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.     

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.     

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.     

Quantum theory as a description of robust experiments: Derivation of the Pauli equation

It is shown that the Pauli equation and the concept of spin naturally emerge from logical inference applied to experiments on a charged particle under the conditions that (i) space is homogeneous (ii) the observed events are logically independent, and (iii) the observed frequency distributions are robust with respect to small changes in the conditions under which the experiment is carried out. The derivation does not take recourse to concepts of quantum theory and is based on the same principles which have already been shown to lead to e.g. the Schrödinger equation and the probability distributions of pairs of particles in the singlet or triplet state. Application to Stern–Gerlach experiments with chargeless, magnetic particles, provides additional support for the thesis that quantum theory follows from logical inference applied to a well-defined class of experiments.     

Analytical treatment of light extraction from textured surfaces using classical ray optics

Regular periodic textures e.g., microlens arrays, micro-pyramids, and cones on substrate surface have been used to enhance light out-coupling in light emitting devices. Photon randomization, often associated with surface roughening, has been suggested as the mechanism for out-coupling enhancement. This article analytically investigates the ray dynamics in a light emitting device when periodic texture is used as an external out-coupler. An attempt has been made to understand the relationship between enhancement in out-coupling and the surface inclination of these structures using classical ray optics.     

A note on the Pauli problem in light of approximate joint measurements

We show that there exist informationally incomplete phase space observables such that the Cartesian margins are informationally equivalent with position and momentum. This shows that it is possible to reconstruct the position and momentum distributions of a quantum system from the statistics of a single observable, and thus a single measurement, even though the state of the system is not uniquely determined by the statistics.     

Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method

A new physical-geometric optics hybrid (PGOH) method is developed to compute the scattering and absorption properties of ice particles. This method is suitable for studying the optical properties of ice particles with arbitrary orientations, complex refractive indices (i.e., particles with significant absorption), and size parameters (proportional to the ratio of particle size to incident wavelength) larger than ∼20, and includes consideration of the edge effects necessary for accurate determination of the extinction and absorption efficiencies. Light beams with polygon-shaped cross sections propagate within a particle and are traced by using a beam-splitting technique. The electric field associated with a beam is calculated using a beam-tracing process in which the amplitude and phase variations over the wavefront of the localized wave associated with the beam are considered analytically. The geometric-optics near field for each ray is obtained, and the single-scattering properties of particles are calculated from electromagnetic integral equations. The present method does not assume additional physical simplifications and approximations, except for geometric optics principles, and may be regarded as a “benchmark” within the framework of the geometric optics approach. The computational time is on the order of seconds for a single-orientation simulation and is essentially independent of the size parameter. The single-scattering properties of oriented hexagonal ice particles (ice plates and hexagons) are presented. The numerical results are compared with those computed from the discrete-dipole-approximation (DDA) method.     

光学教学中的偏振度定义

分析了当前国内部分光学教材中对偏振度定义的歧义,指出依照电矢量在不同方向上的强度来定义偏振度的不完整性,并由此提出教学中的注意点．     

The effect of the counter-rotating terms on the dynamical behaviour in the coherent-state jaynes-cummings model with cavity losses

Summary The effect of the counter-rotating terms in the coherent-state Jaynes-Cummings model with cavity losses is studied. Numerical results for the atomic-population inversion show a significant influence of the counter-rotating terms on the dynamical behaviour.     

A deterministic method study of the impact of the Pauli principle in double-gate MOSFETs

The Pauli principle is included in a multisubband deterministic solver for two-dimensional devices without approximations.The nonlinear Boltzmann equations are treated properly without compromising on accuracy,convergence,or CPU time.The simulation results indicate the significant impact of the Pauli principle on the transport properties of the quasi-2D electron gas,especially for the on state.     

