In this paper, we experimentally demonstrate an approach that “hides” a lowintensity 50 Gbit/s quadraturephasekeying (QPSK) freespace optical beam when it coaxially propagates on the same wavelength with an orthogonal highintensity 50 Gbit/s QPSK optical beam. Our approach is to coaxially transmit the strong and weak beams carrying different orthogonal spatial modes within a modal basis set, e.g., orbital angular momentum (OAM) modes. Although the weak beam has much lower power than that of the strong beam, and the beams are in the same frequency band and on the same polarization, the two beams can still be effectively demultiplexed with little inherent crosstalk at the intended receiver due to their spatial orthogonality. However, an eavesdropper may not readily identify the weak beam when simply analyzing the spatial intensity profile. The correlation coefficient between the intensity profiles of the strong beam and the combined strong and weak beams is measured to characterize the potential for “hiding” a weak beam when measuring intensity profiles. Such a correlation coefficient is demonstrated to be higher than 0.997 when the power difference between the strong fundamental Gaussian beam and the weak OAM beam is
We utilize aperture diversity combined with multiplemode receivers and multipleinputmultipleoutput (MIMO) digital signal processing (DSP) to demonstrate enhanced tolerance to atmospheric turbulence and spatial misalignment in a 10 Gbit/s quadraturephaseshiftkeyed (QPSK) freespace optical (FSO) link. Turbulence and misalignment could cause power coupling from the fundamental Gaussian mode into higherorder 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
 NSFPAR ID:
 10156163
 Publisher / Repository:
 Optical Society of America
 Date Published:
 Journal Name:
 Optics Letters
 Volume:
 45
 Issue:
 11
 ISSN:
 01469592; OPLEDP
 Page Range / eLocation ID:
 Article No. 3042
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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$\sim <\#comment/>8,\sim <\#comment/>10$ , and$\sim <\#comment/>10\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ for the weak OAM$<\#comment/>1,<\#comment/>2$ , and$<\#comment/>3$ beams, respectively. Moreover, a 50 Gbit/s QPSK data link having its$Q$ factor above the 7% forward error correction limit is realized when the power of the weak OAM$<\#comment/>3$ beam is 30 dB lower than that of the strong fundamental Gaussian beam. 
Limitedsize receiver (Rx) apertures and transmitter–Rx (Tx–Rx) misalignments could induce power loss and modal crosstalk in a modemultiplexed freespace link. We experimentally demonstrate the mitigation of these impairments in a 400 Gbit/s fourdatachannel freespace optical link. To mitigate the above degradations, our approach of singularvaluedecompositionbased (SVDbased) beam orthogonalization includes (1) measuring the transmission matrix
$\text{H}$ for the link given a limitedsize 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 multimode beams show that (a) with a limitedsize aperture, the power loss and crosstalk could be reduced by$\sim <\#comment/>8$ and$\sim <\#comment/>23\phantom{\rule{thickmathspace}{0ex}}\text{dB}$ , respectively; and (b) with misalignment, the power loss and crosstalk could be reduced by$\sim <\#comment/>15$ and$\sim <\#comment/>40\phantom{\rule{thickmathspace}{0ex}}\text{dB}$ , respectively. 
We experimentally demonstrate the utilization of adaptive optics (AO) to mitigate intragroup power coupling among linearly polarized (LP) modes in a gradedindex fewmode 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 orbitalangularmomentum (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 100Gbit/s quadraturephaseshiftkeying 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 FMFbased system. An inverse TM is subsequently implemented before the receiver by a spatial light modulator to mitigate the intramodalgroup power coupling. With AO mitigation, the experimental results for$l=+1$ and$l=<\#comment/>1$ modes show, respectively, that (i) intramodalgroup crosstalk is reduced by$><\#comment/>5.8\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ and$><\#comment/>5.6\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ and (ii) nearerrorfree biterrorrate performance is achieved with a penalty of$\sim <\#comment/>0.6\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ and$\sim <\#comment/>3.8\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ , respectively. 
We experimentally demonstrate simultaneous turbulence mitigation and channel demultiplexing in a 200 Gbit/s orbitalangularmomentum (OAM) multiplexed link by adaptive wavefront shaping and diffusing (WSD) the light beams. Different realizations of two emulated turbulence strengths (the Fried parameter
${r}_{0}=0.4,\phantom{\rule{thinmathspace}{0ex}}1.0\phantom{\rule{thickmathspace}{0ex}}\mathrm{m}\mathrm{m}$ ) 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$><\#comment/>5.8\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ , respectively, under the weaker turbulence (${r}_{0}=1.0\phantom{\rule{thickmathspace}{0ex}}\mathrm{m}\mathrm{m}$ ); crosstalk is further improved by$><\#comment/>17.7$ and$><\#comment/>19.4\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ , respectively, under most realizations in the stronger turbulence (${r}_{0}=0.4\phantom{\rule{thickmathspace}{0ex}}\mathrm{m}\mathrm{m}$ ). (2) The optical signaltonoise ratio penalties for the bit error rate performance are measured to be$\sim <\#comment/>0.7$ and$\sim <\#comment/>1.6\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ under weaker turbulence, while measured to be$\sim <\#comment/>3.2$ and$\sim <\#comment/>1.8\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ under stronger turbulence for OAM$l=+1$ and$l=<\#comment/>1$ mode, respectively. 
We study the relationship between the input phase delays and the output mode orders when using a pixelarray structure fed by multiple singlemode waveguides for tunable orbitalangularmomentum (OAM) beam generation. As an emitter of a freespace OAM beam, the designed structure introduces a transformation function that shapes and coherently combines multiple (e.g., four) equalamplitude 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 tradeoff 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$l=\{<\#comment/>2,\phantom{\rule{thickmathspace}{0ex}}<\#comment/>1,\phantom{\rule{thickmathspace}{0ex}}+1,\phantom{\rule{thickmathspace}{0ex}}+2\}$ ), and (c) increased crosstalk within the Cband (from$<\#comment/>23.7$ to$<\#comment/>13.2\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ when the tunable range increases from 2 to 4).