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.     

Spectral Stokesmeter. 1. Implementation of the device

We describe a spectral Stokesmeter: a device for fast simultaneous measurement of the four Stokes parameters of light. It consists of an original optical part, a four-channel scanning optoelectronic system, and a controlling computer system. The original optical scheme was first proposed by us. It is based on two holographic gratings, one of which is a special type of polarization grating. It allows an easy calibration of the device comprising wavelength and sensitivity calibration. The spectral range of the present implementation of the spectral Stokesmeter is 520-750 nm, and the error in the measurement of the normalized Stokes parameters is < or = 0.05.     

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.     

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.     

Differential geometry of normalized Stokes vector trajectories in anisotropic media

Trajectory of the normalized Stokes vector on the Poincaré sphere corresponding to light propagation in anisotropic tissues with birefringence and biattenuance is derived. Analytic expressions are determined from the Serret-Frenet formulas and derivatives of arc length for five quantities including the tangent, normal, and binormal vectors with curvature and torsion. Depth variation of curvature and torsion of normalized Stokes vector trajectories corresponding to light propagating in rodent tail tendon are given. Use of analytic expressions for depth variation of curvature and torsion of the normalized Stokes vector trajectories on the Poincaré sphere is discussed for analysis of polarization-sensitive optical coherence tomography data recorded from anisotropic biological tissues with birefringence and biattenuance.     

Scattering Matrices for Slightly Non-spherical Particles

Abstract

In this paper the theory of light scattering by slightly non-spherical particles is developed and the forms of the amplitude and Stokes scattering matrices are derived. Forward-scatter and backscatter and the information they give about the shape of the particle are discussed as special cases.     

Wave Scattering from Fractal Surfaces

Abstract

In this paper, a normalized band-limited Weierstrass function is presented for modelling 2D fractal rough surfaces. Some conventional statistical parameters, namely the root mean square and the correlation length of rough surfaces, are used to assess between fractal parameters and the roughness of surfaces. An analytic solution of the scattered light field from these fractal surfaces is derived based on Kirchhoff theory. Three statistical parameters, namely the average scattering coefficient, the average intensity of scattered field, and the root mean square of scattered field, are introduced to study the influence of various fractal parameters on the scattered field by theoretical analysis and numerical calculations.     

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.     

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.     

Stimulated Raman Scattering of Squeezed Light with Pump Depletion

Abstract

Using the approximation of small fluctuations around a stationary point, photon statistics and squeezing of vacuum fluctuations are derived in stimulated Raman scattering including the coupling of photon-photon and photon-phonon modes. The depletion of pump light is described and it is shown that a regime of inversion of the process is related to an increase in quantum fluctuations, which are finally reduced again, more in the anti-Stokes mode than in the Stokes mode. If the anti-Stokes coupling is stronger than the Stokes coupling, then an oscillating behaviour of the statistical characteristics occurs and substantial squeezing can be found in photon-phonon modes.     

An analysis of high efficiency stimulated Raman scattering in water with a frequency-doubled pulsed Nd:YAG source

Abstract

Unexpectedly high stimulated Raman scattering (SRS) has been seen with a frequency-doubled Nd:YAG pump laser (532 nm) in water. The pump beam was propagated, both focused and unfocused, through a 4m long tank. Threshold pump irradiance for SRS was measured to be 2 × 10¹³ Wm^?2 and Stokes transitions were identified at approximately 3230 and 3380 cm^?1. The maximum conversion efficiency to the Stokes frequencies seen was 13% of pump input, for a focused beam, 4% for unfocused. SRS from an unfocused beam was seen to arise from high irradiance filaments caused by self-focusing in the water. The term Raman Interaction Function (RIF) has been defined here as the irradiance of the pump beam integrated over the interaction length (distance over which the pump beam irradiance is above threshold). The RIF model was been designed to describe the relationship between pump laser parameters and the output at the dominant Stokes frequencies.     

Synchrotron Radiation. Techniques and Applications

The polarization properties of scattered monochromatic light fields are described by stochastic Stokes parameters S ₀, S ₁, S ₂ and S ₃ which fluctuate in space. We determine the theoretical first-order probability density functions of these Stokes parameters assuming a chi-square density for the intensity of orthogonal linear polarized field components, a uniform density for the relative phase between the corresponding fields and statistical independence of these stochastic quantities. If these assumptions hold, the density of S 0 equals the probability density of a sum of two speckle fields and S ₁, S ₂ and S ₃ are Laplace variates.     

Measurement method of Stokes parameters using a quarter-wave plate with phase difference errors

The Stokes parameters (S0, S1, S2, and S3) of monochromatic light can be measured using the adjustable azimuth settings of a quarter-wave plate and a polarizer. When measuring the Stokes parameters of light of an arbitrary wavelength, the measurement of S3 is affected by the phase difference error Δq(λi), due to the mismatch with respect to wavelength with the quarter-wave plate. In this method, Δq(λi), due to such a mismatch of incident light of arbitrary wavelength, can be overcome by a judicious choice of azimuth settings of the quarter-wave plate and the use of a polarizer; however, the use of a precision quarter-wave plate is necessary. The present paper proposes a measurement method of Stokes parameters of incident light of arbitrary wavelength using a quarter-wave plate with phase difference errors.     

