Quantum Fluctuations in the Stokes Parameters of Light Propagating in a Kerr Medium

Abstract

The quantum theory of light propagation in a nonlinear Kerr medium is applied to calculate the Stokes parameters and their variances in the process of light propagation. Exact quantum formulae are derived for the expectation values of the Stokes operators and thus for the azimuth θ and ellipticity η of the beam. The role of quantum fluctuations in light polarization characteristics is discussed. The periodic behaviour of quantum evolution of the light polarization is revealed explicitly. It is shown that the degree of polarization is diminished at early stages of each period of the evolution but then reverts to its initial state of complete polarization at the end of the period. The variances of the Stokes parameters are also periodic and intensity-dependent; however, they never fall below their coherent state values.     

Quantum phase measurements and non-classical polarization states of light

Abstract

In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.     

Spinor–electron waveguided optics based on the Dirac equation

A preliminary quantum analysis, based on the Dirac equation, of the propagation of spinor–electron waves in electron waveguides is presented. The wave equations for spin-up (SU) and spin-down (SD) electron waves in electron guides are derived and their analogy with TE and TM light modes in dielectric guides is stressed. The spinor–electron waveguided propagation in a electron wave slab waveguide is solved exactly using the Dirac equation, that is, the exact amplitudes and dispersion equations of the spinor–electron waveguided modes are calculated. The main consequences related to the spinor modal structure are discussed: phase retardations (spin polarization), modal cutoff conditions and the non-relativistic limit.     

Beam modes in graded-index media and topological phases

The change in the polarization plane of light vector beams retaining their shape (beam modes) under propagation through gradient-index media is evaluated as a topological phase acquired by cyclic and noncyclic evolutions of these beams on their projective Hilbert space (momentum sphere). The polarization changes are evaluated by means of the characteristic parameters of the light beam selected.     

Polarization Splitting Coupler with Metal Intermediate Layer Theoretical Analysis

Abstract

An analytical model of the polarization splitting coupler with a metal intermediate layer is presented. Fields and propagation constants of the coupler modes are found assuming some specific form of the mode fields. Attenuation characteristics of the coupler are calculated in terms of the local normal mode method.     

Superposition Phases and Squeezing

Abstract

Quadrature variances of a radiation field depend not only on the photon number distribution in the field but also on the relative phases of the photon number probability amplitudes. Two fields with the same photon number distribution can show different degrees of squeezing if photon number states are superposed with different relative phases. It is thus possible, for example, for a radiation field with Poissonian photon statistics to exhibit squeezed quadrature fluctuations. Since different relative superposition phases in general yield different maximum and minimum values of the quadrature variances, measurement of the variances can yield information concerning the relative phases between different number states.     

Polarization Aberration Effects Propagated in Optical Systems

Abstract

The propagation and imaging of polarized light through optical systems described by a polarization aberration expansion is treated by combining a scalar operator calculus with the Jones calculus. The martrix-operator framework provides a means for handling diffraction and propagation in optical systems containing polarization aberrations. An expansion for the polarization aberration function of an optical system, similar to the expansion of the wavefront aberration function into defocus, tilt, piston, and higher-order terms, is analysed. These polarization aberration terms introduce phase changes in the diffraction image proportional to the first and second derivatives of the non-polarization aberrated image structure.     

Some Comments on Designs for Cox's Mixture Polynomial

Designs are suggested for estimating the restricted parameters in Cox's mixture polynomial. The variances of the restricted estimates of the parameters are minimum when using the simplex-lattice designs suggested by Scheffé The precision of the estimates, in terms of their variances, as affected by the location of the design points as well as the location of the standard mixture s is also discussed. It is shown for the vertex design centered at s that if s is positioned on the axis of an individual component, the closer s lies to the vertex of the simplex representing the individual component, the more precise will be the parameter estimates associated with the individual component relative to the other components. A numerical example is presented to illustrate the difference in the interpretations given to the parameter estimates associated with the Cox polynomial and the Scheffé polynomial.     

