Introduction

The discovery of optical frequency combs in the late 1990s by Hall and Hänsch1 has since contributed to widespread technological developments in fundamental and applied research areas, in both classical2,3,4,5,6,7 and quantum domains8,9,10,11. Unlike traditional schemes for comb generation that require bulky and expensive systems12,13,14, microcombs, produced in optical microcavities2,15,16,17, (e.g., microdisks, microring resonators (MRRs), or photonic crystals), represent a stable and compact alternative. Microcombs arise by exploiting the nonlinear interactions of the injected optical field with the material composing their structure. Such nonlinear optical processes, including optical parametric conversion18,19,20,21,22,23, are mediated by the strong modal confinement due to the reduced dimensions of the waveguide and can thus produce a broad spectrum with high conversion efficiency15,17. This aspect makes them suitable for a variety of out-of-the-lab applications, such as for light detection and ranging (LIDAR)24, chip-scale atomic clocks25, portable sensors26, as well as for application towards photonic artificial intelligence-assisted data processing4,27,28, enabling new smart applications for the Internet of Things and the forthcoming industry 4.0 revolution29.

In the domain of microcomb-based telecommunication, microcombs have been applied, e.g., as optical filters30 and for on-chip wavelength division multiplexing enabling high-capacity data transmission17,31,32,33. Spectral instability and uneven power distribution in the comb lines decrease the communication performance, resulting in degraded signal quality and reduced efficiency, which affects data transfer rates and available bandwidth34. Therefore, precise control of the microcomb’s spectral envelope is required to comply with the performance demands of such applications.

Different solutions to this hurdle have been proposed, including  active or passive schemes. For example, frequency stabilization, involving external reference lasers and phase-lock loops18, multipumping schemes35, electro-optical modulation36, or self-injection locking37, have been developed to tailor and stabilize the microcomb features. Passive frequency stabilization, including detuning scanning35 and filter-driven four-wave mixing6,38, also represents a valid alternative to control the output frequency of the microcomb. However, these advanced techniques still encounter several challenges.

Achieving and maintaining the desired output characteristics of the microcomb requires the attainment of the appropriate dynamical regime that allows their stable formation, in turn necessitating precise control over the set of accessible experimental parameters, which can be demanding due to the nonlinear behavior of the MRRs39. Thus, a smart, efficient, and reliable approach that can autonomously search for and locate the optimal parameters to obtain microcombs with the targeted features is highly needed. This task represents a global optimization problem40, which can generally be tackled with different regularization techniques41, as well as with more advanced smart optimization algorithms, such as gradient descent, particle swarm optimization42, or genetic algorithms (GAs)43, among others.

GAs are a class of metaheuristic optimization algorithms inspired by the principles of natural selection and evolution investigated in  biology44. They have been employed in diverse multiparameter global optimization problems across different areas of physics and engineering, including parameter estimation45, image reconstruction46, and tomography47. In recent years, GAs have shown immense potential in the domain of smart photonics, particularly for inverse design problems relating to the development of new photonic systems and devices with optimized operation, such as the microcomb-to-geometry inverse design of microcavities48,49,50,51 and photonic crystals design with engineered dispersion52. They have also been applied towards experimental optimization, such as for increasing the conversion efficiency of dispersive wave generation53. In contrast to conventional gradient-based optimization algorithms41, GAs are highly effective in problems where the model that describes the system dynamics is nonlinear or unknown, yielding a parameter space that exhibits multiple local minima and even discontinuities, for which gradient-based approaches often fail. As such, they have been demonstrably useful for problems that arise in smart photonics applications, where targeting specific operating regimes is paramount, yet the quality and stability of solutions are dependent on a complex multi-dimensional space of cavity parameters, such as on-chip pulse tailoring42, soliton54, and supercontinuum optimization55,56, as well as extremum seeking for laser mode-locking57,58,59 and self-driving lasers60.

In this work, we propose a smart scheme for autonomous and optimized control of microcomb regimes in an integrated MRR to tailor the cavity output. Using microcomb features such as line spacing, intensity envelope, and intracavity power as targets, we employ GAs to find the optimal set of experimental parameters corresponding to the desired intracavity dynamics controlling microcomb formation. We generate a wide range of microcombs corresponding to distinct dynamical regimes through simple modification of the GA, including modulation instability (MI)15,61 and soliton crystal (SC) regimes4,62, in turn demonstrating the reconfigurability of our scheme.

