Fanchao Meng

Coraline Lapre

Cyril Billet

Thibaut Sylvestre

Jean-Marc Merolla

Christophe Finot

Sergei K Turitsyn

Goëry Genty

John M Dudley
email: john.dudley@univ-fcomte.fr

Intracavity incoherent supercontinuum dynamics and rogue waves in a broadband dissipative soliton laser

Understanding dynamical complexity is one of the most important challenges in science. Significant progress has recently been made in optics through the study of dissipative soliton laser systems, where dynamics are governed by a complex balance between nonlinearity, dispersion, and energy exchange. A particularly complex regime of such systems is associated with noise-like pulse multiscale instabilities, where sub-picosecond pulses with random characteristics evolve chaotically underneath a much longer envelope. However, although observed for decades in experiments, the physics of this regime remains poorly understood, especially for highly-nonlinear cavities generating broadband spectra. Here, we address this question directly with a combined numerical and experimental study that reveals the physical origin of instability as nonlinear soliton dynamics and supercontinuum turbulence. Real-time characterisation reveals intracavity extreme events satisfying statistical rogue wave criteria, and both real-time and time-averaged measurements are in quantitative agreement with modelling.

INTRODUCTION

Recent years have seen tremendous advances in understanding nonlinear complexity through studies in optical systems that allow real-time observation of ultrafast instabilities. For example, studies in optical fibres have yielded new insights into the modulation instability of the nonlinear Schrödinger equation (NLSE) [START_REF] Solli | Fluctuations and correlations in modulation instability[END_REF][START_REF] Närhi | Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability[END_REF][START_REF] Tikan | Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation[END_REF][START_REF] Mussot | Fibre multi-wave mixing combs reveal the broken symmetry of fermi-pasta-ulam recurrence[END_REF][START_REF] Kraych | Nonlinear evolution of the locally induced modulational instability in fiber optics[END_REF], improving our understanding of noise-driven nonlinear dynamics, and stimulating new approaches to classify localised soliton structures using machine learning [START_REF] Närhi | Machine learning analysis of extreme events in optical fibre modulation instability[END_REF].

Other studies have focused on instabilities in dissipative soliton lasers, where the laser operation is governed by the balance between nonlinearity and dispersion, and energy input and loss [START_REF]Dissipative Solitons[END_REF][START_REF] Grelu | Dissipative solitons for mode-locked lasers[END_REF][START_REF] Turitsyn | Dissipative solitons in fiber lasers[END_REF][START_REF] Ryczkowski | Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser[END_REF][START_REF] Peng | Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers[END_REF][START_REF] Liu | Revealing the behavior of soliton buildup in a mode-locked laser[END_REF]. Such lasers are usually configured to produce highly regular pulse trains of ultrafast solitons [START_REF] Woodward | Dispersion engineering of mode-locked fibre lasers[END_REF][START_REF] Fu | Several new directions for ultrafast fiber lasers[END_REF], but they can also exhibit a range of more complex temporal and spectral characteristics.

Specifically, the coupling between nonlinearity and dispersion in the cavity can result in instabilities arising from the intrinsic chaotic dynamics of NLSE and NLSE-like systems [START_REF] Blow | Global and local chaos in the pumped nonlinear schrödinger equation[END_REF][START_REF] Herbst | Numerically induced chaos in the nonlinear schrödinger equation[END_REF]. The particular dynamics that are observed depend on the dimensionality of the system under study [START_REF] Strogatz | Nonlinear Dynamics and Chaos[END_REF], and for certain laser designs, it has been possible to see clear signatures of low-dimensional nonlinear dynamics such as the development of complex temporal pattern formation [START_REF] Haelterman | Hopf sideband bifurcation and chaos in fiber lasers with injected signal[END_REF], and bifurcation routes to chaos [START_REF] Soto-Crespo | Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser[END_REF].

More commonly, however, fibre lasers possess a very large number of degrees of freedom so that instabilities are high-dimensional such that the particular operating point of stable pulse train generation can be viewed as an attractor in a multi-dimensional parameter space. In some cases, variation of the cavity parameters about these stable points can induce transition into unstable regimes involving interactions between a small number of circulating pulses (typically 1-10) in the cavity. Studying these instabilities with real-time measurement techniques has led to improved insight into processes such as soliton molecule coupling [START_REF] Krupa | Real-Time Observation of Internal Motion within Ultrafast Dissipative Optical Soliton Molecules[END_REF][START_REF] Herink | Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules[END_REF][START_REF] Liu | Real-time observation of the buildup of soliton molecules[END_REF], complex temporal pattern formation in lasers [START_REF] Huang | Versatile patterns of multiple rectangular noise-like pulses in a fiber laser[END_REF][START_REF] Klein | Ultrafast rogue wave patterns in fiber lasers[END_REF][START_REF] Zhou | Versatile multi-soliton patterns of noise-like pulses in a passively mode-locked fiber laser[END_REF], soliton explosion and rogue wave emergence [START_REF] Klein | Ultrafast rogue wave patterns in fiber lasers[END_REF][START_REF] Runge | Coherence and shot-to-shot spectral fluctuations in noise-like ultrafast fiber lasers[END_REF], and complex intermittence [START_REF] Churkin | Stochasticity, periodicity and localized light structures in partially mode-locked fibre lasers[END_REF][START_REF] Lapre | Real-time characterization of spectral instabilities in a mode-locked fibre laser exhibiting soliton-similariton dynamics[END_REF]. In fact, from a more general perspective, these regimes are neither pure mode-locked pulses, nor continuous wave generation. These highly complex lasing regimes are characterised by the co-existence of both localised nonlinear structures and linear dispersive waves.

In addition to regimes involving only a small number of interacting pulses, a more complex multiscale laser instability has been shown to involve a much greater number (100-1000) of ultrafast pulses evolving randomly underneath a much broader envelope. This multiscale regime of noise-like pulse operation was first discovered by Silberberg et al. in 1997 [START_REF] Horowitz | Noiselike pulses with a broadband spectrum generated from an erbium-doped fiber laser[END_REF], and has since been seen in a wide range of different laser configurations, and with both normal and anomalous dispersion [START_REF] Jeong | On the formation of noise-like pulses in fiber ring cavity configurations[END_REF]. The majority of studies have typically focused on instabilities generating spectral bandwidths of 10's of nm [START_REF] Tang | Soliton collapse and bunched noise-like pulse generation in a passively mode-locked fiber ring laser[END_REF][START_REF] Kobtsev | Generation of double-scale femto/picosecond optical lumps in mode-locked fiber lasers[END_REF][START_REF] Pottiez | Adjustable noiselike pulses from a figure-eight fiber laser[END_REF][START_REF] Lecaplain | Rogue waves among noiselike-pulse laser emission: An experimental investigation[END_REF][START_REF] Li | Unveiling femtosecond rogue-wave structures in noise-like pulses by a stable and synchronized time magnifier[END_REF][START_REF] Wang | Buildup of incoherent dissipative solitons in ultrafast fiber lasers[END_REF][START_REF] Du | Alternation of the mode synchronization and desynchronization in ultrafast fiber laser[END_REF], but in a highly nonlinear regime with significant spectral broadening in the cavity, bandwidths much greater than the gain bandwidth (100's of nm) have been observed [START_REF] Vazquez-Zuniga | Super-broadband noise-like pulse erbium-doped fiber ring laser with a highly nonlinear fiber for raman gain enhancement[END_REF][START_REF] North | Raman-induced noiselike pulses in a highly nonlinear and dispersive all-fiber ring laser[END_REF][START_REF] Santiago-Hernandez | Generation and characterization of erbium-Raman noise-like pulses from a figure-eight fibre laser[END_REF][START_REF] Wang | Generation of noise-like pulses with 203 nm 3-db bandwidth[END_REF]. In addition to their clear interest from a dynamical systems perspective, such lasers have found several important applications [START_REF] Jeong | On the formation of noise-like pulses in fiber ring cavity configurations[END_REF][START_REF] Pan | Fiber-laser-generated Noise-like Pulses and Their Applications[END_REF]. Significantly, while some applications such as tomography and metrology explicitly build on the low temporal coherence of such sources [START_REF] Keren | Interrogation of fiber gratings by use of low-coherence spectral interferometry of noiselike pulses[END_REF], applications in material processing exploiting the burst-like nature of the pulsed output have also been demonstrated [START_REF] Özgören | W, 31 MHz, square-shaped, 1 ns-pulsed all-fiber-integrated laser for micromachining[END_REF].

Somewhat paradoxically, the large number of experimental studies of noise-like pulse lasers under so many different conditions has made it difficult to clearly identify the underlying physics.

Also, the multiscale nature of the laser operation has not always been appreciated in experiments measuring only the envelope or burst output characteristics. Nonetheless, the underlying role of NLSE-like instabilities has been suggested from numerical studies, using both cubic-quintic Ginzburg-Landau equation modelling [START_REF] Chernykh | Soliton and collapse regimes of pulse generation in passively modelocking laser systems[END_REF][START_REF] Chang | Spiny solitons and noise-like pulses[END_REF][START_REF] Komarov | Mechanism of formation of noiselike pulses in passively modelocked fiber lasers[END_REF] and iterative cavity simulations [START_REF] Jeong | On the formation of noise-like pulses in fiber ring cavity configurations[END_REF][START_REF] Tang | Soliton collapse and bunched noise-like pulse generation in a passively mode-locked fiber ring laser[END_REF]. Further modelling [START_REF] Donovan | Dynamics and statistics of noise-like pulses in modelocked lasers[END_REF][START_REF] Lauterio-Cruz | Numerical study of complex dynamics and extreme events within noise-like pulses from an erbium figure-eight laser[END_REF] has revealed how these dynamics can lead to rogue wave statistics, confirming previous experiments in the narrowband noise-like pulse regime [START_REF] Lecaplain | Rogue waves among noiselike-pulse laser emission: An experimental investigation[END_REF][START_REF] Li | Unveiling femtosecond rogue-wave structures in noise-like pulses by a stable and synchronized time magnifier[END_REF][START_REF] Runge | Raman rogue waves in a partially mode-locked fiber laser[END_REF].

Significantly, the results of these previous studies have now extended traditional notions of laser operation beyond average dynamical models to include concepts such as strong dissipation, regenerative saturable absorption [START_REF] Liu | Megawatt peak power from a mamyshev oscillator[END_REF], random lasing [START_REF] Turitsyn | Random distributed feedback fibre laser[END_REF], and intracavity turbulence [START_REF] Turitsyna | The laminar-turbulent transition in a fibre laser[END_REF]. The study of turbulent behaviour in lasers is a subject of particular interest, and can be physically interpreted as a consequence of the large number (∼ 10 4 -10 6 ) of interacting frequency modes underneath the evolving broadband field [START_REF] Barviau | Wave-turbulence approach of supercontinuum generation: Influence of self-steepening and higher-order dispersion[END_REF][START_REF] Picozzi | Optical wave turbulence: Towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics[END_REF][START_REF] Churkin | Wave kinetics of random fibre lasers[END_REF]. Moreover, linking irregular dynamics to turbulence is also interesting from the perspective of understanding intracavity extreme events, which have already been observed in single-pass experiments [START_REF] Hammani | Emergence of rogue waves from optical turbulence[END_REF][START_REF] Suret | Single-shot observation of optical rogue waves in integrable turbulence using time microscopy[END_REF].

