multi-Gaussian Schell-model Beam Research Articles

Propagation dynamics of multi-Gaussian Schell model beams in strongly nonlocal nonlinear media

The analytical propagation formulae of a single multi-Gaussian Schell model (MGSM) beam and two MGSM beams in strongly nonlocal nonlinear media (SNNM) are derived, and the optical breather characteristics of a single MGSM beam and two MGSM beams in SNNM are studied, respectively. It is found that a MGSM soliton is never formed because of the self-shaping feature of MGSM beams, but a MGSM breather can be formed. Furthermore, for a MGSM breather, the Gaussian-like profile and the flat-top profile alternate periodically during propagation. On the other hand, even if the separation distance is large enough, two MGSM breathers can be combined into a single breather due to nonlinearity when the threshold critical power arrives. Furthermore, the relationship between the threshold critical power and the MGSM beam parameters is also investigated.

Degree of paraxiality of radially polarized twisted multi-Gaussian Schell-model beams.

The degree of paraxiality (DOP) of a radially polarized twisted multi-Gaussian Schell-model (RPT MGSM) beam is discussed, and the influence of the source parameters on its DOP is studied. It is shown that the parameters of the beam source, including the boundary characteristic, the beam waist width, the coherence width of the source correlation, and the twist factor, have a significant impact on the DOP of the RPT MGSM beam. To explain the behaviors of the DOP, the far-field divergence angle of this beam is also discussed.

Evolution properties of a radially polarized fractional multi-Gaussian Schell-model beam propagating in anisotropic turbulence

Evolution properties of a radially polarized fractional multi-Gaussian Schell-model beam propagating in anisotropic turbulence

Spreading properties of partially coherent multi-Gaussian Schell-model and modified Bessel-correlated vortex beams in anisotropic turbulent plasma

We investigate the propagation characteristics of partially coherent multi-Gaussian Schell-model (MGSM) and modified Bessel-correlated (MBc) vortex beams traveling in a turbulent plasma. Based on the extended Huygens-Fresnel principle, the cross-spectral density expressions for partially coherent MGSM and MBc vortex beams propagating through turbulent plasma were derived. The results show that the dark spot at the center of the partially coherent MGSM beams disappears in the low-coherence states and remains in the high-coherence states only. In contrast, the intensity of partially coherent MBc vortex beams exists in low- and high-coherence states and does not change during propagation in a weak turbulent plasma.

Changes in the statistical properties of electromagnetic double multi-Gaussian Schell-model beams on propagation in free space.

A class of electromagnetic random sources with a multi-Gaussian functional form in the spectral density and in the correlations part of the cross-spectral density matrix is introduced based on the genuine cross-spectral density-matrix theory. The analytic propagation formulas of the cross-spectral density matrix of such beams propagating in free space are derived by use of Collins' diffraction integral. With the help of analytic formulas, the evolution of statistical characteristics, i.e.,the spectraldensity, the spectral degree of polarization, and the spectral degree of coherence for such beams in free space are analyzed numerically. Employing the multi-Gaussian functional form in the cross-spectral density matrix introduces one more freedom in the modeling of Gaussian Schell-model sources.

Orbital angular momentum evolution of twisted multi-Gaussian Schell model beams in anisotropic turbulence

Twist phase is an unconventional phase that allows a partially coherent beam to carry orbital angular momentum (OAM). In this work, based on the Mercer’s expansion and the nonnegativity of the cross-spectral density function, we obtain a twistable condition for the multi-Gaussian Schell model (MGSM) correlation structure. The expression of an elliptical twisted multi-Gaussian Schell model (TMGSM) beam through non-Kolmogorov anisotropic atmospheric turbulence is rigorously derived, and its spectral density and OAM variation in anisotropic turbulence are studied in detail. The results show that the spectral density and OAM flux density distributions rotate with increasing transmission distance, and increasing the multi-Gaussian modulus and twist factor can significantly suppress the negative effects of atmospheric turbulence. The difference of turbulence anisotropy, beam modulus, and coherence length can affect the distribution of OAM. Furthermore, the twist phase affects both the OAM distribution and magnitude. Our work is helpful for exploring new forms of OAM sources, and promote the application of free-space optical communications.