Enhanced backward stimulated Raman scattering by coupling between the forward and backward processes

Abstract

A new scheme of backward Raman scattering, in which coupling between the forward and backward Stokes processes is caused by injecting an additional backward pump field, is demonstrated both experimentally and theoretically. Four wave mixing among the pump and Stokes fields leads to gain enhancement of backward Raman scattering. A factor of gain enhancement of 2 was obtained with injection of a 0.4 mJ seed Stokes and a 5 mJ backward pump wave.     

Model of Gain Saturation in A Two-mirror Laser

Abstract

An approximate method of analysis of nonlinear operation of Fabry-Perot lasers including longitudinal electric field dependence and the spatial hole burning effect is presented. The method is based on a semiclassical approach and provides an approximate expression relating the normalized small signal gain to the normalized output power and laser parameters. The influence of the spatial hole burning effect on the laser characteristics is investigated. It is shown that this effect determines the value of the optimal coupling strength, as well as causing changes in the laser characteristics.     

Quantum statistics and dynamics of nonlinear couplers with nonlinear exchange

Abstract

In this paper we derive the quantum statistical and dynamical properties of nonlinear optical couplers composed of two nonlinear waveguides operating by second subharmonic generation, which are coupled linearly through evanescent waves and nonlinearly through non-degenerate optical parametric interaction. Main attention is paid to generation and transmission of non-classical light, based on a discussion of the squeezing phenomenon, the normalized second-order correlation function and quasiprobability distribution functions. Initially coherent, number and thermal states of optical beams are considered. In particular, results are discussed with dependence on the strength of the nonlinear coupling relatively to the linear coupling. We show that if the Fock state |1〉 enters the first waveguide and the vacuume state |0〉 enters the second waveguide, the coupler can serve as a generator of squeezed vacuum state governed by the coupler parameters. Further, if thermal fields enter initially the waveguides the coupler plays a similar role as a microwave Josephson-junction parametric amplifier to generate squeezed thermal light.     

Mueller-matrix Ellipsometry on Electroformed Rough Surfaces

Abstract

Automated Mueller-matrix ellipsometry was used to investigate the optical properties of electroformed standard rough surfaces as a function of r.m.s. surface roughness heights and angle of incidence. The r.m.s. roughness of the specimens examined varied from 50 to 12 500 nm. Six different surface finishes and 22 different specimens were examined and Mueller matrices were obtained at angles of incidence that varied from 30 to 80°. Measurements were conducted at a wavelength of 633 nm with the use of a division-of-amplitude photopolarimeter capable of simultaneously measuring all four Stokes parameters of arbitrarily polarized light. Values of ψ and Δ, the ellipsometric parameters, were derived from the measured Mueller matrices. The results demonstrate firstly the monotonic variations in the derived values of Δ with surface roughness for fixed angles of incidence, which include a ‘resonance’ effect for specimens with r.m.s. roughness heights close to the wavelength of light, secondly a systematic variation of ψ with the angle of incidence for different specimen roughness values and a reversal in these trends beyond the pseudo-Brewster angle, thirdly a monotonic variation in Δ values with the angle of incidence for different roughness values, fourthly relatively large variations in ψ values for roughness values close to the wavelength of light and fifthly relatively little change in ψ and Δ values for roughness values that greatly exceeded the wavelength of light.     

Intensity-dependent Phase Shifts in Nonlinear Coupling Devices

Abstract

For nonlinear coupling devices, general solutions using Stokes parameters fail to give complete information of phase shifts, as they only provide the phase-shift difference between the two outputs of coupling waveguides (or two cores for fibre coupling devices). Thus the standard Stokes parameter formulation is not sufficient for some applications in which the nonlinear phase shifts through the devices are of great concern. The analysis given here presents complete and exact solutions for nonlinear phase shifts in optical coupling devices for the first time. This reveals unusual behaviour of the nonlinear phase shifts because, in a certain input power range, a small change of input power can bring about a large change in the nonlinear phase shift. Some basic characteristics of the nonlinear phase shifts and their potential influence on application of coupling devices to all-optic signal processing are discussed.     

Hindered Settling in Unflocculated Suspensions

Abstract

The hindered settling of three sizes of microcapsules suspended at four different concentrations in silicone fluids with four viscosities was determined at 25°C in suspensions.

The viscosities of the various suspensions determined by a Stormer Viscometer indicated pseudoplastic behavior. A viscosity constant was calculated using the power law of the form

ηs^N = ηk^G

The sedimentation rate of suspensions of microcapsules was determined at low Reynolds numbers. An equation

V_s = [(ρ_s - ρ)g/18η] · f(d,C, η_k)

was proposed in which the exponent of [(ρ_s - ρ)g/18 η] was shown to be one. Various sedimentation parameters were fitted by multiple linear regression method to a curve. The empirical equation obtained was

V_s = [(ρ_s - ρ)g/18 η] d^1.63 (1/C^1.27) ηk ^0.07 e^?4.31

A comparison of sedimentation rate against suspension concentration was made for values calculated from the classical Stokes equation, experimental values, and predicted values from the fitted equation.