Enhancement of spin polarization in asymmetrically coupled CdSe and CdZnMnSe quantum dots in ZnSe matrix

An asymmetrically coupled double quantum dot (QD) system consisting of adjacent CdSe and CdZnMnSe QD layers in a ZnSe matrix was investigated using polarization-selective magneto-photoluminescence (PL). Two well-resolved PL peaks are observed corresponding, respectively, to the CdSe and the CdZnMnSe QDs. The peaks exhibit significant change in the intensity and energy position when a magnetic field is applied. The enhancement of the degree of σ⁻ circular polarization emitted by the non-magnetic CdSe QDs is observed in the double layer system, as compared to that observed in CdSe QDs without the influence of neighboring CdZnMnSe QDs. This behavior was discussed in terms of antiferromagnetic interaction between carrier spins localized in pairs of CdSe and CdZnMnSe QDs that are electronically coupled.     

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators.     

Generation and detection of spin polarization in parallel coupled double quantum dots connected to four terminals

A four-terminal parallel double quantum dots (QDs) device is proposed to generate and detect the spin polarization in QDs. It is found that the spin accumulation in QDs and the spin-polarized currents in the upper and down leads can be generated when a bias voltage is applied between the left and right leads. It is more interesting that the spin polarization in the QDs can be detected using the upper and down leads. Moreover, the direction and magnitude of the spin polarization in the QDs, and in the upper and down leads can be tuned by the energy levels of QDs and the bias.     

Differential algebraic method for computing the high order aberrations of practical electron lenses

Differential algebraic method is of an effective technique in computer numerical analysis. It implements exactly differentiation up to arbitrary high order based on the nonstandard analysis. Some complicated nonlinear dynamics problems including high order aberrations of electron optics systems can be solved by mapping properties of differential algebraic quantities. However, the existing electron optical differential algebraic method can only be applied to those problems where the electric and/or magnetic fields are expressed in analytic forms. In this paper, the principle of differential algebraic method is applied to practical electron lenses whose electric/magnetic fields are in the forms of discrete arrays, for example, the files computed by FEM or FDM method. Thus the developed new differential algebraic method is applicable to engineering design. The programs were written for computing the high order aberrations of practical electron lenses. An example is given to show that the numerical results have good accuracy compared with the results computed by using the electric fields expressed in analytical form; the accuracy is limited only by the accuracy of the numerical computation of the fields and the arithmetic errors, and it is enough for engineering design.     

Strong Pauli paramagnetic effect in the upper critical field of KCa2Fe4As4F2

Recently, 12442 system of Fe-based superconductors has attracted considerable attention owing to its unique double-Fe As-layer structure. A steep increase in the in-plane upper critical field with cooling has been observed near the superconducting transition temperature, Tc, in KCa2Fe4As4F2 single crystals. Herein, we report a high-field investigation on upper critical field of this material over a wide temperature range, and both out-of-plane(H∥c, Hc2c) and in-plane(H∥ab, Hc2ab ) directions have been measured.A sublinear temperature-dependent behavior is observed for the out-of-plane Hc2c , whereas strong convex curvature with cooling is observed for the in-plane Hc2ab . Such behaviors could not be described by the conventional Werthamer-Helfand-Hohenberg(WHH) model. The data analysis based on the WHH model by considering the spin aspects reveals a large Maki parameter α=9,indicating that the in-plane upper critical field is affected by a very strong Pauli paramagnetic effect.     

TracePro在“光的偏振实验”中的应用

为提高光的偏振实验教学效果和教学质量,在教学中引入专业的光学设计软件--TracePro,利用该软件仿真了光的双折射过程和现象,以及偏振片的原理;建立光的偏振实验系统实体模型,完成光的偏振态判断实验;仿真光通过波片后的偏振态转换现象;验证马吕斯定律,并仿真了多层介质膜对光的分离和旋光现象.结果表明该方法可以提高教学效率,激发学生探索科学的主观能动性,仿真结论与理论推导和实际实验结果一致.     

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.