Results

Principle of operation

The experimental setup used for microcomb generation and tailoring is shown in Fig. 1a. A continuous-wave laser (CWL) serves as the optical source and is coupled to a temperature-controlled integrated MRR (doped silica glass waveguide with a free spectral range (FSR) of 48.9 GHz63, see Methods section). The optical output signals are collected at the drop port, using an optical spectrum analyzer (OSA) and a power meter (PM).

Fig. 1: Smart microcomb generation scheme.
figure 1

a Experimental setup for microcomb generation and tailoring in a microresonator. CWL continuous-wave laser, EDFA erbium-doped fiber amplifier, FPC fiber polarization controller, MRR microring resonator, PD photodiode, PM power meter, OSA optical spectrum analyzer, PC personal computer. CWL, EDFA, OSA, and PM are controlled remotely and interfaced with the genetic algorithm (GA) to set the experimental parameters. b Operation scheme to implement our GA for microcomb generation. The highlighted steps are applied iteratively for all individuals of the population in the Equipment Control phase and for all selected individuals of the Population Formation phase.

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The CWL output intensity is boosted with an erbium-doped fiber amplifier (EDFA) to pump the MRR around the center frequency of 193.4 THz, which triggers Kerr microcombs through cascaded degenerate four-wave mixing processes64. When the intracavity power is sufficiently high, mode-crossing between orthogonal modes from different families emerges due to geometrical imperfections and high field confinement as we detune the pump with respect to the center frequency, allowing different degenerate modes to exchange energy15. This, in turn, leads to broadband microcombs, whose spectra can fill the entire telecom C-band64. However, to trigger this mechanism, a simultaneous fine-tuning of several setup parameters is required to control such nonlinear processes. To this end, we implement a scheme interfacing the setup components with a genetic algorithm (GA), which controls the laser scan parameters and optimizes the output, as represented in Fig. 1b.

The parameters defining the properties of the microcombs are contained in a vector \({{{{{{\bf{P}}}}}}}_{i}^{n}\), which is referred to as an i-th individual of the n-th generation in the GA formulation. A set of S individuals comprises a population Xn at a given step n of the evolution, with their respective parameters, \({p}_{{ij}}\), also referred to as genes:

$${{{{{{\boldsymbol{X}}}}}}}^{n}=\left[\begin{array}{c}{{{{{{\boldsymbol{P}}}}}}}_{1}^{n}\left({p}_{11},{p}_{12},{p}_{13},{p}_{14},{p}_{15}\right)\\ {{{{{{\boldsymbol{P}}}}}}}_{2}^{n}\left({p}_{21},{p}_{22},{p}_{23},{p}_{24},{p}_{25}\right)\\ \vdots \\ {{{{{{\boldsymbol{P}}}}}}}_{S}^{n}\left({p}_{S1},{p}_{S2},{p}_{S3},{p}_{S4},{p}_{S5}\right)\end{array}\right]\,$$
(1)

In our case, there are five genes corresponding to tunable parameters of the setup, comprising the center frequency of the pump, ω0, frequency span of the sweep, Δω0, sweep step size, dω, and dwell time, dt, as well as the EDFA current setting I.

After initializing the algorithm, the boxed steps shown in Fig. 1b are applied iteratively for each individual in the population: the parameters are passed on to the experimental setup to initiate the comb generation, and the corresponding MRR output is collected in the form of the optical spectrum and power trace. The output is then passed on to the fitness evaluation phase, where it is assigned a score according to its proximity to the target microcomb shape. The fitness function F assigns a score to the candidate individuals, which we define as a weighted sum of our microcomb shape-related objectives fi

$$F={\sum }_{i}^{N}{f}_{i}{w}_{i},$$
(2)

in which each fi is a metric measuring the discrepancy between the MRR output and the individual target microcomb features (see Methods section). The choice of  the weight values wi to be used in Eq. (2) is empirically found and made once, prior to running the algorithm.

