed. This technique utilizes the azimuthal spatial degree of freedom of the input field. We find that only a small set of low-order azimuthal spatial harmonics contributes to the focused field on axis, and a simple transformation exists between the linear vector space of these harmonics and the three-dimensional polarization-vector space. Controlling the relative complex weights of these azimuthal harmonics produces any desired three-dimensional state of polarization.     

非线性克尔效应对飞秒激光偏振的超快调制

研究了近红外飞秒激光的偏振在太赫兹频率的超快调制.利用抽运-探测光谱技术,通过改变两个脉冲之间的延迟时间可以控制光脉冲的旋转角.在Li：NaTb（WO₄）₂磁光晶体中观察到探测光的偏振随延迟时间变化的高速振荡,振荡信号的中心频率为0.19 THz.这种超快偏振调制现象可以解释为,抽运-探测实验构置中,前向传播的抽运光诱导的光学克尔非线性引起被晶体远端表面所反射的背向传播的探测光脉冲偏振面的额外旋转.通过改变抽运光的圆偏振旋性可以控制探测光调制信号的相位和振幅.实验结果表明,非线性光学克尔效应可以作为一种全新的手段,在磁光晶体中实现近红外飞秒激光以太赫兹频率的超快偏振调控.这将在超快磁光调制器等全光器件中得以应用.实验结果将有助于偏振依赖的超快动力学过程的研究.     

Relation of vectorial structures of diffracted plane waves with the elliptical aperture configuration and the light polarization in the far field

The analytical vectorial structure of a linearly polarized plane wave diffracted by an elliptical aperture is studied in detail based on the vector angular spectrum representation. It is found that the energy flux density spot sizes and the energy fluxes of the TE and TM term depend on the elliptical aperture configuration and the polarization direction of the incident plane wave. And the far fields can have smaller spots and larger energy fluxes for an elliptical aperture compared to a circular aperture with the same input wave amplitude. And its potential application in information encoding and transmission for free space communications is proposed apart from re-focusing to enhance the optical storage density. This encoding scheme has the benefit of easy implementation without modulating any properties of the light source.     

An Algebraic Characterization of Vacuum States in Minkowski Space. III. Reflection Maps

Employing the algebraic framework of local quantum physics, vacuum states in Minkowski space are distinguished by a property of geometric modular action. This property allows one to construct from any locally generated net of observables and corresponding state a continuous unitary representation of the proper Poincaré group which acts covariantly on the net and leaves the state invariant. The present results and methods substantially improve upon previous work. In particular, the continuity properties of the representation are shown to be a consequence of the net structure, and surmised cohomological problems in the construction of the representation are resolved by demonstrating that, for the Poincaré group, continuous reflection maps are restrictions of continuous homomorphisms.     

Nonlinear polarization bistability in optical nanowires

Using the full vectorial nonlinear Schr?dinger equations that describe nonlinear processes in isotropic optical nanowires, we show that there exist structural anisotropic nonlinearities that lead to unstable polarization states that exhibit periodic bistable behavior. We analyze and solve the nonlinear equations for continuous waves by means of a Lagrangian formulation and show that the system has bistable states and also kink solitons that are limiting forms of the bistable states.     

Bessel beams: Effects of polarization

An approximation to a Bessel beam produced by tightly focusing linearly polarized light is known to produce a smaller central lobe than focusing plane polarized light. This is because the plane polarized wave gives a broad central lobe caused mainly by a parasitic longitudinal field component. It is known that this problem can be overcome by focusing radially polarized light. Here we demonstrate that other polarization distributions based on a linear combination of transverse electric (TE1) and transverse magnetic (TM1) fields can give a beam even narrower than for the radially polarized case. Special cases of this combination are identified, corresponding to the smallest width (TE1), and the maximum peak intensity compared with the side lobes (electric dipole polarization). Axially-symmetric forms can be generated by illumination with elliptically polarized light. A particular case is azimuthal polarization with a phase singularity, which is equivalent to TE1. For a semi-angular aperture of 60°, the TE1 case gives a central lobe width 9% narrower than for radially polarized illumination, while for plane polarized illumination it is 12% wider than the radially polarized case.     

The spatial polarization distribution over the dome of the sky for abnormal irradiance of the atmosphere

The paper deals with the polarized radiative transfer within a slab irradiated by a collimated infinitely wide beam of arbitrary polarized light. The efficiency of the proposed analytical solution lies in the assumption that the complete vectorial radiative transfer solution is the superposition of the most anisotropic and smooth parts, computed separately. The vectorial small-angle modification of the spherical harmonics method is used to evaluate the anisotropic part, and the vectorial discrete ordinates method is used to obtain the smooth one. The azimuthal expansion is used in order to describe the light field spatial distribution for the case of abnormal irradiance and to obtain some known neutral points in the sky especially useful for polarized remote sensing of the atmosphere.     

