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1. Demonstration of using two aperture pairs combined with multiple-mode receivers and MIMO signal processing for enhanced tolerance to turbulence and misalignment in a 10  Gbit/s QPSK FSO link

   https://doi.org/10.1364/OL.391120  

   Song, Haoqian ; Li, Long ; Pang, Kai ; Zhang, Runzhou ; Zou, Kaiheng ; Zhao, Zhe ; Du, Jing ; Song, Hao ; Liu, Cong ; Cao, Yinwen ; et al ( May 2020 , Optics Letters)

   We utilize aperture diversity combined with multiple-mode receivers and multiple-input-multiple-output (MIMO) digital signal processing (DSP) to demonstrate enhanced tolerance to atmospheric turbulence and spatial misalignment in a 10 Gbit/s quadrature-phase-shift-keyed (QPSK) free-space optical (FSO) link. Turbulence and misalignment could cause power coupling from the fundamental Gaussian mode into higher-order modes. Therefore, we detect power from multiple modes and use MIMO DSP to enhance the recovery of the original data. In our approach, (a) each of multiple transmitter apertures transmits a single fundamental Gaussian beam carrying the same data stream, (b) each of multiple receiver apertures detects the signals that are coupled from the fundamental Gaussian beams to multiple orbital angular momentum (OAM) modes, and (c) MIMO DSP is used to recover the data over multiple modes and receivers. Our simulation shows that the outage probability could be reduced from$><\#comment/>0.1$to$<<\#comment/>0.01$. Moreover, we experimentally demonstrate the scheme by transmitting two fundamental Gaussian beams carrying the same data stream and recovering the signals on OAM modes 0 and$+1$at each receiver aperture. We measure an up to$\sim <\#comment/>10\mathrm{d}\mathrm{B}$power-penalty reduction for a bit error rate (BER) at the 7% forward error correction limit for a 10 Gbit/s QPSK signal.

    

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2. Simultaneous turbulence mitigation and channel demultiplexing for two 100  Gbit/s orbital-angular-momentum multiplexed beams by adaptive wavefront shaping and diffusing

   https://doi.org/10.1364/OL.383714  

   Zhang, Runzhou ; Song, Hao ; Zhao, Zhe ; Song, Haoqian ; Du, Jing ; Liu, Cong ; Pang, Kai ; Li, Long ; Zhou, Huibin ; Willner, Ari N. ; et al ( January 2020 , Optics Letters)

   We experimentally demonstrate simultaneous turbulence mitigation and channel demultiplexing in a 200 Gbit/s orbital-angular-momentum (OAM) multiplexed link by adaptive wavefront shaping and diffusing (WSD) the light beams. Different realizations of two emulated turbulence strengths (the Fried parameter$r_0=0.4,1.0\mathrm{m}\mathrm{m}$) are mitigated. The experimental results show the following. (1) Crosstalk between OAM$l=+1$and$l=-<\#comment/>1$modes can be reduced by$><\#comment/>10.0$and$><\#comment/>5.8\mathrm{d}\mathrm{B}$, respectively, under the weaker turbulence ($r_0=1.0\mathrm{m}\mathrm{m}$); crosstalk is further improved by$><\#comment/>17.7$and$><\#comment/>19.4\mathrm{d}\mathrm{B}$, respectively, under most realizations in the stronger turbulence ($r_0=0.4\mathrm{m}\mathrm{m}$). (2) The optical signal-to-noise ratio penalties for the bit error rate performance are measured to be$\sim <\#comment/>0.7$and$\sim <\#comment/>1.6\mathrm{d}\mathrm{B}$under weaker turbulence, while measured to be$\sim <\#comment/>3.2$and$\sim <\#comment/>1.8\mathrm{d}\mathrm{B}$under stronger turbulence for OAM$l=+1$and$l=-<\#comment/>1$mode, respectively.

    

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3. Utilizing adaptive optics to mitigate intra-modal-group power coupling of graded-index few-mode fiber in a 200-Gbit/s mode-division-multiplexed link

   https://doi.org/10.1364/OL.394307  

   Zhang, Runzhou ; Song, Hao ; Song, Haoqian ; Zhao, Zhe ; Milione, Giovanni ; Pang, Kai ; Du, Jing ; Li, Long ; Zou, Kaiheng ; Zhou, Huibin ; et al ( June 2020 , Optics Letters)

