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.     

Phase Properties of Elliptically Polarized Light Propagating in a Kerr Medium

Abstract

Phase properties of elliptically polarized light propagating through a nonlinear Kerr medium are considered within the framework of the Pegg-Barnett Hermitian phase formalism. The joint phase probability distribution function for the phases of two orthogonal modes describing elliptical polarization of the field is calculated and its evolution discussed and illustrated graphically. The marginal phase probability distribution for the individual phases are also calculated and discussed. Analytical formulae for phase expectation values and variances are derived for the individual phases as well as for the phase difference. It is shown that in the course of propagation the correlation between the phases of the two modes builds up. This correlation is responsible for lowering phase difference variance. The expressions for the sine and cosine functions and their variances of the individual phases as well as the phase difference are obtained and discussed. The effect of randomization of individual phases and the phase difference, which is a purely quantum effect, is shown to appear during propagation. The relation between phase randomization and degradation of the degree of polarization of the light is established.     

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.     

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.     

Influence of the quantum uncertainty on the two-beams approach of reconstruction for one-photon mixed states of partially polarised light

Abstract

In this paper we discuss the reconstruction process of one-photon mixed states of partially polarised light. To solve this issue, we obtain the Stokes parameters by means of the degree of polarisation. The density operator describing the examined state is represented with these parameters. In the proposed two-beams method the degree of polarisation is measured on the analysed beam combined with reference beams containing photons with a settled state of polarisation. Coupling these beams allows one to obtain the Stokes parameters from the intensity contrast behind the rotating polariser. We discuss the influence of the quantum uncertainty on this technique of one-photon states reconstruction and we consider it for three aspects – the possibility of reducing the number of reference beams that are needed, the optimal state of polarisation of reference beams and the accuracy of the reconstruction method.     

Ray picture of polarization and coherence in a Young interferometer

We apply a polarization Wigner formalism to the propagation of polarization in a Young interferometer within paraxial approximation. With a very simple ray picture, we obtain complete and rigorous information about polarization evolution via the superposition of the spatial-angular Stokes parameters associated with three light rays. We compare the degree of polarization in the interference region with several measures of the degree of coherence for vectorial fields.     

Error propagation in polarimetric demodulation

The polarization analysis of light is typically carried out using modulation schemes. The light of an unknown polarization state is passed through a set of known modulation optics, and a detector is used to measure the total intensity passing the system. The modulation optics is modified several times, and, with the aid of several such measurements, the unknown polarization state of the light can be inferred. How to find the optimal demodulation process has been investigated in the past. However, since the modulation matrix has to be measured for a given instrument and the optical elements can present problems of repeatability, some uncertainty is present in the elements of the modulation matrix or covariances between these elements. We analyze in detail this issue, presenting analytical formulas for calculating the covariance matrix produced by the propagation of such uncertainties on the demodulation matrix, on the inferred Stokes parameters, and on the efficiency of the modulation process. We demonstrate that even if the covariance matrix of the modulation matrix is diagonal, the covariance matrix of the demodulation matrix is in general nondiagonal because matrix inversion is a nonlinear operation. This propagates through the demodulation process and induces correlations on the inferred Stokes parameters.     

Mueller-matrix ellipsometry using the division-of-amplitude photopolarimeter: a study of depolarization effects

A fully automated Mueller-matrix ellipsometer with a division-of-amplitude photopolarimeter as the polarization-state detector is described. This device achieves Mueller-matrix ellipsometry by measuring the Stokes parameters of reflected light as a function of the fast axis C of a quarter-wave retarder, which, in combination with a fixed linear polarizer, determines the polarization state of incident light. The reflected Stokes parameters were Fourier analyzed to give the 16 elements of the Mueller matrix. We investigated depolarization of polarized light on reflection from rough, heterogeneous, and anisotropic surfaces by obtaining measurements on rolled aluminum and plant leaves. The results demonstrate (1) a variation of degree of polarization of reflected light with the input polarization state, (2) the precision with which the measured matrices describe the depolarization results, (3) effects of surface anisotropy (rolling direction) on depolarization and cross polarization by reflection from aluminum surfaces, and (4) large values and differences in the depolarization effects from conifer and deciduous leaves. Depolarization of light reflected by the aluminum surfaces was most sensitive to the angle between the plane of incidence and the rolling direction when the incident Stokes parameters S(1), S(2), and S(3) were equal.     

Pancharatnam's Phase for Polarized Light

Abstract

This paper presents a classical theoretical analysis of the geometric phase arising in a cyclic change of the polarization state of light beams. We compare the results obtained this way with the quantum mechanical analysis.     

Entanglement transfer from light to atoms

Abstract

We describe an approach to mapping of a quantum polarization state of free propagating light on a collective spin of an atomic ensemble. Recent experimental results on generation of a macroscopic spin squeezed ensemble of cold atoms via interaction with squeezed light are analysed in detail.     

Polarimetry of scattered light using heterodyne detection

Abstract

Heterodyne detection has been used to measure the polarization state of light back-scattered from various targets (including flame-sprayed aluminium, sandpaper and painted surfaces). The samples are illuminated with a linearly polarized single-frequency continuous-wave CO₂ laser operating at a wavelength of 10.6 μm. The back-scattered co-polarized and cross-polarized components are both coherently detected by beating with an optical local oscillator. This process allows the relative amplitudes and phases of the two components to be measured and hence the light's polarization state can be evaluated. When the target undergoes movement, the scattered light demonstrates the usual properties of dynamic speckle, and the technique allows observation of the time evolution of the polarization ellipse.     