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

The correction pointed out by Nemes [J. Opt. Soc. Am. A39, 667 (2022)JOAOD60740-323210.1364/JOSAA.435756] to our paper [J. Opt. Soc. Am. A37, 89 (2020)JOAOD60740-323210.1364/JOSAA.37.000089] is welcome. The author claims that the beam propagation factors Mx2, My2 are inadequate to characterize twisted elliptical multi-Gaussian Schell-model (TEMGSM) beams, which are introduced in our paper. Further, the author points out that there are two pairs of independent, normalized invariants to classify the TEMGSM beams. In this reply, we present the numerical example of the normalized intrinsic propagation invariants of the TEMGSM beams.

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

The inadequacy of using beam propagation factors Mx2, My2 for general astigmatic beams as those analyzed in the paper J. Opt. Soc. Am. A37, 89 (2020)JOAOD60740-323210.1364/JOSAA.37.000089 is discussed, and the appropriate beam invariants to be considered are presented.

Radially Polarized Twisted Rectangular Multi-Gaussian Schell-Model Beam and Its Propagation Properties

Radially Polarized Twisted Rectangular Multi-Gaussian Schell-Model Beam and Its Propagation Properties

Twisted electromagnetic elliptical multi-Gaussian Schell-model beams and their transmission in random media.

We extend the scalar elliptical multi-Gaussian Schell-model (EMGSM) beams with twist phase to the electromagnetic domain and obtain the analytical expression for the propagation of the electromagnetic twisted EMGSM beams through random media. The twist phase-induced changes of the spectral density and degree of polarization of such beams on propagation are studied numerically. Results show that by adjusting the twist factor and the correlated parameters of the source, both the spectral density and degree of polarization not only rotate around the propagation axis but also exhibit diverse shapes. The flattopped ellipse-like and diamond-like shape maintain over a relatively long propagation distance and finally involve into Gaussian-like shape due to stronger atmospheric turbulence. The results will be useful in optical trapping and optical communication.

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.

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

The degree of paraxiality (DOP) of an electromagnetic fractional multi-Gaussian Schell-model (EM-FMGSM) beam is discussed, and the effect of the properties of the light source on its DOP is also studied. It is shown from the numerical results that the DOP of an EM-FMGSM beam is determined by the rms widths of the auto-correlation functions, the truncated parameter, the degree of polarization, and the boundary characteristics of its source. Moreover, the far-field divergence angle of the beam source is also investigated to illustrate the behaviors of the DOP.

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

Degree of paraxiality (DOP) of an anisotropic hollow multi-Gaussian Schell-model (HMGSM) beam is discussed, and the influence of parameters of the beam source on its DOP is studied. It is shown that the parameters of the beam source, including the anisotropy, boundary characteristic, beam waist width, and beam coherence width, may play an important role in its DOP. Moreover, in order to illustrate the behaviors of DOP, the far-field divergence angle of this beam source has also been investigated.

Partially coherent sources with the combined quadratic phase

We construct a class of partially coherent sources with a new phase, which is consisted of separable and inseparable quadratic phases. As examples, the Gaussian distribution and rectangular flat-topped Gaussian distributions are selected as weight functions, respectively. The analytical propagation formulas of anisotropic Gaussian Schell-model (AGSM) beams and rectangular multi-Gaussian Schell-model (RMGSM) beams with the combined quadratic phase are derived. We investigate the propagation characteristics of the AGSM beam and the RMGSM beam carrying the combined quadratic phase. The twist effects of the combined quadratic phase on the spectral density (SD) and the degree of coherence (DOC) of the AGSM beam are quantitatively analyzed, and a specific method for calculating the critical value of the phase parameter is proposed. In addition, we qualitatively analyze the twist effects of the combined quadratic phase on the SD and the DOC of the RMGSM beam. We find that the propagation of the RMGSM beam is similar to that of the AGSM beam. These results may provide new inspiration for applications of synthesizing rotating beams in optics.

