Classical Coherence Research Articles

Gauge invariance and transport properties in superconductors above Tc.

We have developed a theory of transport phenomena for superconductors above [ital T][sub [ital c]] in the fluctuating region in dirty and clean limits. We show that it is possible to construct a phenomenological theory based on Ginzburg-Landau equation and its gauge invariance, and as a result we can express the fluctuating corrections to the conductivity tensor in a magnetic field in terms of the classical conductivity and coherence lengths. We find that the sign of the Hall conductivity is universal and is determined by [partial derivative] ln[ital T][sub [ital c]]/[partial derivative] ln[mu].

Analysis of Low-coherence Excitation of a Two-mode Fibre Waveguide in the Michelson Interferometer Configuration

Abstract Low-coherence excitation of a two-mode fibre waveguide that leads to a suppressed interference pattern at its exit face is analysed. The use of classical coherence formalism and guided modes field representation reveals that the principle of coherence modulation can be used, i.e., the optical path difference between guided modes that exceeds the source coherence length can be compensated in the Michelson interferometer configuration. General considerations presented here also show the role played by the effect of second-order dispersion which substantially affects the use of this new fibre waveguide interferometer configuration for sensing applications.

Spectral and Dispersion Analysis of Laser Sources and Multimode Fibres Via the Statistics of the Intensity Pattern

Abstract The statistics of an intensity pattern at the exit face of a multimode fibre excited by a quasimonochromatic source is analysed by means of an expression for speckle pattern contrast. Theoretical considerations that take advantages of both classical coherence formalism and guided-mode field representation of light propagating in multimode fibres lead to two equivalent expressions for speckle pattern contrast; the first is expressed in the time domain by using a source temporal coherence function and the second is expressed in the frequency domain by using a frequency correlation function of the source spectral density. Moreover, the modal guiding conditions in multimode fibre are in both expressions governed by a maximum group delay time difference. The feasibility of both expressions, especially the second, is demonstrated by analytic expressions for the speckle pattern contrast for seven different spectra, that is the influence of the source temporal coherence as well as the modal dispersion is thus clearly shown.

Spatial and Temporal Coherence of Light in a Fibre Waveguide

Abstract A general expression for the mutual coherence function of an electromagnetic field propagating in a fibre waveguide is presented by means of classical coherence formalism and the guided modes field representation. Moreover, this expression is applied to a limiting case of the fibre waveguide excitation by cross-spectrally pure, spatially coherent and quasi-monochromatic source with a symmetrical spectrum. In particular, the complex degree of both spatial and temporal coherence at the exit face of a two-mode, weakly-guiding, step-index fibre waveguide is discussed as a function of an exciting condition of guided modes, an intermodal dispersion and a temporal coherence of the source, respectively.

Discussion: A Mistake in Dynamic Coherence Arguments?

Maher (1992b) advances an objection to dynamic Dutch-book arguments, partly inspired by the discussion in Levi (1987; in particular by Levi's case 2, p. 204). Informally, the objection is that the decision maker will “see the dutch book coming” and consequently refuse to bet, thus escaping the Dutch book. Maher makes this explicit by modeling the decision maker's choices as a sequential decision problem. On this basis he claims that there is a mistake in dynamic coherence arguments. There is really no formal mistake in classical dynamic coherence arguments, but the discussions in Maher and Levi do suggest interesting ways in which the definition of dynamic coherence might be strengthened. Such a strengthened “sequentialized” notion of dynamic coherence is explored here. It so happens that even on the strengthened standards for a Dutch book, the classic dynamic coherence argument for conditioning still goes through.

Supercoherence

The basic technical point of this paper is that a pseudo-simplicial category can be produced from primitive data consisting of face functors and degeneracy functors, natural isomorphisms corresponding to the standard simplicial identities, and a small list of higher order commutativity conditions relating these isomorphisms. A similar machine exists for constructing contravariant pseudo-functors on Segal's category Γ. Thus, a monoidal category M gives rise canonically to a pseudo-simplicial category BM which enjoys many of the properties of a classifying space construction, while a symmetric monoidal category A determines a Γ o category Γ o A which then can be used to directly construct a Γ o -space Γ o ∗ A and a spectrum Spt( A). These constructions generalize the basic classical categorical coherence results, and they lead to several applications in homotopy theory and algebraic K-theory. The applications given here include a generalized Quillen S 1 S-construction, a pseudo-functional version of the group-completion theorem, an explicit construction to the K-theory and L-theory presheaves of spectra, and a presheaf level delooping of the Q = + theorem.

