Circular Polarization States Research Articles

A new type of EPR experiment using light quanta produced by nonlinear optical process

A pair of correlated light quanta of 532 nm wavelength with the same linear polarization but divergent directions of propagation was produced by non-linear optical parametric down conversion in a crystal of deuterated potassium di-hydrogen phosphate from a 100 ps duration laser pulse of 266 nm wavelength. Each light quantum was converted to a circular polarization state or a linear polarization state (orthogonal) and was reflected by a turning mirror to superpose with the other at a beam splitter to produce a two-quanta superposition state. For coincident detection of the two light quanta at separated detectors, correlations of the Einstein-Podolsky-Rosen type for the polarizations have been observed as predicted by our analysis. In preliminary runs with limited data we have measured a violation of Bell's inequality by three standard deviations. We are planning to extend our experiments to include a truly random delayed choice between two analyser settings at each detector while maintaining a spacelike separation between the detections.

All-fiber-optic polarization state azimuth control: application to Faraday rotation

An all fiber-optic system for the control and modulation of the azimuth of a linearly polarized beam is described. The experimental configuration is basically that of a Mach-Zehnder interferometer but with the birefringence of the two fiber arms controlled to produce orthogonal circular states of polarization which recombine in the final directional coupler. Azimuth control is then achieved by relative phase modulation using a piezo-electric element. The system has required the use of monomode fiber directional couplers of accurately characterized polarization properties, and the development of fiber linear retarders. The application of the system in the measurement of electric currents via Faraday rotation is described, although extensions to other types of optical instrument are equally feasible.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fourier transform Raman optical activity

Raman optical activity (ROA) is conventionally measured by modulating the incident laser polarization between right and left circular polarization states and detecting the difference in the scattered Raman intensities using a dispersive spectrograph attached to a multichannel detector. In this article, a Fourier transform technique using a Martin-Puplett interferometer is shown to be suitable for measuring both the ROA and ordinary Raman intensities in a single measurement. Novel features in this technique include: (a) incident laser radiation is plane polarized; (b) the scattered Raman light is collected without an analyzer.

Reflective thin-film device for generating spatial binary patterns of orthogonal circular polarization states

A novel device is described that generates, by reflection, polarized optical wavefronts of juxtaposed fields of alternating orthogonal circular polarization states. It consists of a dielectric substrate coated by a transparent thin film of certain refractive index and of thickness that alternates between two discrete values over adjacent areas of the substrate, in a pattern that corresponds to the desired binary polarization pattern of the reflected wave. Devices that use Ge and Si substrates at wavelengths of 10.6 and 0.6328 μm, respectively, are presented as examples.

A note on helicity

We give a formal definition of the helicity operator for integral spin fields, which does not involve their momentum-space decomposition. We base our discussion upon a representation of the Pauli–Lubanski operator in terms of the action on tensor fields by the Killing vectors associated with the generators of the Poincaré group. This leads to an identification of the helicity operator with the duality operator defined by the space–time alternating tensor. Helicity eigenstates then correspond to self-dual or anti-self-dual fields, in agreement with usage implicit in the literature. In addition, we discuss the relationship between helicity eigenstates, which are intrinsically nonclassical, and states of right or left circular polarization in classical electrodynamics

Measurement of flow-birefringence using a circularly polarized laser beam

A method of measuring flow-birefringence is reported. In this method, a circularly polarized light wave is transmitted through the flow-birefringent medium. The transmitted elliptically polarized wave is compensated by a Babinet-Soleil plate to convert it back into a circularly polarized wave. The state of circular polarization is confirmed using the rotating-analyser method. Measurements can be carried out with a sample having a fixed azimuth. The minimum detectable optical retardation angle was 5 × 10 -3 degree. This corresponds to a birefringence of Δ n = 1 × 10 -10, when the optical path length of the sample cell is 100 mm.

Parity violation induced by weak neutral currents in atomic physics. part II

The first part of this paper gives a detailed account of the evaluation of the electric dipole amplitude induced in alkali one-photon S-S transitions, by the parity violating electron-nucleus short range potential Vp.v. associated with the weak neutral currents. Two methods are presented : the first involves an explicit sum over the contributions of the P-states admixed with the S-states and incorporates the best information available on S-P electric dipole amplitudes. The second method, mathematically more elegant, avoids with the help of Green's function techniques any explicit sum over the P states, and, provided that some spin-orbit corrections are neglected, leads to a fairly simple formula involving Coulomb integrals tabulated in the literature and the interpolated quantum defects for S and P waves. The second part is devoted to a description of possible ways to detect parity violation induced in radiative S-S transitions, with a brief discussion of physical processes which could be a source of experimental difficulty. The last section of the paper deals with a theoretical analysis of the influence of a static electric field on the radiative S-S transitions. An evaluation of the induced electric dipole amplitude in the case of cesium indicates that it will compete with the magnetic dipole amplitude for electric fields larger than 10 V/cm. An interference effect between these two amplitudes gives rise to an electronic polarization in the final atomic state proportional to the vector product of the static electric field by the photon momentum which, in a typical case, could be as large as 64 %; the measurement of this interesting and rather peculiar effect will lead to a determination of the sign of the magnetic dipole amplitude. Moreover parity violation could manifest itself by a dependence of this electron polarization on the state of circular polarization of the incident photon.