Radially polarized twisted Multi-Gaussian Schell-model beams and their statistical properties

A radially polarized twisted Multi-Gaussian Schell-model (RPT MGSM) beam based on the unified theory of coherence and polarization is introduced. The reliability conditions for the beams are also derived. We derive the analytical expressions for the elements of the cross-spectral density matrix of such beam propagating in free space and investigate the statistical properties, such as spectral density, degree of coherence, degree of polarization and state of polarization. It is found that the statistical properties of the RPT MGSM beams are closely related to the twist phase, e.g. the twist phase induces not only the rotation of the beam spot but also changes of the degree of coherence, degree of polarization and state of polarization on propagation. Specially, an interesting phenomenon is found. In the far field, when the beams without carrying twist factor, the state of polarization in the flat-top area of intensity distribution is azimuthally polarized rather than radially polarized. Our results may be useful in optical trapping and free-space optical communications.

Propagation of a rectangular multi-gaussian schell-model vortex beam in uniaxial crystal

The cross-spectral density of a rectangular multi-Gaussian Schell-model vortex beam propagating in uniaxial crystal orthogonal to the optical axis has been derived, and the normalized intensity and effective beam widths are investigated by using numerical analysis. The results indicate that the rectangular multi-Gaussian Schell-model vortex beam propagating in uniaxial crystal will evolve from circular dark hollow beam into an elliptical flat-topped beam due to the influences of uniaxial crystal. The effective beam width Wx will gradually increase as the propagation distance z increase, and the beam with larger M and N1=N2 or smaller σ will have a larger effective beam width Wx at the same propagation distance.

Optical trapping Rayleigh particles with a twist effect

We theoretically and numerically investigate the focusing properties and the radiation forces produced by a focused rotating anisotropic generalized multi-Gaussian Schell model (RAGMGSM) beam. We find that for different parameters at the trapped plane, the intensity distribution would evolve into an elliptical dark hollow or elongated Gaussian beam profile. Compared to the focal plane, the trapped plane has an axial displacement due to the twist effects. Further, we demonstrate that two types of particles at different positions of the trapped plane can be trapped and rotated simultaneously by such a focused beam. Moreover, the influences of the beam index M, the coherence width δ, and the twist factor u on the radiation forces is elucidated respectively. The limits of each parameter for stability of optical trapping under a certain condition are explicitly discussed.

Spreading and coherence properties of a rectangular multi-Gaussian Schell-model beam propagating in biological tissues

Based on the extended Huygens–Fresnel integral, the cross-spectral density function of a rectangular multi-Gaussian Schell-model (RMGSM) beam propagating in biological tissues has been derived, and the spreading properties and spectral degree of coherence of an RMGSM beam propagating in biological tissues were studied by using the numerical examples. The results show that an RMGSM beam propagating in biological tissues will first evolve into a rectangular flat-topped beam and then evolve into a Gaussian-like beam due to the influences of the turbulence of biological tissues. It is also found that an RMGSM beam with smaller coherence length can maintain the rectangular flat-topped beam spot at the longer propagation distance.

Propagation of Rectangular Multi-Gaussian Schell-Model Array Beams through Free Space and Non-Kolmogorov Turbulence

In this paper, rectangular multi-Gaussian Schell-model (MGSM) array beams, which consists N×D beams in rectangular symmetry, are first introduced. The analytical expressions of MGSM array beams propagating through free space and non-Kolmogorov turbulence are derived. The propagation properties, such as normalized average intensity and effective beam sizes of MGSM array beams are investigated and analyzed. It is found that the propagation properties of MGSM array beams depend on the parameters of the MGSM source and turbulence. It can also be seen that the beam size of Gaussian beams translated by MGSM array beams will become larger as the total number of terms, M, increases or coherence length, σ , decreases, and the beam in stronger non-Kolmogorov turbulence (larger α and l 0 , or smaller L 0 ) will also have a larger beam size.