Experimental investigation of a coherent quantum measurement of the degree of polarization of a single-mode light beam

Abstract

A novel method for the direct measurement of the degree of polarization is described. It is one of the first practical implementations of a coherent quantum measurement, the projection on the singlet state. Our first results demonstrate the successful operation of the method. However, because of the nonlinear crystals used at present, its application is limited to spectral widths larger than about 8 nm.     

Geometric approach to the degree of polarization for arbitrary fields

Abstract

The eigenvalue decomposition of the polarization matrix is employed to find out the geometric interpretation of the traditional degree of polarization and, in particular, of the degree of polarization for arbitrary electromagnetic fields put forward recently by Setälä et al. [2002, Phys. Rev. Lett., 88, 123902]. It is shown that both measures have similar geometric meaning as a measure for the purity of the polarization state. Possible extensions to the analysis are discussed.     

Extension of a model analysis of the degree of polarization of light

A theoretical approach is developed in which partially polarized radiation can be represented as a sum of coherent and incoherent components and also of the action of some imaginary device with time-dependent birefringence. This approach allows the Jones vector matrix method to be used for the calculations, which is important for theoretical calculations of the polarization state. Pis’ma Zh. Tekh. Fiz. 25, 74–78 (April 12, 1999)     

White-light interferometry with polarization phase-shifter at the input of the interferometer

Abstract

In white-light interferometry the surface profile is determined by measuring the fringe contrast function of the white-light interferogram. One of the techniques proposed for the measurement of the fringe contrast function is the use of the phase shifting technique with the help of an achromatic phaseshifter. The available phase-shifters employ a rotating polarization component at the output end of the interferometer. Using a rotating polarization component at the input end, rather than at the output end, has certain advantages. In this paper we investigate a rotating half-wave plate phase-shifter at the input end for its applications to a white-light interferometer.     

Local polarization reversal of LiNbO3 by scanning the surface perpendicular to the axis of spontaneous polarization with a needle-shaped electrode

The principle of local polarization reversal of ferroelectrics using a moving needle-shaped electrode¹ was used to make a comparative study of the characteristics of polarization reversal of LiNbO₃ from the Z(001) and Y(010) surfaces. In addition to chemical etching, an optical polarization method was used to visualize the domain structure. It was noted that the different dependences of the domain length on the polarizing voltage observed for the different crystal surfaces may be caused by the conducting and polarization properties of the regions in which the domain growth occurs. It is shown that the depth of penetration of the created domains in the sample may be set. Pis’ma Zh. Tekh. Fiz. 24, 52–57 (March 26, 1998)     

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.     

Optical field-strength generalized polarization of multimode single photon states in integrated directional couplers

A quantum analysis of the generalized polarization properties of multimode single photon states is presented. It is based on the optical field-strength probability distributions in such a way that generalized polarization is understood as a significant confinement of the probability distribution along certain regions of the multidimensional optical field-strength space. The analysis is addressed to multimode integrated waveguiding devices, such as N?×?N integrated directional couplers, whose modes fulfil a spatial modal orthogonality relationship. For that purpose a definition of the quantum generalized polarization degree in a N-dimensional space, based on the concept of distance to an unpolarized N-dimensional Gaussian distribution, is proposed. The generalized polarization degree of pure and mixture multimode single photon states and also of some multi-photon states such as coherent and chaotic ones, is evaluated and analyzed.     

Real-time polarization state measurement based on a birefringent crystal wedge

Abstract

We present a method of single-shot polarization state measurement based on a birefringent crystal wedge. The phase delay and amplitude angle of detected light are encoded into two groups of fringes through the interference in a crystal wedge and further decoded by fringe position locations. This method has the merit of real-time measurement, a compact set-up and simple calibration. The principle, set-up, calibration and error analysis are presented in details. In the end, a single-shot measurement set-up with 80 kHz temporal resolution is demonstrated to investigate the molecule dynamic behaviour in a TN liquid crystal under a rectangular voltage.     

Multimode polarization degree of mixture optical states in integrated directional couplers

Mixture multimode optical field classical states propagating in N?×?N integrated directional couplers are analyzed by using the density matrix formalism in a N-dimensional optical space. These mutimode optical fields present a kind of generalized polarization and accordingly a definition of a multimode polarization degree is proposed. It is based on the distance measure between a mixture state and an unpolarized state in a N-dimensional optical space so that in the case N=2 the standard polarization degree is recovered. It is shown that directional couplers can reduce or increase remarkably the multimode polarization degree of a mixture state. Likewise a simple measurement technique, based on Y junctions, of this multimode polarization degree is proposed. Finally all the results can be formally extended to the special case of multimode single photon quantum states.     

