Laguerre-Gaussian Schell-model Research Articles

Orbital angular momentum spectra of twisted Laguerre-Gaussian Schell-model beams propagating in weak-to-strong Kolmogorov atmospheric turbulence.

The presence of atmospheric turbulence in a beam propagation path results in the spread of orbital angular momentum (OAM) modes of laser beams, limiting the performance of free-space optical communications with the utility of vortex beams. The knowledge of the effects of turbulence on the OAM spectrum (also named as spiral spectrum) is thus of utmost importance. However, most of the existing studies considering this effect are limited to the weak turbulence that is modeled as a random complex "screen" in the receiver plane. In this paper, the behavior of the OAM spectra of twisted Laguerre-Gaussian Schell-model (TLGSM) beams propagation through anisotropic Kolmogorov atmospheric turbulence is examined based on the extended Huygens-Fresnel integral which is considered to be applicable in weak-to-strong turbulence. The discrepancies of the OAM spectra between weak and strong turbulence are studied comparatively. The influences of the twist phase and the anisotropy of turbulence on the OAM spectra during propagation are investigated through numerical examples. Our results reveal that the twist phase plays a crucial role in determining the OAM spectra in turbulence, resisting the degeneration of the detection mode weight by appropriately choosing the twist factor, while the effects of the anisotropic factors of turbulence on the OAM spectra seem to be not obvious. Our findings can be applied to the analysis of OAM spectra of laser beams both in weak and strong turbulence.

A study of effects of a turbulent jet engine exhaust on partially coherent Laguerre-Gaussian Schell model vortex beam

In this study, based on the generalized Huygens-Fresnel principle, the evolution properties, such as spectral density, degree of coherence, and beam width of the propagation of partially coherent Laguerre-Gaussian Schell model vortex beam (PCLGSMvB) in jet engine exhaust are studied. Our results show that the spectral density of the corresponding beam can change their form shape during its propagation as the source coherence varies. When the source coherence width is high, the profile of PCLGSMvB changes from initially dark hollow into two spot beams at short propagation distances. If the source coherent width is very small, the shape of PCLGSMvB is converted to a Gaussian shape and keeps its form upon propagation. Also, we found that the spreading of PCLGSMvB is related with their initial parameters, and it will be spread faster with smaller source coherence width, larger mode order n, and longer wavelength. Furthermore, the beam width of the PCLGSMvB increasing as the structural constant increases and it means that the beam can resist to stronger fluctuation of turbulence. Outputs of this study has potential application on deriving the requirements of optical systems on aircrafts like laser range finder, laser designator, optical communication systems and directed infrared countermeasure (DIRCM).

Propagation properties of Laguerre-Gaussian Schell-model beams with a twist phase

In this paper, we introduce a new class of twisted partially coherent beams with a prescribed correlation function, twisted Laguerre-Gaussian Schell-model (TLGSM) beams, whose twist factor not only exists in the twist phase but also in correlation function. Analytical expressions for the cross-spectral density function propagating in free space and in turbulence are derived based on the extended Huygens-Fresnel integral. The evolution of the spectral intensity and orbital angular momentum (OAM) are discussed. Our results show that adjusting both the mode order and twist factor of the proposed beams to enhance the total OAM of the beams and, simultaneously, improve their resistance to turbulence. With multiple degrees of freedom that can be adjusted to optimize the beam for different turbulence conditions, TLGSM beams are an excellent candidate for use in optical applications in challenging media.

Self-reconstruction of twisted Laguerre-Gaussian Schell-model beams partially blocked by an opaque obstacle.

Twisted Laguerre-Gaussian Schell model (TLGSM) beams are a novel type of partially coherent beams, which carry the twist phase and the vortex phase simultaneously. In this paper, the self-reconstruction (SR) of the TLGSM beam partially blocked by an opaque obstacle and propagating through a thin lens focusing system is studied in detail. Implementing the pseudo-mode expansion method, we represent the TLGSM beam as a superposition of spatially coherent modes, which is applicable for calculating the cross spectral density (CSD) and spectral degree of coherence (SDOC) of such a beam using the Fourier transform. The numerical results reveal that the twist parameter, a measure of the strength of a twist phase, determines the characteristics of the SR. In the case of the topological charge of the vortex is positive, the SR capability of spectral density is significantly improved with the increase of the twist parameter. The physical mechanism behind these phenomena is analyzed in detail from the point view of mode expansion. Further, the dependence of the side ring intensity and SR capability of the SDOC on the twist parameter are also investigated. It is found that the SR capability and side ring intensity of the SDOC are simultaneously enhanced for a large twist parameter, providing an efficient way to determine the number of topological charge. Our study results may find application in communication and information recovery applications.

Twisted Laguerre-Gaussian Schell-model beam and its orbital angular moment.

