Laguerre-Gaussian Correlated Schell-model Research Articles

Impact of joint turbulence of jet engine and marine environment on the propagation quality of partially coherent generalized Laguerre–Gaussian correlated Schell model beams

Impact of joint turbulence of jet engine and marine environment on the propagation quality of partially coherent generalized Laguerre–Gaussian correlated Schell model beams

Radial phased-locked Laguerre-Gaussian correlated schell-model beam array

A new beam array called radial phased-locked Laguerre-Gaussian correlated Schell-model (LGCSM) beam array is presented, the beamlet of this beam array is partially coherent beam with Laguerre Gaussian-Schell model correlation. The propagation expression of a radial phased-locked LGCSM beam array in free space is derived. It is aimed to give the effect of beam parameters on evolutions of beam array composed by LGCSM beam. The radial phased-locked LGCSM beam array has unique properties on propagation, the intensity of such beam array will evolve from a beam array composed of Gauss beams into a beam array formed of LGCSM beams. Furthermore, the intensity evolutions of such beam array are modulated by coherence length and beam order of beamlets. The obtained results are important in areas such as light field shaping, and free space optical communication.

Propagation of a rectangular Laguerre-Gaussian correlated Schell-model beam in uniaxial crystal

The analytical equation of a rectangular Laguerre-Gaussian correlated Schell-model (LGCSM) beam in uniaxial crystal orthogonal to the optical axis is derived. The intensity and coherence properties of a rectangular LGCSM beam in uniaxial crystal are investigated by numerical simulations. It is shown that the symmetry of intensity and coherence distribution can be modulated by the ne/no. When ne/no>1 of uniaxial crystal, the multiple beams generating by a rectangular LGCSM beam will spread faster along x-direction than y-direction at the longer distance. The physical explanations of evolutions are analyzed in detail.

Periodic properties of Laguerre-Gaussian correlated Schell-model beams in a gradient-index fiber

The explicit expressions of the cross-spectral density (CSD) and the propagation factor of Laguerre-Gaussian correlated Schell-model (LGCSM) beams propagation in a gradient-index (GRIN) fiber were derived. The statistical properties, such as the spectral intensity, the spectral degree of coherence (DOC) and the propagation factor of LGCSM beams in a GRIN fiber are illustrated numerically. Our results show that the beams spectral intensity and spectral DOC change periodically in a GRIN fiber. We can adjust the initial beam parameters of LGCSM beams, such as the beam order, the transverse beam width and the transverse coherence width, to control the distributions of the spectral intensity and the spectral DOC of the beams in the output plane of a GRIN fiber. Furthermore, the propagation factor of the beams remains invariant on propagation and it is determined only by the initial beam parameters. Our results may be useful in optical fiber communications.

Evolution properties of the radially polarized Laguerre-Gaussian-correlated Schell-model beams propagating in uniaxial crystals.

In this paper, we discuss, both analytically and numerically, the paraxial propagation of the radially polarized Laguerre-Gaussian-correlated Schell-model (LGCSM) beams orthogonal to the optical axis in uniaxial crystals. The analytical expression for the cross-spectral density function and the second-order moments of the radially polarized LGCSM beams are derived, and the evolution properties of the normalized intensity distribution, the spectral degree of the coherence (SDOC), and the spectral degree of the polarization (SDOP) in uniaxial crystals are elucidated by numerical examples. It is found that the intensity distribution of the radially polarized LGCSM beams evolves from a doughnut shape into a solid shape and finally converts into an elliptical symmetric hollow-ring profile in uniaxial crystals due to the combined effect of special correlation functions and the anisotropy effect of the uniaxial crystals. The evolution of the SDOC and SDOP for the radially polarized LGCSM beams is quite different from that of the radially polarized Gaussian-Schell-model beams. In addition, the propagation properties of the radially polarized LGCSM beams are closely related to the spatial coherence length, the mode order, and the ratio of extraordinary and ordinary reflective indices. The results show that the uniaxial crystals could modulate the evolution properties of the radially polarized LGCSM beams.

Propagation properties of rectangular Laguerre–Gaussian-correlated Schell-model beams in atmospheric turbulence

ABSTRACTBased on the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function (WDF), the analytical expressions for the cross-spectral density (CSD) and the propagation factor of a rectangular Laguerre–Gaussian-correlated Schell-model (LGCSM) beam propagating in atmospheric turbulence are derived. The statistical properties, such as the average intensity, the spectral degree of coherence (SDOC) and the propagation factor, of a rectangular LGCSM beam in free space and atmospheric turbulence are comparatively analysed. It is illustrated that a rectangular LGCSM beam exhibits self-splitting and combing properties on propagation in atmospheric turbulence, and the self-splitting properties of such beam are closely related to its beam orders m and n, which is quite different from other self-splitting beams. In addition, the rectangular LGCSM beam has an advantage for reducing the turbulence-induced degradation compared with the conventional partially coherent beams.

