Near-field Fourier transform polarimetry by use of a discrete space-variant subwavelength grating

We present a unique method for real-time polarization measurement by use of a discrete space-variant subwavelength grating. The formation of the grating is done by discrete orientation of the local subwavelength grooves. The complete polarization analysis of the incident beam is determined by spatial Fourier transform of the near-field intensity distribution transmitted through the discrete subwavelength dielectric grating followed by a subwavelength metal polarizer. We discuss a theoretical analysis based on Stokes-Mueller formalism, as well as on Jones calculus, and experimentally demonstrate our approach with polarization measurements of infrared radiation at a wavelength of 10.6 microm.     

Jones matrix for image-rotation prisms

The polarization-transforming properties of rotational prisms are analyzed with polarized light by using the Jones calculus and the exact ray-trace. A general expression of the Jones matrix for a rotational prism is derived, incorporating an explicit dependence on the image-rotation angle or the wave-front-rotation angle. The Jones matrix for the Pechan, Dove, Reversion, and Delta prisms is derived where the explicit dependence on the angle of rotation of the image is given. An experiment with a rotating Dove prism is also conducted to determine the output states of polarization for incident linearly polarized light. Experimental results agree with theoretical expectations.     

Three-dimensional polarization ray-tracing calculus I: definition and diattenuation

A three-by-three polarization ray-tracing matrix method for polarization ray tracing in optical systems is presented for calculating the polarization transformations associated with ray paths through optical systems. The method is a three-dimensional generalization of the Jones calculus. Reflection and refraction algorithms are provided. Diattenuation of the optical system is calculated via singular value decomposition. Two numerical examples, a three fold-mirror system and a hollow corner cube, demonstrate the method.     

Color modulation properties of a liquid-crystal device

The color modulation properties of a twisted-nematic liquid-crystal device are studied based on the Jones calculus. The usefulness of Jones calculus is demonstrated for the blue mode of a supertwisted birefringent liquid-crystal device, after which some experimental results of the color modulation effect for a twisted-nematic liquid-crystal television are presented. We investigated the color dependence of the transmitted light on the applied voltage by using a chromaticity diagram. Most of the experimental results are well explained by the theory derived from the Jones calculus.     

Full-field optical coherence tomography by achromatic phase shifting with a rotating polarizer

We demonstrate two-dimensional detection optical coherence tomography (OCT) using achromatic phase shifting with a rotating polarizer. This phase shifting, which experiences a light beam with a cyclic change in its polarization state, is, in principle, independent of wavelength. We simulated the wavelength dependence of an achromatic phase shifter using Jones calculus and found that the achromatic region exceeded 145 nm when the deviation of the phase retardation was less than +/- 0.5 degrees. Using the achromatic phase shifter and a conventional phase-shift calculation method, we obtained en face OCT images of an onion at different depths. This method is effective to enhance the quality of OCT with an ultrabroad-spectrum light source.     

Three-dimensional polarization states of monochromatic light fields

The 3×1 generalized Jones vectors (GJVs) [E(x) E(y) E(z)](t) (t indicates the transpose) that describe the linear, circular, and elliptical polarization states of an arbitrary three-dimensional (3-D) monochromatic light field are determined in terms of the geometrical parameters of the 3-D vibration of the time-harmonic electric field. In three dimensions, there are as many distinct linear polarization states as there are points on the surface of a hemisphere, and the number of distinct 3-D circular polarization states equals that of all two-dimensional (2-D) polarization states on the Poincaré sphere, of which only two are circular states. The subset of 3-D polarization states that results from the superposition of three mutually orthogonal x, y, and z field components of equal amplitude is considered as a function of their relative phases. Interesting contours of equal ellipticity and equal inclination of the normal to the polarization ellipse with respect to the x axis are obtained in 2-D phase space. Finally, the 3×3 generalized Jones calculus, in which elastic scattering (e.g., by a nano-object in the near field) is characterized by the 3-D linear transformation E(s)=T E(i), is briefly introduced. In such a matrix transformation, E(i) and E(s) are the 3×1 GJVs of the incident and scattered waves and T is the 3×3 generalized Jones matrix of the scatterer at a given frequency and for given directions of incidence and scattering.     

