multi-Gaussian Schell-model Beam Research Articles

Twisted elliptical multi-Gaussian Schell-model beams and their propagation properties.

We introduce a new kind of partially coherent source whose cross-spectral density (CSD) function is described as the incoherent superposition of elliptical twisted Gaussian Schell-model sources with different beam widths and transverse coherence widths, named twisted elliptical multi-Gaussian Schell-model (TEMGSM) beams. Analytical expression for the CSD function propagating through a paraxial ABCD optical system is derived with the help of the generalized Collins formula. Our results show that the TEMGSM beam is capable of generating a flat-topped elliptical beam profile in the far field, and the beam spot during propagation exhibits clockwise/anti-clockwise rotation with respect to its propagation axis. In addition, the analytical expressions for the orbital angular momentum (OAM) and the propagation factor are also derived by means of the Wigner distribution function. The influences of the twisted factor and the beam index on the OAM and the propagation factor are studied and discussed in detail.

Radial phased-locked multi-Gaussian Schell-model beam array and its properties in oceanic turbulence

The radial phased-locked multi-Gaussian Schell-model (MGSM) beam array composed by the N MGSM beamlets is first given to describe a new laser array. The evolution properties of radial phased-locked MGSM beam array in free space and oceanic turbulence are discussed in detail. Based on the extended Huygens-Fresnel principle, the MCF and the effective size of radial phased-locked MGSM beam array in oceanic turbulence are derived. The effects of beam parameters and the oceanic turbulence parameters on the spreading and spectral degree of coherence of radial phased-locked MGSM beam array propagating in oceanic turbulence are investigated by using numerical examples. This research may be useful in underwater optical wireless optical communication.

Evolutions of random electromagnetic multi-Gaussian Schell-model vortex beams propagating in uniaxial crystals orthogonal to the optical axis

The analytical expressions of random electromagnetic multi-Gaussian Schell-model vortex beams propagating in uniaxial crystals orthogonal to the optical axis are derived. The effects of ratio of extraordinary index to ordinary index of uniaxial crystal on propagation properties of random electromagnetic multi-Gaussian Schell-model vortex beam are discussed by using numerical simulations. It is shown that the circular symmetry of random electromagnetic multi-Gaussian Schell-model vortex beam will translate into elliptical symmetry due to the influences of uniaxial crystal, and the beam propagation in uniaxial crystal with larger ratio of extraordinary index to ordinary index will evolve into an elliptical flat-topped beam with larger width along x-axis.

Evolution of stokes parameters in quasi homogeneous electromagnetic sources in the far field

The evolution of Stokes parameters of an electromagnetic field generated by a quasi-homogeneous electromagnetic source in the far field is studied. It is shown that under Fraunhofer approximation, the Stokes parameters of a propagation plane is related to the Stokes parameter of the source by a 4D-Fourier Transform. Some simulation results are presented for propagation in electromagnetic multi-Gaussian Schell model beams.

Propagation properties of radially polarized multi-Gaussian Schell-model beams in oceanic turbulence.

By utilizing the extended Huygens-Fresnel principle, we derive the analytical formulas for the cross-spectral density matrix elements of a radially polarized multi-Gaussian Schell-model (RPMGSM) beam propagating in oceanic turbulence. Effects of beam parameters and oceanic turbulence parameters on the propagation properties of RPMGSM beams are investigated in detail by numerical simulation. Our results show that the RPMGSM beam with larger beam order M has an advantage over the radially polarized Gaussian Schell-model beam for reducing turbulence-induced degradation. Compared with temperature-induced turbulence fluctuation, the salinity-induced turbulence fluctuation makes a greater contribution to the influence on propagation properties of RPMGSM beams.

Properties of multi-Gaussian Schell-model beams carrying an edge dislocation propagating in oceanic turbulence**Project supported by the National Natural Science Foundation of China (Grant Nos. 11604038, 11875096, and 11404048) and the Fundamental Research Funds for the Central Universities, China (Grant Nos. 3132019182 and 3132019184).

