Three-dimensional polarization states of monochromatic light fields

The 3×1 generalized Jones vectors (GJVs) [E(x) E(y) E(z)](t) (t indicates the transpose) that describe the linear, circular, and elliptical polarization states of an arbitrary three-dimensional (3-D) monochromatic light field are determined in terms of the geometrical parameters of the 3-D vibration of the time-harmonic electric field. In three dimensions, there are as many distinct linear polarization states as there are points on the surface of a hemisphere, and the number of distinct 3-D circular polarization states equals that of all two-dimensional (2-D) polarization states on the Poincaré sphere, of which only two are circular states. The subset of 3-D polarization states that results from the superposition of three mutually orthogonal x, y, and z field components of equal amplitude is considered as a function of their relative phases. Interesting contours of equal ellipticity and equal inclination of the normal to the polarization ellipse with respect to the x axis are obtained in 2-D phase space. Finally, the 3×3 generalized Jones calculus, in which elastic scattering (e.g., by a nano-object in the near field) is characterized by the 3-D linear transformation E(s)=T E(i), is briefly introduced. In such a matrix transformation, E(i) and E(s) are the 3×1 GJVs of the incident and scattered waves and T is the 3×3 generalized Jones matrix of the scatterer at a given frequency and for given directions of incidence and scattering.     

Homodyne tomography of classical and non-classical light

Abstract

States with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analysed by tomographical methods. Wigner functions, photon-number distributions, density matrices and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub-Poissonian and super-Poissonian photon statistics, bifurcations of the phase distribution, and loss of coherence were observed, demonstrating the usefulness of quantum state reconstruction as an analysing tool in quantum optics experiments.     

Generation of amplitude squeezed states of light from phase squeezed coherent states

Abstract

We propose a scheme to generate a displaced macroscopic superposition of phase squeezed coherent states by incorporating an optical parametric oscillator (OPO) and a nonlinear Kerr medium in a Mach-Zhender interferometer configuration. We show that the phase squeezed coherent state generated by the OPO evolves into a macroscopic superposition of phase squeezed coherent states on spending a specific amount of time inside a Kerr medium. The phase space displacement is achieved by the interference of the intense reference beam with the signal in the final beam splitter of the interferometer. The noise of the reference beam contaminating the signal is prevented by making this beam splitter highly reflective. We have calculated the photon number uncertainty of the outcoming beam and have shown that it is smaller than the usual amplitude squeezed coherent state's value.     

Measurements and simulations of polarization states of underwater light in clear oceanic waters

Polarization states of the underwater light field were measured by a hyperspectral and multiangular polarimeter and a video polarimeter under various atmospheric, surface, and water conditions, as well as solar and viewing geometries, in clear oceanic waters near Port Aransas, Texas. Some of the first comprehensive comparisons were made between the measured polarized light, including the degree and angle of linear polarization and linear Stokes parameters (Q and U), and those from Monte Carlo simulations that used concurrently measured water inherent optical properties and particle volume scattering functions as input. For selected wavelengths in the visible spectrum, measured and model-simulated polarization characteristics were found to be consistent in most cases. Measured degree and angle of linear polarization are found to be largely determined by an in-water single-scattering model. Model simulations suggest that the degree of linear polarization (DoLP) at horizontal viewing directions is highly dependent on the viewing azimuth angle for a low solar elevation. This implies that animals can use the DoLP signal for orientation.     

Quantum limits for minimum-uncertainty (MU) angular momentum polarization squeezed states

It is shown that there are certain quantum limits to angular momentum minimum-uncertainty (MU) obtained by polarization squeezing Hamiltonians, beyond which the MU cannot be realized. The analysis is made for two cases: (a) when a strong coherent state is in one mode and a squeezed vacuum is in the other mode. (b) For the interference between two optical modes which are amplitude squeezed, with equal squeezing and intensities’ magnitudes.     