Focus shaping of the radially polarized Laguerre-Gaussian-correlated Schell-model vortex beams.

In this paper, we introduce a new kind of partially coherent vector beam with special correlation function and vortex phase named radially polarized Laguerre-Gaussian-correlated Schell-model (LGCSM) vortex beam as a natural extension of scalar LGCSM vortex beam. The realizability conditions for such beam are derived. The tight focusing properties of a radially polarized LGCSM vortex beam passing through a high numerical aperture (NA) objective lens are investigated numerically based on the vectorial diffraction theory. We find that not only the transverse component but also the longitudinal component of the focal field distributions can be shaped by regulating the structures of the correlation functions, which is quite different from that of the conventional radially polarized partially coherent beam. Moreover, a series of wildly used focal field with novel structure, e.g., focal spot, flat-topped or doughnut beam profiles, needle-like focal field and controllable three-dimensional (3D) optical cage, were obtained. These results indicate that the focus shaping can be achieved by combining the regulation of the structures of the correlation functions with the regulation of beam parameters effectively. Our results may be useful for potential applications in optical trapping, optical high-resolution microscopy and optical data storage.

Propagation of multi-cosine-Laguerre-Gaussian correlated Schell-model beams in free space and atmospheric turbulence.

We introduce a class of random stationary, scalar source named as multi-cosine-Laguerre-Gaussian-correlated Schell-model (McLGCSM) source whose spectral degree of coherence (SDOC) is a combination of the Laguerre-Gaussian correlated Schell-model (LGCSM) and multi-cosine-Gaussian correlated Schell-model (McGCSM) sources. The analytical expressions for the spectral density function and the propagation factor of a McLGCSM beam propagating in turbulent atmosphere are derived. The statistical properties, such as the spectral intensity and the propagation factor, of a McLGCSM beam are illustrated numerically. It is shown that a McLGCSM beam exhibits a robust ring-shaped beam array with adjustable number and positions in the far field by directly modulating the spatial structure of its SDOC in the source plane. Moreover, we provide a detailed insight into the theoretical origin and characteristics of such a ring-shaped beam array. It is demonstrated that these peculiar shaping properties are the concentrated manifestation of the individual merits respectively associated with the Laguerre- and multi-cosine-related factors of the whole SDOC. Our results provide a novel scheme to generate robust and controllable ring-shaped beam arrays over large distances, and will widen the potentials for manipulation of multiple particles, free-space optical communications and imaging in the atmosphere.

Propagation of a Laguerre-Gaussian correlated Schell-model beam in strongly nonlocal nonlinear media

Analytical expressions for the cross-spectral density function and the second-order moments of the Wigner distribution function of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in strongly nonlocal nonlinear media are derived. The propagation properties, such as beam irradiance, beam width, the spectral degree of coherence and the propagation factor of a LGCSM beam inside the media are investigated in detail. The effect of the beam parameters and the input power on the evolution properties of a LGCSM is illustrated numerically. It is found that the beam width varies periodically or keeps invariant for a certain proper input power. And both the beam irradiance and the spectral degree of coherence of the LGCSM beam change periodically with the propagation distance for the arbitrary input power which however has no influence on the propagation factor. The coherent length and the mode order mainly affect the evolution speed of the LGCSM beam in strongly nonlocal nonlinear media.

Trapping Two Types of Particles Using a Laguerre–Gaussian Correlated Schell-Model Beam

Based on the Rayleigh scattering theory, the radiation forces and the trap stiffness on Rayleigh dielectric sphere induced by a focused Laguerre–Gaussian correlated Schell-model (LGCSM) beam are theoretically studied. It is found that by choosing the appropriate transverse coherence width, mode orders, transverse beam width, and focus lengths, a Rayleigh particle whose refractive index is larger or smaller than the ambient medium can be trapped. Our results will have some theoretical reference value for optical trapping.

Propagation properties of Laguerre-Gaussian correlated Schell-model beam in non-Kolmogorov turbulence.

Analytical formulas are derived for the average intensity, the root-mean-square (rms) angular width, and the M2-factor of Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in non-Kolmogorov turbulence. The influence of the beam and turbulence parameters on the LGCSM beam is numerically calculated. It is shown that the quality of the LGCSM beam can be improved by choosing appropriate beam or turbulence parameter values. It is also found that the LGCSM beam has advantage over the Gaussian Schell-model (GSM) beam for reducing the turbulence-induced degradation. Our results will have some theoretical reference value for optical communications.

The tight focusing properties of Laguerre-Gaussian-correlated Schell-model beams

Based on the Richards–Wolf vectorial diffraction theory, the tight focusing properties, including the intensity distribution, the degree of polarization and the degree of coherence, of the Laguerre–Gaussian-correlated Schell-model (LGSM) beams through a high-numerical-aperture (NA) focusing system are investigated in detail. It is found that the LGSM beam exhibits some extraordinary focusing properties, which is quite different from that of the GSM beam, and the tight focusing properties are closely related to the initial spatial coherence and the mode order n. The LGSM beam can form an elliptical focal spot, a circular focal spot or a doughnut-shaped dark hollow beam at the focal plane by choosing a suitable value of the initial spatial coherence , and the central dark size of the dark hollow beam increases with the increase of the mode order n. In addition, the influences of the initial spatial coherence and the mode order n on the degree of polarization and the degree of coherence are also analysed in detail, respectively. Our results may find applications in optical trapping.