Based on the theory of coherence, the model of multi-Gaussian Schell-model (MGSM) beams carrying an edge dislocation generated by the MGSM source is introduced. The analytical cross-spectral density of MGSM beams carrying an edge dislocation propagating in oceanic turbulence is derived, and used to study the evolution properties of the MGSM beams carrying an edge dislocation. The results indicate that the MGSM beam carrying an edge dislocation propagating in oceanic turbulence will evolve from the profile with two intensity peaks into a flat-topped beam caused by the MGSM source, and the beam will evolve into the Gaussian-like beam due to the influences of oceanic turbulence in the far field. As the propagation distance increases, the MGSM beam carrying an edge dislocation propagating in oceanic turbulence with the larger rate of dissipation of mean-squared temperature () and ratio of temperature to salinity contribution to the refractive index spectrum (ς) or the smaller rate of dissipation of kinetic energy per unit mass of fluid (ε) evolves into the flat-topped beam or a Gaussian beam faster.

Focus shaping of partially coherent radially polarized vortex beam with tunable topological charge

In this paper, we have introduced a new class of partially coherent vector vortex beams, named radially polarized multi-Gaussian Schell-model (MGSM) vortex beam, carrying the vortex phase with tunable topological charges (i.e., both integral and fractional values) as a natural extension of the radially polarized MGSM beam. The tight focusing properties of the radially polarized MGSM vortex beam passing through a high numerical aperture (NA) objective lens are investigated numerically based on the vectorial diffraction theory. Numerical results show that the focal intensity distributions of the radially polarized MGSM vortex beam can be shaped by regulating the structure of the correlation functions and the topological charge of vortex phase. In contrast with the integral vortex beam, the most intriguing property of the fractional vortex beam is that the focal intensity distribution at the focal plane can be nonuniformity and asymmetry, while such unique characteristics will vanish when the spatial coherence length is sufficiently small. Furthermore, some focal fields with novel structure, such as a focal spot with nonuniform asymmetric or an anomalous asymmetric hollow focal field, can be formed by choosing suitable fractional values of topological charge and spatial coherence length. Our results will be useful for optical trapping, especially for trapping of irregular particles or manipulation of absorbing particles.

Model of a rectangular multi-Gaussian Schell-model vortex beam and its properties

Considering the theory of coherence, the rectangular multi-Gaussian Schell-model vortex beam (RMGSMV) beam generated by multi-Gaussian Schell-model source has been introduced, and the propagation properties of RMGSMV beam propagating in free space has been analyzed by using the derived equations. The effects of beam parameters on the properties of RMGSMV beam propagating in free space have been discussed. The results show that the RMGSMV beam propagating in free space can remain the dark hollow center at the short propagation distance, and the beam will gradually evolve into a beam with similar rectangular flat-topped profile as the propagation distance increases.

Degree of paraxiality of an electromagnetic multi-Gaussian Schell-model beam.

The degree of paraxiality (DOP) of an electromagnetic multi-Gaussian Schell-model (EM-MGSM) beam was discussed, and the dependence of DOP on the characteristics of beam sources was investigated. It is shown that the parameters of beam sources, including the rms widths of the auto-correlation functions, the degree of polarization, and the boundary characteristics, play an important role in the DOP of the beam. To explain these phenomena, the far-zone divergence angle of the EM-MGSM beam was further discussed.

Partially Coherent Flat-Topped Beam Generated by an Axicon

The intensity distribution of a partially coherent beam with a nonconventional correlation function, named the multi-Gaussian Schell-model (MGSM) beam, focused by an axicon was investigated in detail. Our numerical results showed that an optical needle with a flat-topped spatial profile and long focal depth was formed and that we can modulate the focal shift and focal depth of the optical needle by varying the width of the degree of coherence (DOC) and the parameters of the correlation function. The adjustable optical needle can be applied for electron acceleration, particle trapping, fiber coupling and percussion drilling.