Once the fitness of every individual in the population Xn is evaluated in step n of the GA, a subset of the best individuals is selected to compose a new population Xn+1 in the next step n+1. Each individual in the new population contains parameters chosen from a pair of these (best-selected) individuals, through crossover C and mutation M, operations forming what is known as offspring according to the GA formulation40. The operator C uniformly mixes the genes from two selected individuals, \({{{{{{\bf{P}}}}}}}_{l}^{n}\) and \({{{{{{\bf{P}}}}}}}_{m}^{n}\), following a uniform probability distribution D∈[0,1]. The mutation operator M then introduces a probability that any one (or more) of these genes would change to a random value within the gene boundaries. The two operators respectively act according to:

$${{{{{\boldsymbol{C}}}}}}{\left({{{{{{\boldsymbol{P}}}}}}}_{l}^{n},{{{{{{\boldsymbol{P}}}}}}}_{m}^{n}\right)}_{k}={\bar{p}}_{{kj}}^{n+1}=\left\{\begin{array}{c}{p}_{{lj}}^{n}\\ {p}_{{mj}}^{n}\end{array}\begin{array}{c}\,{if}\,\begin{array}{c}{D}_{j}\le 0.5\\ {D}_{j} \, > \, 0.5\end{array}\end{array}\,l,m=1\cdots S ; \,j=1\cdots 5,{with}\,l \, \ne \, m\right.,$$
(3)
$${{{{{\boldsymbol{M}}}}}}{\left({\bar{{{{{{\boldsymbol{P}}}}}}}}_{k}^{n+1}\right)}_{k}={p}_{{kj}}^{n+1}=\left\{\begin{array}{c}{p}_{j}^{* }\,\\ {\bar{p}}_{{ij}}^{n+1}\end{array}\,{if}\,\begin{array}{c}{r}_{j}\le \, {M}_{r}\\ {r}_{j} \, > \, {M}_{r}\end{array}\right.i=1\cdots S ; \, j=1\cdots 5$$
(4)

in which \({\bar{p}}_{{kj}}^{n+1}\) is the j-th gene of the k-th offspring generated from crossover operation prior to mutation, while \({p}_{{kj}}^{n+1}\) is the gene after mutation. rk is a uniformly distributed random number, while Mr is the mutation rate. The random values \({p}_{j}^{* }\) are, in turn, selected from a uniform distribution, whose lower and upper limits are given by the gene boundaries (see the subsection “Genetic algorithm parameters” in the Methods Section for more details).

These two operations allow the parameter space to be explored beyond the current population such that, over many iterations, the algorithm can access different dynamical regimes for microcomb formation by trying various combinations of laser frequency scan settings and intracavity power. We also implement an elitism mechanism, in which the best-performing individual in a population is retained as-is to the next generation.

The process of collecting and evaluating the MRR output is repeated for every individual of the new population until the defined stopping criteria is reached. In our implementation, the algorithm stops after no improvement in the fitness score is observed for ten consecutive generations, indicating that the algorithm has converged to a minimum of the fitness function.

Targeting microcombs

We apply our scheme to target different microcomb spectral envelopes corresponding to different regimes, such as primary combs, MI microcombs, and dissipative Kerr solitons, including SCs. Fig. 2 shows the performance of the GA: Fig. 2a reports the convergence plots for three such GA realizations with different targets, depicting the best and average fitness score per generation as the algorithm progresses, while Fig. 2b–d display the corresponding microcomb shapes at each of the points of improvement in the convergence plots. We note that the number of iterations required to obtain the target spectrum depends on the microcomb state; however, in the realizations we report here, we achieved convergence after around 20 generations.

Fig. 2: Convergence of the genetic algorithm towards target microcomb.
figure 2

a Convergence plots for three separate realizations of the genetic algorithm (GA) that show the fitness score improvement as the generation number increases, eventually converging to better values. Dotted lines depict the average fitness score corresponding to each realization of the GA, while solid lines represent the best score within each generation. The line colors—blue, green, and purple—correspond to the microcombs displayed in b–d, respectively. b–d Spectral output at the labeled points of each convergence plot. Each drop in the convergence plots in a shows a progress in refining the output microcombs (b–d), enabling us to observe the improvement in intermediate microcomb states, as we approach the desired target. The GA realization corresponding to c was initiated with a better gene pool compared to b and d. Hence, the corresponding average fitness plot in a achieves overall lower values compared to the others.

