Vectorial Pauli algebraic approach in polarization optics. II. Interaction of light with the canonical polarization devices

A theoretical approach to the interaction between polarized light and polarization devices, based on the vectorial and pure operatorial form of the Pauli algebra, is presented. In the first part of the paper we have established the vectorial Pauli-algebraic forms of the operators corresponding to various polarization devices and states of light polarization. In this second part we give the vectorial Pauli-algebraic treatment of the interaction between the canonical polarization devices and the various forms of light polarization. Unlike the standard (Jones and Mueller) approaches, this formalism does not appeal to any matrix representation of the involved operators. This approach establishes a bridge between the Hilbert space of the density operators of the polarization states and the Poincaré space of their geometric representations and gives a rigorous justification of the handling of the interactions between the polarization states and polarization systems on the Poincaré sphere and in the Poincaré ball. In such an approach, unlike the standard ones, the three relevant quantities that characterize the interaction - the gain, the Poincaré vector of the outgoing light and its degree of polarization - result straightforwardly, in block. A generalized form of Malus’ law, for any dichroic device and partially polarized light is also obtained this way.     

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.     

偏振光的杨氏干涉

在基础光学框架内,通过杨氏双孔干涉实验中线偏振光的干涉及线偏振光经过两任意厚度晶片的干涉等几个实例,说明了基于矢量波叠加概念的电磁干涉的基本思想、基本分析方法和基本现象.偏振光干涉时,观测平面上可以出现或不出现光强的周期性空间调制,但一般都产生光场偏振态的周期调制.它表明了光的矢量性对干涉的重要影响,并可揭示只分析强度条纹时被掩盖的一些物理效应.     

Polarization of light and topological phases

The phase shifts experienced by a polarized light wave when it propagates through media with arbitrary birefringence, dichroism and depolarizing properties, while on the one hand provide the basis for a variety of optical devices and experiments, on the other provide a powerful means of understanding unitary evolution, nonunitary evolution and decoherence of two-state quantum systems by virtue of a mathematical isomorphism of the two systems. These also help understand aspects of evolution of classical systems under the group of rotations in three-dimensional space, namely the SO(3) group, by virtue of its homomorphism with the group SU(2) governing unitary evolution of polarized light waves. In this review we present a survey and analysis of recent work on topological phases with polarization of light which has revealed several counterintuitive features of such phase shifts such as 2nπ anholonomies, nonlinear and discontinuous behaviour originating hi singularities, peculiar spectral dependence, etc. We point out several areas where these results may find practical application, for example endless phase correction in interferometric sensors, fast switching spatial light modulators, phase shifters with unusual chromatic properties, phasing of antenna arrays, etc. Several useful theoretical insights relevant to polarization optics, quantum mechanics, classical mechanics and other areas of physics, obtained from the work on polarization states are described and some directions for future work are indicated.     

Generation and Manipulation of Spin-Orbit Coupling mode via Four-Wave Mixing with Quantum Interference

Recently, the vectorial nonlinear optical processes driven by spin-orbit coupling (SOC) light have come to the fore, leading to striking optical phenomena and important applications both in classical and quantum optics. However, research on the SOC-mediated light-atom interactions is still in its infancy. Here, the generation and manipulation of SOC mode through a vectorial four-wave mixing (FWM) process in ⁸⁵Rb vapor is demonstrated. Under the excitation of two SOC pump beams, multiple FWM paths can be simultaneously established due to the rich atomic Zeeman sublevels coupling with different circularly polarized components of SOC fields. A higher-order cylindrical or more general SOC FWM signal is observed in the vectorial FWM process, which obeys angular momentum conservation and Gouy phase matching. In particular, quantum interference between different FWM paths plays a crucial role in manipulating the SOC mode of the generated FWM signal, revealing that the conversion of SOC mode is intrinsically quantum. This work provides a pathway toward deeper insight into the vectorial nonlinear optical processes and may advance technology for shaping spatially structured light, which is essential in applications such as nonlinear polarization imaging and the optical communication realm.     