Squeezing in Second-harmonic Generation

Abstract

The production of squeezed states in second-harmonic generation is discussed theoretically from the viewpoint of the structure of the nonlinear medium, phase-matching conditions, and the polarization state of the fields. The nonlinear coupling constants are derived in explicit form for all 102 magnetic symmetry groups for crystalline as well as electrically polarized isotropic media. The phase-matching conditions are discussed in detail. Phase mismatch is shown to accumulate along the optical path, and is calculated in full detail for various media and geometries. We refer to this as the mismatch accumulation effect. General formulae for normally ordered variances of the second-harmonic and fundamental fields are derived by perturbative procedure, and are specified for some special cases of practical interest.     

Time Evolution for a Three-level Atom in Interaction with Two Modes

Abstract

The problem of a three-level atom and two modes is treated quantum mechanically and constants of motion are obtained. The evolution operator is calculated for the case of exact two-photon resonance. The probability distribution functions are calculated for the atom in one of its states. Some statistical quantities of the fields and the atomic systems are given. The interaction with squeezed light is investigated.     

Theoretical study of surface acoustic waves in (n11) GaAs-cuts

The propagation characteristics of true and leaky or pseudo surface acoustic waves (TSAW and PSAW=LSAW) on (n11) GaAs-cuts, n=1, 2, 3 and 4, are theoretically calculated as a function of propagation direction. They include phase velocity (V), electromechanical coupling constant (K(2)), and attenuation factor (alpha) of wave propagation on a metallized surface. The results show that PSAW mode velocities are significantly higher than corresponding TSAW velocities, and for certain propagation directions the attenuation factor is extremely small (10(-5) dB/lambda). Highly coupled PSAW modes exist for propagation directions where the TSAW are very poorly coupled. For certain isolated directions, attenuation of the wave is null (alpha=0), PSAW becoming a non-leaky SAW with partial polarization. And in this case the corresponding TSAW are decoupled from the surface electric excitation. Analysis of relations between various modes (TSAW, PSAW and SSBW, surface skimming bulk wave) is made with the help of the effective surface permittivity function and the generalized slowness diagram. A coupling constant definition different from the usual 2DeltaV/V is used, its validity and application conditions are discussed.     

Measuring the phase variance of light

Abstract

The results of experiments designed to measure the operational phase cosine and sine variances of weak states of light disagree with the variances predicted by canonical phase formalisms. As these variances are fundamental manifestations of the quantum nature of phase, it is important to be able to measure the canonical variances also. A recent suggestion to do so, based on the use of a two-component probe, involves the difficult preparation of exotic states of light which have not yet been produced. In this paper we show how the variances can be measured with simple coherent state inputs. The retrodictive formalism of quantum mechanics provides useful insight into the physics involved.     

Changes in Polarization of a Light Beam with Arbitrary Autocoherence Propagating in a Birefringent Crystal

Based on the Mueller-Stokes matrix formalism and the Wolf autocorrelation functions, a general approach is developed for studying the polarization characteristics of a light beam with arbitrary autocoherence during its interaction with various media. This makes it possible to take into account the dispersion of the medium and the coherence properties of the light field. It is shown that the propagation of a polychromatic light beam with spectrally pure polarization in a certain medium can be described by an integrated Mueller matrix. For a linear phase plate, the matrix elements can be expressed by means of the modulus and the phase of the complex degree of autocoherence. The polarization of a light beam emitted by a black-body radiator and the influence of the dispersion in a KDP crystal in quasi-monochromatic light are discussed as applications.     

Phase auto-compensating high-dimensional quantum cryptography in elliptical-core few-mode fibres

High-dimensional quantum cryptography through optical fibres with several spatial modes requires an efficient quantum key distribution (QKD). However, optical modes acquire different phases and lags due to modal dispersion and random fluctuations, and a modal crosstalk appears under propagation. At present, special optical fibres for spatial multiplexing are being proposed in order to reduce notably the modal crosstalk, however, arbitrary relative phases and lags between modes are always present, which prevents getting an efficient phase encoding QKD. In this work, we take advantage of elliptical-core few-mode optical fibres presenting a very low modal crosstalk and propose an exact phase auto-compensating method by making photons travel several times the path between Alice and Bob (rounds) and by using appropriate modal inversions in each round trip. In order to make clear the proposed phase auto-compensating method, we study in detail a four-dimensional BB84 QKD case with single photon states excited in both polarization and spatial LP modes.     