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In the case corresponding to Fig. 2b, we set the line spacing of the target microcomb to the MRR’s fundamental FSR (48.9 GHz) and the spectral envelope to an absolute sinusoidal shape, obtaining primary and secondary comb line formation. The latter process can be associated with the presence of cavity multi-solitons as it has been widely demonstrated62,65,66,67,68. The other two realizations of the GA reported in the convergence plot correspond to target microcombs defined by a line spacing of ~150 GHz (3 FSR) in Fig. 2c, resembling a MI microcomb, and a line spacing of 48.9 GHz in Fig. 2d, with minimized intensity variations among its frequency lines and the signature step in intracavity power, corresponding to SC formation4,62.

As shown in Fig. 2, the fitness scores are initially higher, corresponding to off-resonance laser scan parameters. All three realizations exhibit a significant drop in the convergence plot occurring around generation 5, reflecting the fact that the worst genes in the initial population are quickly ‘bred out’, since better genes have a higher probability of being selected. With continued evolution, the algorithm traverses the landscape of the parameter space with successive iterations, yielding a better score, resulting in the general descending trend in Fig. 2a. For the case represented by the blue line, corresponding to the microcomb in Fig. 2b, the convergence plot shows a flat region after the initial drop, where the algorithm is converging to a local minimum. Around generation 17, however, mutations have introduced enough variation in the individuals’ parameters to locate a better solution corresponding to a lower minimum, as evident in the second more significant drop in the convergence plot. The corresponding traces at each point I-VI in Fig. 2b illustrate the GA’s findings during this search: II is when more comb lines first start to appear, yielding a substantial improvement in the line spacing requirement, hence the large drop in the convergence plot. Point III, then, is the first sign of more complex dynamics as seen in the spectral envelope, with the line spacing reaching the 48.9 GHz target, reflecting the drop in the convergence plot. However, such a state is unstable, as the asymmetric shape shows. Minor improvements with respect to stability and envelope are achieved between III and V as seen in Fig. 2a, until at point VI the desired sinusoidal spectral envelope shape is achieved, leading to the final drop in the convergence plot. This is reflected in the quality of the spectrum shown in Fig. 2b. Fitness evaluation is detailed in the Methods section.

Similarly, we can visually track the progression of the GA for the other two realizations. For the case corresponding to Fig. 2c, the associated (green) plot in 2 (a) converges in fewer generations, as only a single objective is defined in the fitness function: a target line spacing of ~150 GHz. In Fig. 2d we search for a SC with the characteristic flat spectrum shape reported in the literature4,5. We target such a state by requiring a line spacing of 48.9 GHz (MRR FSR), a criterion to minimize intensity variations of the comb lines, in addition to the characteristic SC step in the transmitted power trace. The evolution of the optical trace along the corresponding convergence plot shows that the GA quickly locates a microcomb that satisfies the line spacing criterion, then fine-tuning takes place, decreasing the intensity variations to +/− 3 dBm in the C-band. The flat spectrum is achieved by imposing a large weight on the intensity variation criterion in the fitness function, as represented by the marked drop between II and III in the convergence plot.

Following this principle for which the algorithm can converge to better solutions over generations, our GA can explore a rich landscape of different dynamical regimes for microcomb formation. Figure 3 shows a gallery of different microcomb states achieved using our implementation of the GA by simply redefining the objectives fi in the fitness function (Eq. 2) to describe the target microcomb in terms of its line spacing, spectral envelope, and average intracavity power. Table 1 shows the parameters found by the GA to yield the corresponding subfigures shown in Fig. 3. The spectral traces determined by the algorithm, as in Fig. 3, illustrate its ability to target distinct line spacings (as in Fig. 3a, e), flatter spectra (as in Fig. 3b, with intensity variation +/− 3 dBm in the C-band), as well as explicit spectral envelope definitions (as in Fig. 3c, d, and f), for the generation of distinct microcombs with over 10 THz bandwidth, spanning the entire C-band.

