We assess the robustness of a principal modes approach to scalable space-division multiplexing transceivers in the presence of mode-dependent loss. Results show resilience to several mode-dependent loss regimes

Barbosa, Fabio Aparecido

Marques Ferreira, Filipe

English

UCL Discovery

Scaling Spatial Multiplexing with Principal Modes1st Fabio Aparecido BarbosaOptical Networks GroupUniversity College London,London, UKfabio.barbosa@ucl.ac.uk2nd Filipe Marques FerreiraOptical Networks GroupUniversity College London,London, UKf.ferreira@ucl.ac.ukAbstract — We assess the robustness of a principal modes approach to scalable space-division multiplexing transceiversin the presence of mode-dependent loss. Results show resilience to several mode-dependent loss regimes.Keywords — Principal modes, multimode fibres, mode-dependent loss.I. INTRODUCTIONSpace-division multiplexing (SDM) has been proposed as a strategy to meet future capacity demands and to cope withsustainable cost- and energy-per bit. Amongst the candidate solutions, the transmission over multimode fibres (MMFs) offersthe highest spatial information density and potential integration gains in transceivers, wavelength selective switches, opticalamplifiers and both fibre- and chip-to-fibre interfaces. The multitude of modes adds new linear impairments, namely groupdelay (GD) spread [1, 2], stemming from the interplay between differential mode delay (DMD) and linear mode coupling, andmode-dependent loss (MDL) [3]. The GD spreading can be undone using multiple-input multiple-output (MIMO) equalisation.However, conventional transceivers require all guided modes to be detected and processed for successful equalisation, bindingthe number of coherent front-ends required to that of the fibre modes. This limits the deployment of fibres with higher numberof modes. A spatially scalable multimode transceiver would unlock MMFs approaching 1000 spatial and pol. modes [4, 5].In MMFs, a set of modes that are frequency independent to 1st order can be identified. These modes are referred to asprincipal modes (PMs) and have initially been proposed as a way to overcome modal dispersion in direct detection systems[6, 7]. In [8], we consider the use of PMs as a platform for scaling the number of spatial tributaries in MMFs coherent opticalsystems in line with traffic demand. T spatial and pol. tributaries are transmitted over a M -mode fibre (T < M ) by exciting TPMs and using T (or T/2 dual pol.) receivers. In the present work, we assess the robustness of such approach in the presenceof different MDL regimes, since link MDL can considerably affect the PMs orthogonality and bandwidth [9, 10].II. SDM TRANSMISSION USING PMSThe coherent SDM transmission system considered for transmission simulations in this work is shown in Fig. 1. To estimatethe M×M matrix H(ω) that describes the MMF channel, a least-square approach based on frequency-domain training sequences(TSs) with 4096 symbols is used. H(ω) can also include impairments of the transmission link. Estimates of the input principalmodes, Ue, and their corresponding group delays can be calculated as the eigenvectors and eigenvalues, respectively, of a groupdelay operator defined as G(ω) = j ∂ωHe(ω)H−1e (ω) [11], where He(ω) is the estimate of the MMF channel. The output PMs,Ve, can be calculated using He(ω) and Ue. The frequency independent characteristic of PMs allows to assume, over a certainfrequency interval, that He(ω) = VeΛe(ω)UHe [6], where (·)H is the Hermitian and Λ(ω) is a diagonal matrix accounting forthe overall group delays and mode gain/loss. Estimates of mode gain/loss can be obtained as the logarithm of the eigenvaluesof D(ω) = He(ω)HHe (ω). The estimation of PMs are sensitive to artefacts on He(ω). As in [8], we also modify the outputPMs by zero-forcing the residual channel, i.e. the end-to-end channel obtained after using the PMs for transmission. This newset of PMs (including both input and output PMs) is indicated as PMs* hereafter.Feedback of Channel State InformationI1I2I3I4I5I6IT -1ITX(ω)UeDP-IQM1DP-IQM2DP-IQM3DP-IQMT/2Tx LaserVeMMFH(ω)CoRx1CoRx2CoRx3CoRxT/2LO LaserMIMORX-DSPO1O2O3O4O5O6OT -1OTY(ω)MIMOTX-DSPFig. 1. Schematic diagram of the optical transmission system.Assuming that channel state information can befed back from the receiver to the transmitter, asdepicted in Fig. 1, the input PMs (or PMs*) Ueare exploited for mode multiplexing. At the channeloutput, the output PMs (or PMs*) Ve are used formode demultiplexing. Both Ue and Ve are applied inthe optical domain by an ideal programmable modemultiplexer [5, 12]. This approach reduces channelmemory and partially suppresses mode coupling at thereceiver front-end [8], an effort focused at reducingto T (or T/2 for dual pol. receivers) the number ofThis work was supported by the UKRI Future Leaders Fellowship MR/T041218/1. Underlying data at doi.org/10.5522/04/20004266.PMs*, T = 12 PMs*, T = 6PMs, T = 12 PMs, T = 6SMs, T = 120.2 0.4 0.6 0.8 1 1.2 1.4 1.62426283032OSNR = 25 dBTheoryPMs*PMsSMs(a)σMDL [dB]SNR[dB]0.2 0.4 0.6 0.8 1 1.2 1.4 1.63.544.55PMsPMs*(b)σMDL [dB]CIRCompressionFig. 