Spatial coherence of anisotropic and astigmatic sources in interference electron microscopy and holography

The lateral coherence properties of two illumination modes in electron interferometry and holography are investigated within the framework of the mutual coherence function. It is shown that the results obtained can be considered particular realizations of the general, anisotropic, Gaussian Schell model, which plays an important role in the classical coherence theory in optics. Another property of this model is described: the ratio between the coherence and illumination areas is constant along every section of the beam. This invariant parameter is shown to be related to another geometric optical invariant of the beam, i.e., its etendue. Numerical calculations showing the relation between illumination and coherence areas in the image, Fresnel, and far-field (Fraunhofer) regions are presented and discussed with regard to the experimental implications.

Speckle patterns in small angle light scattering: The spatial autocorrelation function

The study deals with the determination of the spatial autocorrelation function of speckle patterns caused by the small-angle light scattering from polymer films. The autocorrelation function determines the shape, size and anisometry of the speckle. The effect of the inner structure and orientation of samples (polypropylene foil, poly(decamethylene terephthalate) and a sample of polypropylene filaments) is discussed; it is shown that under the usual experimental conditions the spatial autocorrelation function of speckle patterns can be determined on the basis of the van Cittert-Zernike theorem of the classical coherence theory. The good agreement between the theoretical and experimental dependences of anisometry, the angular dependence of speckle size and the dependence of speckle size on the sample thickness confirm the suitability of a uniform description based on the classical theory of coherence. From the standpoint of the theory of speckle effect, the results presented in this study allow us to infer that in the light scattering from polymer films under usual conditions the assumptions of the application of the central limit theorem are fulfilled: in the scattering volume there is a sufficient number of scattering units, and path fluctuations due to the scattering foil exceed the wavelength of light.

Intensity Correlation Metrology: A Comparative Study

The statistical theory of fully developed, coherent speckle patterns is compared to classical coherence theory. It is shown that speckle correlations are directly analogous to the Hanbury Brown and Twiss effect. On that background a unified description is given for a number of measurement techniques based on intensity correlation measurements in scattered laser light: holographic interferometry, speckle pattern interferometry, speckle photography, stellar speckle interferometry, laser Doppler velocimetry and intensity correlation spectroscopy.

Exploration of the eight-dimensional spin space of a spin-1 particle by NMR

NMR experiments that demonstrate classical spin rotations, spinor behavior, and coherence transfer have been performed on deuterium nuclei (spin 1) in the solid state. Double quantum transitions as well as quantum beats are observed. A connection to other fields of current interest such as optical beats and quarks is shown.

A note on the scattering of partially polarized radiation by free charges

The scattering of partially polarized radiation by free charges is analyzed from the standpoint of the classical coherence theory, introducing the second-order coherence tensor and the degree of polarization in a stationary ergodic incident field. A simple expression for the scattering cross section is obtained.

Relativistic Correlation Theory of the Electromagnetic Field in the Presence of Random Sources*

Relativistic formulation is presented of the second-order classical coherence theory of the electromagnetic field in the presence of random sources. It is shown that the dynamics of the second-order correlation tensors may be reduced to a simpler form in terms of certain tensor potentials. The gauge transformations of these tensor potentials are considered. In particular, two gauges of special interest are found, analogous to the Lorentz gauge and the radiation gauge in Maxwell’s electromagnetic theory. Some interesting relations and conservation laws are presented.

A Study of Partial Coherence and Its Application to the Collimation of Pulsed Multimode Laser Radiation

Classical coherence theory as presented by Wolf with the modification proposed by Neugebauer is used to describe mathematically and experimentally the collimation and focusing of the time-averaged intensity of pulsed multimode laser radiation. Measurements of the double-slit Fraunhofer pattern and the near and far zone intensity patterns were made on two pulsed ruby lasers by both still and streak photography to examine the spatial coherence and the collimation of the beam. Our result showed that the time-averaged collimation and focusing characteristics of the beam can be treated as the superposition of noncoupled spatially coherent modes.

Quantum and classical coherence of stationary modes

Quantum and classical coherence of stationary modes

Coherence effects in ultra-relativistic electron bremsstrahlung

The ultra-relativistic-electron bremsstrahlung in dense media is considered, using classical coherence conditions. General expressions for the reduction of bremsstrahlung in dense media have been obtained, which account for the Landau-Pomerancuk effect (effect of multiple scattering) and the Ter-Mikaeljan effect (effect of medium polarization). The problem of the bremsstrahlung angular distribution in the medium is considered. It has been shown that for sufficiently high energies of the electrons the reduction of bremsstrahlung is due not only to the polarization and multiple-scattering effects but also to the absorption of quanta in the medium. The bremsstrahlung spectrum in the frequency range dominated by the absorption effect has been obtained.