Multi-Gaussian Schell-model source with a complex coherence state

The effects of non-trivial phase of the source degree of coherence on the far-field spectral density for the class of one-dimensional, multi-Gaussian Schell-model beams are explored. While in the absence of the phase, the flat-top spectral density profile with a Gaussian edge drop is symmetrically formed in the far field about the optical axis, various phase functions introduce asymmetric modifications to such distribution. Since the phase of the source degree of coherence must be an odd function, three such examples are considered in detail: linear phase leading to shift, signum phase producing either tilt or split, and cubic phase forming Airy-like radially accelerating profiles. We have established that unless the phase of the source degree of coherence is sufficiently small at all separations, the resulting far-field spectral density profiles are qualitatively very different from those with the trivial phase.

Experimental study: underwater propagation of super-Gaussian and multi-Gaussian Schell-model partially coherent beams with varying degrees of spatial coherence

We report on experiments where super-Gaussian and flat-top, multi-Gaussian Schell-model spatially partially coherent beams, with varying degrees of spatial coherence, were propagated underwater. Two scenarios were explored—calm and mechanically agitated water. The main objective of our study was the experimental comparison of the scintillation statistics. For a similar degree of coherence widths, the results show a potentially improved performance of scintillation index for the multi-Gaussian Schell-model beams as compared to the super-Gaussian beams. It should be noted that the presented results pertain only to the given experimental scenarios and further investigation is necessary to determine the scope of the findings.

Electromagnetic fractional multi-Gaussian Schell-model beams and their statistical properties

A recently introduced class of scalar fractional multi-Gaussian Schell-model beams is extended to electromagnetic domain. The conditions on source parameters guaranteeing that the source generates a physical beam are derived. Analytical formulas for the cross-spectral density matrix elements of the electromagnetic fractional multi-Gaussian Schell-model (EM FMGSM) beams propagating in non-Kolmogorov turbulence are derived. The behaviour of the statistical characteristics, including the spectral density, the degree of coherence and the degree of polarization, of the beam on propagation in free space and non-Kolmogorov turbulence are investigated. It is shown that by choosing appropriate parameters of the beam and the turbulence, we can alleviate influence of the turbulent atmospheric effects effectively. Our findings may be useful in material surface processing and free-space optical communications.

Evolution properties of the radially polarized multi-Gaussian Schell-model beam in uniaxial crystals.

The evolution properties of the normalized intensity distribution, the spectral degree of coherence (SDOC), and the spectral degree of polarization (SDOP) of the radially polarized multi-Gaussian Schell-model (MGSM) beam in uniaxial crystals are illustrated. Numerical results show that the intensity distribution of the radially polarized MGSM beam gradually evolves from a doughnut shape into an elliptical symmetric flattop shape and retains its elliptical flattop shape on further propagation in anisotropic crystals. The evolution behavior of the SDOC and SDOP for the radially polarized MGSM beam is quite different from that of the linearly polarized one. In addition, the influences of the spatial coherence length δ0, beam index M, and the ratio of the extraordinary refractive index to the ordinary refractive index ne/no of the uniaxial crystals on the evolution properties of the normalized intensity distribution, the SDOC, and the SDOP of the radially polarized MGSM beam are discussed in detail.

Propagation properties of a twisted rectangular multi-Gaussian Schell-model beam in free space and oceanic turbulence.

With the paraxial approximation, we derive the analytical formulas for the propagation of a twisted rectangular multi-Gaussian Schell-model (TRMGSM) beam in free space and oceanic turbulence. The spectral density and degree of coherence of the TRMGSM beam both in free space and oceanic turbulence are investigated. We found that the oceanic turbulence barely had any influence on the rotation effect both of the spectral density and degree of coherence. In addition, we found that the spot could degenerate into a Gaussian profile caused by a turbulence medium. Furthermore, for stronger turbulence, the beam spot spreads more rapidly, and the coherence region decreases faster. In this paper, we also study the effect of the twisted factor on the propagating properties.

Transmission of a polychromatic electromagnetic multi-Gaussian Schell-model beam in an inhomogeneous gradient-index fiber.

