Electromagnetic Gaussian Schell-model Sources Research Articles

Spectral polarization of Gaussian Schell-model beams.

We present a class of broadband electromagnetic Gaussian Schell-model sources whose state of polarization is both uniform and identical for all frequencies, but whose far-zone polarization properties strongly depend on wavelength. Also, these sources can produce beams whose polarized portion is always linearly polarized but with a polarization angle that evolves on propagation. Our results offer new insights into the behavior of broadband partially coherent sources.

Reconstruction of an electromagnetic Gaussian Schell-model source from far-zone intensity measurements.

An electromagnetic Gaussian Schell-model source that produces a random beam may be characterized by eight independent quantities. We show how far-zone measurements of the Stokes parameters, together with the Hanbury Brown-Twiss coefficient, allow one to determine all the source parameters. This method provides, to the best of our knowledge, a new tool to identify distant sources.

Nonparaxial, quasihomogeneous electromagnetic sources and their wide-angle far fields

Abstract We consider random, three-component, planar, quasihomogeneous electromagnetic sources and the nonparaxial far fields which they produce. We show that by measuring the far-field spectral polarization matrix on a spherical surface throughout a half-space enables to reconstruct the low spatial-frequency parts of the degrees of correlation between the parallel source field components. Further, detecting, in addition, the far-zone angular cross-spectral density matrix for all pairs of directions with significant intensity allows to deduce the low spatial-frequency contributions to the spectral densities of the source field components as well as the degrees of correlation between the orthogonal components. The validity of the formalism is demonstrated by considering a three-component, electromagnetic Gaussian Schell-model source. The results are important for the research on electromagnetic wide-angle radiators such as many thermal and fluorescent sources and light-emitting diodes.

Monte Carlo simulations of three-dimensional electromagnetic Gaussian Schell-model sources.

This article presents a method to simulate a three-dimensional (3D) electromagnetic Gaussian-Schell model (EGSM) source with desired characteristics. Using the complex screen method, originally developed for the synthesis of two-dimensional stochastic electromagnetic fields, a set of equations is derived which relate the desired 3D source characteristics to those of the statistics of the random complex screen. From these equations and the 3D EGSM source realizability conditions, a single criterion is derived, which when satisfied guarantees both the realizability and simulatability of the desired 3D EGSM source. Lastly, a 3D EGSM source, with specified properties, is simulated; the Monte Carlo simulation results are compared to the theoretical expressions to validate the method.

Three-dimensional electromagnetic Gaussian Schell-model sources.

We introduce three-dimensional (3D) stationary, electromagnetic Gaussian Schell-model (GSM) sources in the space-frequency domain and derive the realizability conditions that the source parameters must obey. In particular, we extend to 3D GSM sources two approaches to the realizability conditions presented previously for beam-like GSM sources. The results are of interest in the analysis and synthesis of tunable non-paraxial, partially coherent, partially polarized light fields.

Modeling random screens for predefined electromagnetic Gaussian-Schell model sources.

In a previous paper [Opt. Express22, 31691 (2014)] two different wave optics methodologies (phase screen and complex screen) were introduced to generate electromagnetic Gaussian Schell-model sources. A numerical optimization approach based on theoretical realizability conditions was used to determine the screen parameters. In this work we describe a practical modeling approach for the two methodologies that employs a common numerical recipe for generating correlated Gaussian random sequences and establish exact relationships between the screen simulation parameters and the source parameters. Both methodologies are demonstrated in a wave-optics simulation framework for an example source. The two methodologies are found to have some differing features, for example, the phase screen method is more flexible than the complex screen in terms of the range of combinations of beam parameter values that can be modeled. This work supports numerical wave optics simulations or laboratory experiments involving electromagnetic Gaussian Schell-model sources.

Polarization properties of three-dimensional electromagnetic Gaussian Schell-Model sources

The polarization properties of the recently introduced three-dimensional electromagnetic Gaussian Schell-model sources [Opt. Lett. 42, 1792 (2017)] are examined. Both cases of uniform and non-uniform polarization are considered. The three-dimensional polarization states are characterized via the eigenvalues of a 3×3 source polarization matrix and, more specifically, via the indices of polarimetric purity. We show that the considered sources exhibit a variety of polarization states throughout their volumes conveniently controlled by several physically accessible source parameters.

Laguerre-Gaussian functions and generalized formulation of electromagnetic Gaussian Schell-model sources.

Fourier transform of the combination of Gaussian function and power functions of even exponents 2n(n=0,1,2,…) gives rise to a class of physically realizable electromagnetic sources with correlation properties expressible in terms of Laguerre-Gaussian functions. Relatively simple mathematical expressions of the electromagnetic beams produced by the Laguerre-Gaussian Schell-model sources are given for an investigation of the coherence and polarization properties and the higher-order coherence effect of the correlations between intensity fluctuations in the Laguerre-Gaussian Schell-model beams (Laguerre-GSMB) of any order n. Results obtained are compared numerically with the predictions of the classic electromagnetic Gaussian Schell-model beam that is the lowest-order Laguerre-GSM beams.

