Electromagnetic Gaussian Schell-model Beam Research Articles

Propagation-induced changes in non-isotropically correlated vector vortex beams

We study the propagation of non-isotropically correlated vector vortex beams (NCVVBs) through an ABCD optical system. The statistical properties, namely, intensity, state of polarization, degree of polarization (DoP), and degree of coherence (DoC) of these beams are investigated. The terminology non-isotropically correlated is used for electromagnetic Gaussian Schell-model beams, that exhibit the distinguishability of spatial correlations between parallel and orthogonal electric field components. The non-isotropic feature of the correlation widths introduces an azimuthal asymmetry in the intensity, DoP, and DoC distributions. The azimuthal asymmetry in the intensity and DoC distributions become prominent around the focal plane. However, this asymmetry can be clearly observed in DoP distributions even at a very short propagation distance. It is found that the statistical properties of NCVVBs are dependent on both Poincaré–Hopf index (PHI) and the source correlation parameters. The number of beamlets in the intensity distribution is twice the magnitude of the PHI of the input beam. Unlike isotropically correlated vector vortex beams, correlation-induced polarization around the central core of the NCVVB is observed. The DoC distribution exhibits the evolution of correlation singularities in the form of dislocations at the far field plane. These dislocations in the DoC profile under lower correlations depend on the PHI, which provides a feasible approach to measure the index of NCVVBs. This study provides a technique to synthesize beams with structured correlation and polarization features.

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.

An advanced method for evaluating Lommel integral and its application in marine environment

In this work, our main aim is to examine theoretically the so-called “Lommel integral”. By introducing a new hypergeometric function of three variables, some new mathematical derivations are performed and a closed form of this integral is established for the first time. As an application of our main result we also examine an analysis of the fiber coupling efficiency for a partially coherent electromagnetic Gaussian Schell-model beam propagating through a turbulent marine medium by using two new power spectrum densities.

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.

Turbulence-induced changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating through anisotropic turbulence

The changes in the state of polarization of partially polarized, partially coherent pulsed electromagnetic beams propagating along a horizontal path through anisotropic turbulence are investigated. Unpolarized and partially polarized, partially coherent pulsed electromagnetic Gaussian Schell-model beams are compared in terms of the turbulence-induced changes in the spectral degree of polarization. Our analysis is focused on models pertaining to electromagnetic Gaussian Schell-model pulsed beams but can either be readily reduced to scalar or be readily generalized to other beam classes. Within the framework of the anisotropic generalized exponential spectrum, considering simultaneously the finite inner and outer scales of turbulence and the asymmetric property of turbulence eddies in the orthogonal x y -plane throughout the propagation path, we derive analytical expressions for the cross-spectral density matrix, spectral degree of polarization, orientation angle, and degree of ellipticity. Finally, we study the effects of the anisotropic turbulence parameter on the spectral degree of polarization, orientation angle, and degree of ellipticity of the beams. Our results can be useful for applications involving partially polarized, partially coherent pulsed beams propagating through atmospheric turbulence.

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.

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.

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.

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.

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.

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.

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.

Coherence and polarization properties of laser propagating through biological tissues

Based on the extended Huygens-Fresnel principle, the analytical expressions of the cross-spectral density matrix elements for random electromagnetic Gaussian Schell-model (GSM) beam propagating in biological tissues are derived, and used to study the changes in spectral degree of coherence μ and spectral degree of polarization P of random electromagnetic GSM beams with the propagation distance z propagating through the different biological tissues. It is shown that the changes closely depend on the species of the biological tissues, beam wave length, the interval between two field points and propagation distance. The spectral degree of coherence μ and the spectral degree of polarization P of the ultraviolet ray (λ=0.325μm) will quickly decrease during the propagation process, which implies that the damage of the ultraviolet ray to biological tissues is strong. The bigger structure constant of the refractive-index Cn2 corresponds to the smaller change of μ and P. There exists the obvious effect of the interval between two field points on the spectral degree of coherence and the spectral degree of polarization of random electromagnetic GSM beams passing biological tissues. The obtained results can provide the theoretical and experimental basis for the analysis to the coherence and polarization properties of random electromagnetic beams propagating through the complex biological tissues.