Stochastic Electromagnetic Beams Research Articles

Propagation characteristics of stochastic electromagnetic array beams

A stochastic electromagnetic array beam that is generated by an electromagnetic Gaussian Schell-model source is introduced by using tensor method. An analytical expression for the cross-spectral density matrix of the stochastic electromagnetic array beam propagating in a paraxial ABCD optical system is derived after performing vector integration. Some numerical calculations are illustrated for the propagation characteristics of such an array beam in free space and fractional Fourier transform (FRFT) system as application examples.

Determination of the coherency matrix of a broadband stochastic electromagnetic light beam

The statistical ensemble of a fluctuating, statistically-stationary electromagnetic light beam is presented in terms of a 2 × 2 matrix, so-called coherency matrix. The method to determine such matrix for a quasi-monochromatic light beam has been proposed for many years. In this paper, we demonstrate that the method needs to be only slightly modified to determine the matrix elements of a broadband stochastic electromagnetic light beam, if one uses the representation of statistical wave fields in the space–frequency domain. The implementation of the method is demonstrated, and the coherency matrix measurement is validated using a well-defined elliptically polarized beam.

Spectral changes of polychromatic stochastic electromagnetic vortex beams propagating through turbulent atmosphere

The unified theory of coherence and polarization and the propagation law of 2 × 2 cross-spectral density are employed to investigate spectral changes of the polychromatic stochastic electromagnetic vortex beam propagating in turbulent atmosphere. It is shown that the spectral changes of a polychromatic stochastic electromagnetic vortex beam in turbulent atmosphere differ from those of the beam without vortex. Specially, the on-axis relative spectral shifts exhibit not only blue-shift, but also red-shift. It is also shown that the topological charge, the correlation length and the refractive index structure constant influence the spectral changes of polychromatic stochastic electromagnetic vortex beams in a turbulent atmosphere.

Changes in generalized Stokes parameters of stochastic electromagnetic beams on propagation through ABCD optical systems and in the turbulent atmosphere

Using the derived formulas for the transformation of 2 × 2 cross-spectral density matrix of the stochastic electromagnetic beams propagating through ABCD optical systems and in the turbulent atmosphere, the changes in the generalized Stokes parameters of the beams propagating under these conditions can be investigated directly. Some typical numerical calculations are illustrated relating to the electromagnetic Gaussian Schell-model beams passing through free space, focal system, dual-focus system, and the turbulent atmosphere with different structure parameters. Further extensions are also pointed out.

An inverse problem in the theory of stochastic electromagnetic beams

The cross-spectral density matrix of an electromagnetic beam has been playing increasingly important role in studies of changes of spectra, of coherence and of polarization as the beam propagates. In this paper we derive solution to an inverse problem, which makes it possible to determine the cross-spectral density matrix of the beam in the source plane z = 0 , from the knowledge of the matrix in any cross-section z = z 0 > 0 in the half-space into which the beam propagates. We apply the result to the theory of so-called Stokes beams, which were introduced not long ago.

Criterion for keeping completely unpolarized or completely polarized stochastic electromagnetic Gaussian Schell-model beams on propagation

The cross-spectral density matrixes of electromagnetic Gaussian Schell-model sources that are completely unpolarized or completely polarized are derived. We find that both the completely unpolarized stochastic electromagnetic Gaussian Schell-model beam and the completely polarized stochastic electromagnetic Gaussian Schell-model beam will keep their spectral degree of polarization or become partially polarized under different constraint conditions during their propagation in free space or through turbulent atmosphere. We give necessary theoretical explanation to the physical phenomena. They are considered as coherence-induced polarization changes and spectral density-induced polarization changes.

Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere

Propagation of stochastic electromagnetic beams through paraxial ABCD optical systems operating through turbulent atmosphere is investigated with the help of the ABCD matrices and the generalized Huygens-Fresnel integral. In particular, the analytic formula is derived for the cross-spectral density matrix of an electromagnetic Gaussian Schell-model (EGSM) beam. We applied our analysis for the ABCD system with a single lens located on the propagation path, representing, in a particular case, the unfolded double-pass propagation scenario of active laser radar. Through a number of numerical examples we investigated the effect of local turbulence strength and lens' parameters on spectral, coherence and polarization properties of the EGSM beam.

Polarization and coherence properties of a beam formed by superposition of a pair of stochastic electromagnetic beams

General expressions are derived for the spectral degree of polarization and for the spectral degree of coherence of a beam generated by the superposition of two stochastic electromagnetic beams. A method to calculate the mutual cross-spectral density matrix of the superposed beam is discussed, as well as experiments to determine it.

Generalized Stokes parameters of a stochastic electromagnetic beam propagating through a paraxial ABCD optical system

On the basis of the generalized diffraction integral formula for an ABCD optical system in the spatial domain, a propagation law for the generalized Stokes parameters of a stochastic electromagnetic beam passing through an ABCD optical system is obtained. We describe the Stokes parameters of the source as linear combinations of the elements of the cross-spectral density matrix, and study the changes in the spectral degree of polarization and in the state of the polarization ellipse of a stochastic electromagnetic Gaussian Schell-model beam propagating through a gradient-index fiber with the help of generalized Stokes parameters and the cross-spectral density matrix. The medium has significant effect on the change of the spectral degree of polarization. However, when the correlation coefficients of the source satisfy the relation delta(xx)=delta(yy)=delta(xy)=delta(yx), the medium does not influence the spectral degree of polarization.

