Stochastic Electromagnetic Gaussian Schell-model Beam Research Articles

Correlations between intensity fluctuations in stochastic electromagnetic Gaussian Schell-model beams

Recent researches about the vector theory of the Hanbury Brown–Twiss effect at optical frequencies have shown that a new statistical quantity, called the degree of cross-polarization, is needed to predict the correlations between intensity fluctuations in stochastic electromagnetic beams. This note is devoted to an investigation of the variations of the degree of cross-polarization and then to a comparison of the distributions of degree of coherence and the correlations between intensity fluctuations across the cross-section of stochastic electromagnetic Gaussian Schell-model (GSM) beams. Analysis leads to a generalization of scalar theory of the degree of global coherence that describes the GSM sources that generate the electromagnetic GSM beams of either spatially very coherent or spatially very incoherent in the global sense.

Coincidence fractional Fourier transform with a stochastic electromagnetic Gaussian Schell-model beam

Based on classical theory of optical coherence and polarization, coincidence fractional Fourier transform (FRT) with a stochastic electromagnetic Gaussian Schell-model (EGSM) beam is investigated. Dependences of the quality and visibility of the coincidence FRT pattern of an object on the degree of polarization and correlation coefficients of the EGSM beam are studied numerically. It is shown that the quality and visibility of the coincidence FRT pattern of an object are determined by the polarization and coherence of the EGSM beam together.

Degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model beam

The concept of the degree of paraxiality introduced recently for monochromatic fields is extended to the domain of stochastic electromagnetic fields. Analytical expression for the degree of paraxiality of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam is derived. Numerical results show that the degree of paraxiality of an EGSM beam is determined by the degree of polarization, r.m.s. widths of the spectral densities and of the correlation functions of its source. Degree of paraxiality of an EGSM beam after passing through a linear polarizer is also analyzed. Our results show that one can modulate the degree of paraxiality of an EGSM beam by a linear polarizer.

Focusing of stochastic electromagnetic Gaussian Schell-model beams through a high numerical aperture objective

Based on vectorial Debye diffraction theory, the focusing properties of stochastic electromagnetic Gaussian Schell-model beams in the focal region of high numerical aperture objective are investigated. Expressions for the intensity distribution and the degree of polarization are derived near the focus. Numerical calculations are performed to analyze the influences of varying corresponding parameters on the changes in the intensity distribution and in the degree of polarization in the focal region.

Propagation factor of a stochastic electromagnetic Gaussian Schell-model beam

Analytical formula is derived for the propagation factor (known asM(2)-factor) of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam in free space and in turbulent atmosphere. In free space, the M(2)-factor of an EGSM beam is mainly determined by its initial degree of polarization, r.m.s. widths of the spectral densities and correlation coefficients, and its value remains invariant on propagation. In turbulent atmosphere, the M(2)-factor of an EGSM beam is also determined by the parameters of the turbulent atmosphere, and its value increases on propagation. The relative M(2)-factor of an EGSM beam with lower correlation factors, larger r.m.s. widths of the spectral densities and longer wavelength is less affected by the atmospheric turbulence. Under suitable conditions, an EGSM beam is less affected by the atmospheric turbulence than a scalar GSM beam (i.e. fully polarized GSM beam). Our results will be useful in long-distance free-space optical communications.

Generalized formulas for stochastic electromagnetic beams on inverse propagation through nonsymmetrical optical systems

Generalized propagation formulas for the elements of the cross-spectral density matrix of stochastic electromagnetic beams on inverse propagation through an axially symmetrical or nonsymmetrical optical system are derived with the help of Fourier transform and inverse Fourier transform. As an example, we apply the formula to the inverse source problem of stochastic electromagnetic Gaussian Schell-model beams.

Propagation of a stochastic electromagnetic Gaussian Schell-model beam through an optical system in turbulent atmosphere

A generalized diffraction integral formula for stochastic electromagnetic beams propagating through an optical system in turbulent atmosphere is derived with the help of tensor method. Some analyses are illustrated by a numerical example relating to changes in the average intensity and the degree of polarization of an electromagnetic Gaussian Schell-model beam propagating through a double-lenses system. It is shown that the optical system has strong influence on the propagation properties of the beam. The method used in this paper can be widely applied to the propagation of astigmatic beams through an optical system in turbulent atmosphere.

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.

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.