   We experimentally demonstrate the utilization of adaptive optics (AO) to mitigate intra-group power coupling among linearly polarized (LP) modes in a graded-index few-mode fiber (GI FMF). Generally, in this fiber, the coupling between degenerate modes inside a modal group tends to be stronger than between modes belonging to different groups. In our approach, the coupling inside the${\mathrm{L}\mathrm{P}}_{11}$group can be represented by a combination of orbital-angular-momentum (OAM) modes, such that reducing power coupling in OAM set tends to indicate the capability to reduce the coupling inside the${\mathrm{L}\mathrm{P}}_{11}$group. We employ two output OAM modes$l=+1$and$l=-<\#comment/>1$as resultant linear combinations of degenerate${\mathrm{L}\mathrm{P}}_{11\mathrm{a}}$and${\mathrm{L}\mathrm{P}}_{11\mathrm{b}}$modes inside the${\mathrm{L}\mathrm{P}}_{11}$group of a$\sim <\#comment/>0.6\text{-}\mathrm{k}\mathrm{m}$GI FMF. The power coupling is mitigated by shaping the amplitude and phase of the distorted OAM modes. Each OAM mode carries an independent 20-, 40-, or 100-Gbit/s quadrature-phase-shift-keying data stream. We measure the transmission matrix (TM) in the OAM basis within${\mathrm{L}\mathrm{P}}_{11}$group, which is a subset of the full LP TM of the FMF-based system. An inverse TM is subsequently implemented before the receiver by a spatial light modulator to mitigate the intra-modal-group power coupling. With AO mitigation, the experimental results for$l=+1$and$l=-<\#comment/>1$modes show, respectively, that (i) intra-modal-group crosstalk is reduced by$><\#comment/>5.8\mathrm{d}\mathrm{B}$and$><\#comment/>5.6\mathrm{d}\mathrm{B}$and (ii) near-error-free bit-error-rate performance is achieved with a penalty of$\sim <\#comment/>0.6\mathrm{d}\mathrm{B}$and$\sim <\#comment/>3.8\mathrm{d}\mathrm{B}$, respectively.

    

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4. Utilizing phase delays of an integrated pixel-array structure to generate orbital-angular-momentum beams with tunable orders and a broad bandwidth

   https://doi.org/10.1364/OL.396447  

   Song, Hao ; Zhao, Zhe ; Zhang, Runzhou ; Song, Haoqian ; Zhou, Huibin ; Pang, Kai ; Du, Jing ; Li, Long ; Liu, Cong ; Su, Xinzhou ; et al ( July 2020 , Optics Letters)

   We study the relationship between the input phase delays and the output mode orders when using a pixel-array structure fed by multiple single-mode waveguides for tunable orbital-angular-momentum (OAM) beam generation. As an emitter of a free-space OAM beam, the designed structure introduces a transformation function that shapes and coherently combines multiple (e.g., four) equal-amplitude inputs, with the$k$th input carrying a phase delay of$(k-<\#comment/>1)\mathrm{\Delta <\#comment/>}\mathrm{\phi <\#comment/>}$. The simulation results show that (1) the generated OAM order ℓ is dependent on the relative phase delay$\mathrm{\Delta <\#comment/>}\mathrm{\phi <\#comment/>}$; (2) the transformation function can be tailored by engineering the structure to support different tunable ranges (e.g., $l=\{-<\#comment/>1\},\{-<\#comment/>1,+1\},\{-<\#comment/>1,0,+1\}$, or$\{-<\#comment/>2,-<\#comment/>1,+1,+2\}$); and (3) multiple independent coaxial OAM beams can be generated by simultaneously feeding the structure with multiple independent beams, such that each beam has its own$\mathrm{\Delta <\#comment/>}\mathrm{\phi <\#comment/>}$value for the four inputs. Moreover, there is a trade-off between the tunable range and the mode purity, bandwidth, and crosstalk, such that the increase of the tunable range leads to (a) decreased mode purity (from 91% to 75% for$l=-<\#comment/>1$), (b) decreased 3 dB bandwidth of emission efficiency (from 285 nm for$l=\{-<\#comment/>1\}$to 122 nm for$l=\{-<\#comment/>2,-<\#comment/>1,+1,+2\}$), and (c) increased crosstalk within the C-band (from$-<\#comment/>23.7$to$-<\#comment/>13.2\mathrm{d}\mathrm{B}$when the tunable range increases from 2 to 4).

    

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5. Experimental mitigation of the effects of the limited size aperture or misalignment by singular-value-decomposition-based beam orthogonalization in a free-space optical link using Laguerre–Gaussian modes

   https://doi.org/10.1364/OL.405399  

   Pang, Kai ; Song, Haoqian ; Su, Xinzhou ; Zou, Kaiheng ; Zhao, Zhe ; Song, Hao ; Almaiman, Ahmed ; Zhang, Runzhou ; Liu, Cong ; Hu, Nanzhe ; et al ( November 2020 , Optics Letters)

   Limited-size receiver (Rx) apertures and transmitter–Rx (Tx–Rx) misalignments could induce power loss and modal crosstalk in a mode-multiplexed free-space link. We experimentally demonstrate the mitigation of these impairments in a 400 Gbit/s four-data-channel free-space optical link. To mitigate the above degradations, our approach of singular-value-decomposition-based (SVD-based) beam orthogonalization includes (1) measuring the transmission matrix$\text{H}$for the link given a limited-size aperture or misalignment; (2) performing SVD on the transmission matrix to find the$\text{U}$,$\mathrm{\Sigma <\#comment/>}$, and$\text{V}$complex matrices; (3) transmitting each data channel on a beam that is a combination of Laguerre–Gaussian modes with complex weights according to the$\text{V}$matrix; and (4) applying the$\text{U}$matrix to the channel demultiplexer at the Rx. Compared with the case of transmitting each channel on a beam using a single mode, our experimental results when transmitting multi-mode beams show that (a) with a limited-size aperture, the power loss and crosstalk could be reduced by$\sim <\#comment/>8$and$\sim <\#comment/>23\text{dB}$, respectively; and (b) with misalignment, the power loss and crosstalk could be reduced by$\sim <\#comment/>15$and$\sim <\#comment/>40\text{dB}$, respectively.

    

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