A particular challenge is to understand the dynamics of noise-like pulse lasers generating the broadest bandwidths, because the presence of highly nonlinear fibre in the cavities used suggests a major role played by supercontinuum broadening. In this case, any modelling in a laser context is computationally very expensive, and measuring these multiscale instabilities in the laboratory is also extremely challenging. These different factors clearly represent a serious limitation when a full understanding of such a rich dynamical laser system is of evident interest from both fundamental and applied perspectives.

Here, we report a combined numerical and experimental study of an extreme dissipative soliton noise-like pulse laser generating an output supercontinuum spectrum of ∼1000 nm bandwidth, and with intracavity spectral width varying two orders of magnitude over one roundtrip. Our stochastic numerical simulations allow us to identify the origin of the laser instability as due to the sensitivity to noise of nonlinear soliton dynamics, particularly multiple interactions and collisions between incoherently evolving sub-picosecond Raman solitons. Our experiments use time and frequency domain techniques to characterise the multiscale dynamics, and our simulations reproduce quantitatively the supercontinuum broadening, and the probability distributions of temporal and spectral fluctuations, including rogue wave events.

RESULTS

Modelling and Dynamics

We first use numerical modelling to illustrate the general features of the noise-like pulse instability regime. Figure 1 shows the dissipative laser system upon which our modelling is based. Typical of dissipative soliton systems, we consider a unidirectional ring cavity consisting of a number of discrete segments where the intracavity field experiences qualitatively different evolution [START_REF] Turitsyn | Dissipative solitons in fiber lasers[END_REF][START_REF] Woodward | Dispersion engineering of mode-locked fibre lasers[END_REF].

The modelling uses an iterative map approach describing each cavity element by a suitable transfer function. For a given set of system parameters, the model seeks convergence to a particular operating state after injection of an initial seed (see Methods). Although scalar models have been shown to reproduce aspects of dissipative soliton laser dynamics qualitatively [START_REF] Meng | Instabilities in a dissipative soliton-similariton laser using a scalar iterative map[END_REF], for quantitative comparison with experiments we implement a more complete approach based on coupled generalised vector nonlinear Schrödinger equations (NLSE). This was found essential to obtain quantitative agreement with experiments. Indeed, it is important to stress that although mean-field models such as those based on the Ginzburg-Landau equation are able to reproduce general features of dissipative soliton lasers [START_REF] Chang | Spiny solitons and noise-like pulses[END_REF], the iterative cavity approach is necessary when describing a system with such dramatic variation in evolution between the different cavity segments.

The simulations use a standard approach, with initiation from a low amplitude noise seed [START_REF] Oktem | Soliton-similariton fibre laser[END_REF] injected at point A before the EDF. The intracavity field then evolves over multiple roundtrips until convergence to a particular operating state. For a stable state, the spectral and temporal field characteristics at any point in the cavity reproduce themselves after one roundtrip, whilst in a noise-like pulse state, the temporal and spectral characteristics at any point fluctuate significantly with roundtrip but the energy nonetheless has a well-defined mean. Typical energy fluctuations after build-up to the noise-like pulse regime are ∼10%, and the physical origin of this behaviour is the chaotic nature of the NLSE and gain/loss dynamics when seeded by noise.

In our experiments, segment AB consists of 11 m of Erbium-doped fibre (EDF), segment BC consists of 2.87 m of standard single mode fibre (SMF), segment CD consists of 10.3 m of highly nonlinear fibre (HNLF), and segments DE and FA consist of 4.45 m and 7.80 m of SMF. A 28.1 cm bulk-optics free space segment EF includes a nonlinear polarisation rotation based saturable absorber (using waveplates and a polarisation beamsplitter) [START_REF] Hofer | Mode locking with cross-phase and self-phase modulation[END_REF], and a narrowband spectral filter to control the bandwidth of the pulses reinjected into the EDF [START_REF] Woodward | Dispersion engineering of mode-locked fibre lasers[END_REF][START_REF] Chong | Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress[END_REF]. The cavity uses nonpolarisation-preserving fibre, and the repetition rate is 5.59 MHz (roundtrip time of ∼179 ns.) The dispersion and nonlinearity parameters of the fibres used are given in Methods. The loss due to splicing and output coupling was ∼6 dB (with primary output coupling of 40% in segment DE), and the total energy loss at the spectral filtering stage is ∼10 dB (associated with the bandwidth reduction from the supercontinuum spectrum at the HNLF output to the much narrower bandwidth at the EDF input.)

Our study of this particular design is motivated by the need to understand noise-like pulse dynamics in the broadband regime. Specifically, the majority of previous studies of noise-like pulse lasers have focussed on narrowband systems with 10's of nm bandwidth [START_REF] Jeong | On the formation of noise-like pulses in fiber ring cavity configurations[END_REF], where modelling and simulations have shown how the dynamics arise from the interaction between self-phase modulation and group-velocity dispersion in the cavity [START_REF] Woodward | Dispersion engineering of mode-locked fibre lasers[END_REF][START_REF] Jeong | On the formation of noise-like pulses in fiber ring cavity configurations[END_REF][START_REF] Chernykh | Soliton and collapse regimes of pulse generation in passively modelocking laser systems[END_REF][START_REF] Chang | Spiny solitons and noise-like pulses[END_REF][START_REF] Komarov | Mechanism of formation of noiselike pulses in passively modelocked fiber lasers[END_REF], with only minor contributions from higher-order effects. With the addition of anomalous dispersion HNLF, however, the dynamics change qualitatively and quantitatively with the processes of incoherent soliton fission and the Raman soliton self-frequency shift combine to dominate the intracavity spectral broadening [START_REF] Dudley | Supercontinuum Generation in Optical Fiber[END_REF][START_REF] Kelleher | Fission of solitons in continuous-wave supercontinuum[END_REF]. Moreover, in contrast to other dissipative soliton laser designs that can exhibit both stable soliton and noise-like pulse operation [START_REF] Smirnov | Wide Variability of Generation Regimes in Mode-Locked Fiber Lasers[END_REF], the use of such a long length of HNLF results in this system operating only in the noise-like instability regime, irrespective of the laser gain or waveplate orientations. In the simulation results that follow, we therefore focus on the dynamics of this unstable broadband operating state with parameters corresponding to our experiments, although we refer when appropriate to Supplementary Information which show simulations for other parameters in order to clarify certain features of the underlying physics.

We begin by showing typical simulation results in the noise-like pulse regime for our experimental parameters as above. Figure 2(a) shows typical simulated spectral and temporal evolution over one cavity round trip, after build-up when the pulse has entered the regime of constant mean energy.

These results were obtained after scanning the simulation parameters to obtain energy and noisy envelope durations comparable to experiment (see Methods), and correspond to a mean intracavity energy (over 1000 roundtrips) at the EDF output of 10.5 nJ. We plot the total intensity of both polarisation components (see Methods). The different propagation steps A-F refer to the different points in the cavity shown in Fig. 1.

In the frequency domain, Fig. 2(a) shows how the spectral characteristics vary significantly over one roundtrip. We see amplification in the EDF (segment AB), dramatic supercontinuum spectral broadening in the HNLF (segment CD), and the strong effect of spectral filtering in the bulk segment EF. Indeed the spectral extent varies by two orders of magnitude over one roundtrip, from ∼10 nm FWHM immediately after the spectral filter, to a supercontinuum with spectral components spanning ∼1000 nm at the HNLF output. In segment DE, the reduced nonlinearity of the SMF (coupled with reduced power due to output coupling) yields essentially linear propagation without additional spectral broadening. As we will see in Figs 3 and4, the shot-to-shot spectra exhibit significant fine structure, but this is not apparent in Fig. 2 because of the false-color visualisation used.

The associated time-domain evolution in Fig. 2(a) reveals significant variation in the subpicosecond temporal structure over one roundtrip, while the slower ∼300 ps envelope remains largely unchanged. The simulations also reveal the presence of clusters of solitons under the envelope (see for example timebase values in the range ∼[-150, -50] ps), an effect previously suggested by low-resolution temporal measurements, and associated with an additional scale of time-domain structure [START_REF] Torres-Muñoz | Simultaneous temporal and spectral analysis of noise-like pulses in a modelocked figure-eight fiber laser[END_REF]. Note that we also confirm the presence of these clusters in our experiments below.

After the HNLF propagation phase, the linear evolution in the subsequent SMF segment DE is associated with dispersive broadening of the solitons formed in the HNLF. Note that the apparent temporal refraction of the pulse trajectories across the HNLF-SMF boundary (point D) arises from the differences in group velocity dispersion in the two fibres. We also see how the spectral filtering in the bulk segment EF has a significant effect on the temporal evolution by removing all field components outside the filter bandwidth, particularly the long-wavelength shifted highest intensity Raman solitons. To more clearly show the temporal evolution after this filtering step, the intensity colormap in segment FA has been scaled by a factor of ×10. the dominant physics associated with the temporal compression of the T FWHM ∼500 fs random pulses at the input to yield ejection of strongly-localised sub-100 fs pulses that then undergo typical supercontinuum dynamics of soliton collisions and Raman shifting to longer wavelengths [START_REF] Dudley | Supercontinuum generation in photonic crystal fiber[END_REF]. Indeed, using P 0 ∼70 W and T 0 = T FWHM /1.76 ∼300 fs as estimates of the mean peak power and duration of the random pulses at the input to the HNLF, the corresponding soliton number is N = (γP 0 T 2 0 /|β 2 |) 1/2 ≈ 4.5, supporting this interpretation [START_REF] Agrawal | Nonlinear Fiber Optics[END_REF]. Associated with these multiple soliton dynamics in the HNLF is the generation of multiple dispersive waves at shorter wavelengths extending to below ∼1100 nm, as seen clearly in the spectral evolution in Fig. 2(a). We note here that the evolution of the Raman soliton trajectory in Fig. 2(a) appears to show spectral broadening, but this is in fact an artefact associated with the fact that we are plotting spectral evolution against wavelength. When plotted against frequency, the soliton bandwidth remains constant once it has clearly separated from the central spectral region. On the other hand, soliton evolution in the presence of the Raman effect and higher-order dispersion can exhibit complex accelerating beam characteristics [START_REF] Efremidis | Airy beams and accelerating waves: an overview of recent advances[END_REF], and this is especially apparent in the trajectories of the time-domain solitons seen in the false colour plot in Fig. 2(b).

