Statistical properties of a radially polarized twisted Gaussian Schell-model beam in a uniaxial crystal

We derive the analytical formulas for the elements of the cross-spectral density matrix of a radially polarized partially coherent beam with a twist phase named radially polarized twisted Gaussian Schell-model (RPTGSM) beam propagating in a uniaxial crystal, and explore the statistical properties, such as the intensity distribution, the degree of polarization (DOP) and the state of polarization (SOP) of such beam in a uniaxial crystal with the help of the derived formulas. It is found that the statistical properties of a RPTGSM beam are closely related with the twist phase and the anisotropy of the uniaxial crystal, e.g. the twist phase leads to the rotation of the intensity, DOP and SOP distributions, and the anisotropy of the uniaxial crystal leads to the asymmetry distributions of these statistical properties. Our results will be useful for designing light field with prescribed intensity, DOP and SOP distributions, and may be useful in optical manipulations and free-space optical communications.     

光纤型偏振OCT 系统中光偏振特性的研究

建立了偏振光在生物组织中传播的模型,并利用该模型模拟了偏振光在生物组织中传播的过程,重建了多种偏振态输入光的情况下光偏振态在生物组织中的分布及生物组织的偏振特性模型.分析了光偏振度与光被生物组织散射次数的关系,阐明了由于偏振光在组织中传播,其偏振态逐渐改变而造成的偏振OCT 干涉计两臂光束失去相干性及偏振OCT 图像质量下降现象.通过分析斯托克斯(Stokes)矢量和穆勒(Muller)矩阵在光纤型偏振OCT系统中的应用,说明Muller 矩阵不受输入光偏振态的影响,因此它比Stokes 矢量更适用于光纤型偏振OCT 系统研究.     

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.     

Polarization phase-shifting interferometric technique for complete evaluation of birefringence

A full-field technique for simultaneous measurement of the magnitude of birefringence and its orientation is presented. This is achieved using a monolithic birefringence sensitive interferometer where the interference fringes carry the information of both the birefringence phase and the orientation of the fast axis of an optically transmissive anisotropic material placed at the output of the interferometer. The interferometer consists of a suitably polarization-masked cube beam splitter, orientated as in the Gates interferometer, which serves to generate a pair of orthogonally polarized and collinearly propagating light beams. Experimental results are obtained through an algorithm incorporating eight polarization phase-shifted interferograms.     

New approach to determine the effects of polarization mode dispersion and chromatic dispersion on pulse and RF signals

We present a novel analytical expression relating the output state of polarization (SOP) and the polarization mode dispersion (PMD) vector, including polarization-dependent chromatic dispersion (PCD), in terms of the angle of precession of the output SOP around the PMD vector. We derive a number of new expressions incorporating for the first time this angle of precession. First, a general relation to study the effect of differential group delay, PCD, and chromatic dispersion on pulses of arbitrary shapes is given. From this general relation, we derive expressions for pulse broadening and power penalty for Gaussian pulses. Moreover, a new expression for PMD-induced power fading for single-sideband modulated radio frequency signals is also derived. Measured experimental results are presented to support the derived expressions.     

Fiber-based single-channel polarization-sensitive spectral interferometry

We present a novel, to our knowledge, fiber-based single-channel polarization-sensitive spectral interferometry system that provides depth-resolved measurement of polarization transformations of light reflected from a sample. Algebraic expressions for the Stokes parameters at the output of the interferometer are derived for light reflected from a birefringent sample by using the cross-spectral density function. By insertion of a fiber-optic spectral polarimetry instrument into the detection path of a common-path spectral interferometer, the full set of Stokes parameters of light reflected from a sample can be obtained with a single optical frequency scan. The methodology requires neither polarization-control components nor prior knowledge of the polarization state of light incident on the sample. The fiber-based single-channel polarization-sensitive spectral interferometer and analysis are demonstrated by measurement of phase retardation and fast-axis angle of a birefringent mica plate.     

