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Biomedical subjects

Emil Wolf

Publications and source records attributed to Emil Wolf.

At least 19 recordsLinked to original sources
PubMed2006

Can two planar sources with the same sets of Stokes parameters generate beams with different degrees of polarization?

It is shown that two stochastic electromagnetic beams that propagate from the source plane z = 0 into the half-space z > 0 may have different degrees of polarization throughout the half-space, even though they have the same sets of Stokes parameters in the source plane. This fact is due to a possible difference in the coherence properties of the field in that plane, but other reasons are also possible. The result is illustrated by an example.

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PubMed2006

Invariance and noninvariance of the spectra of stochastic electromagnetic beams on propogation.

It has been known for some time that the spectrum of light may change on propagation, even in free space. The theory of this phenomenon was developed within the framework of scalar theory. We generalize it to electromagnetic beams, generated by planar, secondary, stochastic sources. We also derive an electromagnetic analog of the so-called scaling law. When this law is satisfied the normalized spectrum of the beam is the same throughout the far zone and across the source.

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PubMed2006

Effects of coherence on the degree of polarization in a young interference pattern.

Recent predictions concerning the relationship between the degree of polarization at a typical point of a Young interference pattern and the degree of coherence of the electromagnetic field at the pinholes are tested by a simple experiment. In particular, it is shown that light that is completely unpolarized at the pinholes can become partially polarized across the fringe pattern.

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PubMed2006

Polarization of completely coherent random electromagnetic beams.

It is shown that the spectral degree of polarization rho(r, omega) of a fluctuating electromagnetic beam which is completely coherent throughout a domain D is necessarily the same at every point in D. It can take on any value in the range 0 < or = rho < or = 1. In particular, the fully coherent beam can be completely polarized or completely unpolarized throughout D.

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PubMed2006

Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber.

Expressions are derived for the cross-spectral density matrix of an electromagnetic Gaussian Schell-model beam propagating through a paraxial ABCD system. Using the recently developed unified theory of coherence and polarization of electromagnetic beams and the ABCD matrix for gradient-index fibers, we study the changes of the spectral density, of the spectral degree of polarization, and of the spectral degree of coherence of such a beam as it travels through the fiber. Effects of material dispersion are also considered.

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PubMed2006

Scattering of light from quasi-homogeneous sources by quasi-homogeneous media.

The field generated by scattering of light from a quasi-homogeneous source on a quasi-homogeneous, random medium is investigated. It is found that, within the accuracy of the first-order Born approximation, the far field satisfies two reciprocity relations (sometimes called uncertainty relations). One of them implies that the spectral density (or spectral intensity) is proportional to the convolution of the spectral density of the source and the spatial Fourier transform of the correlation coefficient of the scattering potential. The other implies that the spectral degree of coherence of the far field is proportional to the convolution of the correlation coefficient of the source and the spatial Fourier transform of the strength of the scattering potential. While the case we consider might seem restrictive, it is actually quite general. For instance, the quasi-homogeneous source model can be used to describe the generation of beams with different coherence properties and different angular spreads. In addition, the quasi-homogeneous scattering model adequately describes a wide class of turbulent media, including a stratified, turbulent atmosphere and confined plasmas.

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PubMed2005

Wave-front spacing in the focal region of high-numerical-aperture systems.

The wave-front spacing in the focal region of an aplanatic focusing system is investigated by use of the vector theory of electromagnetic diffraction for monochromatic, linearly polarized incident light. It is shown that, in systems of high numerical aperture, the wave-front spacing near the focus is significantly larger than the wavelength of the incident light and that the wave-front spacing changes significantly within a few wavelengths of the focus and can be less than a wavelength.

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PubMed2005

Generalized stokes parameters of random electromagnetic beams.

A generalization of the Stokes parameters of a random electromagnetic beam is introduced. Unlike the usual Stokes parameters, which depend on one spatial variable, the generalized Stokes parameters, depend on two spatial variables. They obey precise laws of propagation, both in free space and in any linear medium, whether deterministic or random. With the help of the generalized Stokes parameters, the changes in the ordinary Stokes parameters upon propagation can be determined. Numerical examples of such changes are presented. The generalized Stokes parameters contain information not only about the polarization properties of the beam but also about its coherence properties. We illustrate this fact by expressing the degree of coherence of the electromagnetic beam in terms of one of the generalized Stokes parameters.

