Stochastic Electromagnetic Beams Research Articles

Generation of stochastic electromagnetic beams based on modified degenerate cavity lasers

This study introduces a technique for generating stochastic electromagnetic (SEM) beams using a modified degenerate cavity laser in which one mirror is substituted with a spatial light modulator (SLM). We propose two methods to manipulate the spatial coherence of SEM beams: the first involves adjusting the size of a spatial filter within the laser cavity, which alters the number of oscillating transverse modes and thus varies the spatial coherence. The second method employs phase modulation by applying a dynamic random phase to the SLM. This dual approach allows for precise control over the spatial coherence properties of SEM beams. Experimental results demonstrate the generation of SEM beams using an SLM within a modified degenerate cavity laser and reveal a correlation between two orthogonal polarization components of the beams.

The Effect of Anisotropic Gaussian Schell-Model Sources in Generalized Phase Space Stokes Parameters

Phase-space transforms describe spatial and angular information about light sources where one example is the Wigner functions in wave optics. Stokes parameters, on the other hand, supply information about the polarization of light beams. The generalized phase space Stokes parameters of 2D stochastic electromagnetic beams are already developed. In this article, the application of anisotropic light sources in generalized phase space Stokes parameters is theoretically investigated and numerically analyzed. There are several different ways of studying electromagnetic light beams depending on the spatial domain. But, most measure of the polarization of random light fields is carried out within the Stokes parameters context. In this account we study the electromagnetism, Stokes parameters, phase space, and the anisotropy properties of random light beams at once. We find here that when an anisotropy introduced in phase space then the cross terms of the Wigner matrix depart from the diagonal terms, which is not the same in configuration space. As a result, anisotropy has a different effect in Phase space, i.e. an anisotropic source introduces a phase and a variance change only in the cross terms of Wigner matrix. This is due to the use of anisotropy in the shifted kernel of Wigner transform.

Polarization-resolved scintillations in Young's experiment.

The conventional scintillation, or intensity fluctuation, that occurs in random electromagnetic beams is just one member of a broader class of four interconnected, polarization-resolved scintillations. We examine these generalized scintillations, called Stokes scintillations, that occur when two stochastic electromagnetic beams are made to interfere in Young's experiment. We find that the magnitude of the conventional scintillation can be decreased, within certain limits, at the expense of an increase of one or more of the other Stokes scintillations. For certain applications however, it may be beneficial to suppress the latter.

Vortex phase induced evolution of propagation properties of a spatiotemporally partially coherent partially polarized pulsed beam in atmospheric turbulence

Here, a novel family of stochastic electromagnetic sources called spatiotemporally partially coherent partially polarized multi-Gaussian Schell-model vortex pulsed beams is proposed. With the extended Huygens–Fresnel principle, we derive the analytical formulas for the propagation of our beam in atmospheric turbulence. The spectral density and spectral degree of polarization of such beam both in free space and atmospheric turbulence are investigated. For comparison, we also study the behavior of the partially polarized multi-Gaussian Schell-model non-vortex pulsed beams during transmission. Our theoretical models enrich the classical theory of propagating stochastic electromagnetic beams and may provide a feasible method for further explorations to the novel kind of optical field modulation.

Twisted Electromagnetic Multi-Gaussian Schell-Model Pulsed Source and Its Propagation

Here, a novel family of random electromagnetic sources (twisted electromagnetic multi-Gaussian Schell-model pulsed beams) exhibiting transverse orbital angular momentum is proposed. The physically realizable conditions for these sources are established, and the analytical formulas of the cross-spectral density matrix elements of the beam propagating through an ABCD optical system are derived within the framework of the extended Collins formula. The behaviors of the spectral density, and the spectral degree of coherence of the beam during transmission are investigated numerically. This work enriches the classical theory of stochastic electromagnetic beams propagation, and may benefit applications requiring a specified degree of beam coherence with transverse orbital angular momentum.