Circular and near-circular polarization states of evanescent monochromatic light fields in total internal reflection

Conditions for the production of near-circular polarization states of the evanescent field present in the rarer medium in total internal reflection of incident monochromatic p-polarized light at a dielectric-dielectric planar interface are determined. Such conditions are satisfied if high-index (>3.2) transparent prism materials (e.g., GaP and Ge) are used at angles of incidence well above the critical angle but sufficiently below grazing incidence. Furthermore, elliptical polarization of incident light with nonzero p and s components can be tailored to cause circular polarization of the resultant tangential electric field in the plane of the interface or circular polarization of the transverse electric field in a plane normal to the direction of propagation of the evanescent wave. Such polarization control of the evanescent field is significant, e.g., in the fluorescent excitation of molecules adsorbed at solid-liquid and solid-gas interfaces by total internal reflection.     

Method of determining the phase center of an antenna using polarization measurements

A method of determining the single or partial phase center of an antenna using polarization measurements at two points of the radiation field in the antenna for zone is proposed. The method is based on a determination of the directions of the Poynting vector at these points. An example of the determination of the phase center of an antenna with a known axis is given. Translated from Izmeritel'naya Tekhnika, No. 4, pp. 55–57, April, 1998.     

Analytical description of backscattered states of polarization in polarization optical time-domain reflectometry measurements on uniformly twisted linearly birefringent optical fiber

We present a detailed derivation of the locus of Rayleigh backscattered states of polarization for polarization optical time domain reflectometry in uniformly twisted optical fiber with intrinsic linear birefringence. The locus is algebraically a quartic whose topology is determined by the relative orientation on the Poincaré sphere of the input SOP and the effective birefringence vector. We present an analysis that indicates how experimental data may be interpreted, through geometric parameters of the locus, for evaluating the fiber parameters. The analysis also indicates the minimum number of experimental data points required for meaningful values for the fiber parameters to be obtained.     

Heterodyne measurements of laser light scattering by a turbulent phase screen

We report experiments in which a fiber-coupled heterodyne laser system operating at a wavelength of 1.5 microm is used to measure the phase fluctuations induced on a laser beam by passage through a thin layer of turbulent air and subsequent propagation through free space. We investigate the statistical properties and power spectra of the phase and its rate of change, in addition to the intensity statistics. We find that the power spectrum of the rate of change of phase has a simple negative exponential form. We discuss our results in the context of the problem of detection of phase variations over an extended turbulent atmospheric path.     

Mixture of two-mode unpolarized and pure quantum light states: quantum polarization and application in quantum communication

Quantum polarization is an important property that has been extensively used for quantum communication purposes. In this work, the mixture of an unpolarized two-mode state and a two-mode pure state is analysed. This mixture is controlled by a single parameter, namely the degree of purity. The quantum polarization of the two-mode mixed state is discussed using the quantum Stokes parameters and the quantum degree of polarization. A relation between the degree of purity and the quantum degree of polarization is established. The mixture is used to model coherent light amplified by an erbium-doped fibre amplifier, which focuses the loss of polarization due to the unpolarized light resulting from spontaneous emission. Finally, the use of such a mixed state in the quantum key distribution using multiphoton pulses is analysed.     

Some non-classical properties of a class of new nonlinear coherent states

Some of the properties of a nonlinear coherent state associated with the centre of mass motion of trapped atoms are considered. Especially the autocorrelation function, motional quanta number distribution, the phase properties, the Husimi–Kano Q function and the Wigner–Moyal W function of this nonlinear coherent state are discussed. Jumps in the motional quanta distribution function are reported depending on the dependence on the Lamb–Dicke parameters.     

Generating non-classical light inside an optical cavity by depositing photons

The creation of non-classical states of light is an interesting problem, that we solve sending atoms through an optical cavity. We show that it is possible to add or subtract many photons from a cavity field by interacting it resonantly with a two-level atom. The atom, after entangling with the field inside the cavity and exiting it, may be measured in one of the Schmidt states, producing a multiphoton process (in the sense that can add or annihilate more photons than a single transition allows), i.e. adding or subtracting several photons from the cavity field. By plotting the quadratures and the Husimi Q-function, we also show that the non-classical state produced by such measurements is a squeezed state.     