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PubMed2005

Coherence and polarization properties of far fields generated by quasi-homogeneous planar electromagnetic sources.

In studies of radiation from partially coherent sources the so-called quasi-homogeneous (QH) model sources have been very useful, for instance in elucidating the behavior of fields produced by thermal sources. The analysis of the fields generated by such sources has, however, been largely carried out in the framework of scalar wave theory. In this paper we generalize the concept of the QH source to the domain of the electromagnetic theory, and we derive expressions for the elements of the cross-spectral density matrix, for the spectral density, the spectral degree of coherence, the degree of polarization, and the Stokes parameters of the far field generated by planar QH sources of uniform states of polarization. We then derive reciprocity relations analogous to those familiar in connection with the QH scalar sources. We illustrate the results by determining the properties of the far field produced by transmission of an electromagnetic beam through a system of spatial light modulators.

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PubMed2004

Correlation matrix of a completely polarized, statistically stationary electromagnetic field.

It is shown that, for a 3 x 3 correlation matrix Wij(r, r, omega), (i, j = x, y, z) of the electric vector of a random, stationary electromagnetic field to represent a field that is completely polarized at a point r and frequency omega, each element of the matrix must factorize. More precisely, a necessary and sufficient condition for the correlation matrix to represent a fully polarized field at a point r is that the matrix has the form Wij(r, r, omega) = epsilon(i)*(r, omega)epsilon(j)(r, omega), where epsilon(i)(r, omega) (i = x, y, z) are deterministic functions, i.e., that all pairs of the Cartesian components of the electric field at a point r and frequency omega are completely correlated.

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PubMed2004

Beam conditions for radiation generated by an electromagnetic Gaussian Schell-model source.

It was shown recently that the basic properties of a fluctuating electromagnetic beam can be derived from knowledge of a 2 x 2 cross-spectral density matrix of the electric field in the source plane. However, not every such matrix represents a source that will generate a beamlike field. We derive conditions that the matrix must satisfy for the source to generate an electromagnetic Gaussian Schell-model beam.

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PubMed2004

Coherence properties of sunlight.

The coherence properties of sunlight were first studied by Verdet around 1869 and were later examined by other scientists. However, all the previous calculations assumed that the Earth is in the far zone of the Sun, an assumption that is incorrect. An investigation of why Verdet's result is nevertheless correct reveals a surprising property of radiation from incoherent sources.

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PubMed2004

New generalized Bessel-Gaussian beams.

Analytical expressions are derived for a new set of optical beams, in which the radial dependence is described by a sum of Bessel distributions of different orders, modified by a flat-topped Gaussian function expressed in the form 1 - [1 - exp(-xi2)]M, where xi is a dimensionless parameter and M(> or = 1) is a scalar quantity. The flat-topped Gaussian function can be readily expanded into a series of the lowest-order Gaussian modes with different parameters; this situation makes it possible to express the optical beam as a series of conventional Bessel-Gaussian beams of different orders. The propagation features of this new set of optical beams are investigated to reveal how a windowed Bessel beam passes progressively from a smooth Gaussian window toward the hard-edge limit.

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PubMed2004

Coherence and polarization of electromagnetic beams modulated by random phase screens and their changes on propagation in free space.

The spectral degree of coherence and of polarization of some model electromagnetic beams modulated by a polarization-dependent phase-modulating device, such as a liquid-crystal spatial light modulator, acting as a random phase screen are examined on the basis of the recent theory formulated in terms of the 2 x 2 cross-spectral density matrix of the beam. The phase-modulating device is assumed to have strong polarization dependence that modulates only one of the orthogonal components of the electric vector, and the phase of the phase-modulating device is assumed to be a random function of position imitating a random phase screen and is assumed to obey Gaussian statistics with zero mean. The propagation of the modulated beam is also examined to show how the spectral degrees of coherence and of polarization of the beam change on propagation, even in free space. The results are illustrated by numerical examples.

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PubMed2004

Spectral degree of coherence of a random three-dimensional electromagnetic field.

The complex spectral degree of coherence of a general random, statistically stationary electromagnetic field is introduced in a manner similar to the way it is defined for a beamlike field, namely, by means of Young's interference experiment. Both its modulus and its phase are measurable. We illustrate the definition by applying it to blackbody radiation emerging from a cavity. The results are of particular interest for near-field optics.

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