Fig. 3: Customization of various microcomb regimes.
figure 3

Gallery of microcombs achieved via the genetic algorithm (GA) by setting constraints on line spacing and spectral envelope: Targeting, a a line spacing of ~150 GHz (=3 FSR), b a line spacing of 48.9 GHz (=1 FSR) and minimized intensity variance (+/− 3 dBm), and c–f a line spacing of 48.9 GHz and desired spectral envelopes (solid red lines). The variety of microcombs achieved demonstrates the GA’s ability to search for and locate optimal spectral features as specified by the objectives.

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Table 1 Parameter list for microcomb tailoring reported in Fig. 3
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Figure 4 shows each individual’s fitness score as a function of detuning and laser sweep speed in a single GA run. We calculate the laser sweep speed and detuning from the parameters of each individual, that is, dω and dt for the former, ω0 and Δω0 for the latter. Each plot in Fig. 4a–c corresponds to a different objective in the fitness function, measuring proximity to target line spacing, spectral envelope, and intracavity power, respectively. Fig. 4d shows the weighted sum, that is, the fitness landscape of the parameter space as measured by the fitness function of Eq. (2). This resultant fitness landscape exhibits better contrast between regimes that would otherwise yield similar fitness scores when measured via a single objective, as can be seen when comparing Fig. 4a–c with Fig. 4d. For example, Fig. 4a and b exhibit two regions of similar quality fitness (indicated in the figure with arrows, with a score closer to zero) for two adjacent resonances. Without measuring the power trace (Fig. 4c), the algorithm would incorrectly assume that those two regions yield microcomb states with the same target features (implied by Fig. 4a and b), which would in turn skew the convergence of the algorithm towards sub-optimal solutions. Thus, formulating the fitness function in terms of multiple objectives is imperative to set our GA’s ability to interpret and, hence, search for and correctly locate, the target microcomb. The sparsity of the plots in Fig. 4 is due to the GA’s exploration of the parameter space being concentrated around the best-performing regions, rather than exhaustively searching the entire space.

Fig. 4: Fitness scores for the collected genetic algorithm iterations.
figure 4

a–c Scores of individual objectives fi in the fitness function described in Eq. (2), represented by the scattered plots. d Overall fitness function scores comprising the weighted sum of a–c. The axes are detuning from the microring resonator cold resonance and laser scan speed, calculated from the experimental parameters of each individual: ω0 and Δω0 for the former, dω and dt for the latter. The arrows indicate the regions of optimized solutions (lower score). The color bars of the scattered plots indicate the corresponding objective function score a–c and compound fitness value d.

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We note that the microcomb states accessible by our algorithm are exclusively defined by the fabrication and design properties of the MRR itself (e.g., the dispersion profile of the material, the geometry, etc.). Thus, our GA approach does not alter any of these properties during its application. Rather, it enables intelligent and user-friendly location of the optimal experimental parameters required to access the dynamical regimes allowed by the MRR. For example, one may consider the parameters of the laser frequency scan. Frequency scanning of the pump laser has been established as a method to achieve stable phase-locked states in microcavities that exhibit Kerr and thermal nonlinearities15. As the pump is tuned into a MRR resonance, the Kerr effect introduces an intensity-dependent contribution to the refractive index, which induces the resonances to drift. At the same time, the strong intensity of the pump field leads to thermo-optical effects, causing the resonator to heat up. This, in turn, produces variations in the temperature-dependent refractive index and alters the optical path length, contributing to the overall drift of resonances15. In such a scenario, a stable operational regime can be reached by setting the pump frequency above the cold cavity resonance and then approaching it by scanning the pump towards smaller frequencies69. Thus, the pump frequency tuning speed is an important parameter affecting the accessibility of microcomb states. For soliton states, in which a loss in intracavity power induces the transition from chaos to a phase-locked regime69, the correct speed would allow for losses to be compensated for by the residual resonator heating after the laser scan, thus maintaining the system equilibrium. Hence, the use of GA yields insight into the magnitude of the resonance drift and, when combined with the inclusion of the frequencies defining the start and end point of the scan, allows for the consistent achievement of the same effective detuning for a given microcomb state and by extension, the targeting of stable operational regimes for these microcombs.

