Change in spatial coherence of light on refraction and on reflection.

A theory of refraction and reflection of partially coherent electromagnetic beams has been recently developed. In this paper, we apply it to study the change in spatial coherence caused by refraction and by reflection more fully. By considering a Gaussian Schell-model beam, we show that the change is, in general, dependent on the angle of incidence.

Propagation of electromagnetic beams of any state of spatial coherence and polarization through multilayered stratified media.

We present a theory of propagation of a partially coherent and partially polarized electromagnetic beam through a multilayered stratified medium. The analysis shows that spatial coherence and polarization properties of the beam change, in general, on propagation through such a medium. We illustrate the results by an example.

Diffraction of radiation of any state of spatial coherence on media with periodic structure.

A general formula is derived for the spectral density distribution in the far zone, produced by the diffraction of a beam of any state of spatial coherence on a medium with a spatially periodic structure. The formula may be used to determine the structure of crystals from the diffraction of partially coherent x-ray beams.

Negative refraction of a partially coherent electromagnetic beam.

A theory of usual (positive) refraction of partially coherent electromagnetic beams has been developed recently. In this Letter, we discuss the theory of negative refraction of a partially coherent electromagnetic beam. We show that negative refraction can produce change in spatial coherence of such a beam.

Spectral changes of stochastic beams scattered on a deterministic medium.

It is well known that scattering of a polychromatic plane wave by a random medium, i.e., by a medium whose refractive index varies randomly with position, may produce frequency shifts of spectral lines.

Observation of the Gouy phase anomaly in astigmatic beams.

The Gouy phase anomaly, well established for stigmatic beams, is validated here for astigmatic beams. We simulate the predicted Gouy phase anomaly near astigmatic foci using a beam propagation algorithm integrated within lens design software. We then compare computational results with experimental data acquired using a modified Mertz-Sagnac interferometer.

Statistical similarity and cross-spectral purity of stationary stochastic fields.

In practical situations, one often generates a beam by superposition of two or more light beams. The beam generated by superposition displays, in general, different spectral properties than do the original beams. However, there are some optical beams, called cross-spectrally pure beams, which can generate a light beam of identical spectral distribution on superposition.

Coherence effects in Mie scattering.

The scattering of a partially coherent beam by a deterministic, spherical scatterer is studied. In particular, the Mie scattering by a Gaussian Schell-model beam is analyzed. Expressions are derived for (a) the extinguished power, (b) the radiant intensity of the scattered field, and (c) the encircled energy in the far field.

Implications of complete coherence in the space-frequency domain.

It was shown not long ago that complete spatial coherence of light at a pair of points in the space-time domain may be interpreted as a manifestation of so-called "statistical similarity" between the fluctuating field at the two points. In this Letter, we consider complete spatial coherence at a pair of points in the space-frequency domain and derive a condition that the field at those points must obey. We illustrate the usefulness of the condition by an example.

Relationship between complete coherence in the space-time and in the space-frequency domains.

We present some new results relating to properties of completely coherent optical fields. Our analysis elucidates the relationship between the theories of such fields in the space-time and in the space-frequency domains. We also show that the concept of cross-spectral purity, introduced by L.

The influence of the degree of cross-polarization on the Hanbury Brown-Twiss effect.

We show, by an example, that the knowledge of the degree of coherence and of the degree of polarization of a light beam incident on two photo detectors is not adequate to predict correlations in the fluctuations of the currents generated in the detectors (the Hanbury Brown-Twiss effect). The knowledge of the so-called degree of cross-polarization, introduced not long ago, is also needed.

Effects of spatial coherence on the angular distribution of radiant intensity generated by scattering on a sphere.

In the analysis of light scattering on a sphere it is implicitly assumed that the incident field is spatially fully coherent. However, under usual circumstances the field is partially coherent. We generalize the partial waves expansion method to this situation and examine the influence of the degree of coherence of the incident field on the radiant intensity of the scattered field in the far zone.