The results in Fig. 2(b) clearly show that the input field to the HNLF consists of a large number of irregular localised pulses. As a result, the field injected in the HNLF does not excite narrowband processes such as modulation instability [START_REF] Peng | Real-time observation of dissipative soliton formation in nonlinear polarization rotation mode-locked fibre lasers[END_REF][START_REF] Genty | Collisions and turbulence in optical rogue wave formation[END_REF][START_REF] Chouli | Soliton rains in a fiber laser: An experimental study[END_REF], but rather the dynamics are dominated by incoherent soliton fission. In this case, the decoherence that develops during propagation arises from the effect of noise on soliton interaction and collisions [START_REF] Dudley | Supercontinuum Generation in Optical Fiber[END_REF][START_REF] Kelleher | Fission of solitons in continuous-wave supercontinuum[END_REF] and these results highlight the importance of incoherent soliton fission in noise-like pulse lasers. Of course, under certain conditions, both modulation instability and incoherent soliton fission yield similar characteristics with very large numbers of interacting solitons, and in this case a description in terms of soliton turbulence is more appropriate in both cases [54-56, 70, 72, 73]. This is also the regime where extreme event rogue wave statistics can be observed [START_REF] Hammani | Emergence of rogue waves from optical turbulence[END_REF][START_REF] Suret | Single-shot observation of optical rogue waves in integrable turbulence using time microscopy[END_REF][START_REF] Solli | Optical rogue waves[END_REF][START_REF] Erkintalo | On the statistical interpretation of optical rogue waves[END_REF].

Additional insight into these dynamics is shown in Fig. 3. Here we plot the computed timefrequency spectrogram at the HNLF output, together with the corresponding temporal and spectral intensity profiles (see Methods). Note that we also display the temporal intensity on a logarithmic axis to illustrate the strongly-localised burst-like nature of the noise-like pulse emission. The spectrogram reveals a time-frequency structure typical of Raman-dominated supercontinuum dynamics [START_REF] Dudley | Supercontinuum Generation in Optical Fiber[END_REF], highlighting how each of the solitons generates its own dispersive wave component, and also highlighting the prominent dispersive wave tail associated with the longest wavelength soliton. An accompanying animation (Supplementary Movie 1) shows the evolution of the spectrogram over one cavity roundtrip, and is valuable in revealing the specific dynamics occurring in each segment.

To confirm the soliton nature of the sub-picosecond peaks in the temporal intensity, the highest peak (A) is shown in expanded view on a logarithmic scale (black solid line), and compared with a hyperbolic secant soliton fit (red dashed line). In fact, since the spectrogram allows us to determine the wavelength associated with each temporal peak, we can readily compute the associated soliton number using wavelength-corrected HNLF nonlinearity and dispersion parameters (see Methods). This analysis yields N ∼ 1 for all the strongly localised temporal peaks seen at the HNLF output, further confirming the importance of intracavity soliton dynamics.

The Raman self-frequency shift of the ejected solitons yields the long wavelength spectral extension. And indeed, reaching short wavelengths around 1100 nm would not be possible without the associated dispersive wave generation. However, the presence of Raman scattering is not in itself a necessary condition to observe noise-like pulse operation, and simulations with no HNLF in the cavity still show unstable pulse characteristics for certain parameter regimes. However, without the HNLF, the system operates only in the narrowband regime (see Supplementary Information and Supplementary Fig. 1), as seen in a number of previous studies [START_REF] Horowitz | Noiselike pulses with a broadband spectrum generated from an erbium-doped fiber laser[END_REF][START_REF] Tang | Soliton collapse and bunched noise-like pulse generation in a passively mode-locked fiber ring laser[END_REF][START_REF] Kobtsev | Generation of double-scale femto/picosecond optical lumps in mode-locked fiber lasers[END_REF][START_REF] Pottiez | Adjustable noiselike pulses from a figure-eight fiber laser[END_REF][START_REF] Lecaplain | Rogue waves among noiselike-pulse laser emission: An experimental investigation[END_REF][START_REF] Li | Unveiling femtosecond rogue-wave structures in noise-like pulses by a stable and synchronized time magnifier[END_REF][START_REF] Wang | Buildup of incoherent dissipative solitons in ultrafast fiber lasers[END_REF][START_REF] Du | Alternation of the mode synchronization and desynchronization in ultrafast fiber laser[END_REF]. The essential design parameter here is of course the HNLF length, but additional simulations show that broadband noise-like pulses can be generated with short lengths of HNLF down to ∼1 m (see Supplementary Fig. 2). Of course, the role of the Raman soliton dynamics and the overall bandwidth increase with longer lengths of HNLF, as would be expected on physical grounds (see Supplementary Fig. 3).

The key characteristic of the noise-like pulse regime is of course the dramatic shot-to-shot fluctuations, and to illustrate random field evolution over sequential roundtrips, Figs 4(a

Experiments and Comparison with Simulations

Both time-averaged and statistical predictions of our numerical model have been confirmed using experiments. The overall design of our laser system has been described above (and in Fig. 1). The EDF was pumped at 976 nm, with a pump power threshold of 40 mW for pulsed operation, although we did not observe stable mode-locked operation at any pump power or waveplate orientation [START_REF] Lapre | Real-time characterization of spectral instabilities in a mode-locked fibre laser exhibiting soliton-similariton dynamics[END_REF].

On the other hand, over a wide range of pump powers up to 500 mW, suitable adjustment of the waveplates yielded noise-like pulse operation with chaotic envelope emission at the cavity repetition rate, and broadband spectral output. The results reported below at a pump power of 225 mW are typical of this regime. For this value of pump, the average power at the primary output in branch DE was 13 mW (see Methods).

We used a range of diagnostics to characterise the laser output. Real time shot-to-shot characterisation was possible for the ∼10 nm (3 dB) bandwidth pulses input to the HNLF (point C in Fig. 1) using several different techniques: direct measurement of overall envelope fluctuations via a fast photodiode, a time-lens system to measure sub-picosecond soliton structure on the circulating pulses, and a dispersive Fourier transform (DFT) setup for spectral measurements. At the HNLF output, the large spectral bandwidth of the supercontinuum pulses exceeded the measurement bandwidths of our real-time devices, but time-averaged measurements of the spectra over the full bandwidth of 1000-2100 nm were performed using a an OSA and a near-infrared spectrometer.

In this context, we note that temporal measurements using intensity autocorrelation are of partial utility, as they indicate just the presence of instability through a coherence spike on a broad envelope, and give only an indirect measure of the average sub-structure pulse duration [START_REF] Jeong | On the formation of noise-like pulses in fiber ring cavity configurations[END_REF].

Figure 5 shows the instability properties of the laser measured using direct photodetection.

Figure 5(a) plots data from a fast photodiode over a time span of 20 µs to illustrate the emission of highly unstable pulses at the 5.59 MHz repetition rate (period of ∼179 ns). Although these measurements do not resolve structure faster than the system response time of ∼25 ps, we can still accurately characterise the ∼300 ps envelope, and, within the detection bandwidth, we can even observe variation in the envelope structure with roundtrip. Figure 5(b) unwraps the raw photodiode data to plot the roundtrip variation of the envelope, and reveals the presence of subcluster structure evolving over ∼500 -1000 roundtrips. Although these results clearly reveal shot-to-shot instability on the envelope, the temporal resolution is limited, as seen in the selection of intensity profiles plotted in Fig. 5(c). However, these results are important, because the subclusters seen on the envelope confirm previous studies of similar envelope sub-structure [START_REF] Torres-Muñoz | Simultaneous temporal and spectral analysis of noise-like pulses in a modelocked figure-eight fiber laser[END_REF], and are a clear illustration of random pattern formation and multiscale dynamics in a dissipative soliton laser [START_REF] Huang | Versatile patterns of multiple rectangular noise-like pulses in a fiber laser[END_REF][START_REF] Klein | Ultrafast rogue wave patterns in fiber lasers[END_REF][START_REF] Zhou | Versatile multi-soliton patterns of noise-like pulses in a passively mode-locked fiber laser[END_REF]. In particular, although they are unstable, the sub-clusters are relatively long-lived over multiple roundtrips ∼100's of µs and they consist of a large number of localised solitons of ∼500 fs duration. Of course, the photodiode measurements are unable to resolve both these long timescale characteristics as well as to directly measure the ultrafast soliton structure, and it is for this reason that we performed time-lens measurements for shot-to-shot characterisation on the sub-ps scale.

The time-lens system used is described in the Methods section and had a temporal resolution of ∼ 340 fs and a physical (i.e. demagnified) measurement window of ∼100 ps. Although the finite acquisition window precludes characterisation across the full ∼300 ps pulse envelope, by operating the time-lens asynchronously [START_REF] Ryczkowski | Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser[END_REF], we are nonetheless able to sample the random pulse structure across the envelope over multiple laser round trips. Because of the time-lens measurement bandwidth of ∼12 nm, real-time characterisation was possible only for the input pulses to the HNLF, but as we shall see, these measurements clearly reveal both the sub-ps pulse structure and the rogue wave statistics expected from the underlying nonlinear dynamics. The intensity normalisation was relative to the mean of each respective time series. The inset plots the density functions on a logarithmic scale.

We first note excellent agreement between the simulated and experimental results, with simulations reproducing the experimentally measured intensity probability density function over 3 orders of magnitude. The inset also shows the very good agreement between the simulation statistics and a negative exponential fit (green line), where an exponential distribution is expected here on physical grounds given the randomness of the intensity fluctuations in the noise-like pulse regime. Indeed, such negative exponentially distributed statistics have been seen in previous experiments studying statistics of modulation instability and noise-like pulse lasers [START_REF] Närhi | Machine learning analysis of extreme events in optical fibre modulation instability[END_REF][START_REF] Li | Unveiling femtosecond rogue-wave structures in noise-like pulses by a stable and synchronized time magnifier[END_REF]. In addition to clearly revealing the statistical behaviour of the sub-ps soliton structure of noise-like pulses, these results also strongly confirm the fidelity of the model in reproducing the time-domain properties of the laser system.

We also see (from both simulation and experiment) that a significant fraction of the measured intensity peaks exceed twice the significant intensity threshold (see Methods), thus meeting the statistical criterion to be formally classified as intracavity rogue waves. Indeed, the rogue wave intensity thresholds computed from experiment (I exp RW = 3.64) and simulation (I sim RW = 3.68) are in very good agreement, and the experimental threshold is shown in the figure as the dashed blue line. From this data, it is also straightforward to calculate the fraction of temporal peaks satisfying the rogue wave criterion, which yields 0.43% from simulation, and 0.10% from experiment.