Microcomb characterization

We study the validity of our approach by characterizing the microcombs generated using the experimental parameters located by the GA. We measure the spectral coherence of the microcombs across the entire spectrum, using a delayed Mach-Zender interferometer and calculating the visibility V per comb line from the resulting spectral fringes. The visibility of the interference fringes observed at the output of the Mach-Zender interferometer corresponds to the modulus of the (wavelength-dependent) complex degree of the first-order coherence70,71.

In Fig. 5 we reproduce three spectrally distinct microcombs previously located by the GA, related to multi-soliton and SC states. The spectra are superimposed with their associated line-by-line visibility data for three different delays. Fig. 5a–c show delay values of 20 ps, 5 ns, and 15 ns, corresponding to 0.04, 1, and 3 photon lifetimes, respectively. As expected, all three microcombs show high average visibility \(\bar{V}\) above 91% at zero photon lifetime. For one photon lifetime,\(\bar{V}\) remains above 83% for all states reported. At 3 photon lifetimes, \(\bar{V}\) starts to decrease to around 64%. Still, several comb lines maintain visibility fringes above 80% for all three microcombs, indicating high coherence and minimal noise for such lines70,72. These results demonstrate the ability of our approach to target application-suitable microcomb states, such as for coherent communications32 and precise spectroscopy73.

Fig. 5: Spectral coherence of microcombs.
figure 5

Gray scatter plots show the visibility calculated at each comb line as a measure of spectral coherence70, to characterize microcomb shapes located by the genetic algorithm at a–c 20 ps delay (~0τph), d–f 5 ns delay (~1τph), and g–i15 ns (~3τph), respectively, for each presented microcomb state. Each panel is also labelled with the average visibility value \(\bar{V}\) as an inset.

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Additionally, Fig. 6 shows stability characterization measurements for a particular microcomb shape, reported in Fig. 3e. The main plot displays line-by-line stability in terms of the standard deviation. The stability measurement exhibits minimal variation in the comb line peaks, with a standard deviation value below 0.1 for all frequencies, over one day. The inset of Fig. 6 illustrates power transmission as the pump laser is scanned to generate the microcomb. We note a distinct drop in power associated with SC formation within the trace, as widely reported74.

Fig. 6: Stability of generated microcomb.
figure 6

Grey dots show the standard deviation of intensity value per comb line, measured over one day. The microcomb state (blue) is reproduced using the optimized parameters located by the GA. The inset shows the recorded power transmission trace at the through port of the MRR as the laser frequency is scanned to reproduce the microcomb, clearly showing the step-in power associated with SCs, as specified in the fitness function during the GA search.

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Microcomb modelling

We apply the formalism of the Lugiato-Lefever equation75 (LLE) to describe microcomb dynamics generated by our GA and provide a preliminary understanding of the feasibility of the targeted output regimes. The evolution of the field in MRRs driven by an external pump field is governed by:

$${t}_{r}{\partial }_{t}E\left(t,\tau \right)=\left(-\alpha -i{\delta }_{{\omega }_{0}}-L\frac{{\beta }_{2}}{2}{\partial }_{\tau }^{2}+i\gamma L\,{\left|E\right|}^{2}\right)E+\sqrt{k}\,{F}_{{in}}.$$
(5)

The LLE introduces a reference time \(\tau \in \left[-{t}_{r}/2,{t}_{r}/2\right]\) that is related to the group velocity of the pump field Fin, a center frequency ω0, and a slow time t associated to the number of round-trips N, as \(E\left(t=N{t}_{r},\tau \right)\). tr is the round-trip time of the MRR, α represents the total system losses, \({\delta }_{{\omega }_{0}}\) is the phase detuning of the pumping field with respect to ω0, L is the round-trip length, β2 is the group velocity dispersion, and k is the coupling coefficient of the pump field, which considers the input losses. γ is the nonlinear parameter associated with the Kerr effect, which can be expressed as \(\gamma =\left({\omega }_{0}{n}_{2}\right)/\left(c{A}_{e}\right)\), where Ae is the effective nonlinear mode area of the MRR waveguide while n2 is the Kerr refractive index. Considering the MRR sample in our scheme, the parameters for the simulations are set to \({t}_{r}=22{ps}\), \(L=592\mu m\), \({\beta }_{2}=-10{{ps}}^{2}{{km}}^{-1}\), \(\gamma =220{W}^{-1}k{m}^{-1}\), and k=0.3, while losses and higher-order dispersion terms are neglected. With such values, we sweep the detuning \({\delta }_{{\omega }_{0}}\) around ω0 at a speed \(d\omega /{dt}\), and setting the average power of the field Fin, \({P}_{{F}_{{in}}}=1.8W-2.1W\), compatibly with the GA parameter I. Given the large intra-cavity field intensity in the MRR, we neglect any thermal-induced resonance drift term in the equation15,69. However, our GA accounts for and counterbalances this effect.