Theoretical and experimental studies of a rectangular Laguerre–Gaussian-correlated Schell-model beam

We introduce a new kind of partially coherent beam with nonconventional correlation function named rectangular Laguerre–Gaussian-correlated Schell-model (LGCSM) beam, whose degree of coherence is of rectangular symmetry, and analyze its propagation properties. We find that the rectangular LGCSM beam exhibits self-splitting properties on propagation in free space, i.e., the initial single beam spot evolves into (m + 1) × (n + 1) beam spots on propagation with m and n being the beam orders, which are totally different from that of a circular or elliptical LGCSM beam. The self-splitting properties of a rectangular LGCSM beam are also different from other self-splitting beam whose initial single beam spot only splits into two or four beam spots on propagation in free space. We also find that a focused rectangular LGCSM beam exhibits splitting and combining properties on propagation. Furthermore, we carry out experimental generation of a rectangular LGCSM beam and verify the splitting and combining properties of such beam focused by a thin lens. The rectangular LGCSM beam will be useful for manipulating multiple particles or attacking multiple targets simultaneously.

Propagation of a Laguerre–Gaussian correlated Schell-model beam beyond the paraxial approximation

Recently, Laguerre–Gaussian correlated Schell-model (LGCSM) beam was introduced theoretically [Mei and Korotkova, Opt. Lett. 38(2), (2013), 91–93] and generated experimentally [Wang et al., Opt. Lett. 38(11), (2013), 1814–1816]. In this paper, we treat the propagation of a LGCSM beam beyond the paraxial approximation. Based on the generalized Rayleigh–Sommerfeld diffraction integral, analytical expressions for the intensity and spectral degree of coherence of a nonparaxial LGCSM beam propagating in free space are obtained, and the corresponding results of a paraxial LGCSM beam are also derived as a special case. Our numerical results show that the nonparaxial propagation properties of a LGCSM beam are closely related to the initial beam parameters, such as the beam waist width, the coherence width and the mode order. Furthermore, in the far field, flat-topped, hollow intensity profiles can be formed through varying the initial beam parameters, which is different from that of a nonparaxial Gaussian Schell-model beam.

Evolution properties of a Laguerre-Gaussian correlated Schell-model beam propagating in uniaxial crystals orthogonal to the optical axis.

Analytical expressions for the cross-spectral density function and the second-order moments of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in uniaxial crystals orthogonal to the optical axis are derived. Based on the formulas derived, we study the propagation properties, such as beam irradiance, beam diameters, and the spectral degree of coherence, of a LGCSM beam inside uniaxial crystals in detail. The effect of the initial beam parameters (mode order and spatial coherence length) and the parameters of the uniaxial crystals on the evolution properties of a LGCSM beam is revealed through numerical examples. The uniaxial crystals provide one way to modulate the properties of a LGCSM beam.

Elliptical Laguerre-Gaussian correlated Schell-model beam.

A new kind of partially coherent beam with non-conventional correlation function named elliptical Laguerre-Gaussian correlated Schell-model (LGCSM) beam is introduced. Analytical propagation formula for an elliptical LGCSM beam passing through a stigmatic ABCD optical system is derived. The elliptical LGCSM beam exhibits unique features on propagation, e.g., its intensity in the far field (or in the focal plane) displays an elliptical ring-shaped beam profile, being qualitatively different from the circular ring-shaped beam profile of the circular LGCSM beam. Furthermore, we carry out experimental generation of an elliptical LGCSM beam with controllable ellipticity, and measure its focusing properties. Our experimental results are consistent with the theoretical predictions. The elliptical LGCSM beam will be useful in atomic optics.

Experimental demonstration of a Laguerre-Gaussian correlated Schell-model vortex beam

Laguerre-Gaussian correlated Schell-model (LGCSM) vortex beam is introduced as an extension of LGCSM beam which was proposed [Opt. Lett.38, 91 (2013)Opt. Lett.38, 1814 (2013)] just recently. Explicit formula for a LGCSM vortex beam propagating through a stigmatic ABCD optical system is derived, and the propagation properties of such beam in free space and the focusing properties of such beam are studied numerically. Furthermore, we carry out experimental generation of a LGCSM vortex beam, and studied its focusing properties. It is found that the propagation and focusing properties of a LGCSM vortex beam are different from that of a LGCSM beam, and we can shape the beam profile of a LGCSM vortex at the focal plane (or in the far field) by varying its initial spatial coherence. Our experimental results are consistent with the theoretical predictions, and our results will be useful for particle trapping.