Stochastic electromagnetic beams focused by a bifocal lens

In this paper, we study the focusing of a stochastic electromagnetic beam by a bifocal lens. By taking the electromagnetic Gaussian Schell-model (EGSM) beam as an example, the changes in the spectral density, in the spectral degree of coherence, and in the spectral degree of polarization of the EGSM beam as the beam is focused by an unapertured bifocal lens are investigated. It is shown that the spectral density, the spectral degree of coherence, and the spectral degree of polarization of the focused electromagnetic EGSM beams depend upon the coherence lengths and focal lengths of the bifocal lens. The influence of the coherence lengths and the focal lengths on the focused spectral density, the spectral degree of coherence, and the spectral degree of polarization are investigated in great detail.

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.

Spectral changes in electromagnetic stochastic beams propagating through turbulent atmosphere

It is known that the spectrum of light can change on propagation, even in free space. Such changes are due to its coherence properties. We determine how the spectrum of a stochastic electromagnetic beam of any state of coherence changes on propagation in atmospheric turbulence. We illustrate the results by examining changes in the spectrum of an electromagnetic Gaussian Schell-model beam whose spectrum consists of a single spectral line with a Gaussian profile, which propagates through atmospheric turbulence, with Kolmogorov power spectrum. The results are of interest for optical communications through the atmosphere and for laser radar systems.

Intensity fluctuations and the degree of cross-polarization in stochastic electromagnetic beams

An expression is derived for the correlation between intensity fluctuations at pairs of points in a stochastic electromagnetic beam, obeying Gaussian statistics. The new formula, which is of particular interest for the theory of the Hanbury Brown?Twiss effect, applies to beams of any state of coherence and state of polarization. It contains a new 'two-point' degree of polarization whose presence indicates that, in general, the knowledge of the degree of coherence and of the usual degree of polarization are not adequate for determining the correlation between intensity fluctuations.

Conservation laws for stochastic electromagnetic free fields

Conservation laws for scalar stochastic free fields propagating in free space are generalized to electromagnetic beam-like fields. New conservation laws are derived for the elements of the cross-spectral density matrix of a stochastic electromagnetic beam, and they can be used to show that some integrated polarization properties, for example, Stokes parameters of a beam, are conserved on propagation in free space. We also show that, unlike integrated Stokes parameters, other polarization characteristics of a beam, for instance, its degree of polarization, are not, generally, conserved on propagation. The theory is illustrated by an example relating to the propagation of single-point and integrated Stokes parameters of an electromagnetic Gaussian Schell-model beam.

Scintillation index of a stochastic electromagnetic beam propagating in random media

We study the behavior of the scintillation index (the normalized variance of fluctuating intensity) of a wide-sense statistically stationary, quasi-monochromatic, electromagnetic beam propagating in a homogeneous isotropic medium. In particular, we show that in the case when the beam is treated electromagnetically apart from the correlation properties of the medium in which the beam travels not only its degree of coherence but also its degree of polarization in the source plane can affect the values of the scintillation index along the propagation path. We find that, generally, beams generated by unpolarized sources have reduced level of scintillation, compared with beams generated by fully polarized sources, provided they have the same intensity distribution and the same state of coherence in the source plane. An example illustrating the theory is considered which examines how the scintillation index of an electromagnetic Gaussian Schell-model beam propagates in the turbulent atmosphere. These results may find applications in optical communications through random media and in remote sensing.

Stochastic electromagnetic vortex beam and its propagation

The recent theory formulated in terms of the 2 × 2 cross-spectral density matrix and the propagation law of cross-spectral density are employed to investigate the stochastic electromagnetic vortex beam and its propagation characterization. Based on these, we derived the general formulae for the intensity distribution, degree of coherence and degree of polarization for stochastic electromagnetic vortex beam while propagating in free space. It is shown that the intensity distribution and the degree of polarization of the stochastic electromagnetic vortex beam propagating in free space depend on the correlation length and the topological charge of the vortex beam.

Beam criteria for propagation of electromagnetic beams in the turbulent atmosphere

A recently introduced criterion [O. Korotkova, E. Wolf, Opt. Lett. 32 (2007) 2137] for testing whether a scalar beam preserves its beam-like shape after it propagates some distance through the turbulent atmosphere is generalized to the case of electromagnetic beam propagation. The generalized criterion applies to monochromatic as well as to stochastic electromagnetic beams. The analysis is illustrated by examples.

Propagation characteristics of aberrant stochastic electromagnetic beams in a turbulent atmosphere

In this paper, we investigate the characteristics of stochastic electromagnetic beams with astigmatic aberration propagating through a turbulent atmosphere. Taking the electromagnetic Gaussian Schell-model beam (GSM beam) as an example, the analytic expressions for the intensity and the degree of polarization of the beams propagating through the turbulent atmosphere are derived. It is shown that the intensity distribution and the degree of polarization of the GSM beam in the turbulent atmosphere are severely influenced by the astigmatism coefficient, as well as by the correlation property and the atmospheric turbulence. We show that when beams with astigmatic aberration propagate in a turbulent atmosphere, the beams become asymmetric in the near field and turn out to be symmetric after a quite long distance propagation in the turbulent atmosphere.

Polarization properties of stochastic electromagnetic beams

The behavior of the degree of polarization of a Gaussian Schell-model beam propagating in free space is investigated. Contour diagrams for the degree of polarization, and for the spectral density (‘intensity’) of the polarized and the unpolarized portions of the beam are presented.

Anisotropic-source-induced changes of the degree of polarization of stochastic electromagnetic beams on propagation

It is shown that stochastic electromagnetic beams may have different degrees of polarization on propagation, even though they have the same coherence properties in the source plane. This fact is due to a possible difference in the anisotropy of the field in the source plane. The result is illustrated by some examples.