Statistical properties of a spatiotemporally partially coherent vector cosine-Gaussian-correlated pulsed beam with radial polarization in atmospheric turbulence

In this study, we introduce a novel class of partially coherent vector sources, namely radially polarized spatiotemporally partially coherent cosine-Gaussian-correlated Schell-model pulsed (CGCSMP) beams, which are natural extensions of the scalar Gaussian Schell-model pulsed beams. The conditions for the physical realization of this source are established, and analytical formulae for the two-point, two-frequency cross-spectral density matrix elements of a beam propagating through turbulent atmosphere are derived within the framework of the extended Huygens–Fresnel principle and the atmospheric turbulence spectrum model. The behaviors of the spectral intensity, the spectral degree of polarization (DOP), and the spectral degree of coherence (DOC) of the beam during transmission are investigated numerically. Our work enriches the classical theory of propagating stochastic electromagnetic beams and may be useful for applications requiring a specified degree of beam coherence.

Far-zone behaviors of scattering-induced statistical properties of partially polarized spatially and spectrally partially coherent electromagnetic pulsed beam**Project supported by the National Natural Science Foundation of China (Grant No. 11504286), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2019JM-470), the Fund from the International Technology Collaborative Center for Advanced Optical Manufacturing and Optoelectronic Measurement, and the Science

In this study, we explore the far-zero behaviors of a scattered partially polarized spatially and spectrally partially coherent electromagnetic pulsed beam irradiating on a deterministic medium. The analytical formula for the cross-spectral density matrix elements of this beam in the spherical coordinate system is derived. Within the framework of the first-order Born approximation, the effects of the scattering angle θ, the source parameters (i.e., the pulse duration T0 and the temporal coherence length Tcxx), and the scatterer parameter (i.e., the effective width of the medium σR) on the spectral density, the spectral shift, the spectral degree of polarization, and the degree of spectral coherence of the scattered source in the far-zero field are studied numerically and comparatively. Our work improves the scattering theory of stochastic electromagnetic beams and it may be useful for the applications involving the interaction between incident light waves and scattering media.

Anisotropic turbulence-induced statistical properties evolution of a radially polarized partially coherent pulsed beam on propagation

In this study, we introduce a new kind of partially coherent vector beam with Gaussian distribution in the spatial, temporal and correlation components named a radially polarized partially coherent Gaussian Schell-model pulsed (GSMP) beam as a natural extension of scalar Gaussian Schell-model pulsed beam. Analytical formulas for the two-frequency cross-spectral density matrix elements of this beam are derived based on the extended Huygens–Fresnel theory. Within the frame of extend anisotropic non-Kolmogorov spectrum, the effects of asymmetry anisotropic turbulence eddies on the statistical properties of a radially polarized partially coherent GSMP beam are investigated numerically. Our work improves the classical theory of stochastic electromagnetic beams on propagation and may be useful for applications involving free-space optical communications.

Spectral shifts and spectral switches of polychromatic stochastic electromagnetic vortex beams on scattering from a semisoft boundary medium

Within the accuracy of the first-order Born approximation, the spectrum of a polychromatic stochastic electromagnetic vortex beam on scattering from a semisoft boundary medium is investigated. It is shown from the numerical results that the magnitude of the spectral shift and the position where the spectral switch occurs are affected by the scattering direction, the properties of the incident vortex beam and the scattering medium. It is also shown that the position where the spectral switch takes place will differ for an incident beam with vortex or not.

Weak ghost scattering with stochastic electromagnetic beams

We generalize the theory of ghost scattering with scalar incoherent light sources to the case of stochastic electromagnetic beams under the first-order Born approximation. We derive the expressions for the correlation of intensity fluctuations of the far-zone scattered fields and use them to study the properties of the scatterers. When the incident beam belongs to the class of electromagnetic Gaussian Schell-model beams, we discuss the dependence of ghost scattering results on the parameters such as the coherence lengths, source widths, polarization amplitudes, and degree of coherence. We find under the condition of linear polarized incident beams the scalar ghost scattering results can be retrieved, while the deviation from linear polarization may significantly distort the electromagnetic ghost scattering results.

Polarization properties of stochastic electromagnetic beams modulated by a wavefront-folding interferometer.

We consider the field generated by a wavefront-folding interferometer which is illuminated by a stochastic electromagnetic beam. The specular property and anti-specular property are discussed in the vector case. Take electromagnetic Gaussian Schell-model beam as an example, we investigate the spectral density, the spectral degree of coherence, the spectral degree of polarization as well as the state of polarization of the polarized portion of the field on propagation. Results show that the polarization properties including the degree of polarization, the orientation angle and the degree of ellipse can be adjusted by the phase difference of the interferometer and the phase retardation introduced by the prism. The results may be applied in free-space optical communication.