It is well known that a light beam with vortex phase or twist phase carries orbital angular momentum (OAM), while twist phase only exists in a partially coherent beam. In this paper, we introduce a new partially coherent beam, named twisted Laguerre-Gaussian Schell-model (TLGSM) beam. This TLGSM beam carries both vortex phase and twist phase. Further, the evolutional properties of the spectral density and spectral degree of coherence (SDOC)] of the TLGSM beam passing through a paraxial ABCD optical system are explored in detail. Our results reveal that the vortex and twist phases' handedness significantly affects the evolution properties. When the twist phase's handedness is the same as that of the vortex phase, the beam profile maintains a dark hollow shape during propagation and the side rings in SDOC are suppressed; however, when the handedness of two phases is opposite, then the beam shape evolves into a Gaussian shape and the side rings in SDOC are enhanced. Furthermore, we obtain the analytical expression for the OAM of the TLGSM beam. It is found that the vortex phase's and twist phase's contributions to the OAM are interrelated, which greatly increases the amount of OAM. In addition, the OAM variation of the TLGSM beam passing through an anisotropic optical system is also explored in detail. Our results will be useful for information transfer and optical manipulations.

Propagation Factors of Partially Coherent Model Beams in Oceanic Turbulence

Based on the extended Huygens–Fresnel principle and second-order moments of the Wigner distribution function, we have derived the analytical expressions of the propagation factor of four kinds of partially coherent model beams in oceanic turbulence, including Gaussian Schell-model (GSM), Bessel–Gaussian Schell-model, Laguerre–Gaussian Schell-model, and cosine-Gaussian Schell-model (CGSM). It is found that the modulation of the spectral degree of coherence takes advantage over the GSM beams for reducing the turbulence-induced degradation. The beams with larger index ( $n$ , $\beta $ , $m$ ), initial beamwidth, and the wavelength or the smaller coherent length will be less affected by the oceanic turbulence. In addition, the influences of the oceanic parameters on the beam quality are discussed in detail, and the degradation of beams can be enhanced with the decrease of the rate of dissipation of turbulence kinetic energy per unit mass of fluid and the increase of the rate of dissipation of mean-square temperature, also the salinity fluctuation has greater contribution to the decrease of the beam quality than that of the temperature fluctuation. Moreover, the comparison of the normalized propagation factor of the four kinds of beams demonstrates that the CGSM is more robust against the oceanic turbulence than other partially coherent model beams. Our results can be helpful in the design of an optical communication system in an oceanic environment.

Average intensity and spreading of partially coherent model beams propagating in a turbulent biological tissue

For Gaussian beams with three different partially coherent models, including Gaussian-Schell model (GSM), Laguerre-Gaussian Schell-model (LGSM) and Bessel-Gaussian Schell-model (BGSM) beams propagating through a biological turbulent tissue, the expression of the spatial coherence radius of a spherical wave propagating in a turbulent biological tissue, and the average intensity and beam spreading for GSM, LGSM and BGSM beams are derived based on the fractal model of power spectrum of refractive-index variations in biological tissue. Effects of partially coherent model and parameters of biological turbulence on such beams are studied in numerical simulations. Our results reveal that the spreading of GSM beams is smaller than LGSM and BGSM beams on the same conditions, and the beam with larger source coherence width has smaller beam spreading than that with smaller coherence width. The results are useful for any applications involved light beam propagation through tissues, especially the cases where the average intensity and spreading properties of the light should be taken into account to evaluate the system performance and investigations in the structures of biological tissue.

Average intensity and directionality of partially coherent model beams propagating in turbulent ocean.

We studied Gaussian beams with three different partially coherent models, including the Gaussian-Schell model (GSM), Laguerre-Gaussian Schell model (LGSM), and Bessel-Gaussian Schell model (BGSM), propagating through oceanic turbulence. The expressions of average intensity, beam spreading, and beam wander for GSM, LGSM, and BGSM beams in the paraxial channel are derived. We make a contrast for the three models in numerical simulations and find that the GSM beam has smaller spreading than the others, and the LGSM beam needs longer propagation distance to transform into a well-like profile of average intensity than the BGSM beam in the same conditions. The salinity fluctuation has a greater contribution to the wander of LGSM and BGSM beams than that of the temperature fluctuation. Our results can be helpful in the design of an optical wireless communication link operating in oceanic environment.

Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere

Laguerre-Gaussian Schell-model (LGSM) beam was proposed in theory [Opt. Lett.38, 91 (2013 Opt. Lett.38, 1814 (2013)] just recently. In this paper, we study the propagation of a LGSM beam in turbulent atmosphere. Analytical expressions for the cross-spectral density and the second-order moments of the Wigner distribution function of a LGSM beam in turbulent atmosphere are derived. The statistical properties, such as the degree of coherence and the propagation factor, of a LGSM beam in turbulent atmosphere are studied in detail. It is found that a LGSM beam with larger mode order n is less affected by turbulence than a LGSM beam with smaller mode order n or a GSM beam under certain condition, which will be useful in free-space optical communications.