Structuring of photosensitive material below diffraction limit using far field irradiation

In this paper, we report on in-situ atomic force microscopy (AFM) studies of topographical changes in azobenzene-containing photosensitive polymer films that are irradiated with light interference patterns. We have developed an experimental setup consisting of an AFM combined with two-beam interferometry that permits us to switch between different polarization states of the two interfering beams while scanning the illuminated area of the polymer film, acquiring corresponding changes in topography in-situ. This way, we are able to analyze how the change in topography is related to the variation of the electrical field vector within the interference pattern. It is for the first time that with a rather simple experimental approach a rigorous assignment can be achieved. By performing in-situ measurements we found that for a certain polarization combination of two interfering beams [namely for the SP (?, ?) polarization pattern] the topography forms surface relief grating with only half the period of the interference patterns. Exploiting this phenomenon we are able to fabricate surface relief structures with characteristic features measuring only 140 nm, by using far field optics with a wavelength of 491 nm. We believe that this relatively simple method could be extremely valuable to, for instance, produce structural features below the diffraction limit at high-throughput, and this could significantly contribute to the search of new fabrication strategies in electronics and photonics industry.     

显微物镜聚焦光场任意三维偏振方向的控制

线性偏振光在显微物镜焦斑处入射,与径向偏振光相干叠加产生三维偏振光场,通过调节两束光光强比率和入射线偏振光偏振方向实现聚焦光场任意三维偏振方向的控制.基于矢量光场衍射理论建立了仿真计算模型,对所提三维偏振方向控制方法的可行性进行理论验证和实验评估.构建实际控制光路并进行初步测试,实验结果表明了该方法的可行性,且相比于其他三维偏振控制方法,本文所提方法和其控制光路更为简单易实现.     

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.     

All-Dielectric Multichannel Terahertz Metasurface Empowering Independent Wavefront Manipulation

Metasurfaces have demonstrated unprecedented capabilities in modulating the polarization and phase of electromagnetic waves and formed an emerging field of research, driving the exploitation of versatile compact devices. In this work, one transmission-mode, multichannel all-silicon metasurface platform that can implement functionalities separately in two orthogonally polarized output fields under linearly polarized incidences is proposed, which can effectively promote the design flexibility. Specifically, a single metasurface can realize multiple independent target phase distributions carrying specific phase relationships, thus enabling different information processing in different linear polarization states. For proof-of-principle experimental exhibitions, a monolayer metasurface composed of silicon pillars is designed, fabricated, and characterized to demonstrate the ability of multi-dimensional light field control, such as polarization-switchable focusing beam. Moreover, the other designed metasurface can generate polarization-switchable Bessel vortex beams under linearly polarized incidences, which also verifies the flexibility and practicality of such platform. This metasurface platform may lead to new optical components, involving multichannel singular beam generators, information encoders, and holographic encryption devices.     

Operator for describing polarization states of a photon in terms of Riemann-Silberstein quantized electromagnetic vector

Based on the quantized electromagnetic field described by the Riemann-Silberstein complex vector , we construct the eigenvector set of , which makes up an orthonormal and complete representation. In terms of we then introduce a new operator which can describe the relative ratio of the left-handed and right-handed polarization states of a polarized photon. In s eigenvector basis the operator manifestly exhibits a behaviour which is similar to a phase difference between two orientations of polarization of a light beam in classical optics. Received 8 January 1999 and Received in final form 26 July 1999     

Optical properties of polarization-dependent geometric phase elements with partially polarized light

The behavior of geometric phase elements illuminated with partially polarized monochromatic beams is investigated both theoretically and experimentally. The element discussed in this paper is composed of wave plates with π-retardation and a space-variant orientation angle. We found that a beam emerging from such an element comprises two polarization orders; right-and left-handed circularly polarized states with conjugate geometric phase modification. This phase equals twice the orientation angle of the space-variant wave plate comprising the element. Apart from the two polarization orders, the emerging beam coherence polarization matrix includes a “vectorial interference matrix” which contains information concerning the correlation between the two orthogonal, circularly polarized portions of the incident beam. In this paper we measure this correlation by a simple interference experiment. In addition, we found that the equivalent mutual intensity of the emerging beam is modulated according to the geometric phase induced by the element. Other interesting phenomena concerning propagation will be discussed theoretically and demonstrated experimentally. The experiment made use of a spherical geometric phase element that was realized by use of a space-variant subwavelength grating illuminated with CO₂ laser radiation of 10.6 μm wavelength.     

