# Customizing supercontinuum generation via on-chip adaptive temporal pulse-splitting

## Abstract

Modern optical systems increasingly rely on complex physical processes that require accessible control to meet target performance characteristics. In particular, advanced light sources, sought for, for example, imaging and metrology, are based on nonlinear optical dynamics whose output properties must often finely match application requirements. However, in these systems, the availability of control parameters (e.g., the optical field shape, as well as propagation medium properties) and the means to adjust them in a versatile manner are usually limited. Moreover, numerically finding the optimal parameter set for such complex dynamics is typically computationally intractable. Here, we use an actively controlled photonic chip to prepare and manipulate patterns of femtosecond optical pulses that give access to an enhanced parameter space in the framework of supercontinuum generation. Taking advantage of machine learning concepts, we exploit this tunable access and experimentally demonstrate the customization of nonlinear interactions for tailoring supercontinuum properties.

## Introduction

Complexity is a key characteristic of numerous physical systems, ranging from self-organisation to network access. Based on nonlinear or chaotic dynamics, and relying on a large number of parameters usually difficult to access, these complex systems have an ever-growing impact on our everyday life1. In photonics, numerous systems fall within this category where, for instance, the development of advanced optical sources2,3,4 is of tremendous importance for applications ranging from imaging to metrology5,6,7. A relevant example of this problem is the generation of a supercontinuum (SC)8, a broadband spectrum produced by an optical pulse propagating in a medium under the combined actions of dispersion, nonlinearities, and scattering effects9,10. In fibre-based systems, its underlying formation mechanisms are now well-understood and described within the framework of a modified nonlinear Schrödinger equation3. Significant work recently focused on studying broadening effects triggered by modulation instability processes11, initiated by long (i.e. sup-picosecond, >1 ps) pulses. In this case, the propagation dynamics are widely influenced by noise effects, ultimately resulting in incoherent output spectra12,13. However, many applications, including advanced metrology and imaging, today rely on coherent supercontinua8, where reproducible and controllable features are particularly required6,7. Specifically, for e.g. fluorescence imaging, pump-probe measurement techniques, spectroscopy, as well as coherence tomography, versatile control of both spectral and temporal SC properties is essential7,14,15,16,17. Yet, reproducible SC generation typically requires ultrashort (i.e. sub-picosecond, <1 ps) pulses8, where the means for controlling the propagation dynamics in a reconfigurable manner are limited10,18 (i.e. control is constrained by the design of the initial pulse condition and the properties of the propagating medium19,20,21). Therefore, in spite of numerous, rigorous studies of this regime, the optimization of coherent SC continues to be an experimental challenge14,15,22,23.

Specifically, the properties of single pulses deterministically seeding the generation of coherent supercontinua can be tuned over different degrees of freedom using state-of-the-art techniques (via e.g. pulse shaping, polarization control, or acousto/electro-optic modulation)10,17,18,23,24,25,26,27,28,29. However, these approaches typically rely on external devices that present fundamental limitations in the sub-picosecond regime, on top of being affected by complexity, bulkiness, and costs. More importantly, these techniques only allow for the control of very few single degrees of freedom (e.g. a single pulse’s duration, shape, or power), restricting the available nonlinear dynamics to intra-pulse effects such as soliton deterministic ejection and frequency shifts3,30, thus ultimately hampering the ability to optimize the overall system output.

In contrast, using more than one pulse to seed SC generation not only allows the excitation of multiple independent (intra-pulse) dynamics, but also leads to a richer variety of effects arising from the interaction of different components, i.e. inter-pulse effects such as multi-pulse soliton ejections, dispersive wave radiations, spectral superposition, steering, and collisions3,30,31,32,33,34. Yet, initial efforts towards this direction32,33,35,36,37,38 have only partially unleashed the potential of this concept. Recent approaches have been limited to the use of long (sup-picosecond) incoherent seeds, or to mutually-coherent pulses with very restricted control over their number and properties. Consequently, the full extent of SC control via multi-pulse seeding has yet to be achieved.