In-line interferometer for direction-sensitive displacement measurements by optical feedback detection

We demonstrate a compact in-line interferometer for direction-sensitive displacement measurement by optical feedback detection with a semiconductor laser (SL) light source. Two reflected beams from a semitransparent reference mirror and a reflecting test object interfere in the SL medium, causing a variation in its output power. The reference mirror is located between the SL output facet and the test object. The performance of the interferometer is investigated numerically and experimentally to determine its optimal operating conditions. We have verified the operating conditions where the behavior of the SL output power profile could indicate accurately the displacement magnitude and direction of the moving test object. The profile behavior is robust against variations in optical feedback and scale of the interferometer configuration.     

Stabilization by harmonic intensities for the output signal in heterodyne detection

We experimentally demonstrated that the technique to stabilize the output signal by harmonic intensities is useful in heterodyne detection with an incoherent light source such as a halogen lamp. The relation between the relative standard deviation of an output signal and the fluctuation of the light intensity is analyzed and simulated. Using the fundamental to sixth harmonics increases the stabilities of output signal approximately 3 times, and subtracting the relative standard deviation of the intensity of light source enhances the stabilities 49 times. The fluctuating phase that is due to the fluctuating frequency and temperature and its power spectrum density for an interferometer is also calculated with the Allan variance.     

基于Stokes矢量分析的偏光片光学参数测量

目前偏光片透过率的测量方法依赖偏光片的相对转动,受光源偏振度以及探测器偏振响应的影响大,测量精度低.为解决上述问题,本文提出了基于Stokes矢量分析的方法,通过分析入射到偏光片以及从偏光片出射的偏振光的Stokes矢量的改变,结合最优化算法来解析样品的偏振特性,从而快速、精确地测量偏光片的透过率.该方法测量速度快、可...     

Effects of birefringence on Fizeau interferometry that uses a polarization phase-shifting technique

Interferometers that use different states of polarization for the reference and the test beams can modulate the relative phase shift by using polarization optics in the imaging system. Thus the interferometer can capture simultaneous images that have a fixed phase shift, which can be used for phase-shifting interferometry. As all measurements are made simultaneously, the interferometer is not sensitive to vibration. Fizeau interferometers of this type have an advantage compared with Twyman-Green-type systems because they are common-path interferometers. However, a polarization Fizeau interferometer is not strictly common path when both wavefronts are transmitted by an optic that suffers from birefringence. The two polarized beams see different phases owing to birefringence; as a result, an error can be introduced in the measurement. We study the effect of birefringence on measurement accuracy when different polarization techniques are used in Fizeau interferometers. We demonstrate that measurement error is reduced dramatically and can be eliminated if the reference and test beams are circularly polarized rather than linearly polarized.     

Depth-resolved two-dimensional stokes vectors of backscattered light and mueller matrices of biological tissue measured with optical coherence tomography

Mueller matrices provide a complete characterization of the optical polarization properties of biological tissue. A polarization-sensitive optical coherence tomography (OCT) system was built and used to investigate the optical polarization properties of biological tissues and other turbid media. The apparent degree of polarization (DOP) of the backscattered light was measured with both liquid and solid scattering samples. The DOP maintains the value of unity within the detectable depth for the solid sample, whereas the DOP decreases with the optical depth for the liquid sample. Two-dimensional depth-resolved images of both the Stokes vectors of the backscattered light and the full Mueller matrices of biological tissue were measured with this system. These polarization measurements revealed some tissue structures that are not perceptible with standard OCT.     

Analysis of light noise sources in a recycled Michelson interferometer with Fabry-Perot arms

We present a method by which the effect of laser field variations on the signal output of an interferometric gravitational wave detector is rigorously determined. Using the Laser Interferometer Gravitational Wave Observatory (LIGO) optical configuration of a power recycled Michelson interferometer with Fabry-Perot arm cavities as an example, we calculate the excess noise after the input filter cavity (mode cleaner) and the dependence of the detector strain sensitivity on laser frequency and amplitude noise, radio frequency oscillator noise, and scattered-light phase noise. We find that noise on the radio frequency sidebands generally limits the detector's sensitivity.     

