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Performance Enhancement of an Orbital-Angular-Momentum-Based Free-Space Optical Communication Link through Beam Divergence Controlling

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Performance Enhancement of an Orbital-Angular-Momentum-Based Free-Space Optical Communication Link through Beam Divergence Controlling
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  M2F.6.pdfOFC 2015 © OSA 2015 Performance Enhancement of an Orbital-Angular-Momentum-Based Free-Space Optical Communication Link through Beam Divergence Controlling Long Li 1 , Guodong Xie 1 , Yongxiong Ren 1 , Nisar Ahmed 1 , Hao Huang 1 , Zhe Zhao 1 , Peicheng Liao 1 , Martin P. J. Lavery 2 , Yan Yan 1 , Changjing Bao 1 , Zhe Wang 1 , Nima Ashrafi 3,4 , Solyman Ashrafi 3 , Moshe Tur 5 , and Alan E. Willner 1   1. Dept. of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA,  Email:longl@usc.edu  2. School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK 3. NxGen Partners, Dallas, TX 75219, USA 4. University of Texas at Dallas, Richardson, TX 75080, USA 5. School of Electrical Engineering, Tel Aviv University, Ramat Aviv 69978, ISRAEL Abstract: Using beam divergence controlling to mitigate angular error effects in OAM-based FSO links is investigated through simulation and experiment. Results show that controlling beam divergence allows reducing power loss and angular error induced channel crosstalk.   OCIS codes:  (060.2330) Free-space optical communications; (050.4865) Optical vortices.   1. Introduction Free-space optical (FSO) communication links can potentially benefit from the simultaneous transmission of multiple spatially orthogonal beams through a single aperture pair, such that each beam carries an independent data stream and the total capacity is multiplied by the number of beams [1-2]. Orthogonality of the beams enables efficient multiplexing and demultiplexing at the transmitter and receiver, respectively. An optical beam can carry orbital-angular-momentum (OAM), and such OAM has gained interest for its potential in achieving efficient multiplexing of multiple data-carrying beams [2-5]. A beam that has OAM can be described as having a phase front that “twists” as it propagates. The integer number of 2π phase shifts across the front of the wave will define the OAM value, and OAM beams having distinct OAM values are orthogonal to one another. In addition, there can be positive and negative twisting that is also orthogonal and represents another doubling in the ability to multiplex [3-5]. However, FSO links using OAM present unique challenges due to the beam’s phase and amplitude structure [6]. For example, an OAM beam [7-10]: (i) has a “doughnut” shaped intensity profile, with little power in the center and a higher-intensity annulus, (ii) a circularly-symmetric phase change around the center, in which the OAM value is determined by capturing enough of the phase change, and (iii) higher-order OAM beams diverge faster than the lower orders. Therefore, there is a trade-off between recovering higher signal power that is not in the center and yet recovering the rapid phase change that does occur in the center (and which is needed to ensure orthogonality and low modal crosstalk under lateral displacement as well as angular error between transmitter and receiver in practical systems). These issues necessitate that sufficient recovery of a beam is important for an operational system and will thus limit the distance and number of modes that can be supported [6]. In this paper, we show through simulation and experiment the performance enhancement of an OAM-based FSO communication link through beam divergence controlling, considering power loss and channel crosstalk induced by displacement and angular error. Simulation results indicate that in a 1-km and 10-km OAM-based FSO link, precisely controlling beam divergence allows reducing power loss. Beam divergence controlling could also reduce channel crosstalk induced by receiver angular error and transmitter pointing error, while crosstalk resulting from lateral displacement may increase. A 1-m lab link in which four OAM beams each carrying 50 Gbaud QPSK signal are multiplexed is established. Results show that power loss could be reduced by >20 dB and signal-to-interference ratio (SIR) could be increased by 10~20 dB under receiver angular error using such a technique. Figure 1 (a) Concept of an OAM-multiplexing FSO communication link using transmitter lenses controlling beam divergence. Alignment between transmitter and receiver in a (b) perfectly aligned system, (c) system with lateral displacement, (d) system with Rx angular error, and (d) system with Tx pointing error. Tx: transmitter; Rx: receiver;  f  0 : equivalent focal length; Δ  : lenses spacing shift Data-carrying OAM beamsTxaperture Tx  f  2  f  1  d = Δ +  f  1 +f  2 equivalent focal length  f  0 =  f  12  /  Δ + Δ (a)(d)(c)(e) OAM i OAM  j Transmitter lensesRx