Circular Polarizer for Lyman-alpha Flux*

Polarization and phase shifts of Lyman-alpha flux reflected from Al, Al2O3, ZnS, MgF2, and SiO films were measured. A circular polarizer having a 5° angle of acceptance and 12% transmittance was constructed using Al2O3 and Al mirrors. The amount of flux in the desired state of circular polarization was between 83% and 90%.

Theory for the anomalous polarization of cosmic OH-18-cm radiation and for hyperfine lasers

The theory of Heer and Graft is used to develop expressions for the first- and third-order contributions to the electric polarization of a maser medium undergoing simultaneous maser action on a number of hyperfine transitions. Detailed expressions for the electric polarization of the 2 Π 3 2 state of OH are given for simultaneous maser amplification of the (22)-1667, (11)-1665, (21)-1720, and (12)-1612 megahertz transitions between the hyperfine levels ( F + F −) of the Λ doubled states. If the level occupation and widths are comparable in magnitude for all levels and maser action occurs, the analysis of the resulting nonlinear problem indicates that all four transitions saturate toward circular polarization and is in accord with the suggestion of Heer. The state of circular polarization of the (11), (21), and (12) transitions is strongly dependent on the (22) transition, and each line saturates toward a state of circular polarization opposite to the state of circular polarization of the (22) line. These conclusions require that the saturation line width exceed the Zeeman splitting. A formulation of the exact problem is given and saturation line widths are discussed.

On the Faraday effect in O 2

From Hamiltonians containing the interaction of the magnetic moment of the molecule with the magnetic field of the radiation, the imaginary parts of the magnetic susceptibilities for right and left circular polarization are calculated. The dispersion relations appropriate to tensor media is then applied yielding the difference between the real parts of the magnetic susceptibilities for the two states of circular polarization. Subject to the assumptions that the spin multiplet and adjacent rotational levels spacings are small compared to kT and that the frequency of the radiation is much greater than the frequencies of the absorption bands, an expression for the contribution of the magnetic susceptibility to the Verdet constant is obtained which is frequency independent. This contribution to the Verdet constant is calculated numerically for O 2, under experimental conditions, to be 1.96 μmin per gauss per cm. When the frequency-independent term is combined with a term of the earlier work of Serber, an expression for the total Verdet constant of O 2 in the near infrared, visible, and ultraviolet is obtained which can be fit to the experimental data to 1%. The results obtained here are in complete agreement with those derived earlier by Hougen using a different method.

Recoil Effect in Beta Decay andKCapture

The study of recoil effects in $\ensuremath{\beta}$ decay and $K$ capture is extended to the case of forbidden transitions. Formulas for the angular distribution of recoil nuclei from oriented parent nuclei, the polarization of the recoil nucleus, and the angular correlation between the recoil nucleus and the following $\ensuremath{\gamma}$ ray emitted in given state of circular polarization are presented. For $\ensuremath{\beta}$ decay the results, in which the Coulomb effects have been taken into account only through the Fermi function, are given in closed form for $n$-forbidden transitions. We have considered separately $\mathrm{ST}$ and $\mathrm{VA}$ interactions. The results are quite sensitive to the choice between the two couplings. In particular it is shown that for the so-called unique forbidden transitions of light-nuclei parity-nonconserving effects vanish for a $\mathrm{VA}$ interaction, whereas they are expected to be large with an $\mathrm{ST}$ interaction. The study of recoil effects in $K$ capture, which has been limited to the case of first forbidden transitions, provides a set of experiments which may be used to determine the helicity of the neutrino.

Gamma-gamma angular correlations with circular polarization measurements

The problem of the γ-γ double angular correlation is examined in which the circular polarization state of photons is observed. The relation among the various possible correlations is discussed. The Legendre polynomials of odd order introduce an asymmetry around the valueβ = π/2, whereβ is the. angle between the two radiations. Numerical calculations have been made for the γ-γ cascade of60Co.

Particle Aspect of the Electromagnetic Field Equations

In this paper it is shown that Maxwell's theory of the electromagnetic field in vacuum can be stated in a form closely parallel to Dirac's theory of the electron. The electromagnetic field is described by a three-by-one column matrix whose elements are linear combinations of the three independent spinor components of the field. The Maxwell equations take a form similar to the Dirac equation for a free electron but involving three-by-three matrices. In terms of a wave function normalized so that the integral-square is the number of photons, the classical expressions for the energy, momentum, and angular momentum in the field are related to expected values of the Hamiltonian, momentum, and angular momentum operators. The angular momentum operator consists of an orbital part plus a three-by-three spin-one matrix part. As in Dirac's theory, the contributions from the states of negative Hamiltonian eigenvalue must be subtracted---these are states of opposite circular polarization.