Jones matrix treatment for polarization fourier optics

Abstract

In this work we introduce the use of a Jones matrix method to evaluate the far-field diffraction produced by spatially variant polarization elements. We extend the scalar Fourier optics theory to a vectorial theory by the use of the Jones matrix formalism. With this method it is possible to analyse the diffraction pattern and the local state of polarization in the Fraunhofer approximation by means of the usual Jones matrix calculus.     

Dynamic deuteron polarization in irradiated D-Ammonia (ND3 and its first use in a high energy photon beam

We have dynamically polarized the deutorons in deuterated ammonia (ND₃) at 1 K, 0.5 K and at about 200 mK in a magnetic field of 2.5 T. The paramagnetic radicals were created by irradiating the material under liquid argon at 90 K (‘high temperature’ irradiation) with electrons from the 20 MeV injection linac of the Bonn synchrotron. Electron paramagnetic resonance (EPR) measurements identified the radicals as ?D₂.First target asymmetry measurements of the reaction γd ↑ → pn with ND₃ as target material in a dilution refrigerator were performed at the Bonn 2.5 GeV electron synchrotron. Starting with a deuteron polarization of 31% (using‘ high temperature’ irradiated material) the polarization went up to 44% after additional irradiation at about 200 mK with the photon beam. This polarization value corresponds to an overall polarization of 13.2% of all nucleons in ND₃. The increase of the polarization could be observed up to a dose of 8 × 10¹⁴ equivalent quanta/cm². The subsequent resistance of the polarization to radiation damage is more than one order of magnitude higher than that of butanol. These results mean a considerable improvement with respect to the deuterated alcohol materials which are currently used in high energy physics experiments with polarized deuteron targets.The dependence on the microwave frequency of the polarizations of deuterons and unsubstituted protons was examined at 1 K in order to gain insight into the prevailing mechanism of dynamic nuclear polarization (DNP). These measurements disagree with the equal spin temperature (EST)-hypothesis. They rather give evidence for a more complex behaviour apparently involving more than one polarization mechanism. It is attempted to explain these observations at 1 K with a differential solid state model.Furthermore, we present a series of DNP-signals as measured with our deuteron magnetic resonance (DMR)-system at various microwave frequencies. An unusual change of the DMR-signal shape was observed.     

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.     

Structure of a general pure Mueller matrix

Changes in the radiance and state of polarization of a beam of radiation can often be described by means of a pure Mueller matrix. Such a 4 × 4 matrix transforms Stokes parameters and can be expressed in terms of the elements of a 2 × 2 Jones matrix. Relations between the two types of matrix are discussed. Explicit expressions are given for changes of a pure Mueller matrix that are caused by certain elementary changes of its Jones matrix, such as when its transpose, complex conjugate, or Hermitian conjugate are taken. It is shown that every pure Mueller matrix has a simple and elegant structure, which is embodied by interrelations that involve either only squares of the elements or only products of different elements. All possible interrelations for the elements of a general pure Mueller matrix are derived from this simple structure.     

Frequency-derived distributed optical-fiber sensing technique: theory and characterization

Frequency-derived distributed optical-fiber sensing is a method for remote measurement of the spatial distribution of linear birefringence in an optical fiber, allowing a corresponding measurement of those external measurands that influence this birefringence. The method employs a pump-probe scheme, which, by use of the optical Kerr effect, generates an optical modulation of the probe beam, with a modulation frequency whose temporal variation maps the spatial distribution of birefringence. We provide a complete theoretical analysis of this method by using Jones calculus and graphic representation on the Poincaré sphere. The relevant characterization of the technique and some experimental results are also presented; these show good agreement with the theory.     