Generation of non-uniformly correlated stochastic electromagnetic beams

Until now, there have been many reports concerning the generation and propagation of partially coherent beams due to their less influencing ability in turbulent atmosphere and random media. Of particular interest, a Gaussian-Schell model beam has been widely chosen as a special example of partially coherent beam, since its spatial coherence degree is dependent on position only through the difference between the two position vectors. In the scalar domain, many coherent models have been well studied such as Gaussian and multi-Gaussian Schell-model sources, Bessel-Gaussian and Laguerre-Gaussian Schell-model sources and so on. Based on the theory for devising genuine cross-spectral density matrices for a stochastic electromagnetic beam, several scalar models have been also extended to the electromagnetic domain. In recent years, the propagation of partially coherent beams with spatially varying and non-uniform correlations has become a hot topic, because of their interesting characteristics such as locally sharpened and laterally shifted intensity maxima. In one of our previous studies, we have experimentally investigated the generation of non-uniformly correlated partially coherent beams. However, to the best of our knowledge, so far, there has been no investigation on the generation of non-uniformly correlated stochastic electromagnetic beams. In this paper, we theoretically and experimentally investigate the generation of non-uniformly correlated stochastic electromagnetic beams. Based on the relation between phase correlation and optical coherence, we investigate the 22 cross-spectral density matrix and the coherence distribution of the non-uniformly correlated stochastic electromagnetic beam we generated. It is shown that the coherence degree between two points in the generated beam depends not only on the distance between them, but also on the distances between the points and the center of the beam. In experiment, we use the Matlab rand function to generate a random phase pattern with uniform distribution. The modulation magnitudes of different positions are different and follow an inverse Gaussian distribution in position. Dynamic phase patterns are created from a series of random grey-scale images. Two phase-only liquid crystal spatial light modulators are employed to display computer-generated dynamic phase patterns and modulate the two orthogonally polarized components of the incident coherent light, respectively, and generate a stochastic electromagnetic beam. We measure the correlation distribution of the generated beam in Young's two-pinhole experiment. It is shown that the experimental observations are in agreement with our theoretical analyses. Other kinds of non-uniformly correlated stochastic electromagnetic beams can also be obtained by this approach. Non-uniformly correlated stochastic electromagnetic beams may have some applications in optical manipulation and free-space optical communication.

Propagation of stochastic electromagnetic high-order Bessel-Gaussian beams in the oceanic turbulence

Recently, the laser beam propagation in the oceanic turbulence has become a hot research topic. In addition to the characteristics of free diffraction and self-reconstruction, the high-order Bessel-Gaussian beam is a kind of typical vortex beam because of the existence of a spiral phase factor with orbital angular momentum. Researchers have investigated the self-reconstruction property of the high-order Bessel-Gaussian beams in the free space, also carried out intensive researches on the transmission characteristics of high-order Bessel-Gaussian beam in the ABCD optical system and in the atmospheric turbulence. However, to the best of our knowledge, to date there has been no investigation on the propagation of this laser beam in the oceanic turbulence. In this paper, we will study the propagation characteristics of the random electromagnetic high-order Bessel-Gaussian beams in the oceanic turbulence, and discuss the variation of the normalized spectrum intensity, the spectral degree of polarization, and the spectral degree of coherence. By using the extended Huygens-Fresnel diffraction integral formula, the general expression for the cross spectral density matrix of the stochastic electromagnetic high-order Bessel-Gaussian beams propagating in the oceanic turbulence is obtained, and the statistical properties of the random electromagnetic high-order Bessel-Gaussian beams propagating in the seawater are investigated by numerical calculation. The numerical results show that the oceanic turbulence can affect the normalized spectral intensity distribution of the random electromagnetic beam. With the increase of the transmission distance, the center of the zero-order Bessel-Gaussian beam becomes depressed, and the center of the higher-order Bessel-Gaussian beam will become flat and then depressed. As the transmission distance increases far enough, regardless of the zero-order or higher-order, the intensity distribution will eventually evolve into the quasi Gaussian shaped distribution. The variation of the degree of polarization of each point on the x axis is related to the coherence length (xx，yy) and the oceanic turbulence parameters. The spectral coherence of the origin and any point on the x axis also changes with the increase of x, and the rate of dissipation of mean-square temperature T has influence on the spectral coherence. This research is of great value for applying the high-order Bessel-Gaussian beam to the optical communication, optical imaging and underwater exploration in the ocean.