When we are in the noise like pulse regime generating broadband spectra, the temporal probability distribution as shown in Figure 6(c) is largely insensitive to small changes in the design parameters. Specifically, performing numerical simulations with small changes (within ±10%) in parameters such as f R , E sat , g 0 , and the length of the HNLF have negligible effect on the temporal pulse characteristics, and thus negligible effect on the associated probability density function. This is also seen in experiments when we make small changes in pump power for example. We attribute this insensitivity to the fact that our cavity configuration contains a long length of HNLF such that we observe noise-like pulse behaviour at all pump powers above threshold.

Complementing the time-domain measurements in Fig. 5, we were also able to record realtime spectral data. Specifically, the DFT method was used to record spectral fluctuations at the HNLF input, and Fig. 7(a) shows a false colour representation of the shot-to-shot variation measured over 1000 roundtrips. The fidelity of the DFT method was confirmed by computing the average over this measurement ensemble and comparing with an averaging optical spectrum analyser. The agreement between these measurements is clear from Fig. 7(b), and this figure also shows the average input spectrum obtained from simulations. There is a small difference between the experimental and simulation bandwidth, but this does not influence the interpretation of our results.

As we saw in the simulation results in Fig. 4, the shot-to-shot spectra also show a strong substructure of spectral peaks. Although analysing spectral peak statistics does not have the same direct physical interpretation in terms of soliton dynamics as analysis of temporal peaks, several studies have characterised spectral peak fluctuations in the context of identifying frequency-domain rogue wave events [START_REF] Lecaplain | Rogue waves among noiselike-pulse laser emission: An experimental investigation[END_REF][START_REF] Runge | Raman rogue waves in a partially mode-locked fiber laser[END_REF]. From our real-time spectral measurements, we computed peak statistics in a similar way as for the temporal data, and the corresponding probability density function is shown in Fig. 7(b). Here we also compare with simulation, but note that the simulated spectra were convolved before peak analysis with a response function to model the spectral resolution of the experimental DFT data (see Methods.) The figure plots results on both linear and logarithmic scales, and as with the temporal data, there is very good agreement. The rogue wave spectral peak intensity threshold computed from experiment was (S exp RW = 3.22) and simulation was (S sim RW = 3.20); the experimental threshold is shown in the figure as the dashed blue line. From this data, it is also straightforward to calculate the fraction of spectral peaks satisfying the rogue wave criterion, which yields 0.04% from simulation, and 0.07% from experiment. These density functions were computed from a time series of 57,500 spectral peaks measured experimentally, and 44,900 peaks analysed from simulation. The intensity normalisation was relative to the mean of each respective time series. Finally, we discuss Fig. 7(d) which shows the measured average spectrum at the HNLF output (red curve). The inset uses a logarithmic scale, and plots over an extended wavelength range to show the dispersive wave components by combining measurements from the Anritsu MS9710B OSA and the NIRQuest512 spectrometer (see Methods). The spectrum is highly asymmetric, consisting of a primary spectral peak of ∼40 nm bandwidth, an extended long wavelength tail, as well as the short wavelength dispersive wave structure. The overall span of the measured spectrum approaches ∼1000 nm.

These experimental results are reproduced in our modelling, where the solid black line shows the simulated average spectrum (computed over 1000 roundtrips) based on the full generalised propagation model. There is very good agreement between experiment and simulation and, given the complexity of the dissipative soliton system that we are modelling, we stress at this point the significance of these results. Specifically, although there have been a large number of distinct experimental and numerical studies of noise-like lasers, our simulations here quantitatively reproduce the observed energy characteristics, the time averaged broadband spectrum over a span approaching 1000 nm, as well as the intensity statistics of random sub-picosecond soliton structures. Moreover, they clearly show the role of soliton dynamics, allowing us to physically associate the long wavelength tail with the random evolution dynamics of Raman solitons, and the short wavelength structure from the corresponding dispersive waves. Note that the modulation in the dispersive wave spectral structure arises from cross-phase modulation from the generating soliton pulse [START_REF] Genty | Effect of cross-phase modulation on supercontinuum generated in microstructured fibers with sub-30 fs pulses[END_REF], sometimes described as analogous to event horizon dynamics [START_REF] Webb | Nonlinear optics of fibre event horizons[END_REF]. The importance of the Raman dynamics is explicitly seen by comparing experiment to simulations performed in the absence of the Raman contribution (i.e. f R = 0). These are shown as the dashed black line, and we clearly see that the long wavelength spectral extension in this case is absent. Note that the stronger dispersive wave component here arises from more efficient dispersive wave energy transfer when there is no Raman-induced wavelength shifting.

Despite the fact that the incoherent noise-like pulse regime of optical fibre lasers has been observed for nearly 25 years, its physics has been understood in only very general terms. Indeed, the very appellation of noise-like is a very generic description, and does not provide information or even any hints about the pulse dynamics or possible underlying instability mechanism.

The experiments and modelling reported here have addressed this problem for the particular case of a broadband dissipative soliton laser operating in a highly nonlinear regime. Our experiments reveal multiple ultrafast localised structures with random characteristics typical of soliton turbulence, and our simulations reveal the associated intracavity dynamics of soliton fission, Raman evolution and supercontinuum generation. The simulations predict both time-averaged and statistical properties in quantitative agreement with experiments.

From an experimental viewpoint, our results have provided a further example of the great utility of ultrafast real-time measurements in providing new insights into complex nonlinear dynamics in optical fibre systems. Although we have applied real-time characterisation to the particular case of a broadband incoherent dissipative soliton laser, these methods are general, and we expect future experiments to study similar instability mechanisms in regimes of noise-like pulse laser operation with narrower bandwidths. In particular, developing a more complete understanding of the relative importance of modulation instability and incoherent soliton fission in driving irregular cavity dynamics is likely to be an important area of future study.

Perhaps most significantly, our results suggest that for this case of broadband instability in a highly nonlinear regime, we can clarify the noise-like pulse regime as one where intracavity supercontinuum dynamics play a dominant role. This work extends our knowledge of dissipative soliton systems, and further highlights the rich dynamics of laser oscillators when operated far from a weakly-perturbative dynamical regime.

METHODS

Numerical Modelling.

Numerical simulations of laser pulse evolution used an iterative map with appropriate transfer functions for each cavity element [START_REF] Komarov | Multistability and hysteresis phenomena in passively modelocked fiber lasers[END_REF]. We write the pulse amplitude as A(z, T ) = x u(z, T ) + ŷ v(z, T ) where u(z, T ) and v(z, T ) are the field components along the two principal polarisation axes. The general propagation model for each fibre segment was based on the coupled generalised nonlinear Schrödinger equations (GNLSE) given by:

(∂ z -i∆β 0 /2 + ∆β 1 /2∂ T + iβ 2 /2∂ 2 T -β 3 /6∂ 3 T -ĝ/2)u(z, T ) = iγ(1 + i/ω 0 ∂ T ){(1 -f R ) (|u| 2 + 2/3|v| 2 )u + 1/3v 2 u * + f R u(z, T )h R (T ) * (|u(z, T )| 2 + |v(z, T )| 2 )} (1)
(∂ z + i∆β 0 /2 -∆β 1 /2∂ T + iβ 2 /2∂ 2 T -β 3 /6∂ 3 T -ĝ/2)v(z, T ) = iγ(1 + i/ω 0 ∂ T ){(1 -f R ) (|v| 2 + 2/3|u| 2 )v + 1/3u 2 v * + f R v(z, T )h R (T ) * (|u(z, T )| 2 + |v(z, T )| 2 )} (2)
Here β 2 and β 3 are the second and third-order dispersion coefficients (assumed identical for each axis), and the weak (bend-induced) birefringence in each segment is included via the parameter ∆β 0 = 2π/L B where L B is the beat length. A value of L B = 5 m was used for all segments, consistent with previous studies [START_REF] Tang | Soliton collapse and bunched noise-like pulse generation in a passively mode-locked fiber ring laser[END_REF][START_REF] Huttner | Local birefringence measurements in single-mode fibers with coherent optical frequency-domain reflectometry[END_REF][START_REF] Man | Mechanism of intrinsic wavelength tuning and sideband asymmetry in a passively mode-locked soliton fiber ring laser[END_REF]. The group index term was calculated from the approximation ∆β 1 ≈ ∆β 0 /ω 0 [START_REF] Menyuk | Nonlinear pulse propagation in birefringent optical fibers[END_REF][START_REF] Tang | Mechanism of multisoliton formation and soliton energy quantization in passively mode-locked fiber lasers[END_REF]. Jones calculus was used to model the effect of polarisationselective elements such as wave plates and the polarising beamsplitter in the bulk cavity segment.

The usual Kerr nonlinear coefficient for each segment is γ, and higher-order nonlinear effects of self-steepening and Raman scattering were also included. The Raman contribution is included via the convolution ( * ) with the response function h R (t), which was based on a realistic model for silica [START_REF] Dudley | Supercontinuum generation in photonic crystal fiber[END_REF][START_REF] Agrawal | Nonlinear Fiber Optics[END_REF]. Using a Raman fraction of f R = 0.18 yielded good agreement with experiments, and we neglected orthogonal Raman gain contributions [START_REF] Golovchenko | Unified analysis of four-photon mixing, modulational instability, and stimulated Raman scattering under various polarization conditions in fibers[END_REF]. We stress that the use of this Raman model was essential to quantitatively reproduce the long wavelength spectral broadening seen experimentally. We also note that although some previous studies have used a linear Raman approximation [START_REF] Zhao | 120 nm bandwidth noise-like pulse generation in an erbium-doped fiber laser[END_REF], this cannot accurately describe the dynamics of sub-picosecond pulses [START_REF] Erkintalo | Limitations of the linear Raman gain approximation in modeling broadband nonlinear propagation in optical fibers[END_REF].

We also stress here that the Raman fraction f R is not a fitted parameter, but rather is determined from the peak of the Raman gain profile measured in experiment [START_REF] Stolen | Raman response function of silica-core fibers[END_REF]. Although some small variation in the numerical value of the Raman fraction has been reported, the value of f R = 0.18 has been found to yield good agreement with experiments as suggested in Ref. [START_REF] Agrawal | Nonlinear Fiber Optics[END_REF].

Our modelling used fibre lengths and parameters based on the experimental cavity design.