In this article, we demonstrate a method to drastically enhance the control parameter space for the tailoring of nonlinear interactions in guided fibre propagation and achieved SC generation with highly controllable properties. Using the length scales and stability available with integrated photonics39, custom sets of multiple and mutually-coherent ultrashort optical pulses (with low, 1 ps minimal separation) are prepared using optical pulse-splitting on a photonic chip, also enabling the adjustment of their individual properties (e.g. power, shape, chirp). The size of the control parameter space (i.e. over 1036 unique parameter combinations for 256 pulses) makes traditional experimental approaches, based on trial-and-error or exhaustive parameter sweeps, impossible. However, using machine learning concepts, in a similar fashion to approaches demonstrated in a variety of adaptive control scenarios24,40,41,42,43, we are able to optimize different pulse patterns and experimentally obtain the desired SC outputs. Specifically, we measure the spectral output and employ a genetic algorithm (GA)44,45 to modify the integrated pulse-splitter settings in order to optimize the nonlinear fibre propagation dynamics towards a selected SC criterion (for instance, maximizing the spectral intensity at one or more targeted wavelengths). The results of this proof-of-concept demonstration exhibit versatile control of the output spectra, allowing us to experimentally achieve a seven-fold increase of the targeted SC spectral density when compared to a single pulse excitation with the same power budget. Additionally, we numerically show the potential of this technique, not only for spectral shaping, but also towards the full temporal control of SC generation.

## Results

### Single-wavelength optimization

In order to illustrate the versatility of our scheme for controlling nonlinear pulse propagation, we first demonstrated the enhancement of the power density at a single wavelength of the SC. For this, we limit our study to two cases. As a reference, we used the simplified case of a SC spectrum generated by a single pulse with adjustable power (Fig. 3a). Here, spectral broadening was mediated by the radiation of multiple solitons and dispersive waves, which subsequently experienced Raman self-frequency shifts9,30. For comparison, our second case used multiple excitation pulses (prepared using the integrated splitter), possessing the same power budget as in the single pulse study (50 mW), but with input parameters refined via genetic algorithm optimization (see Methods).

We found that, for target wavelengths across the SC bandwidth, the use of multiple pulses enabled 20–700% spectral density enhancement relative to the reference (see Fig. 3b, c). Examples of optimized spectra for three particular target wavelengths are shown in Fig. 3d–f and illustrate how the resulting spectra can vary significantly for a similar input power but drastically different pulse configurations (see insets). Note that, in this work, we restricted our study to a limited number of pulse seeds (either 16 or 32 pulses in the pattern instead of the 256 maximally-achievable with the chip). Nevertheless, in the propagation regime studied (where SC spectral broadening above 2000 nm is intrinsically limited by fibre losses), the use of such a subset of the available parameter space is sufficient to exhibit notable spectral enhancement while ensuring fast convergence in the optimization process (see Methods and Supplementary Fig. 4, for discussion). As expected, the use of 32 pulse seeds was found to outperform the use of 16 pulse seeds (see Fig. 3c). In this regime, such expected behaviour can be explained by the potential of multiple pulse seeds to judiciously condition the spectral steering and, ultimately, the superposition of independently generated spectral components (see Supplementary Fig. 2). It is foreseen that for other applications and target SC outputs, a greater number of pulses, and consequently larger parameter spaces, will enable even better performances.

### Dual-wavelength optimization

Remarkably, the ability to generate multiple pulses with specific delays and properties further enables the control and optimization of typically complex and interdependent dynamics. This feature is illustrated in Fig. 4, where simultaneous enhancement of the power density at two distinct SC wavelengths can be obtained with our scheme (see Methods). Here, we specifically targeted cases where both wavelength intensities were equivalent (see Methods), but further tunability is accessible depending on the exact optimization criteria used for the algorithm (see Supplementary Discussion and Supplementary Fig. 5). Indeed, arbitrary optimization criteria can be implemented44, in stark contrast to what can be obtained with a single pulse seed. Spectral broadening mediated by soliton radiation is highly deterministic and typically leads to strong spectral correlation in the resulting SC3,31,32,47. In our case however, multiple pulse excitation can seed both independent dynamics and customized nonlinear interaction. This, alone, manifests a powerful example of how our integrated system, along with the implementation of machine learning concepts, can be efficiently used to tailor complex nonlinear processes without extensive system design.