Biphotons,squeezing, and new states of light in polarization quantum optics

The concept of squeezing is discussed for multimode quantum light beams with consideration of polarization using the polarization gaugeSU (2) invariance of free electromagnetic fields. We separate the polarization and biphoton degrees of freedom from other ones, and consider uncertainty relations characterizing polarization and biphoton observables. As a consequence, we obtain a new classification of polarization states of light within quantum optics. We also discuss briefly some interrelations of our analysis with experiments related to some fundamental problems of physics.     

Propagation of polarized light in opals: Amplitude and phase anisotropy

The interaction of linearly polarized light with photonic crystals based on bulk and thin-film synthetic opals is studied. Experimental transmission spectra and spectra showing the polarization state of light transmitted through opals are discussed. A change in polarization is found for waves experiencing Bragg diffraction from systems of crystallographic planes of the opal lattice. It is shown that the polarization plane of the incident linearly polarized wave at the exit from photonic crystals can be considerably rotated. In addition, incident linearly polarized light can be transformed to elliptically polarized light with the turned major axis of the polarization ellipse. Analysis of polarization states of transmitted light by using the transfer-matrix theory and homogenization theory revealed good agreement between calculated and experimental spectra.     

偏光全息研究历程与展望

全息是目前一项极具前景的科学技术,即通过信号光和参考光的干涉,在小小的全息图上记录丰富的信息。相比于传统全息仅记录光波的相位、振幅信息,偏光全息可以将额外的偏振信息记录于偏振态敏感材料中。本文从偏光全息材料入手,详细介绍了偏光全息生产过程;同时介绍基于琼斯理论和张量理论的偏光全息原理和研究进展;最后描述了偏光全息在全息存储和纳米光学领域的发展前景。     

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.     

Polarization and Color Separator Using Binary Phase Grating with Subwavelength Period

A data projector using three liquid crystal display panels has a complex optical system. The illuminating optics separate the beam from a light source into three primary colors and separate those into opposite polarizations using multi-layer films and prisms. A reflection grating with the period of subwavelength has high diffraction efficiency for p polarized light and high regularly reflectance for s polarized light. The diffraction angle of a grating largely depends on the wavelength, because a diffractive optical element (DOE) has large chromatic dispersion. The grating with the period of subwavelength can separate the unpolarized light into polarization components effectively using its polarization dependency and can separate white light into color components using its chromatic dispersion simultaneously. The grating makes the optical system simpler and smaller than those with conventional devices. In this paper the efficiency of polarization separation for the grating is calculated by a rigorous analytical method. Next, the condition for color separation is calculated by Snell#x0027;s law, and an optical system using a grating that performs polarization and color separation is proposed. Experimental results of the DOE fabricated are well matched with those of this simulation.     

The polarized frozen core approximation: Energies and oscillator strengths of C(I) and N(II)

The frozen core and extended frozen core versions of the Hartree-Fock approximation have been improved significantly by means of l-dependent core polarization potentials. The resulting polarized frozen core procedure reproduces most of the observed 2pns, 2pnp and 2pnd terms of C(I) and N(II) with great accuracy; over 60 unobserved terms in N(II) have been calculated, which should prove sufficiently reliable for future identification purposes. Length and velocity forms of electric dipole oscillator strenghts, calculated with these polarized orbitals and the corresponding energies, are generally in excellent agreement, particularly for transitions between the more highly excited states.