## Abstract

The scintillation index of a Gaussian beam and radially polarized beams in turbulent atmosphere is experimentally investigated. The scintillation index of a Gaussian beam and a completely coherent radially polarized beam increases with increasing propagation distance from 0 to 400m. The influence of the coherence of partially coherent radially polarized beam on the scintillation is studied. The result shows that the scintillation index of a partially coherent radially polarized beam can be smaller than that of a completely coherent beam.

© 2014 Optical Society of America

## 1. Introduction

Interest in propagation of laser beams through turbulent atmosphere has increased because of important applications in many areas, such as free space optical communications, remote sensing and imaging. The properties of the laser beams are greatly influenced by the turbulence on propagation, for example, the intensity keeps fluctuating, known as scintillation [1–3]. These optical scintillations result from the distortions of the phase structure of the wavefield by the turbulence, can degrade the performance laser beams in applications. Reducing the fluctuation in the intensity of laser beams through a turbulent atmosphere is critical in some applications. Previous studies showed that appropriately modulating coherence, phase and polarization of input laser beams can reduce the scintillations. Schulz demonstrated that the scintillation of a partially coherent field can be lower than that of a completely coherent counterpart [4]. Since then, investigation of propagation of partially coherent beams in turbulent atmosphere has become a topic of interest, and many optimization schemes have been proposed [5,6]. Qian et al. showed that the degradation of degree of source coherence of pseudo-partially coherent Gaussian Schell-model (GSM) beams may cause reductions of relative beam spreading and scintillation index [5]. Another method for reducing the intensity fluctuation is replacing the single laser beam by beam array [7–11]. Peleg and Moloney found the optimal configuration of the two laser beams with respect to the longitudinal scintillation index, and showed that the value of the longitudinal and radial scintillation for two-beam system is smaller compared with the value for a single beam [9]. The scintillation index can be substantially reduced if the constituent beams overlap at the detector and are properly separated in the transmitter plane [10]. The property of polarization influences the scintillation of a laser beam on propagation in atmospheric turbulence as well [12]. An appropriately chosen nonuniformly polarized beam can have appreciably smaller scintillation than comparable beams of uniform polarization [13]. Cheng et al. demonstrated that the scintillation of radially polarized vector vortex beam is smaller than scalar vortex beams both for strong and weak turbulence [14]. Further study showed that the turbulence-induced scintillation can be further reduced by using an incoherent beam array composed of beamlets with nonuniform polarization [15]. In this study, the scintillation index (SI) of a radially polarized beam (RPB) in atmospheric turbulence is experimentally measured. The experiment is carried out over a 400m outdoor path. The influence of the coherence of a RPB on the intensity fluctuation is discussed.

## 2. Experimental configuration

The experimental configuration for generating a partially coherent RPB and measuring its
intensity fluctuation in atmospheric turbulence is shown in Fig.
1.The linearly polarized He-Ne laser beam with wavelength of 633nm is utilized as a light
source. The beam is magnified by a telescope system constructed from two thin lenses
L_{1} and L_{2} with focal length of 6cm and 30cm respectively. A partially
coherent beam can be generated by introducing a rotating ground glass (RGG). The RGG rotates
continuously, and adds a random phase on the beam, therefore a completely coherent beam converts
into a partially coherent beam [16–18]. The correlation length of the partially coherent beam can
be controlled by the shape or the position of the ground glass [16]. In this study, the ground glass is located in the vicinity of the focus of the
telescope, and beams with different correlation lengths are obtained by changing the position of
the ground glass. Generally, the correlation length of the partially coherent beam becomes
shorter with increasing distance between the RGG and the focus of the telescope. A radial
polarization converter (RPC) is inserted into the optical axis. The RPC is capable to convert a
linearly polarized beam into a beam with perfectly radial polarization distribution. A partially
coherent RPB is formed by propagating the partially coherent beam through the RPC, and then
passes through the atmospheric turbulence. The intensity of the partially coherent RPB keeps
fluctuating on propagation in turbulence. A detector for measuring the scintillation is employed
to measure the SI, in which contains an opto-electron detector with aperture of 5mm ×
5mm. Therefore, the scintillation index measured in this study is aperture averaged
scintillation, but not point scintillation. A computer is connected to the detector to record
the magnitude of the SI. Based on a similar experimental configuration, the scintillation index
of a partially coherent RPB propagating through thermally induced turbulence is studied [2]. The result shows that a partially coherent RPB has a
smaller SI than that of partially coherent linearly polarized beam. In this study, the
experiment is carried out along a 400m outdoor path, which means that our result is obtained in
a real atmospheric environment.

The SI of the beam in a single location of the receiver plane is defined as [1]

*I*(

*x*,

*y*,

*z*) is the intensity of the point.

