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.

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.

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.

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. It has been a common perception that a random medium is required for generation of such spectral shifts by scattering. In this Letter we show that such a phenomenon occurs even when the refractive index of the medium is a deterministic function of position. We also show that this phenomenon may be used to obtain information about the structure of a deterministic medium.

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. Both in simulation and in experiment, results show that a π/2-phase change occurs as the beam passes through each of the astigmatic foci, experimentally validating results derived in a recent paper by Visser and Wolf [Opt. Commun. 283, 3371-3375 (2010)].

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. The relationship between cross-spectral purity and spatial coherence has been the subject of investigations for some time. Recently, a concept of so-called statistical similarity has been introduced which provides a new way to elucidate complete spatial coherence. In this Letter, we discuss some implications of statistical similarity of an optical field on its cross-spectral purity.

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. It is found that the radiant intensity and the encircled energy in the far field depend on the degree of coherence of the incident beam, whereas the extinguished power does not.

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. Mandel many years ago, plays an important role in clarifying this relationship.

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. We show that when the coherence length of the incident field is comparable to, or is smaller than, the radius of the sphere, the angular distribution of the radiant intensity depends strongly on the degree of coherence. The results have implications, for example, for scattering in the atmosphere and colloidal suspensions.

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. We illustrate the result by an example.

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. Cambridge Philos. Soc.9, 399 (1852)] presented a theorem according to which any light beam is equivalent to the sum of two light beams, one of which is completely polarized and the other completely unpolarized. We show that Stokes' proof of this theorem is flawed. We present a condition for the theorem to be valid.

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.

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.