Polarization recording of holograms in partially polarized recording light

A theoretical approach is considered for media whose scalar and anisotropic responses are of opposite sign. The nondiffracted beam, and the imaginary and real images formed by a polarization hologram are analyzed under these conditions. It is shown that the imaginary image has its polarization transformed compared with the object field while a pseudoscopic object field reconstructed in terms of polarization state and degree is formed in the real image. Pis’ma Zh. Tekh. Fiz. 23, 38–42 (February 12, 1997)     

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.     

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.     

Time Reversal for the Polarization State in Optical Systems

Abstract

The time-reversal operator for the polarization state can be successfully implemented in any optical system where a beam retraces its path. A Faraday rotator followed by a mirror realizes a device whose representative matrix is similar to the quantum mechanics time-reversal operator for the spin. Any effect of the medium birefringence is cancelled and, for linear polarization, the beam always returns opposite polarized with respect to the entrance state. Analogies with the operation of a phase-conjugation mirror are pointed out and suggested consequences of the novel optical configuration are given.     

Modulational method of eliminating the zero shift of a fiber ring interferometer induced by polarization nonreciprocity

A new method is proposed to eliminate the zero shift of a fiber ring interferometer induced by polarization nonreciprocity. This method is based on periodic modulation of the polarization state of nonmonochromatic radiation at the entrance to the interferometer ring system. Numerical estimates are given. Pis’ma Zh. Tekh. Fiz. 25, 78–82 (August 26, 1999)     

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.     

A Simple Necessary and Sufficient Condition on Physically Realizable Mueller Matrices

Abstract

Development of simple tools to test physical realizability of measured or computed Mueller matrices is the subject of this paper. In particular, the overpolarization problem, i.e., the problem of ensuring that the output degree of polarization does not exceed unity is solved by finding an easily implementable necessary and sufficient condition. With G being the Lorentz metric, it states that a given matrix M is not overpolarizing if and only if the spectrum of GM ^T GM is real and an eigenvector associated with the largest eigenvalue is a physical Stokes vector. This result is used to characterize some M classes of special interest, and is used to test several examples from recent literature.     

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.     

A simple demonstration of the Pancharatnam phase as a geometric phase

Abstract

To demonstrate the Pancharatnam phase as a geometric (Berry's) phase, each polarization state must be obtained by projecting the previous state on it. We describe a simple interferometric arrangement for such a demonstration which only uses a single rotation linear analyser to introduce a continuously variable phase difference between the two beams.     

Degrees of mutual coherence of a 3D polarization state

Abstract

The absolute values of the three degrees of mutual coherence between the analytic signals representing the components of the electric field of a given three-dimensional (3D) polarization state are relative quantities that depend on the laboratory reference frame considered. The extremal values for the said absolute values are determined and analyzed. The reduction to the well-known conventional 2D case is retrieved in a natural way.     

Modulation of the polarization of semiconductor laser radiation at constant output power

The degree of polarization of “doubly”-modulated (by the pump current and the optical confinement factor) laser radiation is analyzed by applying a method of analyzing the stability of the solutions of systems of Lyapunov differential equations to a system of rate equations. An analysis of the system of rate equations yielded its eigenvalues, also called stability coefficients, which are the characteristic time for a transition of the system from one state to another. The behavior of a doubly modulated laser was modeled mathematically and it was demonstrated that the polarization of the laser output radiation can be controlled with almost constant output power. Pis’ma Zh. Tekh. Fiz. 24, 84–90 (August 26, 1998)     

Wave design and polarization optimization in the interference of four non-coplanar beams for making three-dimensional periodical microstructures

Abstract

A systematic analysis of the interference of four non-coplanar beams for the purpose of making three-dimensional periodical microstructures is described. A general relationship between the four wavevectors, the required wavelength and the desired 3D lattice is formulated based on the reciprocal space theory. A concept of uniform contrast is introduced to evaluate the modulation depth of the resultant pattern as a whole by properly choosing the beam ratio and polarization. A calculation algorithm is developed to determine the optimized polarization of each beam for a given lattice to reach the maximum uniform contrast. Specifically, the effect of non-uniqueness of the wavevector solution for a given lattice on the final result is investigated. It is shown that one can improve the uniform contrast by using a set of waves with less angular divergence.     

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.     

Scaling of decoherence effects in quantum computers

Abstract

The scaling of decoherence rates with qubit number N is studied for a simple model of a quantum computer in the situation where N is large. The two state qubits are localized around well-separated positions via trapping potentials and vibrational centre of mass motion of the qubits occurs. Coherent one and two qubit gating processes are controlled by external classical fields and facilitated by a cavity mode ancilla. Decoherence due to qubit coupling to a bath of spontaneous modes, cavity decay modes and to the vibrational modes is treated. A non-Markovian treatment of the short time behaviour of the fidelity is presented, and expressions for the characteristic decoherence time scales obtained for the case where the qubit/cavity mode ancilla is in a pure state and the baths are in thermal states. Specific results are given for the case where the cavity mode is in the vacuum state and gating processes are absent and the qubits are in (a) the Hadamard state (b) the GHZ state.     

A non-contact technique for determining the depth of zero-order gratings

Abstract

In this work we present a simple, non-contact method for characterizing the depth of deep zero-order diffraction gratings using standard visible optics. Form birefringence exhibited by zero-order structures alters the polarization state of light transmitted through them. The amount of change is dependent on several factors including the depth of the grating grooves. By recording the polarization changes of laser light transmitted through the sample we demonstrate how the depth of any grating with a known pitch may be determined. Results for many different gratings have been analysed and show good agreement with groove depths measured from scanning electron micrographs. From these results a universal relationship between the amount of polarization change and the depth of the grating grooves has been determined.     

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.     

A Novel Beamsplitter for Optical Polarization State Interferometry

Abstract

We propose an evanescent-field optical beamsplitter, ideal for experiments in polarization state interferometry. It splits an incident wave into two beams, both being in the same polarization state, related to the incident state by a predetermined SU(2) operation on the Poincaré sphere. The operational characteristics of such beamsplitters are described.     

On the Gain of a Passive Linear Depolarizing System

Abstract

Transformation of a partially polarized light by a passive linear optical system must satisfy certain physical realizability constraints imposed on the elements of the Jones operator (matrix) characterizing the system. In this note we extend earlier work by Jones, Barakat, and Azzam and Bashara and derive a set of conditions on the elements of the Jones operator which depend explicitly on the input light degree of polarization. This is accomplished by a simple and novel approach based on the Cauchy-Schwartz—Bunyakowski inequality for coherency matrices.     

Simple Scaling Relationships for Calculation of Lidar Returns from Turbid Media in Multiple Scattering Regime

Abstract

Calculations for back-scattered radiation from a turbid medium, for situations such as lidar sounding of a cloud, or in general of measurements aimed at deducing the optical properties of the medium, can involve long-time operation of computers, especially in the cases of dense media, where multiple scattering has to be considered. This paper presents some simple scaling relationships that allow the results obtained for a particular situation to be used to obtain results for situations with different optical or geometrical parameters. The effect of multiple scattering on the polarization of the returns is taken into account. Some numerical examples are presented to check these relationships. In the Appendix some details are given of the Monte Carlo code used to deal with polarization of the returns, as well as comparisons of Monte Carlo results for double scattering with the results of analytical formulas that were presented in an earlier paper.