Group-delay-managed nonlinear medium

Our approach, originally proposed in ref. 21, uses the dispersive walk-off between the WDM channels to avoid FWM and XPM, but at the same time produces no walk-off among the frequency components within each channel, which preserves pulse integrity and enables accumulation of large amounts of SPM. In order to achieve this, we split the nonlinear fibre used for 2R regeneration into a series of short sections separated by spectrally periodic phase filters known as PGDDs, as shown in Fig. 1a. Such filters, usually made of several cascaded Gires–Tournois etalons28, 29, have sawtooth-like group-delay spectra (Fig. 1b). When the PGDD spectrum is added to a straight-line (i.e. constant-dispersion) group-delay spectrum of a section of the nonlinear fibre, the resulting group-delay spectrum of the ʽfibre + PGDDʼ combination exhibits staircase-like behaviour (Fig. 1b). This ensures equal delays (i.e. no dispersion) among all frequency components within each channel, thereby maximising SPM, but at the same time introduces temporal walk-off between different WDM channels, which reduces XPM and FWM. When multiple ʽfibre + PGDDʼ unit cells are concatenated, such walk-off is accumulated, effectively resulting in the creation of a new artificial nonlinear medium with large group-velocity dispersion among different WDM channels and with no dispersion within each channel. In such a medium, which we refer to as ʽGDM nonlinear medium,ʼ the benefits of large SPM can be enjoyed simultaneously by each of many WDM channels without suffering from the FWM and XPM. In this paper we focus on a GDM medium based on nonlinear fibres and commercially available PGDDs29, 30. In the future, it might be possible to implement the entire GDM on a chip using integrated-photonics solutions for both nonlinear31, 32 and PGDD33,34,35 functions.

Fig. 1 Principle of multi-channel 2R regeneration. a Group-delay-managed (GDM) medium is made by concatenation of N ʽfibre + periodic group-delay device (PGDD)ʼ unit cells and processes m WDM channels. b Each cell has a staircase-like group-delay spectrum (whose derivative is dispersion), ensuring strong nonlinearity within each channel, but suppressed nonlinear interactions among the channels. Group-delay spectra are shown for three adjacent WDM channels. c Single-channel Mamyshev 2R regenerator is based on signal’s spectral broadening by self-phase modulation (SPM), followed by off-centre bandpass filtering. d Propagation in the GDM medium results in group-delay walk-off between the adjacent channels (wavelength is normalised to channel spacing) and allows their simultaneous broadening by the SPM without nonlinear inter-channel crosstalk. The coloured map underneath represents evolution of power spectral densities of the three channels. Group delay values in b, d assume the channel spacing of 200 GHz (1.6 nm) and fibre with dispersion D = –120 ps nm−1 km−1 and section length of 1.25 km Full size image

The use of bit walk-off to suppress XPM was originally proposed for conventional long-haul communication lines36, 37 and later was demonstrated with PGDDs for dispersion-managed soliton transmission38, 39. The long-haul communication lines, however, operate in the regime where the nonlinearities are weak, whereas 2R regeneration inherently relies on large SPM, i.e. operates in a strongly nonlinear regime. We found the optimum parameters of operation for the latter regime40, which indicate that an excellent 2R performance, which is also very robust with respect to perturbations of the experimental parameters, can be obtained with as few as five or six ʽfibre + PGDDʼ unit cells with anomalous net dispersion of the cell and large normal dispersion of the nonlinear fibre.

The GDM nonlinear medium can enable the WDM operation in any SPM-based 2R regenerator or other optical signal processor. In this paper we report its application to a particular scheme known as the Mamyshev regenerator22. The operation of the latter is illustrated in Fig. 1c for the case of a single channel. After propagation in nonlinear fibre, a noisy input pulse (ʽONEʼ symbol) with original bandwidth Δν 0 experiences SPM-caused spectral broadening so that the width of the broadened spectrum Δν NL is proportional to the input pulse’s peak power P 0 while the power spectral density of the broadened spectrum is virtually independent of the input power. Hence, by selecting a portion of the broadened spectrum by an optical bandpass filter (OBPF), one can obtain an output pulse of approximately the same duration as the input pulse (if OBPF width Δν F ≈ Δν 0 ), but with the magnitude that does not change with input power fluctuations (regeneration of ʽONESʼ symbols). On the other hand, any noise between the pulses (i.e. taking place of ʽZEROʼ symbols) is too weak to cause SPM broadening and is confined within the input signal’s bandwidth. If the OBPF centre frequency is offset from the centre of the input signal’s spectrum, the noise between the pulses is not transmitted to filter’s output, which constitutes the regeneration of ʽZEROʼ symbols. For proper operation, the Mamyshev scheme requires large amount of SPM (3…12 radians of nonlinear phase shift Φ NL ). Figure 1d illustrates application of the GDM medium to the Mamyshev regenerator.