Segment AB consists of 11 m of OFS R37003 Erbium-doped fibre (EDF) with normal dispersion The gain term ĝ(ω) is non-zero only in the EDF segment, and we model this with a Lorentzian:

β 2 = +40 × 10 -3 ps 2 m -1 ,
ĝ(ω) = 1 1 + E/E sat × g 0 1 + Ω 2 /Ω 2 g , (3)
with g 0 the unsaturated small-signal gain, E = (|u| 2 + |v| 2 )dτ the intracavity pulse energy, and E sat a gain saturation energy parameter. Ω = ω -ω 0 is the detuned angular frequency, and ω 0 is the central transition frequency (corresponding to a wavelength of 1550 nm) and Ω g is the gain (half) bandwidth (corresponding to 20 nm). Note that this approach is widely used in the modelling of EDF amplifiers [START_REF] Woodward | Dispersion engineering of mode-locked fibre lasers[END_REF][START_REF] Yarutkina | Numerical modeling of fiber lasers with long and ultra-long ring cavity[END_REF] and is justified physically because gain recovery timescales for an Erbium-doped amplifier are typically ∼100's of µs [START_REF] Desurvire | Erbium-Doped Fiber Amplifiers: Principles and Applications[END_REF], orders of magnitude slower than any of the characteristic timescales of our laser dynamics: the roundtrip time (179 ns); the noiselike pulse envelope (∼100's of ps); the ultrafast soliton substructure (∼100's of fs). We also note that because of the spectral filtering in the cavity, the bandwidth of the injected signal into the amplifier is effectively reset to ∼10 nm for every roundtrip, which is significantly less than the 40 nm FWHM of the lineshape function. Moreover, there is no appreciable nonlinear spectral broadening in the EDF such that the pulses remain at ∼10 nm bandwidth during amplification.

This means that gain-bandwidth limiting effects [START_REF] Sidorenko | Nonlinear ultrafast fiber amplifiers beyond the gain-narrowing limit[END_REF] are also negligible. Indeed, the fact that we can neglect nonlinear effects in the amplifier is another factor that allows us to focus more on the physics of the dramatic spectral broadening in the HNLF. We also note that our use of a constant distributed gain coefficient g 0 is for consistency with previous studies of similar laser systems that have shown good agreement with experiments [START_REF] Woodward | Dispersion engineering of mode-locked fibre lasers[END_REF]. In fact, we explicitly checked that for our parameter regime, the average and statistical results from simulations do not significantly depend on the longitudinal gain model used. Finally, we note that typical polarisation-dependent gain in our parameter regime is expected to be below ∼0.3 dB [START_REF] Wysocki | Polarization dependent gain in erbium-doped fiber amplifiers: computer model and approximate formulas[END_REF], which can be neglected compared to our small signal and saturated gain of 35 dB and 21 dB respectively over the 11 m EDF length.

Moreover, previous studies of polarisation-dependent gain saturation have also shown negligible effect on nonlinear dynamics in dissipative soliton lasers [START_REF] Grelu | Relative phase locking of pulses in a passively mode-locked fiber laser[END_REF].

A bulk-optics free space segment EF (length 28.1 cm) includes a nonlinear-polarisation based saturable absorber [START_REF] Hofer | Mode locking with cross-phase and self-phase modulation[END_REF][START_REF] Noske | Subpicosecond soliton pulse formation from self-mode-locked erbium fibre laser using intensity dependent polarisation rotation[END_REF], and a narrowband spectral filter to control the bandwidth of the pulses reinjected into the EDF [START_REF] Chong | Ultrafast fiber lasers based on self-similar pulse evolution: a review of current progress[END_REF]. The filter transfer function was modelled on a double supergaussian fit to the experimentally measured intensity transmission function and was given by: T (Ω ) = Numerical simulations were performed using a 1.3 ns time window and 2 18 = 262144 points such that the temporal resolution is ∼5 fs. The frequency grid corresponds to a wavelength span of ∼1019-3238 nm with a frequency resolution of 769 MHz (wavelength resolution ∼6×10 -3 nm around 1550 nm). Although computationally very demanding, this level of time and frequency resolution is necessary to span the full noise-like pulse envelope structure, as well as to capture fine structure in the temporal and spectral domains. The numerical techniques used for the solution of GNLSE-like differential equations are well-known, and examples of numerical code for this purpose are widely available [START_REF] Dudley | Supercontinuum Generation in Optical Fiber[END_REF][START_REF] Agrawal | Nonlinear Fiber Optics[END_REF].

c 1 exp(-(Ω 2 /Ω 2 1 ) m 1 ) + c 2 exp(-(Ω 2 /Ω 2 2 ) m 2 ) with coefficients c 1 = 0.7036, c 2 = 0.2944, m 1 = 1.4483, m 2 = 1.0034, Ω 1 = 4.
A particular simulation is initiated at the input to the EDF (point A in Fig. 1(a)) using a gaussian noise background in the time-domain distributed across the full 1.3 ns time window [START_REF] Liu | Revealing the behavior of soliton buildup in a mode-locked laser[END_REF][START_REF] Renninger | Pulse shaping and evolution in normal-dispersion modelocked fiber lasers[END_REF]. The seed energy (distributed between the two polarisation components) was ∼3 pJ.

Physically, laser operation would be initiated by random amplified spontaneous emission noise from the EDF, but the averaged simulation results and the computed intensity peak statistics were found to be independent of the noise source used. Typically ∼10 2 roundtrips were required for the simulations to converge to the regime with well defined mean energy, and it was only after entering this regime that statistical analysis was performed.

To compare simulations and experiments, we iteratively scanned the simulation parameter space to yield average spectral characteristics that agreed with experiment (Figure 7). This procedure yielded a small signal gain of g 0 = 0.73 m -1 and saturation energy of E sat = 3.5 nJ. For the 225 mW pump power used in our experiments, these parameters were comparable to previous similar modelling of dissipative soliton lasers [START_REF] Renninger | Pulse shaping and evolution in normal-dispersion modelocked fiber lasers[END_REF], and supported by a rate equation analysis of the EDF single pass gain characteristics [START_REF] Desurvire | Erbium-Doped Fiber Amplifiers: Principles and Applications[END_REF]. The simulations yield a mean intracavity energy (averaged over 1000 roundtrips) of 10.5 nJ at the EDF output, compared with the experimental value of 13.6 nJ. Although exact agreement would not be expected because of the approximate model of the gain lineshape function used, the overall agreement is remarkable between the mean energy, the average broadband spectrum with components spanning ∼1000 nm, and computed temporal and spectral statistics. For completeness, we give the waveplate orientations for our simulations as: (QWP1, HWP1,HWP2, QWP2) = (5.4 • , 16.2 • , 64.8 • , 27 • ) although a precise comparison with experiment is not possible here because of the unknown birefringence orientation of each particular fibre segment in the cavity.

Computation of the Spectrogram.

The simulations yield access to the amplitude and phase of the intracavity field, allowing us to calculate a frequency (or wavelength)-time spectrogram which clearly shows the intensity and phase content of the pulse in the time and frequency domains. We compute in particular the total field spectrogram S(ω, τ ) = S u (ω, τ ) + S v (ω, τ ) where the separate component spectrograms are defined by:

S k (ω, τ ) = ∞ -∞ g(T -τ ) f (T ) exp(-iωT )dT 2 (4)
with k = u, v and f (T ) representing either u(z, T ) or v(z, T ) respectively, the field components along the two principal polarisation axes. The function g(T -τ ) a variable delay gate function with delay value τ . The spectrogram trace then plots the spectra of a series of time-gated portions of the field and, especially when plotted against the associated temporal and spectral intensities, it provides a highly intuitive way to interpret the time-frequency structure of a complex field. In our calculation of the spectrogram, we used a gate function of 300 fs duration (full width at half maximum) and Gausssian profile. Note that the use of the total spectrogram over both polarisations has the clear physical interpretation that it projects naturally onto the total temporal intensity profile and total spectrum.

Based on the spectrogram, it is possible to identify the wavelength of each of the Raman-shifted localised temporal peaks in the random HNLF output field, allowing calculation of the associated soliton number using N p = [γ(ω p )P p T 2 p /|β 2 (ω p )|] 1/2 . Here γ(ω p ) and β 2 (ω p ) are respectively the nonlinearity and dispersion parameters at the Raman-shifted peak frequency ω p , and P p and T p are respectively the pulse peak power and duration. The corrected dispersion parameter is then

β 2 (ω p ) = β 2 (ω 0 )+(ω p -ω 0 ) β 3 (ω 0 )
where ω 0 corresponds to a wavelength of 1550 nm. The corrected nonlinearity parameter is then γ(ω p ) = (ω p /ω 0 )γ(ω 0 ) [START_REF] Kibler | Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area[END_REF].

Experimental Setup.

The laser system in Fig. 1 used a unidirectional cavity configuration with fibre lengths as described above. The overall laser repetition rate is 5.59 MHz (roundtrip time of ∼179 ns. The primary laser output after the HNLF (point D) used a 40% coupler, and we used a 1% coupler at point C for diagnostics and a 5% coupler in segment DE for additional spectral measurement.

The spectral filter used (Andover 155FSX-1025) had 10 nm bandwidth (FWHM) and 80% peak transmission. The EDF was co-directionally pumped at 976 nm, and noise-like pulsed behaviour was observed at all values of pump power above the 40 mW pump threshold where pulsed laser operation was first observed. In contrast to similar cavity configurations without the HNLF [START_REF] Lapre | Real-time characterization of spectral instabilities in a mode-locked fibre laser exhibiting soliton-similariton dynamics[END_REF],

we did not observe any stable mode-locked regime for any combination of cavity parameters.

With suitable adjustment of the waveplates, it was possible to observe noise-like pulse operation with broadband spectral output over a wide range of pump powers up to 500 mW. The observed spectra exhibited qualitatively similar characteristics over the full range of pump powers, although the broad temporal envelope duration (as measured with a photodiode) increased to ∼450 ps at the highest pump powers. The results reported here at a pump power of 225 mW corresponded to 13 mW average power at the primary output after the HNLF (point D). This corresponds to an intracavity energy of 7.3 nJ at the HNLF output and an energy at the EDF output of 13.6 nJ when accounting for all coupling and splicing losses between the EDF and HNLF.

