Experimental demonstration of coupling of an electromagnetic Gaussian Schell-model beam into a single-mode optical fiber
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- Zhao, C., Dong, Y., Wu, G. et al. Appl. Phys. B (2012) 108: 891. doi:10.1007/s00340-012-5176-5
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We demonstrate experimentally the procedure of coupling of a stochastic electromagnetic Gaussian Schell-model (EGSM) beam into a single-mode optical fiber. We find that the coupling efficiency depends closely on the coherence and polarization properties of the EGSM beam, which is consistent with theoretical prediction. Our results may find applications in connection with free-space optical communications and LIDARs, where coupling of a stochastic beam into an optical fiber is inevitable encountered.
It has been recently asserted that the intimate relation between the states of coherence and polarization of random light  can be successfully exploited in optical systems, such as free-space communication systems, LIDARs, optical tweezers, and classic imaging systems [2–33]. A special yet broad class of the stochastic electromagnetic Gaussian Schell-model (EGSM) beams was introduced as a natural extension of the well-known stochastic scalar GSM beam and its generation, ghost imaging, detection, and interaction with various media are by now well understood [2–33]. It was revealed that EGSM beams have advantage over scalar GSM beams or coherent Gaussian beams in some applications, such as free-space optical communications, LIDARs, optical imaging, particle trapping, and remote sensing. Several theories have been proposed for describing the polarization and coherence properties of a 3D stochastic electromagnetic field, including the theory introduced by Wolf et al. [8, 28] and the theory introduced by Friberg et al. [29, 30], and two definitions of 3D degree of polarization were proposed, respectively. It was shown that a monotonic one-to-one correspondence exists between two definitions of 3D degree of polarization under certain condition . More recently, Wang et al.  reported experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model source. Zhang et al.  studied the effect of polarization on the degree of paraxiality of an EGSM beam. Wu and Cai  explored modulation of spectral intensity, polarization and coherence of an EGSM beam by a phase aperture.
In 1972, Cohen carried out an experimental study of the coupling of the GaAs injection laser beams into optical fibers . Since then, the coupling of light into optical fibers has been investigated extensively due to its wide applications in optical communications, biomedical optics, LIDARs, stellar interferometry, and wavefront sensing. The majority of the previously published papers were devoted to coupling of coherent beams into optical fibers. In some practical applications, such as free-space optical communications and LIDARs, coupling of a stochastic beam into an optical fiber is inevitable encountered because the coherence of laser beam was degraded by the atmospheric turbulence during propagation [35, 36]. Thus, it is of great importance to study the coupling of a stochastic beam into an optical fiber. Recently, Salem et al. theoretically studied the effects of coherence and polarization on the coupling of an EGSM beam into optical fibers based on the theory of coherence and polarization introduced by Wolf et al. and found that the coupling efficiency is closely related to the states of coherence and polarization [37–39]. To our knowledge, no experimental results have been reported up until now on the coupling of an EGSM beams into optical fibers. In this article, we first offer the experimental results concerning the coupling of an EGSM beam into a single-mode fiber (SMF). We also use Wolf’s theory for describing the coherence and polarization properties of a stochastic electromagnetic beam to be consistent with the theoretical results of Refs. [37–39].
3 Experimental results
After the beam parameters of the generated EGSM beam were measured, we can obtain the value of DOP of the generated EGSM beam and study the coupling of the beam into a SMF. In our experiment, the generated EGSM beam (i.e., the transmitted beam from BS1) is coupled into the SMF with the objective lens. The numerical aperture (NA) of the objective lens equals to 0.1. The SMF with NA = 0.13 is made of fused silica (S460 HP produced by the THORLAB) and its operating wavelength ranges from 450 nm to 600 nm. The power meter is used to measure the power of the beam just before the objective lens and the power at the output of the SMF.
In conclusion, we have carried out experimental study of the coupling of an EGSM beam without anti-diagonal elements into a SMF. The dependency of the coupling efficiency on the correlation coefficients and the DOP of the generated EGSM beam were studied experimentally and were found to be consistent with the theoretical predictions. Our results are crucial for all applications relating to transmission of partially coherent beams through optical fibers.
This study was supported by the National Natural Science Foundation of China under Grant Nos. 10904102 & 61008009 &11104195, the Foundation for the Author of National Excellent Doctoral Dissertation of PR China under Grant No. 200928, the Natural Science Foundation of Jiangsu Province under Grant No. BK2009114, the Huo Ying Dong Education Foundation of China under Grant No. 121009, the Key Project of Chinese Ministry of Education under Grant No. 210081, the Universities Natural Science Research Project of Jiangsu Province Grant Nos. 10KJB140011 & 11KJB140007, the Project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions, and the National College Students Innovation Experiment Program under Grant No. 111028510. O. Korotkova’s research is funded by the US ONR (Grant N00189-12-P-0114).