Conditions for polarization elements to be dichroic and birefringent

The polarization of light when it passes through optical media can change as a result of change in the amplitude (dichroism) or phase shift (birefringence) of the electric vector. The anisotropic properties of media can be determined from these two optical features. We derive the conditions required for polarization elements to be dichroic and birefringent. Our derivation starts from commonly accepted assumptions for dichroism and birefringence. Our main conclusions are that (i) the generalized Jones matrix for dichroic elements has in general nonorthogonal eigenpolarizations and (ii) in the general case, the birefringent and dichroic properties of polarization elements have no direct association with the corresponding phase and dichroic polar forms derived in the polar decomposition of the polarization elements' Jones matrices.     

Polarization contrast imaging of biological tissues by polarization-sensitive Fourier-domain optical coherence tomography

Jones matrix imaging of biological samples by a polarization-sensitive Fourier-domain optical coherence tomography has been demonstrated using a two-dimensional CCD camera to obtain two spectra corresponding to the orthogonal polarization components simultaneously. The measurement results of a quarter-wave plate are compared between the two incident polarization sets, H-V linear and R-L circular polarization. Jones matrix imaging of the bovine tendon is demonstrated. Measured Jones matrix images are converted to equivalent Müller matrix images. Local polarization properties are obtained by longitudinal differentiation of Jones matrix components. The layered structure of the bovine tendon and birefringence are revealed.     

A numerical method for coupled differential equations

This paper describes a numerical method for solving first-order coupled matrix differential equations. Recursive equations are used to find ‘reflection’, ‘transmission’ and ‘source’ coefficients; these coefficients are then used to construct the vector solution to the differential equations. The method can be used to solve linear and non-linear differential equations with specified initial or two-point boundary values. Numerical results for several initial value problems are given in the paper.     

Polarization properties of inversely twisted nematic liquid-crystal gratings

Based on the Jones matrix representation of twisted nematic liquid crystals (LC's), we have carried out a theoretical analysis of the polarization properties of inversely twisted nematic (ITN) LC gratings. Some interesting polarization behaviors are expected in the ITN LC grating. When a linearly polarized light parallel or perpendicular to the grating direction is incident on the ITN LC grating, the diffracted light in the 0th order is linearly polarized with the same polarization direction of incident light, while the diffracted light in high orders is linearly polarized perpendicular to that of incident light. Using a multirubbing alignment technique, we have practically prepared an ITN LC grating with ?45 degrees inversely twisted structures. The experimental investigations of the optical characteristics of the ITN LC grating demonstrate agreement with theoretical expectations.     

Application of the Jones calculus for a modulated double-refracted light beam propagating in a homogeneous and nondepolarizing electro-optic uniaxial crystal

The Jones matrix calculus is applied to an electro-optic crystal with uniaxial symmetry when the light beam is incident nearly normally on the crystal face. The approach allows one to treat refracted waves and rays that diverge in the crystal and are modulated by an external low-frequency field. The effect of partial interference of overlapping refracted beams is allowed for and calculated for the case of uniform intensity of the beam over its cross section. The method is employed to analyze optical systems containing an imprecisely cut and aligned electro-optic crystal plate.     

An optical channel modeling of a single mode fiber

The evaluation of the optical channel model that accurately describes the single mode fibre as a coherent transmission medium is reviewed through analytical, numerical and experimental analysis. We used the numerical modelling of the optical transmission medium and experimental measurements to determine the polarization drift as a function of time for a fixed length of fibre. The probability distribution of the birefringence vector was derived, which is associated to the ‘Poole’ equation. The theory and experimental evidence that has been disclosed in the literature in the context of polarization mode dispersion – Stokes & Jones formulations and solutions for key statistics by integration of stochastic differential equations has been investigated. Besides in-depth definition of the single-mode fibre-optic channel, the modelling which concerns an ensemble of fibres each with a different instance of environmental perturbation has been analysed.     

Quantum Statistics of Scattering between Relativistic Electrons and Interfering Laser Fields in the Zero-gain Approximation

The quantum-statistical properties are examined for two independent laser beams, forming interference fringes, which are in interaction with a particle (electron) beam treated as a ‘two-step’ reservoir system. Using the master equation and generalized Fokker-Planck equation techniques, the photon statistics are derived in closed form. Anticorrelation effects are found, indicating competition between modes, but no sub-poissonian or squeezing effects are possible.