Gaussian Schell-model Vortex Beam Research Articles

Correlation and polarization singularities of a radially polarized Gaussian Schell-model vortex beam propagating in oceanic turbulence

The correlation and polarization singularities as the important parameters of a radially polarized Gaussian Schell-model vortex beam propagating in oceanic turbulence have been investigated in detail. On the one hand, the correlation singularity of the beam will first split, and then generate new correlation singularities, and finally vanish in pairs. The longer the propagating distance, the larger the rate of dissipation of mean-square temperature, and the lower initial correlation lengths reduce the stability of correlation singularities. On the other hand, polarization singularities also split during transmission. The different initial correlation lengths cause the uneven distribution of polarization singularities, and the high order topological charge leads to the generation of new polarization singularities at short distances. Our numerical findings may be of great significance for detection and imaging of the oceanic optical telecommunication links.

Robustness of partially coherent vortex beams to the impact of dynamic Kolmogorov kind of turbulence

The wave propagation characteristics of Gaussian-Schell model vortex beams passing through a dynamic Kolmogorov type of turbulence are analyzed at the laboratory level. The effect of a rotating pseudo-random phase plate, which simulates Kolmogorov-type atmospheric turbulence, on the Gaussian-Schell model beams carrying twist phase is characterized by calculating the scintillation index and intensity line profiles. Our analysis proves the resilience of Gaussian-Schell model vortex beams to the impact of dynamic turbulence. Simulation studies are further used to validate the experimental results. Because of the resemblance between our investigation conditions and real-world atmospheric turbulence, these findings have potential applications in free-space communication systems.

Stable 3D particle manipulation using rotating elliptical Gauss–Schell model vortex partially coherent light sources

The Partially coherent light source can be applied to the noninvasive capture of particles, and increasing the freedom of capturing different types of particles simultaneously is of great significance. This paper studies the optical field distribution of a rotating elliptical Gaussian-Schell model vortex beam focused by a lens and the radiation force acting on Rayleigh particles. The beam’s rotation parameter, the vortex’s topological charge, and the spatial coherence length have different effects on the light intensity, which will determine the optical capture ability of Rayleigh particles with other refractive indices and generate equilibrium points at different positions. The longitudinal equilibrium points of high-refractive-index particles and the transverse equilibrium points of low-refractive-index particles are increased by adjusting the value of the rotation parameter and the topological charge. Finally, the appropriate size range for trapping Rayleigh particles is analyzed according to the comparison of Brownian force and radiant force. The results show that this partially coherent light source has a high degree of freedom in capturing particles with different refractive indices, which provides a new way for optical capture technology and three-dimensional (3D) particle manipulation.

Propagation Properties of an Off-Axis Hollow Gaussian-Schell Model Vortex Beam in Anisotropic Oceanic Turbulence

Based on the extended Huygens–Fresnel principle and the power spectrum of anisotropic oceanic turbulence, the analytical expressions of the average intensity and coherence properties of an off-axis hollow Gaussian-Schell model (OAHGSM) vortex beam propagating through anisotropic oceanic turbulence were derived. The effects of turbulent ocean and beam characteristic parameters on the evolution properties of the OAHGSM vortex beam were analyzed in detail. Our numerical simulation results showed that the OAHGSM vortex beam with a larger position factor is more focusable. Meanwhile, the OAHGSM vortex beam eventually evolves into a Gaussian-like beam after propagating through the anisotropic oceanic turbulent channel. The speed of this process can be accelerated by the decrease of the hollow order, topological charge, beam width, and transverse coherence width of the beam. The results also indicated that the normalized average intensity spreads more greatly and the spectral degree of coherence decays more rapidly for the smaller dissipation rate of the kinetic energy per unit mass of fluid, the smaller anisotropic coefficient, the smaller inner scale factor, the larger dissipation rate of the mean-squared temperature, and the higher temperature–salinity contribution ratio.

Influence of biological tissue and spatial correlation on spectral changes of Gaussian-Schell model vortex beam

Based on the extended Huygens-Fresnel principle, the analytical expressions of the spectrum for Gaussian-Schell model vortex beam (GSMVB) propagating in biological tissues have been derived. The effects of the field point position, the species of the biological tissues, spatial correlation of beams on the relative spectral shift of GSMVB passing biological tissues have been investigated using the contour plots. It is shown that the spectral change is somewhat slow on the area near the z-axis, whereas the spectral redshift, blueshift and jump occur at far off-axis range. The stronger biological tissue turbulence can delay spectral jump, extend the space of observing the beam spectral jump, weaken the phenomenon of spectral jump on the propagation. Simultaneously, the results can well verify the scientificity and rationality of selecting the mouse as the experimental objects in biomedical research. The spatial coherence of beams can speed up the spectral change and slow the spectral jump down. Additionally, several physical explanations have been given to the above phenomena.