Direct pulse envelope measurements used a 35 GHz photodiode (New Focus 1474 A) connected to a 20 GHz channel of a real-time oscilloscope (LeCroy 845 Zi-A, 40 GS/s). The DFT setup used 5.13 km of dispersion compensating fibre (DCF) with group velocity dispersion coefficient of D = -83.6 ps/nm/km (β 2 = +107 × 10 -3 ps 2 m -1 ) at 1550 nm. The signal under test was attenuated before injection into the DCF to ensure linear propagation. The fidelity of the DFT measurements was confirmed by comparing the DFT spectrum with that measured using an averaging OSA (Anritsu MS9710B) for a separate stable mode-locked laser operating around 1550 nm. This comparison was also performed on the average spectra measured at the HNLF input (see results in The time-lens setup was based on a commercial system (Picoluz UTM-1500) described in [START_REF] Salem | Optical time lens based on four-wave mixing on a silicon chip[END_REF],

supplemented by an additional module of dispersion compensating fibre for additional magnification. A time-dependent quadratic phase was applied on the signal after propagation step D 1 by four wave mixing in a silicon waveguide between the signal and linearly-chirped pump pulses from an integrated fibre laser module (a 100 MHz Menlo C-Fiber Sync, a P100-EDFA and a prechirping fibre D p ). The overall system magnification of ×190 was determined experimentally by using Fourier-domain pulse shaping (Finisar Waveshaper 4000 series) to create a picosecond pulse doublet with exactly 10 ps separation, and by measuring the increased temporal separation after passage through the time-lens. The magnification |M | = D 2 /D 1 is associated with total dispersion for the input and output propagation steps of: D 1 = 4.16 ps/nm and D 2 = 790.4 ps/nm. The timelens output was then recorded by a 12.5 GHz photodiode (Miteq DR-125G-A) connected to the 20 GHz channel of the real-time oscilloscope at a sampling rate of 40 Gs/s. The calculated overall time-lens resolution [START_REF] Salem | Application of space-time duality to ultrahigh-speed optical signal processing[END_REF] was 340 fs, and the demagnified time window was ∼100 ps (determined by the duration of the chirped pump pulses into the Silicon waveguide). Since the noise-like pulse envelope duration of ∼300 ps is larger than the time-lens window, we operated in asynchronous mode with free-running acquisition triggered by the arrival of the time-lens signal. To avoid low signal to noise ratio at the edges of the measurement window, all statistical analysis of the time-lens temporal peaks was performed only on the central (70 ps) region of the window.

Rogue Wave Criteria.

Based on the statistical distribution of intensity peaks in both the time and frequency domains, a significant intensity is defined as the associated mean intensity of the upper third of intensity peaks. The temporal and spectral rogue wave thresholds are defined as equal to 2.2 times this significant intensity [START_REF] Dudley | Rogue waves and analogies in optics and oceanography[END_REF].

Data availability Data are available from the corresponding author upon reasonable request.

Code availability

The GNLSE simulation code used in this manuscript is available from the

Figure 2 (

 2 Figure 2(b) provides an expanded view of the evolution in the HNLF segment CD over a 40 ps time window, together with the input and output intensity profiles. These results clearly reveal

  ) and (b) plot the temporal and spectral characteristics at the input and output of the HNLF respectively for 5 sequential roundtrips (after converging to constant mean energy.) The parameters here are the same as in Figs 2 and 3 corresponding to the 10.3 m HNLF used in experiment. These results clearly illustrate the dramatic shot-to-shot variation associated with this operating regime, and the temporal profiles in particular show the expected characteristics of the noise-like pulse regime. Specifically, the temporal profiles (shown over a 500 ps span within the 1.3 ns computation window -see Methods) clearly show the large number (∼300) of chaotic soliton peaks whose intensities vary dramatically from shot-to-shot. The spectral characteristics also show significant fluctuating fine structure. Note that for the spectral results, we also plot the mean spectrum computed over a much larger number of roundtrips (1000) to highlight the fact that these fluctuations are not at all apparent using average spectral measurements. Comparing Figs. 4(a) and (b) further highlights the extent of the HNLF spectral broadening.

Figure 6 (

 6 Figure 6(a) shows 5 typical results from the time-lens measurements, plotting the temporal profiles (after demagnification) over a 50 ps timebase. For comparison, 5 typical results from numerical simulations are also shown in Fig. 6(b), and we clearly see the strong visual similarity between the measured and simulated intensity peaks. To compare these results more quantitatively, Fig. 6(c) plots the computed probability density functions for the peak intensities computed from experiment (red) and simulation (black). These density functions were computed from a time series of 21,000 temporal peaks measured experimentally, and 135,000 peaks analysed from simulation.

  and nonlinear parameter γ = 6.0 × 10 -3 W -1 m -1 . Third-order dispersion in the EDF was neglected. Standard silica fibre Segments BC, DE, and FA were of lengths 2.87 m, 4.45 m, and 7.8 m respectively, and used SMF-28 parameters β 2 = -21.7 × 10 -3 ps 2 m -1 , β 3 = +86.0 × 10 -6 ps 3 m -1 , and nonlinear parameter γ = 1.1 × 10 -3 W -1 m -1 . Although some cavity components (such as wavelength-selective couplers) used short lengths of other silica-based fibre, this was found to have negligible effect on propagation and was not explicitly included in the modelling. The supercontinuum segment CD models propagation in 10.3 m of OFS Highly Nonlinear Fibre with β 2 = -5.23 × 10 -3 ps 2 m -1 , β 3 = +42.8 × 10 -6 ps 3 m -1 (zero dispersion wavelength of 1408 nm), and nonlinear parameter γ = 18.4 × 10 -3 W -1 m -1 . The net cavity dispersion is +0.06 ps 2 . Note that all dispersion and nonlinearity parameters above are specified at 1550 nm.

  2584 × 10 12 rad s -1 , and Ω 2 = 6.8006 × 10 12 rad s -1 . Linear losses in the cavity originate mainly from splicing and coupling and are considered at points C (0.84 dB), D (3.02 dB) and F (3.0 dB) in the simulation. The loss at point F includes the linear loss of the filter (20%).

Fig. 7 (

 7 Fig.7(b)). The real-time DFT signal was measured by a 12.5 GHz photodiode (Miteq DR-125G-A) connected to another 20 GHz channel of the real-time oscilloscope, resulting in a spectral resolution of 0.19 nm. For the results in the inset of Fig. 7(d), the broadband spectrum from the HNLF is plotted over an expanded wavelength range by combining measurements from the Anritsu MS9710BOSA below 1550 nm and the Ocean Optics NIRQuest512 spectrometer (resolution of 6.3 nm) above 1550 nm. The measured spectra were matched in the region of 1550 nm.

FIG. 1 .

 1 FIGURES

FIG. 3 .

 3 FIG. 3. Simulated single-shot spectrogram at the HNLF output. The spectrogram representation is shown together with the projected temporal intensity (top, shown on both linear and logarithmic scales) and spectrum (right). The highest temporal intensity peak from simulation (A) is shown in expanded view on a logarithmic scale (black solid line) and compared with a hyperbolic secant soliton fit (red dashed line). The Supplementary Movie shows the spectrogram evolution over one roundtrip.

FIG. 5 .FIG. 6 .

 56 FIG. 5. Photodiode characterisation results after the EDF and before injection in the HNLF. (a) Measured pulse train plotted over a 20 µs time span. (b) False colour representation of the temporal evolution of the pulse envelope over 2500 roundtrips. (c) Temporal intensity profiles at roundtrip (RT) 1, 500, 1000, 1500 and 2000.

ACKNOWLEDGEMENTS F.M, C.L, C.B, T.S., J.M.M and J.M.D.acknowledge support from the French Investissements d'Avenir programme, project ISITE-BFC (contract ANR-15-IDEX-0003) and project EUR (ANR-17-EURE-0002). G.G. acknowledges support from the Academy of Finland (Grants 318082, 333949, Flagship PREIN 320165). J.M.D. and C. F. also acknowledge project ANR-20-CE30-0004. S.K.T. acknowledges the support of the Russian Science Foundation (grant number 17-72-30006).


Marie-Liesse Pacreau

Olivier Bomme

Sonia Burrel

Dr David Boutolleau
email: david.boutolleau@aphp.fr

High conservation of varicella-zoster virus helicase-primase complex, the target of the new antiviral drug amenamevir

Keywords: Varicella-zoster virus, Helicase-primase complex, Natural polymorphism, Antiviral resistance testing

Varicella-zoster virus (VZV) resistance to current antiviral drugs, that all target the viral DNA polymerase, represents a growing concern, notably among immunocompromised patients. Amenamevir, a novel antiviral that inhibits the VZV helicase-primase (HP) complex, is approved in Japan for the treatment of herpes zoster. In this study, we describe the low natural polymorphism of VZV HP complex (interstrain identity >99.7% both at nucleotide and amino acid levels) among 44 VZV clinical isolates. This work enabled to settle the maps of natural polymorphisms of VZV HP complex and to provide the genotypic tools for the monitoring of the emergence of VZV resistance to amenamevir in patients.

Varicella-zoster virus (VZV) is a ubiquitous alphaherpesvirus that causes varicella (chickenpox), as a primary infection, and herpes zoster (shingles), as a localized reactivation [START_REF] Kennedy | Clinical features of varicella-zoster virus infection[END_REF]. VZV infections are associated with significant morbidity and mortality, especially in immunocompromised populations, due to disseminated and chronic infections [START_REF] Sauerbrei | Resistance testing of clinical varicella-zoster virus strains[END_REF].

The mainstay antiviral therapy for VZV infections over the past decades relies on nucleoside analogues that target the viral DNA polymerase (encoded by open reading frame 28 [ORF28]): acyclovir and penciclovir, and their oral prodrugs valaciclovir and famciclovir [START_REF] Andrei | Advances and perspectives in the management of varicella-zoster virus infections[END_REF][START_REF] Piret | Antiviral resistance in herpes simplex virus and varicella-zoster virus infections: diagnosis and management[END_REF][START_REF] Sauerbrei | Resistance testing of clinical varicella-zoster virus strains[END_REF]. Nucleoside analogues require phosphorylation by VZV thymidine kinase (TK, encoded by ORF36) and cellular kinases before being incorporated into the growing DNA chain by the viral DNA polymerase and inhibiting DNA replication by chain termination mechanism.