Additionally, our approach has the potential of controlling the SC temporal properties, which we confirmed by numerical simulations using a shorter fibre propagation length (in order to ensure reliable and reasonably fast computation of the pulse propagation dynamics—see Methods for details). In particular, by assuming a 200 fs pulse (2 kW peak power), which was randomly split into a train of 64 pulses by our integrated device and propagated through a 50 m-long HNLF, we show how solitons, radiating from the excitation pulses, can individually experience different Raman self-frequency shifts and temporal walk-offs leading to collisions, steering and the generation of novel frequency components14,32,33 (see Fig. 5a). Overall, such an enhanced parameter space can ultimately drive different propagation scenarios and thus provide a high degree of reconfigurability in terms of SC properties (see Supplementary Fig. 2 for different examples of propagation dynamics). Indeed, depending on the initial conditions, highly variable yet coherent SC output spectra3 can be obtained (Fig. 5b), with the additional possibility for selecting the delay and order with which specific spectral components emerge from the fibre (see Fig. 5c)14.

Continuous control of the relative delay between two spectral components can thus be obtained over a large temporal window of ±40 ps (Fig. 5d—see Methods). This ability, obtained by exploiting the multiple pulses of the system, provides a higher flexibility and tuning range with respect to conventional shaping techniques applied to a single pulse (see Fig. 5d and Methods for details)10,17,18,22,26,28. In particular, when considering the propagation regime studied here, single pulse seeding always leads to the formation of soliton(s) and associated dispersive waves, the temporal walk-off of which is intrinsically related to their wavelength (i.e. the most red-shifted solitons will typically exhibit a larger delay due to Raman scattering8,9). In this framework, even conventional shaping techniques are inherently limited to slightly adjusting the absolute value of the relative delays between different spectral components (see Fig. 5d). On the other hand, the use of multiple pulse seeding has shown that versatile temporal control between two (or eventually more) pulses at arbitrary wavelengths of the output spectrum can be obtained. This additional temporal tunability, typically required e.g. in advanced imaging systems14,16,17, will complement the experimentally-demonstrated spectral shaping, and is expected to be further enhanced (e.g., by activating additional interferometers and thus exponentially expanding the accessible parameter space).

## Discussion

We demonstrate how adjustable, integrated path-routing can be used to access a wide and controllable optical parameter space. In combination with the use of genetic algorithms (GAs), we showed the generation of supercontinua with broadly reconfigurable characteristics. Most importantly, this is achieved with the same power budget, meaning no additional amplification was used, and therefore the benefits of pulse splitting far exceed the drawbacks due to the additional optical loss of the integrated device. In particular, the improvements provided by the additional degrees of freedom in the multi-pulse excitation regime can condition the interleaving, superposition, and nonlinear interaction between multiple phase-locked pulses, which in turn significantly expands the controllable SC properties by allowing the customization of both their spectral and temporal power distribution. Besides this demonstration in the telecom range, our approach could be extended to other typical laser wavelengths (e.g. 800 or 1064 nm) and/or fibre designs. Using for instance an optical source to seed a fibre with a judiciously chosen dispersion profile (in order to circumvent the loss-induced spectral broadening limitations observed in the current HNLF), coherent and reconfigurable octave spanning SC generation is expected to be readily obtained with our proposed systems. Similarly, the nonlinear fibre used in our experiments for SC generation could be shortened or readily integrated on a photonic chip46,48,49, thus providing a compact and stable system for the deployment of advanced optical functionalities (such as on-chip f-2f interferometry based on coherent SC50). In this context, we foresee this approach as an invaluable tool for the development of novel optical sources for, e.g. state-of-the-art imaging and metrology applications requiring both spectral and temporal tunability (e.g. pump-probe measurement techniques, hyperspectral imaging, or various schemes for coherent control)4,5,6,7,8,14,16,34.

Additionally, it is worth underlining that we restricted our attention to the use of sub-picosecond pulses (<1 ps) in order to avoid temporal overlap between adjacent excitation pulses during propagation in our integrated system. Yet, the design of a pulse-splitter with shorter relative delays or, equivalently, the use of longer pulses is also expected to unlock novel features in SC adaptive control (via e.g. coherent temporal synthesis39 and tailored pulse superposition31,33), especially within the framework of fundamental studies associated with extreme event formation11,13,35,38. Similarly, such an approach is thus expected to allow the optimal exploitation of complex optical systems without a priori knowledge of their dynamics. This may include applications related to advanced nonlinear signal processing51, the control of frequency comb emission4,5,22, as well as of laser mode-locking2. In turn, this can pave the way towards the next generation of self-adjusting lasers40,52 and ‘smart’ integrated optical systems.