Properties of off-axis hollow Gaussian-Schell model vortex beam propagating in turbulent atmosphere**Project supported by the Natural Science Foundation of Jilin Province, China (Grant No. 20180101031JC) and the Jilin Provincial Science Foundation for Basic Research, China (Grant No. 2019C040-7).

The analytical expression of off-axis hollow Gaussian–Schell model vortex beam (HGSMVB) generated by anisotropic Gaussian–Schell model source is first introduced. The evolution properties of off-axis HGSMVB propagating in turbulent atmosphere are analyzed. The results show that the off-axis HGSMVB with smaller coherence length or propagating in stronger turbulent atmosphere will evolve from dark hollow beam into Gaussian-like beam with a larger beam spot faster. The beams with different values of integer order N or the position for hollow and vortex factor R will have almost the same Gaussian-like spot distribution at the longer propagation distance.

Optical trapping of the low index of refraction particles by focused vortex beams and two face-to-face focused beams

Using the extended Huygens–Fresnel principle and Rayleigh scattering theory, optical trapping of the low index of refraction particles using a focused Gaussian Schell-model (GSM) non-vortex beam, a focused GSM vortex beam, and two face-to-face focused GSM vortex beams have been studied. The results demonstrate that the focused GSM non-vortex beam cannot capture the low index of refraction particles, however, the focused GSM vortex beam can be a two-dimensional trap of particles in the z-axis, and the transverse gradient force Fgrad,x and the trapping equilibrium region increase as the topological charge m increases. As the focal length f or the refractive index of particles np decreases, the radiation forces increase and the trapping ability also enhances. To trap the low index particles in three-dimensional space, we adopt that the two face-to-face focused GSM vortex beams can be used to construct an optical potential well. The transverse gradient force of two face-to-face focused GSM vortex beams is twice that of a single GSM vortex beam. The limit of the radius for the low index of refraction particles that were stably captured has also been determined. The obtained results provide valuable information for trapping and manipulating the low index of refraction particles using GSM vortex beams, which may be applied in micromanipulation, biotechnology, nanotechnology and so on.

Propagation of Gaussian Schell-model vortex beams in biological tissues

Propagation of Gaussian Schell-model vortex beams in biological tissues

Effect of anisotropic non-Kolmogorov turbulence on the evolution behavior of Gaussian Schell-model vortex beams

Abstract The effect of anisotropic non-Kolmogorov turbulence on the evolution behavior of average intensity and coherent vortices for Gaussian Schell-model (GSM) vortex beams is investigated. Based on the extended Huygens–Fresnel principle and power spectrum of the anisotropic non-Kolmogorov turbulence, the analytical expressions for the cross-spectral density and average intensity of GSM vortex beams propagating through anisotropic non-Kolmogorov turbulence are obtained. The evolution behavior of intensity and coherent vortices for GSM vortex beams in anisotropic non-Kolmogorov turbulence has been discussed in detail by numerical simulation. The results shown that the evolution behavior of coherent vortices and intensity profile depends on the effective anisotropic factor, generalized exponent factor and structure constant of anisotropic non-Kolmogorov turbulence, as well as the beam parameters, such as beam waist, wave length and correlation length.

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.

Optical trapping two types of particles using a focused vortex beam

Propagations of Gaussian Schell-model (GSM) vortex beams through a focusing optical system are formulated. The radiation force acting on Rayleigh dielectric sphere with different refractive indices produced by focused GSM vortex beams is investigated theoretically. Numerical results demonstrate that the focused GSM non-vortex beam can not trap the low index of refraction particles, but can capture the high index of refraction particles. The focused GSM vortex beam can be used to trap high index of refraction particles to a bright ring of the focal plane, and simultaneously capture low index of refraction particles to z-axis. The larger the topological charge m is, the larger the value of the spatial correlation length σ0 is, the easier it is to trap two types of particles is. Trapping stability is also analyzed.

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).

Influence of non-Kolmogorov atmospheric turbulence on the beam quality of vortex beams.

Based on the extended Huygens-Fresnel principle and the definition of second-order moments of the Wigner distribution function (WDF), the analytical expressions for the propagation factors (M2-factors) and Strehl ratio SR of the Gaussian Schell-model (GSM) vortex beams and GSM non-vortex beams propagation through non-Kolmogorov atmospheric turbulence are derived, and used to study the influence of non-Kolmogorov atmospheric turbulence on beam quality of the GSM vortex beams. It is shown that the smaller the generalized structure constant and the outer scale of turbulence are, and the bigger the inner scale of turbulence is, the smaller the normalized propagation factor is, the bigger the Strehl ratio is, and the better the beam quality of GSM vortex beams in atmospheric turbulence is. The variation of beam quality with the generalized exponent α is nonmonotonic, when α = 3.11, the beam quality of the GSM vortex beams is the poorest through non-Kolmogorov atmospheric turbulence. GSM vortex beams is less affected by turbulence than GSM non-vortex beams under certain condition, and will be useful in long-distance free-space optical communications.