The compatibility of the Mamyshev regenerator with conventional dispersion management has been experimentally demonstrated for a single channel41 and later investigated with three to four channels15, 42. These experiments used alternating normal- and anomalous-dispersion fibres and did not involve PGDDs. Such conventional dispersion management schemes do not monotonically accumulate walk-off between channels and, hence, are unable to sufficiently suppress XPM and FWM. As a result, these experiments could not be extended to multi-channel operation.

In this paper, we demonstrate multi-channel 2R regeneration in the Mamyshev scheme enabled by the GDM nonlinear medium. In all presented experiments the nonlinear fibre is the conventional dispersion-compensating fibre (DCF) with nonlinear constant γ ≈ 5 (W km)−1, dispersion D = –120 ps nm−1 km−1, and attenuation ≈ 0.5 dB km−1. All signals are OOK modulated by a 231–1 pseudo-random bit sequence (PRBS) and carved into 50% return-to-zero (RZ) pulses. To ensure the worst case of inter-channel nonlinearities (XPM and FWM), all WDM signals are co-polarised. In order to properly characterise the 2R regeneration performance, we decorrelate the clock frequencies and the bit patterns between the neighbouring channels (see ‘Methods’ for more details). Without proper clock decorrelation, one is likely to observe unrealistically optimistic regeneration performance (e.g. when the 50% RZ pulses from the neighbouring channels are interleaved in time), which cannot be achieved in a practical communications system, where the channels have independent (uncorrelated) clocks.

Multi-channel regeneration in a loop-based GDM medium

In order to be able to easily vary the number of ʽfibre + PGDDʼ unit cells in the regenerator without drastic increase in the required resources, and to experimentally confirm the parameters of the theoretically predicted regime40 of multi-channel regeneration in the GDM medium, we have built a recirculating loop23, 24, where we used only one ʽfibre + PGDDʼ unit cell and passed the signals through it multiple times (Fig. 2) to achieve the effect of concatenating multiple identical cells. After each pass (circulation), the spectrum of each WDM channel is increasingly broadened by SPM, until it completely fills the passband width of the PGDD’s amplitude response after five circulations (the PGDD in this experiment has a periodic bandpass amplitude characteristic with –1-dB width of 100 GHz), as shown in Fig. 3a. Hence, using a 10 Gigabit-per-second (Gbps) signal after five circulations as the regenerated output, we have studied the regeneration performance with various numbers of channels (Fig. 3b). Although 2R regeneration cannot improve the intrinsic bit-error rate (BER) of the signal, the compression of noise of ʽZEROʼ and ʽONEʼ symbols makes the signal more robust with respect to subsequent noise addition. This improvement (a.k.a. ʽeye-opening improvement,ʼ because it increases the opening between the ʽZEROʼ and ʽONEʼ levels on the eye diagram) is quantified by the reduction of the signal power level at the receiver’s optical pre-amplifier entrance that is required to obtain BER = 10−9. While the merits of a regenerator are ultimately determined by the reach extension it offers to a specific real transmission system in the field, the eye-opening improvement is the widely accepted laboratory measure of the regenerator’s ability to suppress the signal’s impairments and hence improve the system performance. In three separate experiments, we have found that the eye-opening improvement of the central channel degraded by amplitude jitter does not show any noticeable degradation when the number of WDM channels on a 200-GHz-spaced grid is increased from 1 to 2 (red diamonds in Fig. 3b), from 1 to 12 (purple triangles), or when the number of the channel’s closest neighbours on this grid is changed from 0 to 7 while keeping the total number of channels at 8 (blue squares). In general, the negative impact of XPM and FWM from neighbouring channels on the performance of a given regenerated channel quickly diminishes with the increased frequency separation between the channels. Thus, only a few (5–7) closest neighbours have a potential to degrade the signal channel’s regeneration performance. Our GDM method strongly suppresses this degradation: as the results in Fig. 3b show, the performance is not degraded as we change the number of closest neighbour channels from 0 to 11. Thus, in line with our theoretical prediction in ref. 21, these results experimentally demonstrate that there is no fundamental XPM or FWM limit on the number of channels regenerated in our scheme, i.e. adding more channels would not increase XPM or FWM impairments.