## Methods

### Integrated pulse-splitter

The on-chip photonic pulse-splitter was formed by cascading N = 9 balanced interferometers and M = 8 delay lines based on integrated optical waveguides (see Fig. 2), where the associated delays varied according to the relation ΔτM = 2ΔτM-1. The device was fabricated from a CMOS-compatible, high-refractive index silica glass (Hydex) produced by chemical vapour deposition without the need for high-temperature annealing46. Patterning was done using UV photolithography and reactive ion etching. This material platform is featured by a refractive index of n = 1.7, along with very low linear (0.06 dB cm–1) and negligible nonlinear optical losses (no nonlinear losses measured up to 25 GW cm–2). The waveguide dimensions allowed for single mode TE and TM propagation at telecom wavelengths, where the dispersion and nonlinear properties were similar to those reported in Ref.46, as verified by means of optical vector analyser measurements (Luna OVA 5000). At the central wavelength of the pulses used in our experiments (i.e. λ = 1550 nm) and for the selected polarization, we estimated the waveguide dispersion to be extremely low (β2 = −2.87 ps2 km−1and β3 = −0.0224 ps3 km−1), yet the effective nonlinearity to be significantly high (γ = 233 W−1 km−1).

The input and output bus waveguides featured mode converters and were pigtailed to 1.2 m fibre patchcords (SMF-28) on each side, resulting in coupling losses of 1.4 dB per facet. The total propagation length in the sample varies between 5 and 9.5 cm and depends on the selected paths inside the structure. Overall, the total losses in our pulse-splitter were measured to be between 3.10 and 3.36 dB at 1550 nm, depending on the optical path (including the attenuation from the mode converters and pigtails).

Gold electrodes were deposited on each arm of the nine balanced interferometers (the last is dedicated to the output splitting and pulse recombination but does not introduce any delay), in order to induce a local and variable thermal modification on the adjacent optical waveguide. Such a modification was controlled electronically (see below) to produce a phase difference ΔφN between the two arms of the interferometer (where N is the interferometer number in the sample). For each of the eight interferometers, the waveguide thermal control allowed for a tunable switching of the optical output beam path between the short and the long arm of the following delay line (thus inducing a path difference equivalent to a delay ΔτM). The two output waveguides from such elements were then fed into the two input waveguides of the subsequent balanced interferometer. Via these cascaded blocks, it is possible to generate up to 2M optical pulses with adjustable powers and temporal separation (multiples of Δτ1). We note that in our integrated pulse-splitter, the minimal delay was Δτ1 = 1 ps, and the maximal delay was Δτ8 = 128 ps so that we were able to generate up to 256 pulse replicas with adjustable individual powers and tunable temporal separation (multiples of 1 ps) over the range 1–255 ps. We also note that the photonic chip supports bidirectional optical propagation and can also be used by inverting the input and output ports, as illustrated in Fig. 2a (thus leading to a propagation where the associated delays in the chip decrease according to the relation ΔτM = 0.5 ΔτM-1).

The splitting ratio of the interferometers was computer controlled, via a push-pull architecture implemented by custom computer-controlled driving electronics, used to apply up to the 5.0 ± 0.2 V voltage swing required to completely switch the beam path from one interferometer output to the other. The splitting ratio characterization was carried out by measuring the optical power at each interferometer and we found, for each element, an extinction ratio above 16 dB (i.e. a cross-talk below 2.5%). From both electronic and optical characterizations, we estimated that the splitting ratio can be modified with a resolution of 0.01% (assuming a wavelength independent response) via ~32,000 voltage control levels per interferometer over the voltage range required for a complete path switching. For the overall sample, this corresponds to more than 1036 different setting configurations (i.e. combinations) that can be employed for the versatile generation of multiple pulse replicas. The wavelength dependence of the interferometer splitting ratio was characterized using a tunable CW laser (Tunics-Plus). Over the range 1525–1575 nm (i.e. the bandwidth of the pulses used in our experiments), we found only negligible differences in the measured splitting ratio (i.e. maximal ± 3%) and overall losses (~0.2 dB discrepancies in the worst-case scenario, when propagating along a single waveguide path).