Computational approaches for generating electromagnetic Gaussian Schell-model sources

Two different methodologies for generating an electromagnetic Gaussian-Schell model source are discussed. One approach uses a sequence of random phase screens at the source plane and the other uses a sequence of random complex transmittance screens. The relationships between the screen parameters and the desired electromagnetic Gaussian-Schell model source parameters are derived. The approaches are verified by comparing numerical simulation results with published theory. This work enables one to design an electromagnetic Gaussian-Schell model source with pre-defined characteristics for wave optics simulations or laboratory experiments.

Experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model source

We report the experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model (EGSM) source based on the technique for measuring the fourth-order correlation function (i.e., intensity correlation function). Furthermore, we carry out experimental measurement of the intensity distribution of a focused EGSM beam, and we carry out theoretical simulation using the measured beam parameters. Our experimental results agree reasonably well with the theoretical predictions.

Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence

We present a detailed investigation, qualitative and quantitative, on how the atmospheric turbulence with a non-Kolmogorov power spectrum affects the major statistics of stochastic electromagnetic beams, such as the spectral composition and the states of coherence and polarization. We suggest a detailed survey on how these properties evolve on propagation of beams generated by electromagnetic Gaussian Schell-model sources, depending on the fractal constant alpha of the atmospheric power spectrum.

Parametric study of uniformly polarized stochastic electromagnetic beam and its imaging

A parametric study is performed in investigating the stochastic electromagnetic beam generated by a uniformly polarized electromagnetic Gaussian Schell-model source and passing through ABCD optical systems. Through theoretical analysis, the requirement is derived that the uniformly polarized electromagnetic field can be obtained at the output plane of the imaging optical system. Furthermore, the general imaging formula of the stochastic electromagnetic beam is derived. Numerical examples are also presented to illustrate the application.

Synthesis of electromagnetic Schell-model sources

A procedure for the synthesis of the most general electromagnetic Schell-model light source is proposed. It makes use of the generalized van Cittert-Zernike theorem to produce the electromagnetic source starting from a primary spatially incoherent source, characterized by a suitable position-dependent polarization matrix. By resorting to the spectral decomposition of the polarization matrix, it is shown how such an incoherent source can be synthesized by using a Mach-Zehnder interferometer, with suitable amplitude transmittances placed in its arms, fed by two mutually uncorrelated laser beams. Examples are given for the case of electromagnetic Gaussian Schell-model sources.

Statistical properties of correlated radial stochastic electromagnetic array beams on propagation

A kind of array beam named the correlated radial stochastic electromagnetic array beam that is generated by an electromagnetic Gaussian Schell-model source is introduced by use of tensor method. The analytical expression for the cross-spectral density matrix of this array beam propagating through the turbulent atmosphere and in free space is obtained after performing vector integration. Some typical numerical calculations are illustrated for the changes in the spectral density, spectral degree of polarization, and spectral degree of coherence of the beam on propagation. We find that the atmospheric turbulence can destroy the correlated effect among the beamlets.

Propagation of stochastic Gaussian-Schell model array beams in turbulent atmosphere

Analytical formulas for the elements of the 2x2 cross-spectral density matrix of a kind of stochastic electromagnetic array beam propagating through the turbulent atmosphere are derived with the help of vector integration. Two types of superposition (i.e. the correlated superposition and the uncorrelated superposition) are considered. The changes in the spectral density and in the spectral degree of polarization of such an array beam generated by isotropic or anisotropic electromagnetic Gaussian Schell-model sources on propagation are determined by the use of the analytical formulas. It is shown by numerical calculations that for the array beam composed by isotropic Gaussian-Schell model sources, the spectral degree of polarization in the sufficiently far field returns to the value of the array source; for the array beam composed by anisotropic sources, the spectral degree of polarization in the far field approaches a fixed value that is different from the source.

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.

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.

Vector-mode analysis of symmetric two-point sources

Vector modes and eigenvalues are evaluated for a partially coherent source when only a pair of points is of interest, as in the case of the radiation emerging from the pinholes of a Young interferometer fed by an electromagnetic beam. Analytical results are presented, paying particular attention to those cases when the fields at the two points cannot be distinguished from one another on the basis of their second-order correlation properties. It is shown that the superposition scheme provided by the vectorial modal theory of coherence allows a simple interpretation of the interference pattern and an intuitive understanding of its coherence–polarization features to be given. Examples are given for the case of electromagnetic Gaussian Schell-model sources.

A method of generating electromagnetic Gaussian Schell-model beams

A method of generating an electromagnetic Gaussian Schell-model source from two coherent linearly polarized plane waves is described. This method involves two mutually correlated phase-only liquid-crystal spatial light modulators placed in the arms of a Mach–Zehnder interferometer. The sources produced by this method can be used to generate a wide class of electromagnetic beams with prescribed coherence and polarization properties.

Realizability conditions for electromagnetic Gaussian Schell-model sources

The electromagnetic Gaussian Schell-model (EGSM) beam is the simplest analytical model of a random electromagnetic beam. The model can be successfully used in studies of spectral, polarization and coherence properties of random electromagnetic beams on propagation in free space or in any linear medium, deterministic or random. The most general type of source which produces electromagnetic Gaussian Schell-model beam is characterized by 10 parameters. Using properties of the cross-spectral density matrix of such a beam, we derive necessary and sufficient conditions which the parameters of the source must satisfy in order to generate a physically realizable beam of this type. The conditions provide certain constraints for synthesis, simulations and any application of such beams.