Fig. 2 Experimental recirculating-loop setup. 10-Gbps-modulated signals from 12-channel transmitter enter the recirculating loop containing one GDM unit cell. After five circulations the signals are filtered and detected by a pre-amplified receiver (Rx). The tunable laser is used to generate ±25% amplitude jitter when it is tuned to the wavelength of the signal channel to be measured. MZM: electro-optic Mach–Zehnder modulator, EDFA: erbium-doped fibre amplifier, PC: polarisation controller, AOS: acousto-optic switch, VOA: variable optical attenuator, DCF: dispersion-compensating fibre, OSA: optical spectrum analyser, OBPF: optical bandpass filter, DCA: digital communication analyser Full size image

Fig. 3 Multi-channel 2R regeneration in the recirculating loop. a SPM-broadened spectra of the central (1550.5 nm) channel (out of 12 channels total) after N circulations, obtained with the resolution bandwidth of 0.1 nm. b Eye-opening improvement at BER = 10−9 for the central 1550.5-nm channel after N = 5 circulations versus the number of other simultaneously regenerated channels. Different-coloured traces in b describe three separate experiments using different EDFAs in the loop and should not be compared to one another. Red diamonds correspond to the increase from 1 to 2 and the purple triangles—to the increase from 1 to 12 in the total number of consecutive 200-GHz-spaced WDM channels. Blue squares correspond to the change in the number of the central channel’s closest neighbours on the 200-GHz-spaced grid from 0 to 7, while the total number of channels is kept at 8. Error bars are obtained from the linear fits to BER curves (red diamonds, first and last purple triangles) and from power measurement uncertainties (blue squares, three middle purple triangles) Full size image

The most important results of the recirculating-loop experiment are presented in Fig. 4a–d, demonstrating 2R regeneration of 12 10-Gbps channels with 200-GHz spacing. The data in Fig. 4a, obtained from comparing the curves of BER versus receiver pre-amplifier’s input power (examples of which are given in Fig. 4b–d), clearly indicate that the regenerator improves eye opening by more than 2 dB for all 12 channels. The eye diagrams in the insets of Fig. 4b–d also show significant reduction of the amplitude jitter after the regeneration. The number of channels in this experiment has been limited by the gain-flattened bandwidth of our high-power erbium-doped fibre amplifier (EDFA) (1542–1560 nm) and the 200-GHz channel spacing of the PGDD. The role of gain flattening is evident in Fig. 4a by the better performance of channels 5 and 6, for which the EDFA gain ripple is minimal. This results in the smallest input-to-output power excursion, a more even distribution of the SPM generation among all circulations, and nearly ideal regeneration conditions for these two channels.

Fig. 4 Results of 12-channel 2R regeneration in the recirculating loop. a Eye-opening improvements at BER = 10−9 for 12 simultaneously regenerated channels (left axis); 12-channel spectra at the input (blue) and output (red) of the regenerator (right axis), obtained with the resolution bandwidth of 0.1 nm. N is the number of circulations. Error bars are obtained from the linear fits to BER curves. Numbered circles indicate the channels shown in b–d. b–d BER curves and eye diagrams for amplitude-jitter-degraded signals before (red triangles) and after the regeneration (blue squares) for 1542.5-nm (b), 1550.5-nm (c) and 1560.2-nm (d) channels. BERs for signals without amplitude jitter are also shown (black open circles—before and blue open squares—after the regeneration). b–d Share common legend. The eye diagrams (insets in b–d) exhibit significant reduction in the amplitude jitter after the regeneration Full size image