Finally, the response time of the system was estimated by switching one (or several) interferometer splitting ratios within the sample, and temporally resolving the subsequent SC spectral modification induced after propagation in the HNLF. This was done using a fast spectrometer (see Methods below), which was also used to ensure the long-term stability and excellent repeatability of the pulse-splitter device. For one interferometer, the switching settling time (to reach thermal equilibrium) for the maximal voltage swing, was estimated to be below 100 ms, including the overall lag time of the computer, driving electronics, and detection system (~30 ms overall). Using simultaneous switching of five interferometers, we observed slightly longer settling times that were attributed to thermal cross-talk between adjacent interferometers, as well as longer update times of the sequential commands sent to the electronic drivers (~160 ms). An overall 500 ms settling time was estimated to be sufficient for capturing the main spectral modifications in the experiments performed here while ensuring excellent repeatability. This was confirmed, in case of the optimization routine, by choosing an extremely conservative 3 s settling time, yielding equivalent results to those obtained using a 500 ms settling time.

### Experimental SC generation and control

The fibre laser used in our experiments (Menlo C-Fiber) generated femtosecond pulses at a 250 MHz repetition rate. The initial spectrum, measured with an optical spectrum analyser (OSA), was centred at 1550 nm with a 52 nm bandwidth (full width at half maximum—FWHM). After suitable dispersion management and temporal recompression, the pulse was sent into our integrated pulse-splitter, allowing for the preparation of multiple pulses. The optical pulse had an estimated ~ 200 fs duration (FWHM) and peak power of 300 W when entering the photonic sample. Subsequently, the optical output of the sample (i.e. the set of prepared sub-picosecond pulses) was amplified to the desired power level by using a short length (1.6 m) erbium-doped fibre amplifier (EDFA) before being injected into 1 km of HNLF. At this wavelength, the fibre operates in the anomalous dispersion regime, yet close to the zero-dispersion wavelength (ZDW = 1545 nm, see HNLF parameters below). After propagation in the HNLF, the broadband SC was characterized using a fast spectrum analyser (Avantes—AvaSpec NIR512) allowing measurements over a 954–2580 nm window with a resolution of ~3.5 nm. The spectral intensity(ies) at the wavelength(s) of interest were extracted from these measurements for each iteration and then used to implement the optimization criterion for the GA (see Methods below and Supplementary Discussion). The measurements of the fast spectrum analyser were also performed over the range 600–1750 nm using the OSA (ANDO AQ6317B), thus allowing for consistency verification with improved resolution. Measurements of the initial conditions were carried out at the input of the HNLF: Pulse spectral and temporal diagnostics were done with the OSA as well as with a custom intensity autocorrelator and frequency-resolved optical gating setup (FROG)53.

Temporal broadening of the sub-picosecond optical pulses was controlled via careful dispersion management throughout the setup until injection into the HNLF. Specifically, we used a combination of single mode fibre (SMF-28) and dispersion compensating fibre (DCF-38 from Thorlabs) with patchcords of specifically chosen lengths to (i) minimize the initial chirp of the pulse emitted from the fibre laser, (ii) temporally recompress the pulse (while limiting nonlinear effects) before injection into the integrated splitter, as well as, (iii) maintain the pulse temporal spreading to a minimum during and after propagation in the sample. This configuration, based on controlled dispersion management and subsequent amplification after pulse-splitting, allows obtaining ~ 200 fs pulses both at the HNLF input and throughout propagation in the photonic chip waveguides (thus avoiding temporal overlap between the adjacent prepared pulses) while limiting the overall distortions induced via nonlinear effects before injection into the HNLF.