The alternative option is intravenous foscarnet that inhibits directly the viral DNA polymerase without the need of phosphorylation by viral TK. However, the therapeutic management of VZV infections may be challenged by the emergence of VZV resistance to antivirals. To date, VZV resistance to acyclovir and/or foscarnet has been reported almost exclusively in case-reports of immunocompromised patients who require prolonged or repeated therapies, such as transplant recipients and HIV-infected individuals (Mercier- [START_REF] Mercier-Darty | Utility of ultra-deep sequencing for detection of varicella-zoster virus antiviral resistance mutations[END_REF][START_REF] Piret | Antiviral resistance in herpes simplex virus and varicella-zoster virus infections: diagnosis and management[END_REF][START_REF] Sauerbrei | Resistance testing of clinical varicella-zoster virus strains[END_REF], and in rare cases of immunocompetent individuals with recurrent VZV keratitis [START_REF] Boutolleau | Emergence of varicella zoster virus resistance to acyclovir among both immunocompromised and immunocompetent individuals[END_REF][START_REF] Gueudry | Acyclovirresistant varicella-zoster virus keratitis in an immunocompetent patient[END_REF]. To our knowledge, only one published study reported a prevalence of VZV resistance to antivirals of 27% in a cohort of hematological patients with persistent VZV infection [START_REF] Van Der Beek | Persistence and antiviral resistance of varicella zoster virus in hematological patients[END_REF]. Moreover, in the National Reference Center for Herpesvirus in Pitié-Salpêtrière Hospital (Paris), we observed a prevalence of VZV resistance to antivirals of 11% during the period 2010-2018 among patients with no significant regression of clinical lesions associated with VZV infection despite antiviral treatment for at least 10 days [START_REF] Boutolleau | Emergence of varicella zoster virus resistance to acyclovir among both immunocompromised and immunocompetent individuals[END_REF]. VZV resistance to acyclovir is mostly conferred by mutations in TK and, less frequently, in DNA polymerase [START_REF] Piret | Antiviral resistance in herpes simplex virus and varicella-zoster virus infections: diagnosis and management[END_REF][START_REF] Shiraki | Emergence of varicella-zoster virus resistance to acyclovir: epidemiology, prevention, and treatment[END_REF]. Moreover, the nephrotoxicity of foscarnet may limit its use. Therefore, novel therapeutic options with novel viral targets are highly needed for the management of severe and drug-resistant VZV infections. The VZV helicase-primase (HP) complex constitutes a promising target for novel antiviral agents inhibiting DNA replication. This heterotrimeric complex consists of 2 essential proteins, ORF55 helicase and ORF6 primase, interacting with ORF52 accessory protein, which are well conserved among Herpesviridae [START_REF] Klinedinst | Helicase-primase complex of herpes simplex virus type 1: a mutation in the UL52 subunit abolishes primase activity[END_REF][START_REF] Ligat | Identification of amino acids essential for viral replication in the HCMV helicase-primase complex[END_REF]. The VZV HP complex possesses multiple enzymatic activities that are essential for DNA replication and viral growth: DNA helicase and single-stranded DNA-dependent ATPase localized within ORF55 helicase, and primase localized within ORF6 primase [START_REF] Chono | ASP2151, a novel helicase-primase inhibitor, possesses antiviral activity against varicellazoster virus and herpes simplex virus types 1 and 2[END_REF]. HP inhibitors (HPIs) represent a breakthrough in the development of anti-herpesvirus agents. Conversely to classical antivirals, they do not target the viral DNA polymerase and do not need activation by the viral TK: they inhibit directly the viral HP complex and, therefore, remain active against viruses that are resistant to acyclovir and/or foscarnet [START_REF] Andrei | Advances and perspectives in the management of varicella-zoster virus infections[END_REF][START_REF] Shiraki | Emergence of varicella-zoster virus resistance to acyclovir: epidemiology, prevention, and treatment[END_REF]. The oxadiazolephenyl derivative amenamevir (ASP2151) is an HPI that possesses antiviral activity against not only herpes simplex viruses 1 and 2 (HSV-1 and HSV-2) but also VZV, setting it apart from pritelivir (AIC316) which inhibits only HSV replication and demonstrated clinical efficacy in patients with genital herpes [START_REF] Chono | ASP2151, a novel helicase-primase inhibitor, possesses antiviral activity against varicellazoster virus and herpes simplex virus types 1 and 2[END_REF][START_REF] Wald | Effect of Pritelivir compared with valacyclovir on genital HSV-2 shedding in patients with frequent recurrences[END_REF]. Additionally, amenamevir is active against acyclovir-resistant VZV in vitro [START_REF] Chono | ASP2151, a novel helicase-primase inhibitor, possesses antiviral activity against varicellazoster virus and herpes simplex virus types 1 and 2[END_REF]. Amenamevir appeared to be effective and well tolerated in the treatment of herpes zoster in immunocompetent patients in a randomized, double-blind, valaciclovir controlled phase 3 study and was therefore approved in Japan in September 2017 [START_REF] Kawashima | Amenamevir, a novel helicase-primase inhibitor, for treatment of herpes zoster: A randomized, double-blind, valaciclovir-controlled phase 3 study[END_REF]. To date, one single mutation conferring resistance to amenamevir has been identified in VZV ORF55 helicase [START_REF] Chono | ASP2151, a novel helicase-primase inhibitor, possesses antiviral activity against varicellazoster virus and herpes simplex virus types 1 and 2[END_REF]. Moreover, poor is known regarding the natural polymorphism of VZV HP complex. In this context, the aims of this work were to develop novel techniques for the sequencing of VZV HP complex of 44 VZV clinical isolates and one VZV laboratory strain to investigate the genetic variability and to provide a precise map of VZV HP complex natural polymorphism in order to facilitate the interpretation of VZV genotypic resistance testing toward amenamevir.

The present study included the analysis of the VZV laboratory strain Ellen (ATCC-VR-1367) and 44 VZV clinical isolates recovered in cell culture from mucocutaneous swabs during the period 2012-2019, as previously described [START_REF] Perrier | Complementary assays for monitoring susceptibility of varicella-zoster virus resistance to antivirals[END_REF]. Clinical samples were collected from 44 unrelated patients (21 males, 23 females, median age, 57 years) experiencing VZV infection (varicella, n = 4; herpes zoster, n = 38; unspecified, n = 2). Patients were mainly immunocompromised: solid organ transplantation (n = 7), hematopoietic stem cell transplantation (n = 5), solid cancer (n = 4), hemopathy (n = 2), HIV infection (n = 3), auto-immune disease (n = 10), unknown immune status (n = 13). None of the patients received prior amenamevir therapy. Novel methods were developed for the amplification and sequencing of VZV ORF55 and ORF6 according to previously described procedures [START_REF] Collot | High conservation of herpes simplex virus UL5/UL52 helicase-primase complex in the era of new antiviral therapies[END_REF][START_REF] Perrier | Complementary assays for monitoring susceptibility of varicella-zoster virus resistance to antivirals[END_REF]. Briefly, VZV DNA extraction was performed using the MagNA Pure Compact Instrument (Roche Diagnostics, Meylan, France). The full-length ORF55 (2646 base pairs [bp]) and ORF6 (3252 bp) were amplified by nested PCR using the proofreading enzyme Expand High Fidelity (Roche Diagnostics). Thereafter, amplification products were sequenced by Sanger method using 4 overlapping primer pairs and analyzed with the automated capillary sequencer ABI 3730XL DNA Analyzer (Applied Biosystems) (Table 1). All nucleotide and amino acid sequences obtained were compared with that of VZV reference strain Dumas with GenBank accession number X04370 [START_REF] Davidson | The complete DNA sequence of varicella-zoster virus[END_REF]) using SeqScape v2.5 software (Applied Biosystems). All VZV ORF55 and ORF6 sequences determined in this study have been deposited in the GenBank database under accession numbers MZ152705 through MZ152790.

Our results showed a very low natural polymorphism of VZV HP complex. At the nucleotide level, the interstrain identity of ORF55 and ORF6 ranged from 99.8% to 100% among the 44 clinical isolates and the laboratory strain Ellen investigated (Table 2). In comparison with Dumas reference sequences, 23 and 21 nucleotide substitutions were identified within ORF55 and ORF6, respectively, corresponding to a total number of nucleotide substitutions per strain ranging from 0 to 6 within both genes. The majority (>61%) of those nucleotide substitutions were silent. At the amino acid level, the interstrain identity of VZV HP complex ranged from 99.7% to 100%. Five and 8 different amino acid changes were identified in ORF55 helicase and ORF6 primase, respectively, corresponding to 0.57% and 0.74% of the total codons of the proteins. Each VZV strain harbored 0 to 2 amino acid changes in ORF55 helicase and 0 to 3 in ORF6 primase (Table 2). Overall, the frequency of those amino acid changes related to natural polymorphism of VZV HP complex ranged from 2.2% to 22.2% (Table 3). The most frequent changes were K616R (17.8%) in ORF55 helicase and G496V and H575Q (22.2%) in ORF6 primase. All natural polymorphisms described in this study were evenly distributed alongside VZV helicase and primase, and all but one of them were located outside conserved domains of the proteins. Thus, A1053T change, identified only in the laboratory strain Ellen, was located in the conserved zinc finger motif. The new data obtained in this work together with the data reported so far in the literature enabled to provide the maps of natural polymorphisms of VZV ORF55 helicase and ORF6 primase (Fig. 1) [START_REF] Chono | ASP2151, a novel helicase-primase inhibitor, possesses antiviral activity against varicellazoster virus and herpes simplex virus types 1 and 2[END_REF][START_REF] Tyler | Genomic cartography of varicella-zoster virus: A complete genome-based analysis of strain variability with implications for attenuation and phenotypic differences[END_REF].

The emergence of VZV resistance to standard antiviral drugs, especially acyclovir, represents a growing concern, notably among immunocompromised patients [START_REF] Piret | Antiviral resistance in herpes simplex virus and varicella-zoster virus infections: diagnosis and management[END_REF][START_REF] Sauerbrei | Resistance testing of clinical varicella-zoster virus strains[END_REF]van der Beek et al., 2012), but also in some rare cases of immunocompetent patients with recurrent VZV keratitis [START_REF] Boutolleau | Emergence of varicella zoster virus resistance to acyclovir among both immunocompromised and immunocompetent individuals[END_REF][START_REF] Gueudry | Acyclovirresistant varicella-zoster virus keratitis in an immunocompetent patient[END_REF]. For those patients and other vulnerable ones with severe VZV infections, HPIs, alone or in combination, constitute an alternative possibility of therapeutic management. In the present study, we developed novel techniques for the sequencing of VZV full-length ORF55 helicase and ORF6 primase. Those techniques will be useful for the rapid VZV genotypic resistance testing to HPIs, since molecular approach significantly shortens the time for the detection of drug resistance in a clinically relevant time frame [START_REF] Burrel | Genotypic characterization of UL23 thymidine kinase and UL30 DNA polymerase of clinical isolates of herpes simplex virus: natural polymorphism and mutations associated with resistance to antivirals[END_REF]. This work enabled to describe extensively the natural polymorphism of VZV HP complex in the era of HPIs. Despite the lack of phenotypic test of VZV isolates towards amenamevir, the mutations identified in the present study are most certainly natural polymorphisms since (i) they were detected in VZV clinical isolates recovered from patients with no prior amenamevir therapy and (ii) they were not located within or downstream motif IV of the helicase, where almost all mutations conferring HSV resistance to HPIs have been previously identified [START_REF] Collot | High conservation of herpes simplex virus UL5/UL52 helicase-primase complex in the era of new antiviral therapies[END_REF][START_REF] Sato | Characteristics of helicase-primase inhibitor amenamevir resistant herpes simplex virus[END_REF]. Moreover, some authors showed that minor pre-existing HPI resistant mutations could be detected in HSV-1 clinical isolates at a frequency of 10 -4 to 10 -5 plaque forming units (pfu), but those isolates remained susceptible to pritelivir [START_REF] Biswas | Detection of HSV-1 variants highly resistant to the helicaseprimase inhibitor BAY 57-1293 at high frequency in 2 of 10 recent clinical isolates of HSV-1[END_REF][START_REF] Sukla | Mismatch primer-based PCR reveals that helicase-primase inhibitor resistance mutations pre-exist in herpes simplex virus type 1 clinical isoaltes and are not induced during incubation with the inhibitor[END_REF]. However, it is noteworthy that those low-frequency mutations cannot be detected by the Sanger method used in the present study. Our results obtained from the VZV laboratory strain Ellen and 44 VZV clinical isolates demonstrated a very low natural polymorphism of VZV HP complex. Thus, the interstrain identity was >99.7% at the nucleotide and the amino acid levels for both helicase and primase. This high conservation of VZV HP complex is similar to the high conservation (>99%) that we have previously reported for other viral targets of anti-VZV drugs (ORF36 TK and ORF28 DNA polymerase), and anti-HSV drugs (UL23 TK and UL30 DNA polymerase; UL5 helicase and UL52 primase) [START_REF] Burrel | Genotypic characterization of UL23 thymidine kinase and UL30 DNA polymerase of clinical isolates of herpes simplex virus: natural polymorphism and mutations associated with resistance to antivirals[END_REF][START_REF] Collot | High conservation of herpes simplex virus UL5/UL52 helicase-primase complex in the era of new antiviral therapies[END_REF][START_REF] Perrier | Complementary assays for monitoring susceptibility of varicella-zoster virus resistance to antivirals[END_REF]. These results are also in accordance with the overall nucleotide identity of >99.7% obtained by the comparison of 18 complete VZV genomes [START_REF] Tyler | Genomic cartography of varicella-zoster virus: A complete genome-based analysis of strain variability with implications for attenuation and phenotypic differences[END_REF]. Among all herpesviruses, VZV is known to display the lowest nucleotide variation within its genome, estimated at 0.05-0.06% [START_REF] Quinlivan | Molecular studies of varicella zoster virus[END_REF].

