Electromagnetic Gaussian Schell-model Research Articles

Determination of Stokes fluctuations and Stokes scintillations for an electromagnetic beam

In this article, we report the experimental determination of Stokes fluctuations and Stokes scintillations for a generalized electromagnetic Gaussian–Schell model (EMGSM) beam. We have used an experimental scheme comprising three different interferometers which are aimed to tailor the correlation between orthogonal field components, synthesis of the generalized EMGSM beam, and observation of the spatial features of the light beam in the far zone. Stokes fluctuations matrix elements are measured for a partially polarized and unpolarized light beam. The weight value of the matrix elements is found to be dependent on the correlation strength parameter () of the source. Experimental results for Stokes scintillations are also determined which depend drastically on the modulus value of B xy . For asymmetrical coherence widths, variation in the Stokes scintillations is discerned across the beam diameter. The obtained results show a reasonable match with the theoretically expected values. The study reveals the source properties which can find applications in the areas of optical imaging, optical communication, etc.

Experimental investigation of degree of cross-polarization for an electromagnetic Gaussian-Schell model beam.

We investigate the properties of the degree of cross-polarization (DOCP) for an electromagnetic Gaussian-Schell model (EMGSM) beam in the radial direction of the cross section of the beam. The coherence and polarization features of a partially coherent light beam are engineered to construct the isotropic and non-isotropic EMGSM beams, and the resulting changes in the DOCP are examined. For experimental realization, a double-slit interferometer is utilized at the output to probe the coherence properties for different polarization components across the beam diameter of an electromagnetic source. Experimental observations infer that variation in DOCP does not become apparent for isotropic coherence widths in the orthogonal polarization directions, whereas the variation can be apparent only once both the coherence widths are distinct. Furthermore, experimentally, a special case is also investigated for which the value of DOCP goes beyond unity. The DOCP finds application in areas such as second-order intensity interference, imaging, and characterization of non-homogeneously polarized beams.

Degree of paraxiality of a twist electromagnetic Gaussian Schell-model beam.

The definition of the degree of paraxiality (DOP) for a stochastic electromagnetic field is applied to a twist stochastic electromagnetic field. As an illustrative example, DOP for a wide class of model stochastic fields, i.e., twist electromagnetic Gaussian Schell-model (TEGSM) fields, is discussed. The dependence of the DOP of the light source on its properties is also studied in detail. The numerical results show that the DOP of a TEGSM beam is determined by the rms widths of auto-correlation functions and the twist factor as well as by the degree of polarization. To explain the behavior of DOP, the far-field divergence angle of this beam source is also discussed.

Statistical features of an electromagnetic Gaussian-Schell model beam propagating through a smoke aerosol environment.

In this paper, we investigate both theoretically and experimentally the statistical properties of an electromagnetic Gaussian-Schell model (EMGSM) beam propagating through polluted atmosphere specifically containing smoke aerosol medium. Experimentally, a glass chamber of 1 m length is constructed to mimic the smoky atmosphere inside the laboratory, in which incense sticks are used for smoke aerosol production inside the chamber in a time-controlled manner. An input EMGSM beam having a variable degree of coherence and degree of polarization (DOP) propagates through the aerosol medium, and its coherence and polarization features after propagation are probed. The results show that the coherence features of the vectorial beam are modified significantly by the smoke aerosol medium, while, for the given propagation length of 1 m, the polarization features remain unaffected. We also investigate the coherence features of the EMGSM beam through smoke aerosols in a particular condition when the DOP of the beam is kept zero. These results are expected to provide insights into atmospheric effects on free-space optical communication in real situations when the medium contains air pollution.

Statistical properties of an electromagnetic Gaussian Schell-model beam propagating in uniaxial crystals along the optical axis.