For the reference experiment using only a single pulse, the pulse-splitter was set with all splitting ratios to their minimal values (so that only one pulse follows the shortest possible waveguide path), while the EDFA current was tuned to linearly sweep the average power with 425 incremental steps over the range 0.1–50 mW. Note that we used an additional optical attenuator before the HNLF for measuring SC output spectra with input average powers below 2.5 mW (i.e. the EDFA amplification threshold). The best result within this ensemble of 425 output spectra—with respect to the desired optimization criterion—was used as reference for comparing the results obtained via multiple pulse optimization.

For these experiments, we set the EDFA current to the maximal value used previously (i.e. leading to 50 mW average output power after amplification). In this case, the relative powers of the pulses were directly controlled by modifying each delay interferometer splitting ratio (as well as the output interferometer, for regulating the overall power).

### GA parameters

For the experiments presented, we made use of an optimization process based on a GA implemented directly from the Matlab dedicated function which was employed to adjust the integrated pulse-splitter parameters via driving electronics controlled through a USB connection. Note that no other tuning parameters were used and all other experimental settings were kept constant. For assessing the optimization criteria, we used the spectral intensity measured at one (or two) wavelength(s) in the SC. For the reported experiments, the GA was configured to enhance the discrete spectral intensity at a selected wavelength (i.e. single-objective function—as seen in Fig. 3) or both spectral intensities at two selected wavelengths (i.e. multiple-objective function—as seen in Fig. 4). In the latter case, the optimization process yields a so-called Pareto front (or frontier)44, corresponding to the optimum set of parameters leading to the best trade-offs between the optimization criteria. Note that in Fig. 4, we only illustrate the case where both spectral intensities at the selected wavelength of interest are similar. A detailed analysis of the Pareto front clearly indicates that more sophisticated optimization processes can readily be achieved (e.g. allowing to select the ratio between the spectral intensity at the desired wavelengths—see Supplementary Fig. 5 for additional details). This, in turn, leads to more versatile output properties.

For proof of principle demonstrations, we kept the parameters of the GA function to their default values and selected a crossover of 50%, i.e. the ratio of ‘genes’ (the voltage of a single interferometer) from each ‘individual’ (set of all voltages for the interferometer array) carried from one ‘generation’ to the next44,45. The number of individuals populating each generation (i.e. each iteration step of the GA) was adjusted depending on the number of genes for each individual (i.e. the number of actively-controlled interferometers).

In addition, the maximal number of generations was limited in order to achieve a meaningful optimization towards the targeted SC output in a reasonable time frame (~1 h for each optimization process). Specifically, for five active interferometers (i.e. for generating 16 pulses), we constrained our algorithm to 15 generations with 500 individuals. Correspondingly, when 6 interferometers were actively adjusted (i.e. for 32 pulses), we expanded the population size to 1,000 individuals in order to obtain a better sampling of the initial parameter space (i.e. one additional gene per individual), while reducing the number of generations to 10. Note that, with such a limited number of generations, a systematic convergence (in the strict mathematical definition) of the GA might not be fully reached. However, we obtained a consistent improvement in the desired SC properties even using this limited number of iterations. Such optimization has been carefully verified for various sets of GA parameters (as well as for various settling times—i.e. the time between setting the system and taking the measurement, see Supplementary Fig. 4 and Supplementary Discussion), and was also observed in additional tests for more complex optimization objectives.

### Numerical simulations of nonlinear pulse propagation

Our numerical simulations used a split-step Fourier method to solve the generalized nonlinear Schrödinger equation (GNLSE)3,8 for modelling the pulse evolution in both the on-chip photonic pulse-splitter and the HNLF:

$${\frac{{\partial A}}{{\partial z}} + \frac{\alpha }{2}A - \mathop {\sum}\limits_{k \ge 2} {\frac{{i^{k + 1}}}{{k!}}} \beta _k\frac{{\partial ^kA}}{{\partial T^k}} = i\gamma \left( {1 + i\tau _{{\mathrm{shock}}}\frac{\partial }{{\partial T}}} \right)\left( {A\left( {z,T} \right){\int}_{ - \infty }^{ + \infty } {R\left( {T\prime } \right)} \left| {A\left( {z,T - T\prime } \right)} \right|^2\mathrm{d}T\prime } \right)}$$
(1)

Here A(z, T) is the pulse envelope (in W−1/2), evolving in a comoving frame at the envelope group velocity β1−1, so that T = t − β1z. The model includes higher-order dispersion (shown on the left-hand side of the equation) and nonlinearity (on the right-hand side), as well as the presence of loss α and initial broadband noise (i.e. one photon with random phase per spectral mode)9,10. The overall nonlinearity is represented by a nonlinear coefficient γ and includes the self-steepening effect (through a shock timescale τshock = 1/ω0 = 0.823 fs). The nonlinear response function R(T′) = (1−fR)δ(T′) + fRhR(T′) encompasses both an instantaneous Kerr effect and a delayed Raman contribution hR(T′), the weight of which is given by fR = 0.18.