Figure 7a and b display simulation results for two exemplary microcombs: a multi-soliton state and a stable MI microcomb state, corresponding to the cases shown in Fig. 3c and d. The exact alignment of the spectral traces underscores consistency between experimental and simulated results. The simulated temporal profiles of the intracavity fields, depicted as insets in Fig. 7, offer insights into the nature of these two regimes. The temporal trace in the inset of Fig. 7a reveals a structure consistent with multi-soliton bound states76, previously demonstrated in microresonators77, characterized by sub-picosecond components and spaced by 0.22 ps. The inset in Fig. 7b depicts pulse profiles interspersed with secondary modulated fringes, closely resembling the characteristics of a stable MI microcomb78.

Fig. 7: Microcomb modelling.
figure 7

Simulation results, represented by the red dots, fit exemplary microcombs obtained experimentally through the GA (solid blue line) for (a) the multisoliton regime and (b) the near MI regimes. Insets show the simulated temporal intra-cavity fields for each microcomb.

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Discussion

Our work proposes a smart scheme to target distinct microcomb regimes via GAs for various real-world applications. Given the modular aspect of the fitness function that we employ in our scheme, our smart approach is highly versatile and applicable to other devices for microcomb generation, including (micro) cavities with different geometries and materials (e.g., silicon-based platforms), highly nonlinear fibers, and spiral waveguides79, that feature a third-order nonlinear response to the propagating electrical field (e.g., two-photon absorption). This is due to the model-free nature of our implementation, requiring minimal information on the geometry and properties of the specific waveguide.

In addition, our approach is straightforwardly adaptable to different setup configurations for microcomb generation involving additional components, such as for multiple laser sources80, as well as other tuning mechanisms (e.g., multi-stage scanning or back scanning). In such cases, adapting the GA amounts to introducing new objectives in Eq. 2, whose arguments are associated with the new components’ parameters. Similarly, we can include additional constraints defining the target microcombs that introduce new degrees of freedom to the fitness function, in turn tailoring the microcombs towards specific applications. For example, in telecommunications where it is essential to mitigate microcomb noise, an objective can be included in Eq. 2 to account for noise characteristics during the optimization. In Fig. 2d we observe a flat microcomb, reaching a spectral flatness of ± 3 dBm that fills the C-band of telecommunication (from 190 THz to 196 THz). Thus, our smart scheme is a promising alternative for telecommunication and machine learning applications where current implementations require expensive spectral shapers to achieve flat microcomb spectra4,81.

Furthermore, the experimentally obtained microcombs have shown stability in their spectral features over a period of 12 hours to 1 day, overall extending previous results in the same direction48,82.

In Fig. 3, we demonstrate that our scheme can find optimal combinations of the input parameters that reproduce microcomb spectral envelopes with profiles corresponding to distinct complex comb dynamics, including SCs and multi-soliton states.

We note that our results are reproducible in the sense that, once the optimal set of parameters for a target microcomb shape has been located by the GA, we can reproduce the exact same output by directly inputting these parameters to the experimental setup. Indeed, this has been further demonstrated as we subsequently generated the same output microcombs when performing additional coherence and stability measurements. Moreover, the states that we obtain using the optimized parameters are stable against external perturbations (Fig. 6), such as mechanical vibrations, temperature instabilities, and other environmental factors. Together with the reproducibility claim of our results, our measurements prove the high robustness of our scheme.