Within the angular-spectrum representation, we study the partially coherent beam propagating in uniaxial crystals along the optical axis. By a method of vortex expansion, we derive the analytical solution for the cross-spectral density (CSD) function of an electromagnetic Gaussian Schell-model (EGSM) beam. We demonstrate that the analytical expression of CSD function can be written into a quasi-coherent-mode representation, whose basis vectors are constructed by the elegant Laguerre-Gaussian (eLG) functions. Several limits of the analytical solution are examined and good agreements with previous theories are obtained. Moreover, we calculate the energy density and degree of polarization (DOP) of the EGSM beam, from which the effects of coherent degree on the propagating properties are revealed. It is found that the energy conversion between circularly polarized components becomes rapid when the degree of coherence is decreasing. For all degree of coherence, the energy density and DOP exhibit a similar saturated behavior in the far field.

Characterization of the electromagnetic Gaussian Schell-model beam using first-order interference.

We propose a method for the characterization of electromagnetic Gaussian Schell-model (EMGSM) beams. This method utilizes the first-order interference consisting of polarization-state projections along with the two-point (generalized) Stokes parameters. The second-order field correlations employed in this method enable us to determine both the magnitude and the argument of the complex degree of electromagnetic coherence. We experimentally demonstrate this method by characterizing an EMGSM beam, which is synthesized using a laser beam passing through a rotating ground glass diffuser. This beam-characterization method is expected to be potentially useful for probing the partially coherent and partially polarized beams, and have tremendous applications in broad areas of optical communication and beam propagation.

Generating electromagnetic nonuniformly correlated beams.

We develop a method to generate electromagnetic nonuniformly correlated (ENUC) sources from vector Gaussian Schell-model (GSM) beams. Having spatially varying correlation properties, ENUC sources are more difficult to synthesize than their Schell-model counterparts (which can be generated by filtering circular complex Gaussian random numbers) and, in past work, have only been realized using Cholesky decomposition-a computationally intensive procedure. Here we transform electromagnetic GSM field instances directly into ENUC instances, thereby avoiding computing Cholesky factors resulting in significant savings in time and computing resources. We validate our method by generating (via simulation) an ENUC beam with desired parameters. We find the simulated results to be in excellent agreement with the theoretical predictions. This new method for generating ENUC sources can be directly implemented on existing spatial-light-modulator-based vector beam generators and will be useful in applications where nonuniformly correlated beams have shown promise, e.g., free-space/underwater optical communications.

Detection of a Semi-Rough Target in Turbulent Atmosphere by an Electromagnetic Gaussian Schell-Model Beam

The interaction of an electromagnetic Gaussian Schell-model beam with a semi-rough target located in atmospheric turbulence was studied by means of a tensor method, and the corresponding inverse problem was analyzed. The equivalent model was set up on the basis of a bistatic laser radar system and a rough target located in a turbulent atmosphere. Through mathematical deduction, we obtained detailed information about the parameters of the semi-rough target by measuring the beam radius, coherence radius of the incident beam and the polarization properties of the returned beam.

Propagation factor and beam wander of electromagnetic Gaussian Schell-model array beams in non-Kolmogorov turbulence

The propagation formulae for the propagation factor (known as M2-factor) and beam wander of electromagnetic Gaussian Schell-model (EGSM) array beams in non-Kolmogorov turbulence are derived by using the extended Huygens-Fresnel principle and the second-order moments of the Wigner distribution function. The results indicate that the M2-factor and beam wander depend on the beam parameters and turbulence parameters, and the relative M2-factor has a maximum when the generalized exponent parameter α is equal to 3.1. Otherwise, the changes of the separation distances (x0, y0) have great influence on the relative M2-factor. The relative beam wander increases rapidly when 3<α<3.2; however, it increases slowly when 3.2<α<4. It is also shown that the beam spreading of EGSM array beams is more affected by turbulence than the root mean square beam wander.