The effects of polarization changes of stochastic electromagnetic beams on heterodyne detection in turbulence

The performance of heterodyne systems is discussed for stochastic electromagnetic beams in turbulent atmospheres by introducing a turbulence spectrum of refractive-index fluctuations. Several analytic formulae for the heterodyne detection system are presented by employing the beam coherence polarization matrix of an electromagnetic Gaussian Schell-model beam. Based on the Tatarskii spectrum model, some numerical results are given for the variation of heterodyne efficiency with the misalignment angle, detector diameter, turbulence conditions and parameters of the overlapping beams. According to the numerical results, we find that the change in heterodyne efficiency is dependent on the initial polarization of the beams, and that a turbulent atmosphere degrades the heterodyne efficiency significantly for a lager detector diameter. The change in heterodyne efficiency in a turbulent atmosphere is basically the same as that in free space for a relatively short distance zs. However, the change in heterodyne efficiency is different for a sufficiently long distance. For the deterministic received signal and the detector, the performance of the heterodyne detection can be adjusted by controlling the local oscillator signal parameters.

Generation of stochastic electromagnetic beams with complete controllable coherence.

We generate a stochastic electromagnetic beam (SEB) with complete controllable coherence, that is, the coherence degree can be controlled independently along two mutually perpendicular directions. We control the coherence of the SEB by adjusting the phase modulation magnitude applied onto two crossed phase only spatial light modulators. We measure the beam's coherence properties using Young's interference experiment, as well as the beam propagation factor. It is shown that the experimental results are consistent with our theoretical predictions.

Magnetic spectral Stokes singularities of stochastic electromagnetic beams through an astigmatic lens

Much interest has been aroused in the polarization singularities. A new technique for metrology called singular Stokes polarimetry based on the detection of polarization singularities has been recently developed and used to detect deformations and displacements of samples on a submicron scale, to measure the topology of polarized speckle field and to study the biomedicine as well. The polarization singularities have been extensively studied theoretically, numerically and experimentally. However, most of the studiesare restricted within the frameworks of the fully coherent wave-fields. By using the spectral Stokes parameters introduced by Korotkova and Wolf[Korotkova O, Wolf E 2005 Opt. Lett. 30 198], Yan and L[Yan H, L B 2009 Opt. Lett. 34 1933] have extended the concept of the polarization singularities from fully coherent beams to partially coherent beams. On the other hand, Hajnal[Hajnal J V 1990 Proc. R. Soc. Lond. A 430 413] studied the electric and magnetic polarization singularities in free-space propagation experimentally with microwaves and confirmed that the electric and magnetic polarization singularities are not coincident in general. In this paper, taking the partially coherent edge dislocation beam for example, the explicit magnetic propagation expression for stochastic electromagnetic beam through an astigmatic lens is derived based on the representation of cross-spectral density matrix propagation. Using the spectral Stokes parameters the magnetic spectral singularities are studied in detail. It is shown that there exist magnetic spectral s12, s23 and s31 singularities of stochastic electromagnetic beams through an astigmatic lens. The magnetic spectral Stokes singularities correspond to the zero points of complex Stokes fields sij=0. s12 singularity corresponds to the circular polarization (C-point) of partially coherent beam, and s3 0(s30) means right-(left-) handedness, where the orientations of the major and minor axes of the polarization ellipse become undefined. s23 and s31 singularities must be located on L-lines, where the handedness of the polarization ellipse is undetermined (linear polarization). By suitably varying a control parameter, such as off-axis distance, slope of edge dislocation, spatial correlation length, and astigmatic coefficient or propagation distance, the motion, creation, and annihilation of magnetic spectral Stokes singularities may appear. It has been shown that a pair of C-points with equal but opposite topological charges and with similar handedness may be created or annihilated. The V point and handedness reversal of C point may take place. Compared with the electric spectral Stokes singularities of stochastic electromagnetic beams, the positions are not the same, and the left- and right-handedness spaces do not coincide. The results obtained in this paper would be useful for an in-depth understanding of polarization singularities of stochastic electromagnetic beams.

