Deep learning based atmospheric turbulence compensation for orbital angular momentum beam distortion and communication.

Atmospheric transmission distortion is one of the main challenges hampering the practical application of a vortex beam (VB) which carries orbital angular momentum (OAM). In this work, we propose and investigate a deep learning based atmospheric turbulence compensation method for correcting the distorted VB and improving the performance of OAM multiplexing communication. A deep convolutional neural network (CNN) model, which can automatically learn the mapping relationship of the intensity distributions of input and the turbulent phase, is well designed. After trained with loads of studying samples, the CNN model possesses a good generalization ability in quickly and accurately predicting equivalent turbulent phase screen, including the untrained turbulent phase screens. The results show that through correction, the mode purity of the distorted VB improves from 39.52% to 98.34% under the turbulence intensity of Cn2 = 1 × 10-13. Constructing an OAM multiplexing communication link, the bit-error-rate (BER) of the transmitted signals in each OAM channel is reduced by almost two orders of magnitude under moderate-strong turbulence, and the demodulated constellation diagram also converges well after compensated by the CNN model.

[1]  K. T. Gahagan,et al.  Optical vortex trapping of particles , 1996, Summaries of papers presented at the Conference on Lasers and Electro-Optics.

[2]  Schock,et al.  Method for a quantitative investigation of the frozen flow hypothesis , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[3]  A. Vaziri,et al.  Entanglement of the orbital angular momentum states of photons , 2001, Nature.

[4]  Jennifer E. Curtis,et al.  Dynamic holographic optical tweezers , 2002 .

[5]  Alexander Jesacher,et al.  Quantitative imaging of complex samples by spiral phase contrast microscopy. , 2006, Optics express.

[6]  M. Neifeld,et al.  Turbulence-induced channel crosstalk in an orbital angular momentum-multiplexed free-space optical link. , 2008, Applied optics.

[7]  R. Boyd,et al.  Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum. , 2009, Optics letters.

[8]  Robert W. Boyd,et al.  Quantum Correlations in Optical Angle–Orbital Angular Momentum Variables , 2010, Science.

[9]  M. Padgett,et al.  Orbital angular momentum: origins, behavior and applications , 2011 .

[10]  A. E. Willner,et al.  25.6-bit/s/Hz spectral efficiency using 16-QAM signals over pol-muxed multiple orbital-angular-momentum modes , 2011, IEEE Photonic Society 24th Annual Meeting.

[11]  Miles J. Padgett,et al.  Tweezers with a twist , 2011 .

[12]  S. M. Zhao,et al.  Aberration corrections for free-space optical communications in atmosphere turbulence using orbital angular momentum states. , 2012, Optics Express.

[13]  R. Boyd,et al.  Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding. , 2012, Optics Express.

[14]  A. Willner,et al.  Terabit free-space data transmission employing orbital angular momentum multiplexing , 2012, Nature Photonics.

[15]  D. Simon,et al.  Two-photon spiral imaging with correlated orbital angular momentum states , 2012, 1201.5623.

[16]  A. Willner,et al.  Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers , 2013, Science.

[17]  A. Nicolas,et al.  A quantum memory for orbital angular momentum photonic qubits , 2013, Nature Photonics.

[18]  Min Gu,et al.  Generation of sub-diffraction-limited pure longitudinal magnetization by the inverse Faraday effect by tightly focusing an azimuthally polarized vortex beam. , 2013, Optics letters.

[19]  A. Willner,et al.  100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength. , 2014, Optics letters.

[20]  A. Willner,et al.  Adaptive-optics-based simultaneous pre- and post-turbulence compensation of multiple orbital-angular-momentum beams in a bidirectional free-space optical link , 2014 .

[21]  Yinwen Cao,et al.  Phase correction for a distorted orbital angular momentum beam using a Zernike polynomials-based stochastic-parallel-gradient-descent algorithm. , 2015, Optics letters.

[22]  A. Willner,et al.  Optical communications using orbital angular momentum beams , 2015 .

[23]  Geoffrey E. Hinton,et al.  Deep Learning , 2015, Nature.

[24]  Ebrahim Karimi,et al.  Real-time imaging of spin-to-orbital angular momentum hybrid remote state preparation , 2014, 1404.7573.

[25]  Chunqing Gao,et al.  Pre-turbulence compensation of orbital angular momentum beams based on a probe and the Gerchberg-Saxton algorithm. , 2016, Optics letters.

[26]  Jian Wang,et al.  Encoding/decoding using superpositions of spatial modes for image transfer in km-scale few-mode fiber. , 2016, Optics express.

[27]  Mourad Zghal,et al.  Encoding information using Laguerre Gaussian modes over free space turbulence media. , 2016, Optics letters.

[28]  Jian Wang,et al.  Advances in communications using optical vortices , 2016 .

[29]  Min Zhang,et al.  Adaptive Demodulator Using Machine Learning for Orbital Angular Momentum Shift Keying , 2017, IEEE Photonics Technology Letters.

[30]  Timothy Doster,et al.  Machine learning approach to OAM beam demultiplexing via convolutional neural networks. , 2017, Applied optics.

[31]  Min Zhang,et al.  System impairment compensation in coherent optical communications by using a bio-inspired detector based on artificial neural network and genetic algorithm , 2017 .

[32]  Xiangjun Xin,et al.  Performance Comparison of PS Star-16QAM and PS Square-Shaped 16QAM (Square-16QAM) , 2017, IEEE Photonics Journal.

[33]  Yan Yan,et al.  Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing , 2017, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[34]  A. Willner,et al.  Atmospheric turbulence compensation in orbital angular momentum communications: Advances and perspectives , 2018 .

[35]  Sanjaya Lohani,et al.  Turbulence correction with artificial neural networks. , 2018, Optics letters.