Demonstration of a stand-alone multi-channel 2R regenerator

With the insights gained from the recirculating-loop experiments, we have built a stand-alone 2R regenerator (Fig. 5a) consisting of five PGDDs and six sections of nonlinear fibre (Fig. 5b), described in greater detail in ‘Methods’. Although an ideal PGDD is a pure all-pass filter and there are no fundamental limits on making it virtually lossless, the PGDDs that are commercially available today have finite insertion losses of 3–5 dB, primarily owing to the lack of market incentive to further reduce the loss in their current application (dispersion compensation at the loss-tolerant mid-stage of an EDFA). To compensate for the loss of the PGDDs, nonlinear fibre, couplers, and splices, and to achieve similar amounts of SPM in all fibre sections, we use bi-directional distributed Raman amplification in all sections of the nonlinear fibre. The number of regenerated WDM channels in our experiment is limited by the available Raman pump wavelengths and powers, which determine the spectral shape and magnitude of the saturated Raman gain. In order to avoid confusing 2R regeneration with artifacts of Raman gain saturation (which can suppress low-frequency amplitude jitter), we introduce fast amplitude fluctuations by modulating all channels with broadband (14-GHz-wide) Nyquist–Johnson electronic noise. The multi-channel regeneration is characterised by comparing the eye diagrams and ʽBER versus receiver input powerʼ curves between the regenerator input (point A in Fig. 5a) and regenerator output (point B in Fig. 5a) for all channels.

Fig. 5 Stand-alone regenerator setup. a 10-Gbps-modulated signals from a 16-channel transmitter enter the regenerator, and their performance is characterised by a pre-amplified receiver. b GDM medium in the stand-alone regenerator consists of six Raman-pumped sections of DCF, separated by five PGDDs. PG: pattern generator, SSB: single sideband, SMF: single-mode fibre, RPU: Raman pump unit. c Decorrelation of the even- and odd-channel clock frequencies by frequency modulation (FM) of a single clock source Full size image

The experimental results shown in Figs. 6 and 7 indicate similar amounts of the SPM-induced spectral broadening and similar eye-opening improvements for all 16 regenerated channels. In addition to presenting 16-channel spectra in Fig. 6a, we show detailed view of the spectra of four representative channels (channels 2, 6, 12 and 16) in Fig. 6b–e to illustrate that they indeed have similar shapes and similar amounts of nonlinear spectral broadening. The eye diagrams of these channels (insets in Fig. 6b–e) also exhibit similar and clearly noticeable amounts of the amplitude noise suppression by the regenerator. Figures 7a, b indicate that the eye-opening improvements for all 16 channels are 4.8 dB or better. Building upon the 12-channel recirculating-loop results, this 16-channel experiment represents the first, to the best of our knowledge, demonstration of a truly multi-channel 2R regenerating device. Moreover, it uses 100-GHz WDM channel spacing, which, as of the manuscript’s submission time, is the narrowest channel spacing among any 2R regenerators processing more than one WDM channel.

Fig. 6 Spectra and eye-diagrams before and after the stand-alone 2R regenerator. a–e Optical spectra of the noise-degraded signals at the regenerator input (blue) and output (red) for all 16 channels (a) and four representative channels (detail view, b–e), obtained with the resolution bandwidth of 0.016 nm. Corresponding eye diagrams are shown as insets. Encircled numbers at the top of a show positions of the four channels. f 5-bit pattern before and after regeneration (1555.75-nm channel) Full size image

Fig. 7 BER measurements and spectral ripple before and after the stand-alone 2R regenerator. a Eye-opening improvements at BER = 10−9 level (purple circles pertaining to the left axis) and spectral ripple (blue squares and red triangles pertaining to the right axis) among the 16 simultaneously regenerated channels. By pre-emphasising the channel powers so that the ripple of the WDM spectrum at the GDM medium input (blue squares) is the inverse of that at the GDM medium output (red triangles), we minimise the differences in optical signal-to-noise ratios and nonlinear phase shifts among the 16 channels due to Raman gain ripple66 . Error bars are obtained from the parabolic fits to BER curves. b BER curves for all 16 channels Full size image

We emphasise that the number of channels in this experiment is not constrained by any conceptual limitations of the GDM approach, and is only limited by the bandwidth of the practical Raman amplifiers available in our lab. Hence, we expect this approach to be scalable to much higher channel counts when wider-bandwidth amplifiers are used.