Spectral Stokes singularities of partially coherent edge dislocation beams

The polarization singularities in vector wavefields have been extensively studied analytically and experimentally. The polarization singularities can be analyzed by using electromagnetic theory or Stokes parameters, or be described in terms of complex Stokes scalar fields. In some practical applications, partially coherent beams have more advantages than fully coherent beams. Recently, the concept of the polarization singularities has been extended from fully coherent beams to partially coherent beams. In this paper, using the representation of cross-spectral density matrix propagation, the explicit propagation expressions for the partially coherent edge dislocation beams are derived in free space, and based on the spectral Stokes parameters the spectral singularities are studied in detail. It is shown that there exist spectral s12, s23 and s31 singularities of partially coherent edge dislocation beams in free-space propagation. s12 singularities correspond to circular polarization (C-points) of the partially coherent edge dislocation beams, and s30 (s30) means right-(left-) handedness, where the orientations of the major and minor axes of the polarization ellipse become undefined. s23 and s31 singularities must be located on L-lines, where the handedness of the polarization ellipse is undetermined (linear polarization). The motion, creation and annihilation of spectral Stokes singularities may appear in the variation of a controlling parameter, such as off-axis distance, slope of edge dislocation, spatial correlation length, or in the variation of the propagation distance. By suitably varying the spatial correlation length or propagation distance the V-point, the handedness reversal of C-point, creation and annihilation for a pair of oppositely charged spectral singularities take place. The creation and annihilation occur for a pair of s12 singularities with opposite topological charge but same handedness. The critical points of the controlling parameters and propagation distance, at which pairs of different spectral singularities annihilate, are not the same. The collision of the C-point and L-line results in a V-point (vector singularity), which is unstable. A small perturbation leads to the handedness reversal. At such a point the state of polarization is undetermined and the degree of polarization P=0. The results obtained in this paper would be useful for a deep understanding of polarization singularities of stochastic electromagnetic beams.

Orbital angular moment of an electromagnetic Gaussian Schell-model beam with a twist phase.

We derive the analytical formula for the orbital angular momentum (OAM) flux of a stochastic electromagnetic beam carrying twist phase [i.e., twisted electromagnetic Gaussian Schell-model (TEGSM) beam] in the source plane with the help of the Wigner distribution function. Furthermore, we derive the general expression of the OAM flux of a TEGSM beam on propagation with the help of a tensor method. As numerical examples, we explore the evolution properties of the OAM flux of a TEGSM beam propagating through a cylindrical thin lens or a uniaxial crystal. It is found that the OAM flux of a TEGSM beam closely depends on its twist factors and degree of polarization in the source plane, and one can modulate the OAM flux of a TEGSM beam by a cylindrical thin lens or a uniaxial crystal. Our results may be useful in some applications, such as particle manipulation and free-space optical communications, where light beam with OAM is preferred.

Effects of statistical similarity in Young's interference experiment

Some new results are established on the condition that the fluctuating field at the pinholes in Young's interference experiment is statistically similar at a frequency ω0. It is shown that this condition ensures complete spectral coherence of the light in the plane of observation. Under this circumstance, the spectral degree of polarization and cross-polarization of the stochastic electromagnetic beam in the plane of observation are exactly the same as that in the pinholes. Furthermore, we derive a condition that ensures complete spatial coherence at the pinholes in the space–time domain.

Twist phase-induced changes of the statistical properties of a stochastic electromagnetic beam propagating in a uniaxial crystal.

With the help of a tensor method, an analytical formula is derived for the cross-spectral density matrix of a twisted electromagnetic Gaussian Schell-model (EGSM) beam (i.e., EGSM beam with twist phase) propagating in a uniaxial crystal orthogonal to the optical axis. The twist phase-induced changes of the statistical properties, such as the spectral density, the degree of polarization and the degree of coherence, of an EGSM beam propagating in a uniaxial crystal are illustrated numerically. It is found that the distributions of the spectral density, the degree of polarization and the degree of coherence of a twisted EGSM beam in a uniaxial crystal all exhibit non-circular symmetries, which are quite different from those of a twisted EGSM beam in isotropic medium or in free space. One may use uniaxial crystal to determine whether an EGSM beam carries twist phase or not.