Polarization properties of beam radiated from three-dimensional electromagnetic Gaussian-Schell model source

A recent literature introduced the stationary, three-dimensional (3D), and electromagnetic (EM) Gaussian-Schell model (GSM) source through the analytic approach. In this paper, investigations are performed on the statistical properties of the degree of polarization (DOP) and state of polarization (SOP) of the far-zone radiated beam from such source. The effects of initial widths and correlation coefficients of the source on the DOPs and SOPs of the radiated beam are numerically analyzed. Furthermore, comparisons are held for the DOPs and polarization ellipse shapes of the radiated beam between the uniformly and non-uniformly polarized sources cases. Our results greatly enrich the current knowledge of 3D, EM sources with arbitrary state of polarization.

Free-Space to Fiber Coupling of Electromagnetic Gaussian Schell-Model Beams in Turbulent Marine Atmospheric Channel

We present a method to analyze the fiber coupling efficiency η of electromagnetic Gaussian Schell-model (EGSM) beams propagating through marine atmospheric turbulence. The expression for η is derived from the relation of field distributions between EGSM beam and fiber mode. The influence factors of η are discussed, including the properties of EGSM beam, focusing lens, and turbulence. We find that η declines as the turbulence enhances. A large-aperture lens and an EGSM beam with high coherence, long wavelength, and optimum beam width are able to achieve a higher η in turbulent links. Beam polarization also takes effect on η but the effect is complex. Our investigation has applications in the fiber coupling of vectorial beams in communication systems.

Evolution of degree of polarization of partially coherent beams propagation in slant and horizontal atmospheric turbulence

In this paper, the analytical expressions for the degree of polarization (DoP) of the electromagnetic Gaussian Schell-model (GSM) beam propagating along a slant path in atmospheric turbulence are obtained. The expressions are used to analyze factors such as the waist radius, amplitude ratio, wavelength, and refractive-index structure constant of the polarization properties of the GSM beam, and we come to some new conclusions. The main results that when the components of the waist radius are equal (σx = σy), there is a waist radius within 2 cm < σx < 4 cm that can provide the most concentrated DoP distribution, and the axis point DoP will eventually approach the initial value as the transmission distance increases, implying that it exhibits self-recovering characteristics. In addition, compared to a horizontal path, the DoP distribution of the GSM beam propagating along a slant path is more concentrated, and the propagation distance corresponding to the maximum axis point DoP is longer. Therefore, when the GSM beam propagates along a slant path, the detector can receive information at longer distances. The research results provide a theoretical support for the control of the polarization state of local beam in coherent optical communication systems.

Coherence properties of a random electromagnetic vortex beam propagating in biological tissues

ABSTRACTBased on the extended Huygens-Fresnel principle and the unified theory of polarization and coherence, the coherence properties of random electromagnetic Gaussian Schell model (GSM) vortex beams propagating through biological tissues were investigated. It was shown that with an increasing propagation distance, the change in the spectral degree of coherence |μ(ρ, −ρ, z)| is more complex than that of μ(0, ρ, z). If the change in |μ(ρ, −ρ, z)| is divided into the preceding and latter stages, then the change in μ(0, ρ, z) is similar to that of |μ(ρ, −ρ, z)| at the latter stage. The wavelength of the far-infrared beam (λ = 10.6 µm) is similar to that emitted by the biological tissues, and a resonance with water molecules occurs in the biological tissues. At the initial plane, the larger ρx corresponds to a smaller value of |μ(ρ, −ρ, z)|, and during the propagation process, the spatial coherent interval is wider for |μ(ρ, −ρ, z)| than for μ(0, ρ, z). The fluctuation change depth of |μ(ρ, −ρ, z)| in the biological tissues is somewhat shallower than that of μ(0, ρ, z) under the same conditions, such as the same biological tissue, the same wavelength, or the same interval between two field points. In addition, the spatial self-correlation length σyy has an effect on |μ(ρ, −ρ, z)| and on μ(0, ρ, z) to a different extent, while the changes in these two quantities are independent of the spatial mutual-correlation length σxy of the random electromagnetic GSM vortex beam.