An optimal photon counting polarimeter

We present the experimental results for a method used to perform polarimetry on ensembles of single photons. Our setup is based on a measurement method known to be optimal for estimating the state of two-level systems. The setup has no moving parts and is sensitive to weak sources (emitting single photons) of light as it relies on photon counting, and has potential applications in both classical polarization measurements and quantum communication scenarios. In our implementation, we are able to reconstruct the Stokes parameters of pure polarization states with an average fidelity of 99.9%.     

Scheme to measure quantum stokes parameters and their fluctuations and correlations

Abstract

We propose a scheme to measure quantum Stokes parameters, their fluctuations and correlations. The proposal involves measurements of intensities and intensity-intensity correlations for suitably defined modes, which can be produced by a combination of half-wave and quarter-wave plates.     

Light polarization states of a cholesteric liquid crystal probed with optical ellipsometry

Herein a useful methodology to study optical properties of cholesteric liquid crystals (Ch-LC) is proposed by using the Fourier decomposition ellipsometry technique to calculate the Stokes parameters of transmitted and reflected light in the UV–Vis spectral range. Combining Bragg reflection and optical activity we were able to obtain ∼100% of linear or circular light polarization from the Ch-LC sample using achromatic and non-polarized light source. The photonic bandgap and the polarization components can be controlled with the temperature as a result of alterations in the helix pitch of the cholesteric phase. Finally, it is demonstrated the correlation between the dissymmetry factor (g) calculated via the Stokes parameter S₃ and the reflection spectrum. The data revealed that the maximum value of S₃ is not coincident with the peak of maximum reflection. The reflected or transmitted light analysis via Stokes parameters obtained by ellipsometry showed an alternative and low cost method for optical characterization in Ch-LC.     

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.     

Polarization characterization of a Mach-Zehnder interferometer

Polarization characterization of a Mach-Zehnder interferometer, based on the state of polarization (SOP) and power measurement at the interferometer output, is presented. We study the SOP and degree of polarization (DOP) of the output light, first as a function of the light power in each arm of the interferometer for a fixed input SOP and DOP, and second as a function of the SOP's in each arm of the interferometer for a fixed input power. Stokes formalism and the Poincaré sphere are used for simultaneous representation of the SOP and DOP, as well as their evolution. It is shown that the SOP and DOP stability and also the output light power are highly dependent on the light source coherence. Knowledge of these different parameters leads to configurations that allow simultaneous control of the SOP and DOP. We can hence realize a quasi-monochromatic nonpolarized light source, which is useful for the polarization-independent characterization of optical components.     

Quantum Statistics of Stimulated Raman and Hyper-Raman Scattering of Squeezed Light with Pump Depletion

Abstract

Using the approximation of small fluctuations around a stationary solution, photon statistics and quadrature variances are derived in stimulated Raman and hyper-Raman scattering including the coupling of pumping, Stokes, anti-Stokes and phonon modes. The depletion of pump light is included. Compared to Raman scattering, additional regimes to generate anti-bunched, sub-Poisson and squeezed light were found caused by self-interaction of the pump mode. It was possible to include effects of nonlinear dynamics, initial squeezing of radiation and phonon system, external noise and losses.     

Polarization separation of light in holographic grating reflection in conical mounting

Abstract

We experimentally investigate the interaction of linearly polarized light with a holographic grating in a conical mounting. Due to the periodic structure, the polarization properties of the reflected zeroth-order beam are highly sensitive to the conical angle. When a focused Gaussian beam with linear polarization impinges on an air–grating interface at an exceptional conical angle, a spatial splitting of the reflected beam is observed behind a polarizer. We find that it can be interpreted using the anisotropy of the polarization distribution in holographic grating reflection.     

Ultrasonic Nondestructive Evaluation of Inhomogeneous Plane Strain in Elastic Medium

Abstract

The possibility to enhance the efficiency of ultrasonic nondestructive testing making use of non-linear effects of wave propagation is investigated theoretically. The quasi one-dimensional problem of non-linear longitudinal wave propagation in elastic medium undergoing inhomogeneous plane prestrain is solved. The solution establishes the relations between the physical and geometrical properties of the medium, parameters of its predeformed state and the characteristics of the wave with smooth arbitrary initial profile. The non-linear sine-wave propagation in the medium with two traction-free surfaces is considered in more detail. The algorithm for evaluation of the parameters of plane strain on the basis of wave velocity and its profile evolution measurement data is proposed.     

The Adiabatic Phase and Pancharatnam's Phase for Polarized Light

Abstract

In 1955 Pancharatnam showed that a cyclic change in the state of polarization of light is accompanied by a phase shift determined by the geometry of the cycle as represented on the Poincaré sphere. The phase owes its existence to the non-transitivity of Pancharatnam's connection between different states of polarization. Using the algebra of spinors and 2 × 2 Hermitian matrices, the precise relation is established between Pancharatnam's phase and the recently discovered phase change for slowly cycled quantum systems. The polarization phase is an optical analogue of the Aharonov-Bohm effect. For slow changes of polarization, the connection leading to the phase is derived from Maxwell's equations for a twisted dielectric. Pancharatnam's phase is contrasted with the phase change of circularly polarized light whose direction is cycled (e.g. when guided in a coiled optical fibre).