Compensation of parasitic polarization modulation in a fiber-optic gyroscope

It has been shown that the influence of parasitic polarization modulation on the precision of a fiber-optic gyroscope may be reduced substantially by incorporating reflection-type phase modulators with conversion of polarization modes. Pis’ma Zh. Tekh. Fiz. 23, 90–94 (August 12, 1997)     

Electric polarization and the extinction of the extraordinary reflected ray

Abstract

When light is incident from an isotropic medium on to an interface with a uniaxial crystal, the idea of an effective electric polarization is useful. We show that the same idea may be extended to the reverse situation where the light is incident from the uniaxial crystal. In this case, when the optical axis lies in the plane of incidence, there is a Brewster angle associated with the extinction of the reflected ray, because the waves have a definite polarization. We analyse the relation between the Brewster angle and the effective electric polarization at the interface.     

Faraday compensator of reciprocal optical anisotropy utilizing a polarization ring interferometer

It is shown that a polarization ring interferometer containing a Faraday cell can be used to compensate the reciprocal anisotropy in round-trip optical circuits. It is established theoretically and experimentally that, unlike the case of conventional Faraday mirrors, the quality of the restoration of the polarization in a compensator based on a polarization ring interferometer is practically independent of the Faraday rotation angle. A deviation of the Faraday rotation angle from 45° leads only to an additional power loss. The novel compensators can be used in fiber-optic circuits with a wideband light source or with several sources having different wavelengths. Pis’ma Zh. Tekh. Fiz. 25, 57–63 (May 26, 1999)     

Conversion of the polarization of an electromagnetic wave under cyclotron resonance in a two-dimensional electron system

A theoretical analysis is made of the conversion of the polarization of an electromagnetic wave when cyclotron resonance is excited in a two-dimensional electron system. It is shown that the greatest conversion of the polarization can be achieved in the reflected wave. At high electron concentrations the effect remains very appreciable even in the presence of electron scattering. In this case, the wave polarization conversion effect can be used to obtain information on electron relaxation in a two-dimensional system. Pis’ma Zh. Tekh. Fiz. 25, 21–26 (November 12, 1999)     

Spectral analysis of the device operators in polarization dynamics

Abstract

The spectral analysis of the device (instrument) operators, as an alternative approach to the dynamical polarization phenomena, is presented by means of an example of a classical time-varying optical device, the electrooptical modulator with longitudinal effect in crystals of KDP type. The polarization-spectral structure of the modulated light is analysed on this basis, both in terms of spectral Jones vectors and of spectral polarization matrices. Some experimental results are presented.     

Concerning the polarization vector of a wave reconstructed by a pseudodeep volume grating

It is shown theoretically and experimentally that for non-Bragg readout of a pseudodeep hologram recorded in a thick-layer medium the wave reconstructed by the hologram changes its state of polarization. Pis’ma Zh. Tekh. Fiz. 23, 58–63 (January 26, 1997)     

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.     

Dynamical configurational excitations and the polarization of dielectrics under a load

The polarization of dielectrics, which do not exhibit electrostriction, under a mechanical load is due to dynamical configurational excitations in the loaded crystal. Among these configurations, a dynamical order parameter is identified. It is determined by solving a nonlinear reaction-diffusion equation. The comparatively short buildup time of charge under a load is due to the formation and propagation of a wave of switching. Pis’ma Zh. Tekh. Fiz. 24, 79–82 (April 12, 1998)     

Achromatic phase shifting for polarization interferometers

Abstract

The use of an achromatic phase shifter with a polarization interferometer to make very accurate measurements of small optical path differences with white light is described.     

Optimum signal polarization in two-wave mixing with incoherent erasure of the fanning process

Abstract

We present a study of the optimum polarization states of the pump and signal beams in two-wave mixing amplification using BaTiO₃ where the main objective is to improve the performance by reduction of the beam fanning. We demonstrate numerically and experimentally that at low (less than 50) pump-to-signal ratios it is advantageous to use both pump and signal in mixed polarization states with respect to the principal plane of the crystal.     

Anisotropic polarization of radiation in quantum-confinement whispering-gallery-mode lasers

The polarization of lasing and spontaneous emission from half-disk- and disk-shaped quantum-confinement lasers operating on whispering-gallery modes with wavelengths within 2.18–2.28 μm has been studied. It is established that electric vector E of output radiation is oriented predominantly in the p-n junction plane, which is explained by the fact that radiation is generated due to electron-heavy hole transitions. Modulation of the polarized spontaneous radiation spectra has been observed.