Evolution behavior of Gaussian Schell-model vortex beams propagating through oceanic turbulence.

The analytical expressions for the cross-spectral density and average intensity of Gaussian Schell-model (GSM) vortex beams propagating through oceanic turbulence are obtained by using the extended Huygens-Fresnel principle and the spatial power spectrum of the refractive index of ocean water. The evolution behavior of GSM vortex beams through oceanic turbulence is studied in detail by numerical simulation. It is shown that the evolution behavior of coherent vortices and average intensity depends on the oceanic turbulence including the rate of dissipation of turbulent kinetic energy per unit mass of fluid, rate of dissipation of mean-square temperature, relative strength of temperature salinity fluctuations, and beam parameters including the spatial correlation length and topological charge of the beams, as well as the propagation distance.

Propagation law of partially coherent vortex beam

We propose the analytic solution of cross-spectral density matrix (CSDM) of a partially coherent vortex beam while propagating. The solution to the propagation law is appropriate for a Gaussian Schell-model vortex beam to any order. It is found that the solution of CSDM of a Gaussian Schell-model beam revealed by Emil Wolf is a special instance. By this general solution, the intensity distribution, especially the degree of polarization and the mean-squared beam width of the partially coherent vortex beam, are investigated. It is found that the propagation character of the beam width is decided by the correlation-length, and that the topological charge affects only the value of the beam width.

Experimental study of the focusing properties of a Gaussian Schell-model vortex beam

We carry out an experimental and theoretical study of the focusing properties of a Gaussian Schell-model (GSM) vortex beam. It is found that we can shape the beam profile of the focused GSM vortex beam by varying its initial spatial coherence width. Focused dark hollow, flat-topped, and Gaussian beam spots can be obtained in our experiment, which will be useful for trapping particles. The experimental results agree well with the theoretical results.

Comparative study of partially coherent vortex beam propagations through atmospheric turbulence along a uplink path and a downlink path

Based on the extended Huygens-Fresnel principle, the propagations of a partially coherent vortex beam through atmospheric turbulence along an uplink path and a downlink path are studied, where the Gaussian Schell-model (GSM) vortex beam is taken as a typical example of partially coherent vortex beam. The analytical expressions for the average intensity, rms width and cross-spectral density function of GSM vortex beam propagating through atmospheric turbulence along a slant path are derived and used to study the influence of atmospheric turbulence along an uplink path and a downlink path on GSM vortex beam propagation and on coherence vortex. It is shown that under the same conditions the influence of atmospheric turbulence along a downlink path on GSM vortex beam propagation is smaller than that along a uplink path, and the conservation distance of the topological charge of GSM vortex beam along a downlink path is longer than that along a uplink path. The results are explained in physics.

Generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence

By using the extended Huygens–Fresnel principle, the analytical expressions for the generalized Stokes parameters of random electromagnetic Gaussian Schell-model (GSM) vortex beams propagating through atmospheric turbulence are derived, and used to study the changes in spectral Stokes parameters of random electromagnetic GSM vortex beams in atmospheric turbulence and to compare the results of random electromagnetic GSM vortex-free beams. The influence of atmospheric turbulence on the spectral Stokes parameters is analyzed. The validity of our results is interpreted physically.

Study correlation vortices in the near-field of partially coherent vortex beams diffracted by an aperture

We have derived the analytical expression of the electric cross-spectral density in the near- field of partially coherent vortex beams diffracted by an aperture. Taking the Gaussian Schell-model vortex beam as a typical example of partially coherent vortex beams, the spatial correlation properties and correlation vortices in the near-field of partially coherent vortex beams diffracted by a rectangle aperture are studied. It is shown that the off-axis displacement, spatial degree of coherence parameter, propagation distance, and the opening factor of the aperture affect the spectral degree of coherence and positions of correlation vortices. With the optimization algorithm, we obtain the symmetric distributing coherent vortex.

Partially coherent vortex beams propagating through slant atmospheric turbulence and coherence vortex evolution

Using the extended Huygens–Fresnel principle and the quadratic approximation of the phase structure function, and taking the Gaussian Schell-model (GSM) vortex beam as a typical example of partially coherent vortex beams, the explicit expressions for the cross-spectral density function and average intensity of GSM vortex beams with topological charge m=+1 propagating through slant atmospheric turbulence are derived, and used to study the propagation properties of GSM vortex beams in atmospheric turbulence along a slant path and evolution behavior of coherence vortices. It is shown that the spreading of GSM vortex beams along a horizontal path is larger than that along a slant path in the long atmospheric propagation. The propagation through horizontal atmospheric turbulence can be treated as a special case of the altitude-independent structure constant. The position of coherence vortices in slant atmospheric turbulence does not coincide with that in horizontal atmospheric turbulence, and the dependence of position of coherence vortices on the zenith angle, wavelength and reference point is illustrated by numerical examples. A comparison with the previous work is also made.