We derive analytical expressions for the cross-spectral density matrix of polychromatic electromagnetic multi-Gaussian Schell-model (EMGSM) beam transmission through a gradient-index fiber. The space-spectrum evolution properties for the spectral density, spectral shift, degree of polarization, and electromagnetic coherence state of a polychromatic EMGSM beam with Lorentzian line type spectrum and central wavelength λ0=1550 nm propagation in a silica-clad germania core inhomogeneous graded-index fiber are studied in detail. We show that these statistical properties exhibit periodicity in the fiber, caused by the focusing property of square-law media, which can be reminiscent of the self-imaging effect of optical fields. The effects of the nonconventional correlation functions of the polychromatic EMGSM beam on the transmission properties are also investigated.

Average intensity and spreading of a radially polarized multi-Gaussian Schell-model beam in anisotropic turbulence

Analytical expressions of average intensity and long-term beam width for a radially polarized multi-Gaussian Schell-model (MGSM) beam in anisotropic atmospheric turbulence are developed based on the extended Huygens-Fresnel principle. The influences of anisotropic non-Kolmogorov turbulence and source parameters on the average intensity, polarization and long-term beam spreading of radially polarized MGSM beam are examined in detail. The source correlations, free-space diffraction and turbulent effect jointly affect both the intensity and polarization profiles of the beam propagated in the atmosphere. As a radially polarized MGSM beam propagates in the atmosphere, increasing the associated beam order can lower the evolution rate from its flat-topped beam profile into a Gaussian beam profile because of the turbulent effect. Variations in the average intensity and long-term beam width are closely related to the propagation distance, power spectrum index, inner-scale, initial spatial coherence, and beam width. The atmospheric turbulence-induced beam spreading is generally suppressed with the enhanced anisotropy coefficient.

Laser arrays of partially coherent beams with multi-Gaussian correlation function

We study the laser arrays which are constructed by partially coherent beams with multi-Gaussian correlation function, i.e., circular, rectangular and elliptical multi-Gaussian Schell-model (MGSM) beam arrays. Analytical propagation formulas for circular, rectangular and elliptical MGSM beam arrays through a stigmatic ABCD optical system and in turbulent atmosphere are derived, with which the propagation properties of such laser arrays may be easily determined. It is found that in the near field, the irradiance distributions of circular, rectangular and elliptical MGSM beam arrays are mainly controlled by the distribution of beam arrays in the source plane. In the far field, the irradiance distributions of circular, rectangular and elliptical MGSM beam arrays in free space are determined by their correlation functions respectively; while in turbulent atmosphere, the correlation functions and turbulent atmosphere all influence the irradiance distributions, especially after enough long distance propagation, the turbulent atmosphere may change the irradiance distributions from non-circular symmetry to circular symmetry.

Degree of paraxiality of an anisotropic generalized multi-Gaussian Schell-model beam.

The degree of paraxiality of an anisotropic generalized multi-Gaussian Schell-model (GMGSM) beam is discussed and shown to be affected by the anisotropy and boundary characteristics of the source. Numerical results are presented to show the influence of these factors.

Experimental study: Underwater propagation of polarized flat top partially coherent laser beams with a varying degree of spatial coherence

We report on experiments where spatially partially coherent laser beams with flat top intensity profiles were propagated underwater. Two scenarios were explored: still water and mechanically moved entrained salt scatterers. Gaussian, fully spatially coherent beams, and Multi-Gaussian Schell model beams with varying degrees of spatial coherence were used in the experiments. The main objective of our study was the exploration of the scintillation performance of scalar beams, with both vertical and horizontal polarizations, and the comparison with electromagnetic beams that have a randomly varying polarization. The results from our investigation show up to a 50% scintillation index reduction for the case with electromagnetic beams. In addition, we observed that the fully coherent beam performance deteriorates significantly relative to the spatially partially coherent beams when the conditions become more complex, changing from still water conditions to the propagation through mechanically moved entrained salt scatterers.