In this study, we identified 5 and 8 amino acid changes related to natural polymorphism in VZV helicase and primase, respectively, corresponding to 0.57% and 0.74% of the total codons of the proteins. Only 3 of them, namely K316R in ORF55 helicase, and G496V and H575Q in ORF6 primase, were detected with a frequency over 15%; each of the 9 other polymorphisms was detected in a single VZV strain.

Few previous studies reported natural polymorphisms of VZV HP complex: Tyler et al. performed the genomic cartography of 18 complete VZV genomes and Chono et al. sequenced the helicase and primase subunits from an amenamevir-resistant VZV strain [START_REF] Chono | ASP2151, a novel helicase-primase inhibitor, possesses antiviral activity against varicellazoster virus and herpes simplex virus types 1 and 2[END_REF][START_REF] Tyler | Genomic cartography of varicella-zoster virus: A complete genome-based analysis of strain variability with implications for attenuation and phenotypic differences[END_REF]. In this study, all 5 amino acid changes identified in the ORF55 helicase were described for the first time, and 2 out of the 8 amino acid changes identified in the ORF6 primase, G496V and H575Q, were previously reported in a VZV strain from Canada [START_REF] Tyler | Genomic cartography of varicella-zoster virus: A complete genome-based analysis of strain variability with implications for attenuation and phenotypic differences[END_REF]. The present data together with previous ones enabled to provide the maps of natural polymorphisms of VZV ORF55 helicase and ORF6 primase [START_REF] Chono | ASP2151, a novel helicase-primase inhibitor, possesses antiviral activity against varicellazoster virus and herpes simplex virus types 1 and 2[END_REF][START_REF] Tyler | Genomic cartography of varicella-zoster virus: A complete genome-based analysis of strain variability with implications for attenuation and phenotypic differences[END_REF] (Fig. 1). All but one (20/21) were located outside the conserved motifs of the viral enzymes previously defined [START_REF] Ligat | Identification of amino acids essential for viral replication in the HCMV helicase-primase complex[END_REF][START_REF] Klinedinst | Helicase-primase complex of herpes simplex virus type 1: a mutation in the UL52 subunit abolishes primase activity[END_REF]. The remaining change A1053T, which was detected only in the laboratory strain Ellen, was located in the conserved zinc finger motif of ORF6 primase. However, this polymorphism does not concern the 4 conserved residues involved in the formation of the zinc finger motif [START_REF] Ligat | Identification of amino acids essential for viral replication in the HCMV helicase-primase complex[END_REF].

The use of HPIs in medical practice, a novel class of anti-herpesvirus agents with a different mechanism of action from classical anti-herpesvirus agents used so far, should significantly improve the therapeutic management of HSV and VZV infections. First, HPIs will permit the treatment of infections due to viruses that are resistant to acyclovir and/or foscarnet [START_REF] Andrei | Advances and perspectives in the management of varicella-zoster virus infections[END_REF][START_REF] Shiraki | Emergence of varicella-zoster virus resistance to acyclovir: epidemiology, prevention, and treatment[END_REF]. Moreover, multidrug combination therapies will now be possible. Thus, the combination of HPIs with the nucleoside analogues acyclovir and penciclovir showed a synergistic antiviral effect against HSV and VZV in vitro [START_REF] Chono | Synergistic activity of amenamevir (ASP2151) with nucleoside analogs against herpes simplex virus types 1 and 2 and varicella-zoster virus[END_REF]. Therefore, combination therapies may constitute a potential approach for treating severe, sometimes life-threatening, diseases due to HSV or VZV, such as encephalitis or infections in immunocompromised patients.

To date, no emergence of HSV or VZV resistance to HPIs has been detected in patients treated with those novel drugs. All mutations conferring resistance to HPIs described so far have been selected in cell culture through serial passages of virus in presence of HPIs. For HSV, resistance mutations are mainly located immediately downstream of motif IV of UL5 helicase, but few mutations have also been identified in UL52 primase [START_REF] Collot | High conservation of herpes simplex virus UL5/UL52 helicase-primase complex in the era of new antiviral therapies[END_REF][START_REF] Sato | Characteristics of helicase-primase inhibitor amenamevir resistant herpes simplex virus[END_REF]. For VZV, only one mutation conferring resistance to amenamevir has been identified [START_REF] Chono | ASP2151, a novel helicase-primase inhibitor, possesses antiviral activity against varicellazoster virus and herpes simplex virus types 1 and 2[END_REF]. After the selection of a VZV resistant mutant in cell culture in the presence of increasing concentrations of amenamevir, sequence analysis identified the N336K change in ORF55 helicase of VZV, corresponding to the N342K change in UL5 helicase of HSV-1 that was previously shown to confer resistance to amenamevir [START_REF] Biswas | A mutation in helicase motif IV of herpes simplex virus type 1 UL5 that results in reduced growth in vitro and lower virulence in a murine infection model is related to the predicted helicase structure[END_REF].

Further in vitro studies are needed to extend the catalog of VZV resistance mutations to amenamevir In conclusion, this work enabled to settle a valuable baseline of VZV ORF55 helicase and ORF6 primase natural polymorphisms. The novel genotypic techniques developed will be useful for the monitoring of the emergence of VZV resistance to amenamevir and potential other antiviral compounds that inhibit VZV HP complex in patients included in clinical trials or treated in medical practice.

Table 1

Primers used for amplification and sequencing of VZV full-length ORF55 helicase and ORF6 primase. Frequency per strain (median) 0 -2 (0) 0 -3 (0)

Variation of the total codons (%) 0.57 0.74 (A) ORF55 helicase is a 881-amino-acid protein. The 6 conserved motifs (I to VI) are represented by the grey boxes with the positions (codon numbers) indicated below [START_REF] Ligat | Identification of amino acids essential for viral replication in the HCMV helicase-primase complex[END_REF]. All amino acid positions related to natural polymorphism reported so far in the literature are indicated: those described in this study are underlined, those reported by [START_REF] Tyler | Genomic cartography of varicella-zoster virus: A complete genome-based analysis of strain variability with implications for attenuation and phenotypic differences[END_REF] are represented with an *, and the one reported by [START_REF] Chono | ASP2151, a novel helicase-primase inhibitor, possesses antiviral activity against varicellazoster virus and herpes simplex virus types 1 and 2[END_REF] in an amenamevir-resistant VZV strain is indicated in italic.

The amino acid change conferring resistance to amenamevir described by [START_REF] Chono | ASP2151, a novel helicase-primase inhibitor, possesses antiviral activity against varicellazoster virus and herpes simplex virus types 1 and 2[END_REF] is in bold.

(B) ORF6 primase is a 1083-amino-acid protein. The 5 conserved motifs (I to V) and the DxD and zinc finger motifs are represented by the grey and the black boxes, respectively, with the positions (codon numbers) indicated below [START_REF] Ligat | Identification of amino acids essential for viral replication in the HCMV helicase-primase complex[END_REF][START_REF] Klinedinst | Helicase-primase complex of herpes simplex virus type 1: a mutation in the UL52 subunit abolishes primase activity[END_REF]. All amino acid positions related to natural polymorphism reported so far in the literature are indicated: those described in this study are underlined, those reported by [START_REF] Tyler | Genomic cartography of varicella-zoster virus: A complete genome-based analysis of strain variability with implications for attenuation and phenotypic differences[END_REF] are represented with an *, and the one reported by [START_REF] Chono | ASP2151, a novel helicase-primase inhibitor, possesses antiviral activity against varicellazoster virus and herpes simplex virus types 1 and 2[END_REF] in an amenamevir-resistant VZV strain is indicated in italic.

Fig. 1 .

 1 Fig. 1. Polymorphism map of VZV helicase-primase complex.

Figure legends Fig. 1 .

 legends1 Figure legends

Table 2

 2 Variations of VZV helicase-primase complex, both at nucleotide and amino acid levels, among 44 clinical isolates and the laboratory strain Ellen (ATCC-VR-1367) in comparison with reference strain Dumas (GenBank accession number X04370).

	Parameter	ORF55 helicase	ORF6 primase
	Nucleotide identity (%)	99.85 -100	99.82 -100
	Nucleotide mutations (no.)	23	21
	Strains with nucleotide mutations (%)	17 (37.78)	31 (68.89)
	Frequency per strain (median)	0 -6 (0)	0 -6 (1)
	Silent mutations (%)	17 (73.91)	13 (61.91)
	Amino acid identity (%)	99.77 -100	99.72 -100
	Amino acid changes (no.)	5	8

Table 3

 3 Frequencies of amino acid changes related to natural polymorphism of VZV ORF55 helicase and ORF6 primase identified in this study in comparison with reference strain Dumas (GenBank accession number X04370).

		Amino acid changes	No. of VZV strains (%)
		A227T	1 (2.2)
		R527Q	1 (2.2)
	ORF55 helicase	N593M	1 (2.2)
		K616R	8 (17.8)
		T825A	1 (2.2)
		I139V	1 (2.2)
		M161L	1 (2.2)
		C280R	1 (2.2)
		G496V	10 (22.2)
	ORF6 primase
		T518A	1 (2.2)
		H575Q	10 (22.2)
		A894T	1 (2.2)
		A1053T	1 (2.2)

Acknowledgements

This work was supported in part by the Association pour la Recherche sur les Infections Virales (ARIV).