2. (a) Average SNR of the received constellations versus σMDL. (b) CIR compression versus σMDL. SMs (solid line), PMs (lines with triangles) and PMs*(lines with circles) are used. Solid lines with markers for the 6 PMs case and dashed lines with markers for the 12 PMs case.optical front-ends necessary to transmit&detect T spatial tributaries (T < M ). We then transmit T tributaries by exciting TPMs with the lowest GDs. At the receiver, the residual channel is estimated using TSs transmitted by only the T tributaries,and MMSE MIMO equalisation is then carried out. However, and because, PMs are affected by DMD and MDL, we evaluatetheir performance against the optimal basis provided by the Schmidt modes (SMs). SMs are obtained through singular valuedecomposition of He(ω) [9]. Although forming an optimal multiplexing basis, SMs are not readily suitable for optical domainimplementation due to their frequency dependent nature, thus mode coupling and channel memory reduction would not beachieved at the receiver front-end.We assume a 50-km graded-index MMF with M = 12 spatial and pol. modes – optimised following [13, 4]. To account forlarger link MDL, the mode attenuation vector is varied by changing the core doping contrast. The fibre parameters are available inthe underlying data (see footnote). Transmission considers the semi-analytical channel model in [1], with a linear mode couplingof −20 dB/km. Receiver includes quantisation to 7 bits. We transmit 16-QAM signals at 33 GBd, and consider as performancemetrics the signal-to-noise ratio (SNR) of the received constellations (averaged over T , 1/T∑Ti=1 E|Xi|2/E|Xi − Yi|2).Furthermore, the channel intensity impulse response (CIR) at the receiver front-end is estimated, considering the pulse RMSwidth, to evaluate to what extent channel memory is reduced by the PMs. All results are obtained for an optical SNR of 35 dB.Fig. 2(a) shows the SNR of the received constellations as a function of the standard deviation of the accumulated MDL, σMDL.Performance is shown for T = 12 and for the transmission using the best 6 PMs (T = 6). The results show that correcting thePMs (by zero-forcing) improved performance by 0.7 dB and 1.5 dB for T = 12 and T = 6, respectively. The SNR gap betweenPMs (or PMs*) and SMs is mainly due to errors in the estimation of H(ω) and/or errors in the eigendecomposition of He(ω).Finally, it can be observed that the PMs and PMs* performance are not significantly affected by MDL (for the regimes tested).Fig. 2(b) shows the CIR compression achieved by using PMs (or PMs*) as a function of σMDL – taking as reference CIRrelated to He(ω) without pre- or post-compensation. It can be seen that CIR compression of 4 times can be achieved for theMDL regimes tested.III. CONCLUSIONWe have shown a PMs approach can successfully reduce end-to-end channel memory and suppresses mode coupling at thereceiver front-end for several MDL regimes. Therefore, this is a promising technique to exploit a subset of the fibre spatial andpol. modes while keeping the number of optical front-ends to that of tributaries transmitted.REFERENCES[1] F. Ferreira et al., “Semi-analytical modelling of linear mode coupling in few-mode fibers,” IEEE JLT, vol. 35, no. 18, p. 4011, 2017.[2] A. Mecozzi et al., “Intensity impulse response of SDM links,” Opt. Express, vol. 23, no. 5, p. 5738, 2015.[3] A. Lobato et al., “Impact of mode coupling on the mode-dependent loss tolerance in few-mode fiber transmission,” Opt. Express, vol. 20, no. 28, p.29776, 2012.[4] F. Ferreira et al., “Towards 1000-mode optical fibres,” in submitted to ECOC [available on arXiv], 2022.[5] N. K. Fontaine et al., “Hermite-gaussian mode multiplexer supporting 1035 modes,” in OFC, 2021, p. M3D.4.[6] S. Fan et al., “Principal modes in multimode waveguides,” Opt. Lett., vol. 30, no. 2, p. 135, 2005.[7] A. A. Juarez et al., “Perspectives of principal mode transmission in mode-division-multiplex operation,” Opt. Express, vol. 20, no. 13, p. 13810, 2012.[8] F. Barbosa et al., “On a scalable path for multimode MIMO-DSP,” in submitted to ECOC [available on arXiv], 2022.[9] K.-P. Ho et al., “Linear propagation effects in mode-division multiplexing systems,” IEEE JLT, vol. 32, no. 4, p. 614, 2014.[10] W. Xiong et al., “Spatiotemporal control of light transmission through a multimode fiber with strong mode coupling,” Phys. Rev. Lett., vol. 117, p.053901, 2016.[11] D. Askarov et al., “Long-period fiber gratings for mode coupling in mode-division-multiplexing systems,” IEEE JLT, vol. 33, no. 19, p. 4032, 2015.[12] D. Pohle et al., “Intelligent self calibration tool for adaptive mode multiplexers using multiplane light conversion,” in subm. to ICO, 2022.[13] F. Ferreira et al., “Design of few-mode fibers with m-modes and low differential mode delay,” IEEE JLT, vol. 32, no. 3, p. 353, 2014.

Scaling Spatial Multiplexing with Principal Modes

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Scaling Spatial Multiplexing with Principal Modes

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