光学薄膜诱导偏振像差对大数值孔径光学系统聚焦特性的影响

大数值孔径光学系统表面光线的入射角较大, 会导致薄膜的偏振分离, 诱发偏振像差, 影响光学系统的聚焦特性. 本文利用矢量光衍射理论, 建立了光学薄膜各参量与光学系统聚焦光场的模型. 利用该模型分析了线偏振光入射时, 光学薄膜对光学系统聚焦光斑的扰动. 在此基础上, 探讨了应用了不同约束条件下得到的光学薄膜对最终聚焦光场的影响, 确定了减小薄膜扰动光学系统光斑的设计方法, 即额外添加透射率差和位相差的约束条件, 并且适当增加位相差约束的权重. 利用该方法优化设计的薄膜, 相比于普通减反膜而言, 对系统聚焦光场中心强度的提升可达约12.5%.     

Polarization beam splitters using polarization diffraction gratings

We report a polarization beam splitter that uses polarization gratings written onto a zero-twist nematic liquid-crystal display. We show three configurations. The first two separate the diffracted light into two orthogonally polarized orders that are either linearly or circularly polarized. In the third configuration, we demonstrate a novel case for which the output is separated into two nonorthonormal polarization states. One component is linearly polarized and the second is circularly polarized.     

The Imbert-Fedorov shift of paraxial light beams

We present a solution to the problem of reflection and transmission of a polarized paraxial light beam at an interface between two homogeneous media by using a two-form amplitude and an extension matrix to represent the vectorial angular spectrum of a three-dimensional (3D) light beam. We derive general formulas for the Imbert-Fedorov (IF) shift of the reflected and transmitted beams of a polarized paraxial light beam. The IF shift of two different types of polarized beams is calculated, and the influence of the polarization state and the polarization feature of the vectorial angular spectrum on the IF shift is discussed.     

Flexible Manipulation of the Polarization Conversions in a Structured Vector Field in Free Space

The conversion between different polarizations generally requires an optical element or an optical system. We demonstrate, theoretically and experimentally, that the conversion between different states of polarization (SoP) can be flexibly manipulated in a structured optical field by itself. During the structured optical field propagation in free space, any two orthogonal polarizations can be generated and auto‐focus at any desired propagation positions by purposely designing the initial SoP distribution and a caustic phase in the field cross‐section. The experiment arrangement combines a caustic‐based approach and a 4f optical system. This approach provides a way to flexibly manipulate the polarization conversions in free space propagation by the optical field itself (without any physical element along the propagation path), may lead to more complex and flexible vectorial manipulations of an optical field scenarios and potential applications in corresponding areas.     

Plane-parallel biaxial plates as polarization interferometers

Plane-parallel biaxial plates as polarization interferometers. Knowing the refractive indices and the directions of the rays inside a birefringent crystal, it is possible to calculate the positions of the images formed, when a non-parallel light beam incides on it.We part from general expressions for images in plane-parallel plates of any type of medium and we use vectorial expressions for the incident and refractive rays and waves in both interfaces.From them, we obtained the interference patterns which are observed when the plate is placed between two crossed polarizers. This experimental device constitutes a polarization interferometer. In order to find the shape of the interference patterns, we superposed the wave's fronts emerging from the images determining, in this way, the phase difference curves of phase constant on a screen.     

Transformation matrices for the Mueller-Jones formalism

The Mueller-Jones (MJ) or pure Mueller matrix formulation has been reported by using two different matrix transformations in a condensed representation. The possibility to find other transformation matrices is explored. A complete set of unitary operators (R) is found to be closely related with the MJ matrices and with the evolution of pure states on the Poincaré sphere surface. We propose an alternative deduction for the condensed representation of the MJ matrices, obtained by using the Kronecker product operation and use of R unitary matrices as a tool to combine different Mueller matrices and changes of polarized states on the Poincarè sphere surface. Finally, it is shown explicitly that the columns of the transformation matrices are the eigenvectors of the MJ matrix associated to a non-depolarizing optical system and a corollary is established as a criterion to differentiate a Mueller matrix from an MJ matrix.     

Representations of the Poincaré Semigroup and Relativistic Causality

This paper provides the mathematical tools for addressing issues of two kinds of causality in relativistic scattering theory: general causality, i.e., an effect can only be measured after its cause, and Einstein causality, i.e., no propagation of probability outside of the forward light cone. Starting from Wigner's unitary irreducible representations of the Poincaré group for noninteracting, one particle states, we describe the mathematical tools necessary to describe scattering states, the Lippmann-Schwinger Dirace kets, and to describe resonances and decaying states, the relativistic Gamow ket. An important step for their derivations is the Hardy space hypothesis. Investigating the transformation properties of scattering and resonance states under the dynamical Poincaré semigroup reveals that both kinds of causality result from this hypothesis about nature of the spaces of states and observables.     

Residual polarization of non-coherently backscattered linearly polarized light: the influence of the anisotropy parameter of the scattering medium

The effect of preservation of the residual polarization of backscattered light in the case of multiply scattered disordered media illumination by a linearly polarized plane wave is examined using the path-integral approach and Monte Carlo simulation. Disordered ensembles of non-interacting dielectric particles are considered as the model of scattering media. The influence of the anisotropy parameter of the scattering system on the degree of residual polarization is analysed. Experimental results obtained for various scattering systems at different wavelengths of illuminating light are in satisfactory agreement with the results of theoretical analysis and Monte Carlo simulation. The dependence of statistical properties of the polarization states of backscattered field partial components, such as probability distributions of ellipticity, on the anisotropy parameter is studied.