aperture Rx    >   1   k  m    F   S   O   t  r  a  n  s  m   i  s  s   i  o  n   D  e  m  u   l   t   i  p   l  e  x   i  n  g (b)TxRxDivergence controlled beamCollimated beamTxRxTxRxRxTxperfectly aligneddisplacementangular errorpointing error  M2F.6.pdfOFC 2015 © OSA 2015 2. Concept and simulation results Our simulation model is depicted in Fig. 1(a). Multiple data-carrying OAM beams at 1550 nm are multiplexed and pass through a pair of transmitter lenses (  f  1 and  f  2 ) before transmitting in free space. The equivalent focal length  f  0  of these two lenses is:  f  0  =  f  12  /  Δ + Δ , where the lenses spacing shift Δ  is defined as d  -  f  1 -  f  2  with d   representing the spacing between lenses. Note that such a structure is widely used in traditional FSO systems as a telescope where the output beam is collimated (with Δ =0) [11]. In our OAM-based FSO links, we use these transmitter lenses to precisely control beam divergence by carefully tuning Δ , in order to enhance system performance. In ideal cases, transmitter and receiver are perfectly aligned. However, in a practical system, transmitter and receiver may have lateral displacement, receiver angular error and/or transmitter pointing error, as shown in Fig. 1(b)-(e) [6]. Figure 2 Simulated power loss when only OAM +7 is transmitted with perfect alignment (a) as a function of transmitter and receiver aperture sizes (diameter) in a 1-km link; (b) and (c) as a function of equivalent focal length in a 1-km link and a 10-km link, respectively. Transmitted beam size in (a) and (b) is 10 cm, and in (c) is 30 cm. Transmitter and receiver aperture sizes in (b) and (c) are 10 cm and 30 cm, respectively. Since controlling beam divergence would obtain smaller spot size at receiver than collimated beams, more power could be received with limited size apertures. Figure 2(a) shows when  f  0  is adjusted to be around transmission distance, power loss decreases. Because of faster divergence when propagates, higher order OAM beams would have more benefits on power loss when converged, as shown in Fig. 2(b). We also show using beam divergence controlling to reduce power loss in 10-km links, as illustrated in Fig. 2(c).  Figure 3 (a) Simulated SIR of OAM +3 when OAM +1, +3 are transmitted with lateral displacement, receiver angular error and transmitter pointing error in a 1-km OAM-based FSO link. Transmitted beam size is 10 cm, and transmitter and receiver aperture sizes are 15 cm. Δ = d  -  f  1 -  f  2 , Δ =0 equals to without transmitter lenses in the link. (b) and (c) Illustrations of beams at receiver with lateral displacement and receiver angular error, respectively. An OAM-based FSO link would also have different performance under lateral displacement, receiver angular error and transmitter pointing error using beam divergence controlling. Links which displacement dominates would like to have larger receiver beam sizes because of relatively small mismatch under the same displacement, while links with receiver angular errors would prefer smaller receiver beam sizes for less phase shift would be introduced by the same angular error, as illustrated in Fig.3 (b) and (c). As a combination of displacement and angular error, pointing error would have a trade-off in choosing the receiver beam size. SIR of OAM +3 as a function of Δ   in a 1-km link when OAM +1 and +3 are transmitted under 8 mm displacement, 8 μ rad angular error or 8 μ rad pointing error, is shown in Fig. 3(a). With only angular error, SIR reaches its peak when Δ   is around 0.25 mm, which refers to an  f  0  of about 1-km. Both too large and too small a receiver beam size would decrease SIR under pointing errors. Note that when Δ   increases from 0.3 to 0.5 mm, though receiver beam size increases, SIR under displacement is still decreasing because of large curvature of the beam. 3. Experimental setup and results Figure 4(a) shows the experimental setup of an OAM-based FSO link using beam divergence controlling. A narrow linewidth laser at 1550 nm is sent to a Mach-Zehnder modulator to produce a 100-Gbit/s QPSK signal. This signal is amplified and split into two copies, one of which is delayed using a ~10-m length of single-mode fiber (SMF) to 56102550w/o lens010203040Equivalent Focal Length (km)    P  o  w  e  r   L  o  s  s   (   d   B   )   OAM+7OAM+5OAM+310111213141501020304050Tx and Rx Aperture Diameter (cm)    P  o  w  e  r   L  o  s  s   (   d   B   )   wo/ lensf0=5kmf0=2.5kmf0=1kmf0=600m0.50.612.55w/o lens010203040Equivalent Focal Length (km)    P  o  w  e  r   L  o  s  s   (   d   B   )   OAM+7OAM+5OAM+3 (a) 1-km(b) 1-km(c) 10-km Txbeam size 10 cmTxbeam size 10 cmaperture size 10 cmTxbeam size 30 cmaperture size 30 cm Intensity of large beamIntensity of small beamDisplacement  d  Angular errorLarge phase shift 00.10.20.30.40.50510152025Lenses Spacing Shift (mm)    S   I   R   (   d   B   )   displacementangular errorpointing error (a)(c)(b) Small phase shiftIntensity of small