The second–order moment statistics of a twisted electromagnetic Gaussian Schell-model propagating in a uniaxial crystal

Under the help of extended Huygens–Fresnel integral, we acquire the analytic expressions of second-order moments of the Wigner distribution function (WDF) for a twisted electromagnetic Gaussian Schell-model (TEGSM) beam propagating in a uniaxial crystal. Moreover, we obtain the formulae for propagation factor, the effective radius of curvature and Rayleigh range in which we studied the properties of the TEGSM beam numerically. It is found that the initial beam parameters and the uniaxial crystal parameters play a decisive role in the TEGSM beam propagating in a uniaxial crystal. The TEGSM beam with smaller absolute deviation of coherence width δxx and δyy is less affected by anisotropic diffraction in a uniaxial crystal, which is much different from the evolution properties of an EGSM beam in a uniaxial crystal. The Rayleigh range will decreases while the crystal parameter e increases. Thus, the propagation properties of a TEGSM beam could be controlled in a uniaxial crystal by changing the initial beam parameters and the uniaxial crystal parameters where it is necessary.

Polarization characteristics of partially coherent beam passing through astigmatic fractional Fourier system

The fractional Fourier transform is a powerful tool for analyzing optical resonators. The selection of fractional number and astigmatism coefficient determines the size of the resonator, and influences the polarization, far-field emission angle and focusing power of the laser beam. Researchers often pay more attention to the change of light intensity after the fractional Fourier transform system. However, the effect of polarization changes on the system is also critical. In this article, we took partially coherent electromagnetic Gaussian-Schell model beam as a research object. Based on Collins formula and the fractional Fourier transform system ABCD matrix, we deduced the polarization degree of electromagnetic Gauss Schell model beam passing through the astigmatic lens fractional Fourier transform, elliptical azimuth and ellipticity; and analyzed the distribution of polarization degree, elliptic azimuth and ellipticity output plane of the astigmatism fraction Fourier transform system by numerical simulation. The results show that the distribution of polarization degree, ellipse azimuth and ellipticity on the output plane are no longer uniform after the beam passing through the fractional Fourier transform system with an astigmatic lens. In the non-focal plane, affected by astigmatism, beam waist position in x and y directions do not coincide, and the bigger astigmatism is, the farther separation is. Therefore, the polarization properties are elliptically symmetrical, and the greater the astigmatism is, the greater the eccentricity of the ellipse is. In the focal plane, the beam coincides with the waist position in the x and the y direction, and the polarization characteristics are circularly symmetric. The larger the astigmatism coefficient is, the larger the radius is. The greater the astigmatism coefficient is, the faster the polarization changes on the axis. The astigmatism of the lens leads to the difference of the beam width between the x direction and the y direction. Therefore, the point polarization of the shaft will appear in doublet or double valleys, and the greater the astigmatism coefficient is, the greater the difference between the value with and without astigmatism is. The results of this study have some reference value for the selection of fractional Fourier transform order and astigmatism coefficient under different polarization characteristics, and have important guiding significance for the design of optical resonator.

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.

Propagation of a Vector Cosine-Gaussian Correlated Beam Through an Active GRIN Medium

This paper presents a convenient approach that uses the tensor method to study the propagation of a nonuniformly correlated electromagnetic Cosine-Gaussian Schell-model (ECGSM) beam through an active gradient-index (GRIN) medium. It is shown that the initial correlation structure has a significant influence on the intensity gain; an ECGSM beam ( n = 1) experiences more gain than a conventional electromagnetic Gaussian Schell-model (EGSM) beam ( n = 0). The inhomogeneous gain induced by the medium leads to a nonlinear modulation of beam parameters such as the spectral intensity, coherence, and polarization. Although the gain leads to a broadening of the beam width, the coherence gradually decreases, which yields a useful guideline for manipulating active GRIN materials to generate numerous partially coherent beams. It is found that the polarization ellipse in the center of a conventional EGSM beam gradually evolves into circular polarization. However, the state of polarization of a nonuniformly correlated ECGSM beam gradually changes into linear polarization. The ability to manipulate light beams using active GRIN materials opens an alternative avenue for the generation of complex vector beams, which promises important supports in the fields of waveguide amplifiers, beam shaping, optical sensors, and beam transformer devices.