In this study, the SI is measured by a detector with aperture size of 5mm, which means that the scintillation refers to area scintillation index. Recently, the aperture averaged scintillation is proposed to study the scintillation of an area, which is defined as [19]

## 3. Scintillation index of a Gaussian beam and radially polarized beams

In this section, the experimental measurement of SI of a Gaussian beam (GB) and RPB propagating through a real atmospheric environment is presented. The experiment is carried out in a clear and calm night. Because of the environment limitation, we only measured the SI within a 400m outdoor path. SI of a GB in turbulent atmosphere has been numerically simulated in detail [1]. The on-axis SI of a GB increases gradually with increasing propagation distance in turbulence. The experimental result of on-axis SI of a GB in turbulence is presented in Fig. 2.The evolution of SI of a GB obtained by the opto-electron detector agrees with that of point SI. The SI is small at a propagation distance of 100m, and increases with increasing propagation distance. The scintillation of a completely coherent RPB increases with increasing propagation distance within 400m experimental distance as well. Experimental measurement of a completely coherent RPB shows higher scintillation than that of a GB. This can be in part understood by their intensity distribution. The on-axis point of GB has the maximal intensity. A completely coherent RPB has donut shape irradiance distribution, leading to the intensity null in the center.

As mentioned before, a GB has a Gaussian-shaped intensity profile, the magnitude of the intensity decreases with increasing radial distance from axis. The SI of a GB along the radial axis of the transverse plane is present in Fig. 3.Generally, the SI along a radial axis increases with increasing radial distance, which is the opposite of the evolution of intensity magnitude. A completely coherent RPB has a central dark core surrounded by a bright ring. The magnitude of intensity increases at first, and reaches the maximum, then decreases with the increasing radial distance. Such an intensity evolution leads to an opposite SI evolution. With the radial distance increases, the SI of a completely coherent RPB decreases, and reaches the minimum at the position of maximal intensity, and then increases again. The evolution of the SI and the intensity with increasing distance is opposite, which is similar with that obtained in [20]. The result of Fig. 5 and 6 in [20] showed that the SI of a GB increases with increasing radial distance, and the SI of J-Bessel–Gaussian beams (an example of beams with dark core) decreases and then increases with increasing radial distance.

The properties of beam on propagation in atmospheric turbulence are influenced by the correlation length of the input beam. The effect of correlation length of RPB on its scintillation is studied. In the experiment, the correlation length of beam is modulated by adjusting the position of RGG. Generally, the correlation length of the partially coherent beam becomes shorter with increasing distance between the RGG and focus of the telescope. To compare the result of completely coherent beam and partially coherent beam, and to investigate the influence of correlation length on the SI of partially coherent RPB, two examples of partially coherent beams are considered. These two beams are generated by locating the RGG in two different places of the telescope. The coherent degree is obtained by examining the fringes formed by double-slit experiment. As depicted in Fig. 4, both of two correlation curves have a quasi-Guassian shape. The half width of full maximum (HWFM) of two curves is about 1.46mm and 0.7mm, respectively. These two beams are taken as examples of partially coherent beam with higher and lower coherence.

The experimental result in Fig. 5 shows that SI of a RPB depends on the correlation length of the beam. Over a 400m outdoor path, the SI of the completely coherent RPB increases with increasing propagation distance. The SI of the partially coherent RPB with correlation length of 1.46mm increases as well, but the evolution curve is smoother. The SI of the partially coherent RPB with correlation length of 0.7mm decreases with increasing propagation distance. In particular, the SI of partially coherent RPB can be smaller than that of completely coherent RPB at the propagation distance of 400m.

These behaviors are partly attributed to the intensity property of beams. It is known that the dark core of a RPB fills with light as the coherence of the beam decreases. The central-dip intensity profile of a RPB finally evolves into a Gaussian shape after a sufficiently long propagation distance in atmospheric turbulence. The distance required is shorter for beam has lower coherence. Within the 400m path, the magnitude of normalized intensity (the maximal magnitude of the intensity profile is set to 1) of the on-axis point is larger for beams with lower coherence. Besides that, the scintillation is affected by the RGG and atmospheric turbulence as well. At the short propagation distance, the effect of RGG is more important. The partially coherent beams in the experiment are generated by RGG. Clearly, the rotation and vibration of the ground glass introduces additional intensity fluctuation. Therefore, the partially coherent RPB has a larger scintillation index than completely coherent beam in short propagation distance. The effect of the atmospheric turbulence on the scintillation of beams becomes more apparent with increasing propagation distance. Owing to the intensity and the effect of RGG and atmospheric turbulence, the scintillation of partially coherent RPB is smaller than that of completely coherent RPB at 400m.

## 4. Conclusion

In conclusion, the intensity fluctuation of a GB and RPBs within 400m outdoor path is experimental measured. The SI of a GB and a completely coherent RPB increases with the propagation distance increases from 0 to 400m. The SI of GB increases with radial distance increases as well. The result of SI of partially coherent RPB shows that, the SI of the partially coherent RPB with higher coherence increases with propagation distance, but that of partially coherent RPB with lower coherence decreases with propagation distance. In particular, at the distance of 400m, the SI of a partially coherent RPB is smaller than that of a completely coherent RPB.

## Acknowledgments

This work was supported by the National Natural Science Foundation of China (NSFC) (11304104, and 61178015), and Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (ZQN-PY209).

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