The spectral properties of a partially coherent Lommel-Gaussian beam in turbulent atmosphere

https://doi.org/10.1016/j.optlastec.2019.105940Get rights and content

Highlights

  • Analytical equations of a partially coherent Lommel-Gaussian beam are derived.

  • Propagation properties in turbulent atmosphere are studied.

  • Propagation of the beam is closely related with beam and turbulent parameters.

Abstract

Based on the extended Huygens–Fresnel principle, the analytical propagation equations of a partially coherent Lommel-Gaussian (PCLG) beam propagating in atmospheric turbulence have been introduced. The spectral properties of the PCLG beam in turbulent atmosphere are explored. It is found by numerical simulations that after propagating in turbulent atmosphere, the intensity distribution and spectral degree of coherence (SDOC) of the PCLG beam vary on propagation. The intensity distribution of the PCLG beam depends closely on the strength of atmospheric turbulence and the parameters of the source beam, and will eventually transform into a Gaussian profile at the receiver plane. In addition, with smaller OAM quantum number and structure constant or bigger wavelength, the SDOC of the PCLG beam spreads more rapidly. The results are expected to be useful for understanding the properties of the Lommel-Gaussian beam in turbulence.

Introduction

In recent years, considerable attention has been paid to the propagation of various vortex beams carrying orbital angular momentum (OAM) in turbulent atmosphere, due to their widespread applications in free-space optical communications, quantum state manipulation, optical microscopy, etc [1], [2], [3], [4], [5]. However, theoretical and experimental studies have shown that the vortex beams are seriously induced by the turbulence, and the performances of the beam are inevitably damaged [5], [6], [7], [8], [9]. To reduce the negative effect of the turbulence, many methods and techniques have been proposed and studied. It has been demonstrated that a partially coherent vortex beam is more resistant to the turbulence than a fully coherent vortex beam [10], [11]. It has also been revealed that the beam carrying OAM is also preferable to the beam without OAM [12], [13]. Furthermore, the non-diffracting vortex beams have been applied to reduce the effects of turbulent medium for their excellent properties of non-diffraction and self-healing mechanism [14], [15].

The concept of non-diffracting beams was firstly put forward in 1987 and the zero-order Bessel beam was experimentally generated by illuminating an angular slit located in the focal plane of a lens with a plane wave [16]. After that, other types of nondiffracting beams was proposed: Mathieu beams [17], [18], Hankel–Bessel beams [14] and Airy beams [19]. The high order Bessel beam, as a typical kind of the nondiffracting vortex beams, has been widely studied [20], [21], [22]. However, the ideal nondiffracting vortex beam is characterized as carrying infinite energy and propagating indefinitely in the space without deformation. To restrict its energy, usually a Gaussian windowing function is added, thus the Bessel-Gaussian beam is introduced [23] and is extensively applied in optical manipulation [24], medical imaging [25] and so on [26], [27], [28]. Recently, the Lommel beam has been proposed, which is a linear superposition of Bessel beams and the transverse intensity distribution can be flexibly adjusted [29]. Subsequently, the Lommel beam has been extensively studied [30], [31], [32], [33], [34]. However, to our knowledge, the intensity distribution and SDOC of the partially coherent Lommel-Gaussian (PCLG) beam, which are significant aspects to evaluate laser propagation property, has not been analyzed.

The purpose of the paper is to study the propagation properties of the PCLG beams in atmospheric turbulence. Analytical expressions of the intensity distribution and SDOC of a PCLG beam propagating in atmospheric turbulence are given and the dependences of the propagation parameter on the source and the turbulence parameter are also discussed.

Section snippets

Theoretical model

The source field of a Lommel-Gaussian beam can be expressed as a combination of M decentered Gaussian beams, given below [26], [29]En(s,z=0)=p=0(-1)p(c)2pexp[i(n+2p)ϕ]Jn+2p(βs)exp[-s2w02]1Minp=0(-1)p(c)2pexp(-β24)m=0M-1exp-s2w02+iβ(xcosθm+ysinθm)+iφm,where s=(x,y) is a position vector, θm=mα0, α0=2πM and φm=nmα0, β, c, and n denote beam’s scaling factor, asymmetry parameter, and OAM quantum number, respectively. Also, k=2π/λ is wave number with wavelength λ, w0 is beam waist, and Jn+2p(·)

Numerical results

For easier comparison, the normalized intensity distribution is adopted. The parameters are selected as follows: w0=2cm, σ0=1cm, L0=10m, l0=1cm, λ=632.8nm, Cn2=10-14m-2/3, β=80m-1, z=1km and n=1. Other parameters are specified in the figures.

The intensity distribution of a PCLG beam in turbulence with different asymmetry parameters are depicted in Fig. 1. When at source plane, the beam profile of PCLG beam has a doughnut shape. With the increase of distance, the dark core will become smaller

Conclusion

Analytical expressions of the intensity distribution and SDOC of a PCLG beam in atmospheric turbulence have been derived. The influence of beam and turbulent parameters on the evolution of the PCLG beam has been performed. Within the range of parameters examined, it is shown that the as structure constant Cn2, and wave length λ are smaller, or OAM quantum number n, spatial correlation length σ0, and inner scale l0 are larger, the intensity distributions of the PCLG beam spread slowly. The

Funding

National Nature Science Foundation of China (61675159), Key Projects of Equipment Pre-Research Fund (6140416010102) and Nature Science Foundation of Shaanxi Province (2016JM1001).

Declaration of Competing Interest

The authors declared that there is no conflict of interest.

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