A Method for the Optical Characterization of Thin Uniaxial Samples

An optical characterization procedure for small fragments of uniaxial materials is described involving the simple use of crossed polarizers with one polished face of the material. The reflectance at a fluid-uniaxial slab boundary beyond, but near, the critical angle of incident light is examined for linear incidence polarization using an orthogonal output polarizer. It is found that, as the crossed incident and output polarizers are rotated together, there are, for a given angle of incidence, particular polarization angles for which the reflectivity is a minimum. These angles give information on the optical tensor of the crystal under study. Further the intensity of the reflected light, for incidence angles beyond critical with the input and output polarizers crossed, has as a function of the incident polarization angle an oscillatory form which, when fitted to theory, can also yield the full uniaxial tensor of the material under study. This is confirmed experimentally for a thin single crystal of calcite with one polished face.     

Modelling of a variable optical switch based on the parametric amplification in a photonic crystal fibre

We model an optical switch with a variable gain based on the optical parametric amplification in a photonic crystal fibre (PCF). By solving the coupled amplitude equations, the switch gain as a function of the power, wavelength and the state of polarization (SOP) of the control wave as well as the signal wavelength is simulated. The results show that the switch gain is increased by increasing the control power and the maximum gain is obtained for a specific SOP of the control wave. Also, the proposed switch has ultrahigh speed and provides a very wide and flat gain over the C-band without changing the operating wavelength.     

Self-referenced rectangular path cyclic interferometer with polarization phase shifting

A polarization phase shifting interferometer using a cyclic path configuration for measurement of phase nonuniformities in transparent samples is presented. A cube beam splitter masked by two linear polarizers is used to split the source wavefront into two counter propagating linearly polarized beams that pass through the sample. At the output of the interferometer, the two orthogonally polarized beams are rendered circularly polarized in the opposite sense through the use of a quarter wave plate. Finally, phase shifting is achieved by rotating a linear polarizer before the recording plane. In a rectangular path interferometer, although the two counter propagating wavefronts are laterally folded with respect to each other in the interferometer arms, the beams finally emerge mutually unfolded at the output of the interferometer. This phenomenon is utilized to create a reference if the sample is introduced in one lateral half of the beam in any one of the interferometer arms. The polarization phase shifting technique is used to generate four phase-shifted interferograms, which are utilized to evaluate the phase profile of the phase sample. Experimental results presented validate the proposed technique.     

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.     

Interferometric ellipsometer

We describe an interferometric ellipsometer that, in contrast to previous designs, requires a single reflection from a sample surface so that tanpsi and Delta are measured directly. A reference beam is created in one arm of a modified Mach-Zehnder interferometer such that the p and s polarizations have a common phase and fixed relative amplitude, irrespective of the sample. This beam is combined interferometrically with the measurement beam. The output beam is spatially separated into its polarization components and temporal fringes created at the photodetectors via mechanical scanning of one of the mirrors. Measurements made on a reference SiO(2) film are in excellent agreement with the calibration certificate while those made on a glass surface demonstrate measurement capabilities for low reflectivity samples. Estimates of the noise performance indicate a precision, in air, of approximately 41 pm.     

Passive single-mode fiber depolarizer

We analyze and demonstrate a passive single-mode fiber depolarizer by using cascaded 2 x 2 couplers, recirculating delay lines, and a commercial laser diode. Design criteria and principles are discussed. We reduced the degree of polarization (DOP) to less than 20 dB by using ten cascaded couplers. The DOP can be reduced even further with more couplers. Experiments illustrate that this depolarizer is insensitive to the input polarization state and can eliminate polarization noise in a polarization-sensitive fiber-optic system.     

Optical imaging based on time-resolved Stokes vectors in filamentous tissues

Time-resolved Stokes vector components of light transmitted through filamentous tissues were measured with a view to improving the imaging quality of optical images in such tissues. Temporal profiles of the Stokes vectors and the time-resolved degree of polarization (DOP) were calibrated to produce higher image quality than that of images based on time gating, polarization discrimination, or both. A thin chicken bone inserted into chicken breast tissue with filament orientation in different directions with respect to the direction of input linear polarization was scanned to demonstrate images of higher spatial resolution and contrast based on the measurement of time-resolved DOP.