Solution of the phase problem in the theory of structure determination of crystals from x-ray diffraction experiments.

We present a solution to a long-standing basic problem encountered in the theory of structure determination of crystalline media from x-ray diffraction experiments; namely, the problem of determining phases of the diffracted beams.

Beam condition for scattering on random media.

Properties of random media are frequently investigated by studying their interactions with stochastic electromagnetic fields. However, a stochastic beam does not necessarily retain its beamlike form on scattering, and the theory of stochastic electromagnetic fields that are not beamlike is rather complicated. In this paper a necessary and sufficient condition is derived for a beam to retain its beamlike form after it is scattered on a stochastic medium.

Determination of correlation functions of scattering potentials of stochastic media from scattering experiments.

The classic "Ewald-sphere construction" for determining the structure of crystalline objects from x-ray and neutron diffraction experiments is generalized to determine the correlation functions of scattering potentials of stationary random media from scattering experiments.

Cross-spectral density matrices of polarized light beams.

We show that there is no unique form of the cross-spectral density matrix of completely polarized light beams. We present three kinds of such matrices, each of which represents a beam that is completely polarized at every point. Some of the beams do not imitate monochromatic beams, in contrast to the usual assumption made in polarization optics.

Coherence-induced polarization changes in light beams.

We consider a class of stochastic electromagnetic beams, and we show both analytically and by numerical examples that coherence properties of the electromagnetic field in the source plane affect the polarization properties of the radiated beam.

Can a light beam be considered to be the sum of a completely polarized and a completely unpolarized beam?

In a classic paper that may be regarded as the starting point of polarization optics, G. G. Stokes [Trans.

Application of correlation-induced spectral changes to inverse scattering.

It is shown how the phenomenon of correlation-induced spectral changes generated on scattering of a polychromatic plane wave on a spatially homogeneous random medium may be used to determine the correlation function of the scattering potential of the medium.

Polarization invariance in beam propagation.

It has been known for some time that the degree of polarization of a light beam may change on propagation, even in free space. In this Letter we derive sufficiency conditions for the degree of polarization of a beam generated by a uniformly polarized stochastic, electromagnetic source of a wide class to be the same throughout the far zone and in the source plane.

Diffraction tomography without phase information.

A modified form of diffraction tomography is presented in which measurements of the phase of the scattered field are replaced with measurements of the intensity on two planes beyond the scatterer. The new method is illustrated by an example.

Solution to the inverse scattering problem for strongly fluctuating media using partially coherent light.

We investigate the inverse scattering problem for statistically homogeneous, isotropic random media under conditions of strong fluctuations of optical wavefields. We present a method for determining the spectral density of the dielectric constant fluctuations in such media from scattering of partially coherent light. The method may find applications to a wide class of turbulent media such as the turbulent atmosphere and certain turbulent plasmas where backscattering and depolarization effects are negligible.

Spectral anomalies in a Fraunhofer diffraction pattern.

We show that spectacular spectral changes take place in the vicinity of the dark rings of the Airy pattern formed with spatially coherent, polychromatic light diffracted at a circular aperture.

Polarization-induced spectral changes on propagation of stochastic electromagnetic beams.

It was shown some years ago that the spectrum of a stochastic scalar field depends not only on the source spectrum but also on the degree of coherence of the source. In this paper we show that there are electromagnetic fields for which not only the state of coherence of the source, but also its degree of polarization affect the spectrum of the radiated field. We illustrate the analysis by diagrams which show the far-zone spectra of some stochastic electromagnetic beams generated by sources of different states of coherence and different degrees of polarization.

Scattering matrix theory for stochastic scalar fields.

We consider scattering of stochastic scalar fields on deterministic as well as on random media, occupying a finite domain. The scattering is characterized by a generalized scattering matrix which transforms the angular correlation function of the incident field into the angular correlation function of the scattered field. Within the accuracy of the first Born approximation this matrix can be expressed in a simple manner in terms of the scattering potential of the scatterer.