Photonic metamaterials: a new class of materials for manipulating light waves

Abstract

A decade of research on metamaterials (MMs) has yielded great progress in artificial electromagnetic materials in a wide frequency range from microwave to optical frequencies. This review outlines the achievements in photonic MMs that can efficiently manipulate light waves from near-ultraviolet to near-infrared in subwavelength dimensions. One of the key concepts of MMs is effective refractive index, realizing values that have not been obtained in ordinary solid materials. In addition to the high and low refractive indices, negative refractive indices have been reported in some photonic MMs. In anisotropic photonic MMs of high-contrast refractive indices, the polarization and phase of plane light waves were efficiently transformed in a well-designed manner, enabling remarkable miniaturization of linear optical devices such as polarizers, wave plates and circular dichroic devices. Another feature of photonic MMs is the possibility of unusual light propagation, paving the way for a new subfield of transfer optics. MM lenses having super-resolution and cloaking effects were introduced by exploiting novel light-propagating modes. Here, we present a new approach to describing photonic MMs definitely by resolving the electromagnetic eigenmodes. Two representative photonic MMs are addressed: the so-called fishnet MM slabs, which are known to have effective negative refractive index, and a three-dimensional MM based on a multilayer of a metal and an insulator. In these photonic MMs, we elucidate the underlying eigenmodes that induce unusual light propagations. Based on the progress of photonic MMs, the future potential and direction are discussed.     

Thermodynamic assessment of Sb–Sn system

Abstract

The Sb–Sn system has been assessed in terms of thermodynamic models for the individual phases. Expressions for the Gibbs energy as a function of temperature and composition are obtained and both phase diagram and thermochemical data are calculated and found to be in good agreement with the experimental data. The compound phase SbSn is treated by means of a Bragg–Williams–Gorsky approach.

MST/421     

Far zone spectral shifts in light propagation from the exit face of a few-mode fibre waveguide guiding the frequency-dependent linearly polarized modes

Abstract

Far zone spectral shifts, including free space propagation of light from a planar secondary, partially coherent source represented by the exit face of a few-mode fibre waveguide, are investigated in the paraxial regime by using frequency-dependent linearly polarized (LP) modes guided by the fibre waveguide. The origin of the far zone blue or red spectral shift of individual frequency-dependent LP modes, as well as of their superposition at the particular observation point, is clarified. In particular, the dependence of the wavelength shifts of spectra on the position of the observation point in the far zone plane and the primary source linewidth is studied for the two-mode, weakly guiding, step-index fibre waveguide.     

Mueller matrix analysis of infrared ellipsometry

A Mueller analysis has been done of IR ellipsometry performed with imperfect optical components. Equations linking experimental and calculated Fourier coefficients have been derived and consistently solved. Correction routines for permittivity measurements are demonstrated and discussed with gold and SrTiO(3) as examples. It is shown that such effects as interferometer polarization, detector dichroism, transmission, and phase changes in polarizers can be calculated and effectively removed from the spectra. The problems of calibration and multiple reflections between IR polarizers are discussed, and error propagation in permittivity measurements is analyzed.     

Quantum statistics and dynamics of nonlinear couplers

Abstract

We investigate both codirectional and contradirectional nonlinear couplers composed of two nonlinear waveguides operating by second-harmonic generation. We take into account possible mismatches inside the waveguides and between them. We calculate the photon number distribution, its factorial moments, quadrature and integrated intensity variances and quadrature uncertainty product taking into account the effects of transmission of light between waveguides. Incident beams are assumed to be coherent, squeezed and mixed with external noise. Second-harmonic modes are assumed to be pumped with strong coherent beams. We show that non-classical behaviour of beams generated by the nonlinear waveguides can be transferred between them and controlled by linear and nonlinear mismatches. In the contradirectional regime of propagation, asymptotic non-classical states can be generated.     

Highly convergent focusing of light based on rotating dipole polarization

Focusing properties of transverse circular polarization modes that bring light to a small focal spot are investigated. Two particular illumination polarization distributions are discussed. Rotating electric dipole polarization results in a central lobe diameter 8% smaller than for the circularly polarized aplanatic case at a NA of 0.95 in air and is also smaller than for radial polarization at NAs less than 0.90. Azimuthal polarization with a phase singularity of charge unity results in a small central lobe width that is smaller than that produced by focusing radially polarized light, having a width that is 17% smaller than for circularly polarized illumination at a NA of 0.95.