beamIntensity of large beam  M2F.6.pdfOFC 2015 © OSA 2015 decorrelate the data sequence. The two fiber branches are coupled to collimators, each of which emits a collimated Gaussian beam with a beam diameter of 2.2 mm. One beam is converted to OAM+1 by SLM-1, while the other is converted to OAM+3 by SLM-2. After being combined on a beam splitter, the multiplexed OAM beams are split into two identical copies. One of the copies is reflected by three mirrors to generate OAM -1 and -3, which are then multiplexed with the other copy (i.e., OAM +1 and +3). Afterwards, the resulting four multiplexed OAM beams pass through two lenses with focal lengths of 10 cm, spacing between which is adjustable to control the beam divergence. After 1-m FSO transmission, the beams are sent to SLM-3 loaded with an inverse spiral phase hologram of the particular OAM channel to be detected. Such an OAM beam is converted to a Gaussian-like beam, which is then coupled into an SMF and sent for coherent detection. Figure 4 (a) Experimental setup for an OAM-based FSO communication link using transmitter lenses. (b) Simulated and experimental power loss as a function of receiver aperture size when OAM +3 is transmitted with perfect alignment. (c1) and (c2) Simulated and experimental SIR of OAM +3 when OAM +1, +3 are transmitted with angular error and displacement, respectively. (d1) and (d2) Experimental measurement of BER as a function of OSNR for OAM +3 when OAM ±1, ±3 are transmitted with angular error and displacement, respectively. In (b), (c1) and (c2), lines and markers are simulation and experiment results, respectively. Col.: collimator; SLM: spatial light modulator; BS: beam splitter; Tx: transmitter; Rx: receiver. Figure 4(b) shows simulated and experimental power loss of OAM +3 as a function of receiver aperture size when only OAM +3 is transmitted with transmitter and receiver perfectly aligned. Limited size receiver apertures are implemented by adding a truncated pattern onto SLM-3. A link using beam divergence controlling with  f  0  around 1-m shows a power loss >20dB less than that of a link without divergence controlling in a 1-m link. Figure 4(c1) and Fig. 4(c2) show SIR of OAM +3 when both OAM +1 and +3 are transmitted under angular error and displacement, respectively. Receiver angular errors are introduced to the link by adding tilted phase terms onto SLM-3, and lateral displacements are created by adjusting mirror-1, which can laterally shift the beam. SIR of OAM +3 using beam divergence controlling increases by 10~20 dB under various angular errors, while decreases by 5~10 dB under different lateral displacement. Measured and simulated results in Fig. 4(b)-(c2) show similar trends. Figure 4(d1) and Fig. 4 (d2) show BER of OAM +3 when OAM ±1, ±3 are transmitted with angular error and displacement respectively, with each beam carrying a 50 Gbaud QPSK signal. When angular error is 100 μ rad, a link without beam divergence controlling could not achieve the 7% overhead forward error correlation (FEC) limit of 3.8e-3, while a link using such techniques with  f  0  ~1-m could. Moreover, a link with beam divergence controlling could still achieve the FEC limit under 400 μ rad angular error with little power penalty compared with 100 μ rad case. On the other hand, such a link would have higher power penalty under lateral displacement. Acknowledgement We acknowledge the generous support of NxGen Partners.   References [1] G. Gibson et al., Opt. Ex. 12 , 5448 (2004) [2] L. Allen, et al., Physical Rev. A 45 , 8185 (1992) [3] J. Wang et al., Nat. Photon. 6 , 488 (2012) [4] A. Yao, et al., Advan. in Opt. and Photon., 3 , 161 (2011) [5] JA. Anguita, et al., Applied Opt.  47 , 2414 (2008) [6] G. Xie, et al., accepted by GLOBECOM' 2014  [7] H. Lezec, et al., Science 297 , 820 (2002) [8] R. Phillips, et al., Applied Opt. 22 , 643 (1983) [9] J.Barry, et al., Opt. Eng. 24 , 1049 (1985) [10] A. Farid, et al., JLT, 25 , 1702 (2007) [11] Y. Arimoto, et al., in Proc. ECOC 2008   0.10.20.30.4010203040Rx Aperture Diameter (cm)    P  o  w  e  r   L  o  s  s   (   d   B   )   f0=1mf0=0.7mf0=5mw/o lens 0.10.20.30.40.50510152025Displacement (mm)    S   I   R   (   d   B   )   f0=1mf0=0.7mf0=5mw/o lens 50/50couplerEDFA50 GbaudQPSK signal generatorSLM-1Coherent receiverDelayPCCol.SLM-2SLM-3MirrorBS-1BS-2BS-3  f  1  f  2  f  3  f  4 Tx    1  -  m    f  r  e  e  s  p  a  c  e   t  r  a  n  s  m   i  s  s   i  o  n Rx 1015202510 -4 10 -3 10 -2 OSNR (dB)    B   i   t   E  r  r  o  r   R  a   t  e   0mm w/o lens0.30mm w/o lens0.35mm w/o lens0.30mm w/ lens0.20mm w/ lens 1015202510 -4 10 -3 10 -2 OSNR (dB)    B   i   t   E  r  r  o  r   R  a   t  e   0 µ rad w/o lens80 µ rad w/o lens100 µ rad w/o lens100 µ rad w/ lens400 µ rad w/ lens (c1)(c2)(d1)(d2) 100200300400500051015202530Angular Error (   rad)    S   I   R   (   d   B   )   f0=1mf0=0.7mf0=5mw/o lens (b)(a) Mirror-1marker: simulationline: experiment
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