Beam spreading and M2-factor of electromagnetic Gaussian Schell-model beam propagating in inhomogeneous atmospheric turbulence

The main purpose of this paper is to study the beam spreading and M2-factor of electromagnetic Gaussian Schell-model (EGSM) beam through inhomogeneous atmospheric turbulence. The analytical formulas for the root-mean-square (rms) spatial width, rms angular width, M2-factor of EGSM beam in turbulence are derived by using the second-order moments of the Wigner distribution function and extended Huygens-Fresnel integral. Our results show that the relative M2-factor of EGSM beam decreases with decreasing of zenith angle, initial coherence lengths and initial degree of polarization and with increasing of beam widths and inner scale. It is also shown that as the zenith angle is equal to π/6, the saturated propagation distances of the relative rms angular width, the relative rms spatial width, and the relative M2-factor are about 0.3km, 3km and 20km, respectively. And it also can be found that the relative M2-factor becomes small when the initial degree of polarization closes to 0.

Changes in the degree of polarization of random electromagnetic GSM vortex beams in biological tissues

Based on the Huygens-Fresnel principle, the analytic expressions of the cross-spectral density matrix elements of the random electromagnetic Gaussian Schell model (GSM) vortex beams in biological tissues are derived, and used to study the changes in the on-axis degree of polarization P(0, 0, z), one point degree of polarization P(ρ, ρ, z) and two points (generalized) degree of polarization P(0, ρ, z) of random electromagnetic GSM vortex beams. The results show that with the increment of the propagation distance z, the bigger Cn2 is, the earlier appearance of the inflexion points in P(0, 0, z) and P(ρ, ρ, z) are, but the changes in P(0, ρ, z) are related to the propagation distance. The smaller σxy is, the greater σyy is, the more smooth the change curves of P(0, 0, z), P(ρ, ρ, z) and P(0, ρ, z) are. Besides, the difference values between σxx and σyy also influence the changes in P(0, 0, z), P(ρ, ρ, z) and P(0, ρ, z). On the same conditions, the changes in P(0, ρ, z) are more complicate than those in P(ρ, ρ, z), and the changes in P(ρ, ρ, z) are more complex than those in P(0, 0, z).

Kurtosis parameter K of arbitrary electromagnetic beams propagating through non-Kolmogorov turbulence

General analytical formulae for the kurtosis parameters K (K parameters) of the arbitrary electromagnetic (AE) beams propagating through non-Kolmogorov turbulence are derived, and according to the unified theory of polarization and coherence, the effect of degree of polarization (DOP) of an electromagnetic beam on the K parameter is studied. The analytical formulae can be given by the second-order moments and fourth-order moments of the Wigner distribution function for AE beams at source plane, the two turbulence quantities relating to the spatial power spectrum, and the propagation distance. Our results can also be extended to the arbitrary beams and the arbitrary spatial power spectra of Kolmogorov turbulence or non-Kolmogorov turbulence. Taking the stochastic electromagnetic Gaussian Schell-model (SEGSM) beam as an example, the numerical examples indicate that the K parameters of a SEGSM beam in non-Kolmogorov turbulence depend on propagation distance, the beam parameters and turbulence parameters. The K parameter of a SEGM beam is more sensitive to effect of turbulence with smaller inner scale and generalized exponent parameter. A non-polarized light has the strongest ability of resisting turbulence (ART), however, a fully polarized SEGSM beam has the poorest ART.