For the HNLF, we used the parameters retrieved from the manufacturer datasheet (OFS Fitel—HNLF ZDW1546): At a central wavelength of 1550 nm, the nonlinear parameter is γ = 11.3 W−1 km−1, the dispersion is slightly anomalous with β2 = −0.102 ps2 km−1, β3 = 0.0278 ps3 km−1 and β4 = 4.0 × 10−5 ps4 km−1 and the linear losses are 0.99 dB km−1.

For simulations of the on-chip photonic pulse-splitter, we modelled the pulse evolution through each waveguide element using a split-step method. This included the dual waveguide system with balanced and unbalanced interferometric structures and associated beam splitter transfer functions. The splitting ratio of the MZI structures, allowing for tuning the pulse path and creating delayed pulse replicas, was modelled by adding a tunable phase offset on one arm of the respective balanced interferometer. The parameters of the waveguides at 1550 nm, assuming a pure TM polarization, were taken as β2 = −2.87 ps2 km−1 and β3 = −0.0224 ps3 km−1, with a nonlinear parameter γ = 233 W−1 km−1 and linear losses of 0.06 dB cm–1 (see above and ref. 46).

For the cases shown in Fig. 1, we simulated the evolution of a transform-limited Gaussian pulse of 200 fs duration (FWHM) with a peak power of 1 kW directly injected into 10 m of HNLF with the properties shown above (Fig. 1a), or split into four pulses with different peak powers and 1 ps separation (Fig. 1b). Note that the same individual properties and overall input energy was used for both cases. The corresponding spectrograms were constructed using a 50 fs hyperbolic-secant gate function10,53.

For the proof-of-concept simulations illustrated in Fig. 5, we considered a simple case where the integrated pulse-splitter was directly connected to 50 m of HNLF, with coupling losses of 1.4 dB per chip facet. At the input of the pulse-splitter, we injected a transform-limited Gaussian pulse of 200 fs duration (FWHM) with a peak power of 2 kW (i.e. the typical values associated with a fibre laser producing such pulses at 10 MHz repetition rate and 4 mW average output power). For this analysis, we carried out 10,000 simulations randomly varying the splitting ratio of 6 (+1 output) interferometers (such as to produce 64 pulses with 1 ps separation and adjustable powers). The extraction of each soliton/pulse properties at the HNLF output (see Fig. 5c) was carried out using a spectral filter with a 50 nm bandwidth (FWHM) around the wavelengths of interest. Subsequent analysis of the pulse relative delay at the HNLF output (see Fig. 5d) was obtained by discarding the filtered pulses with a peak power below 20 W (i.e. below 1% of the initial pulse peak power). For this diagram, we post-selected cases where only one pulse was obtained at each wavelength (after filtering) within the ensemble of 10,000 simulations.

The coherence analysis of the supercontinua was carried out by fixing the splitting ratio used in our model and performing 20 stochastic numerical simulations with random noise seeds (i.e. adding one photon with random phase per spectral mode). The degree of spectral coherence |g(1)12 (λ, 0)| was thus retrieved as the mean value for the modulus of the degree of first-order coherence calculated at each wavelength λ over this ensemble of 20 simulations, which we found to be a sufficient number for a meaningful estimation of the SC coherence36. <g> was computed as the mean spectral coherence over the 20 dB SC spectral bandwidth. Note that the coherence value mentioned in Fig. 5 was then obtained by repeating this procedure for 50 different pulse-splitter settings and then averaging the results.