Conditional generation of non-classical states in a non-degenerate two-photon micromaser: Equal-intensity pair-Fock states preparation. I

Abstract

We present the theory underlying a new experimental scheme for the preparation of selected number states of a bimodal high-Q microcavity. The practical feasibility of this method is carefully discussed. In particular we take explicitly into account the existence of fluctuations of the atom–field interaction times as well as the possibility of imperfect atomic detection.     

Intensity and phase measurements of nondiffracting beams generated with a magneto-optic spatial light modulator

Nondiffracting beams are of interest for optical metrology applications because the size of the beam does not change as the beam propagates. However, accuracy can be increased if the diameter of the beam is smaller. One technique for accomplishing this is to use the dark axial intensity profile associated with a higher-order nondiffracting Bessel function beam. We generate these higher-order Bessel function beams with a programmable spatial light modulator. We study the intensity patterns and the phase dependence of these nondiffracting beams. In addition, we examine interference effects caused by recording these patterns onto a binary spatial light modulator.     

Conditional generation of non-classical states in a non-degenerate two-photon micromaser: Single-mode fock states preparation. II

Abstract

A conditional generation of single-mode Fock states in the framework of a non-degenerate two-photon micromaser theory is reported. The exact expression for the probability of success of the experiment is obtained. We show that it is possible to conjugate experimentally interesting values of this probability, with the generation of number states having a controllable high intensity. This objective is reached by constructing analytically detailed rules about the cavity state at t = 0 as well as the atom–field interaction times as functions of the available operating conditions. These rules play a central role in our Fock-state-building process, leading to an essential countering of the Stark-shift-induced detuning effects. The practical reliability of the proposal is carefully discussed from several points of view. Some possible applicative potentialities of our scheme are briefly pointed out.     

Quantum properties and dynamics of X states

X states are a broad class of two-qubit density matrices that generalize many states of interest in the literature. In this work, we give a comprehensive account of various quantum properties of these states, such as entanglement, negativity, quantum discord and other related quantities. Moreover, we discuss the transformations that preserve their structure both in terms of continuous time evolution and discrete quantum processes.     

Halfwave retarder for all polarization states

We show that a device consisting of an optical rotator placed between two identically oriented quarter-wave plates always acts as a halfwave retarder for some pair of orthogonal elliptically polarized states that can be selected by linear adjustment of the optical rotation and orientation of the quarter-wave plates.     

Quantum mechanical law of corresponding states

The structure and thermodynamic properties of the quantum liquids ⁴He and H₂ near the liquid-gas critical point are calculated with the effective potential approximation, in which the two-body Slater sum replaces the Boltzmann factor; the statistical mechanics problem is formally equivalent to that of a fictitious classical fluid. Approximate integral equation methods from the theory of classical fluids are then used to calculate the critical point parameters and the radial distribution function g(r). The results from the approximate integral equations are compared both with experimental data and with the results of an exact Monte Carlo calculation for the fictitious fluid for a range of densities at the temperatures 7 and 8 K in ⁴He and 36 and 40 K in H₂.Work supported in part by the National Science Foundation.Work supported in part by the National Research Council of Canada.Work supported in part by the National Science Foundation Award No. SMI77-17458.     

Quantum theory of light diffraction

At present, the theory of light diffraction only has the simple wave-optical approach. In this paper, we study light diffraction with the relativistic quantum theory approach. We find that the slit length, slit width, slit thickness and wavelength of light affect the diffraction intensity and form of diffraction pattern. However, the effect of slit thickness on the diffraction pattern cannot be explained by wave-optical approach, but it can be explained in quantum theory. We compare the theoretical results with single- and multiple-slits experimental data, and find the theoretical results are in accordance with the experimental data. In addition, we give some theory predictions. We think all new predictions will be tested by the light diffraction experiment.