Compared to a single input pulse with adjustable properties, the use of multiple and controllable pulses leads to enhanced tunability in the SC properties, which is illustrated in Fig. 5d. For this comparison, we repeated the previous set of 10,000 stochastic simulations replacing our integrated pulse-splitter by an arbitrary pulse shaper25. In particular, we modelled the random variation of the pulse properties by first modifying its peak power P0 and temporal profile asymmetry ε. The pulse envelope A(T) was constructed from two half-Gaussians with different widths being respectively $$T_{\mathrm{0}}^ \pm = \left( {1 \pm \varepsilon } \right)T_{\mathrm{0}}$$. These half-Gaussians were added so that their maxima overlap, forming a pulse of duration T0 = 200 fs (FWHM) with variable trailing/leading edge steepness. We then added a random quadratic and cubic spectral phase of the form $$\exp \left( {i\eta \nu ^2 + i\kappa \nu ^3} \right)$$ on top of the pulse spectrum $$\tilde A(\nu )$$, before finally implementing an additional nonlinear phase shift, i.e. a self-phase modulation with random and tunable nonlinearity of the form $${\mathrm{exp}}\left( {i\varphi _{{\mathrm{NL}}}\left| A \right|^2/P_{\mathrm{0}}} \right)$$. Each of these parameters was randomly changed for 10,000 different realizations, and uniformly distributed over the ranges:P0 = [0 2] kW; ε = [−0.5 0.5]; η = [−0.5 0.5] ps2; κ = [−0.05 0.05] ps3; φNL = [−3π 3π]. Although not exhaustive, such adjustable properties are typical of common optical processing systems (e.g. extra fibre length, pulse spectral shaping, etc.) and allow for a direct comparison with our pulse-splitter-based simulations, as the typical SC output bandwidths and coherence degrees remained quantitatively similar for such pulse durations3. Note that the SC filtering, processing, and post-selection described above remained otherwise unchanged.

In order to verify the overall validity of the dynamics observed in our experiments, we also performed simulations of the evolution of a single pulse directly injected into 1 km of HNLF with variable input powers (see Supplementary Fig. 1). In this case, numerical simulations were carried out for propagation in the HNLF only, using the input conditions measured at the HNLF input from spectral (OSA) and temporal (autocorrelator/FROG) experimental characterization.

## Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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## Acknowledgements

We gratefully acknowledge the experimental support of Robin Helsten for the sample packaging and control. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through the Steacie, Strategic, Discovery and Acceleration Grants Schemes, by the MESI PSR-SIIRI Initiative in Quebec, by the Canada Research Chair Program and by the Australian Research Council Discovery Projects scheme (DP100000104327). This project has also received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme Grant agreement no 725046. B.W. acknowledges the support from the People Programme (Marie Curie Actions) of the European Union’s FP7 Programme under REA grant agreement INCIPIT (PIOF-GA-2013-625466). M.K. acknowledges funding from the European Union’s Horizon 2020 Research and Innovation programme under the Marie Sklodowska-Curie grant agreement number 656607. P.R. and C.R. acknowledge the support of NSERC Vanier Canada Graduate Scholarships. B.E.L. acknowledges support from the Strategic Priority Research Program of the Chinese Academy of Sciences (grant number XDB24030300). A.P. and M.P. acknowledge additional support by the Engineering and Physical Sciences Research Council (EPSRC) (EP/M013294/1); MC REA (630833,327627); EU-H2020. R.M. acknowledges additional support by the Government of the Russian Federation through the ITMO Fellowship and Professorship Program (grant 074-U 01) and from the 1000 Talents Sichuan Program.

## Author information

Authors

### Contributions

B.W. developed the idea and the experimental setup. B.W., M.K., C.R., P.R., P.L.G. and M.R. performed the experiments and analysed the experimental results. B.W. and M.K. performed the numerical studies. B.E.L. and S.T.C. designed and fabricated the integrated device. A.P., M.P., E.A.V. and D.J.M. contributed to discussions. R.M. supervised and coordinated the project. All authors contributed to the writing of the manuscript.

### Corresponding authors

Correspondence to Benjamin Wetzel or Roberto Morandotti.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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Wetzel, B., Kues, M., Roztocki, P. et al. Customizing supercontinuum generation via on-chip adaptive temporal pulse-splitting. Nat Commun 9, 4884 (2018). https://doi.org/10.1038/s41467-018-07141-w

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