In comparison with exhaustive search methods using standard sweeping approaches, which are limited in their ability to explore a large or complex solution space and are sensitive to noise and measurement errors, our proposed scheme is time- and resource-efficient with significant benefits towards real-world applications, as we quantitatively report in Fig. 4. The use of GAs drastically reduces the need for time-consuming and labor-intensive trial-and-error experiments to find a desired microcomb. It can quickly explore a large parameter space to identify the optimal input parameters that lead to the best performance.

The microcombs obtained by our smart approach can be numerically reproduced using the well-established theoretical framework of the LLE, as shown in the exemplary cases reported in Fig. 7, which can offer a preliminary understanding on the feasibility of the targeted states. On the other hand, the realization of complex spectral envelopes that would be otherwise difficult to predict numerically (e.g., due to model complexity limiting the accuracy and resource consumption of numerical simulation), are, instead, experimentally obtainable with this scheme as shown in Fig. 3.

Conclusions

Our work demonstrates a smart approach for locating and generating distinct, specific microcomb states according to their desired intracavity power and spectral profiles. Our approach exhibits remarkable stability under external perturbations, and user-friendly reproducibility of the located microcombs.

Our findings have significant implications for developing portable, highly precise microcombs that can function robustly in uncontrolled environments. Indeed, our approach eliminates the need for additional stabilization mechanisms, thereby facilitating the utilization of microcomb dynamics across a broad range of out-of-lab applications. With the precise control of individual microcomb lines offered by GA, we can exploit individual frequency components to achieve ultra-dense, broadband data encoding for optical signal processing. This can improve existing spectral tailoring techniques, and enable the realization of photonic artificial neural networks. These advances open new avenues for real-time processing in high-capacity communication networks, providing significant advantages over current methods.

Methods

Experimental setup for microcomb generation

We generate our microcombs in a four-port doped silica glass MRR63, with an FSR of 48.9 GHz and featuring low linear loss (~0.06 dB cm−1) and nonlinearity (~220 W−1km−1), operating in the anomalous dispersion regime, with a group velocity dispersion β2=−3.1 ps2km−1 TM and −10 ps2km−1 TE mode at 193 THz. The MRR exhibits a mode crossing around 1552 nm. In our experimental setup, the MRR is pumped by a tunable CWL source (Santec TSL-710) that is amplified from 20 mW to ~1.8 W by an EDFA (Pritel PMFA-33), as shown in Fig. 1a. The MRR is mounted on a commercial thermoelectric cooler (TEC), to maintain the chip temperature near 30 °C.

Genetic algorithm parameters

The GA used in this study is based upon the open-source Python library ‘geneticalgorithm’83. The library’s source code was modified to tailor the algorithm towards the microcomb generation task in this work. In particular, the crossover and parent selection operations were customized. The fitness function and multi-objective formulation of the optimization problem were fully developed for this work.

Following established approaches in evolutionary-based optimization techniques, we set the hyperparameters of the GA based upon preliminary manual exploration of the microcomb generation procedure, accounting for the trade-off between convergence time and quality of solution. As such, we set a population size of 20 individuals, a 20% mutation probability, a 50% crossover probability, and a 1% elitism ratio. The elitism ratio defines the portion of high-quality individuals allowed to continue ‘as-is’ to the next generation to retain the best-performing individuals within the gene pool. Furthermore, we select the parents according to a ‘roulette wheel’ approach, where higher quality candidates have a better chance of being selected as parents. Finally, we also utilize uniform crossover, where each gene is chosen from either parent with equal probability (as opposed to other mixing ratios, such as one- or two-point crossover, which would favour inheritance from one parent over another)84. Each realization of the GA takes around 12 hours, although the total time includes the hardware-related bottlenecks (e.g., time required to scan and poll the OSA over GPIB connections was around 1 minute per scan, with each generation requiring hundreds of scans).

Our implementation also sets boundaries for the gene values as dictated by the specifications of the equipment and minimal knowledge of the system: the centre wavelength for the pump is limited between 1539 nm and 1552 nm, corresponding to the known range of the microring in which resonances near the mode crossing occur. The pump scan span boundaries are limited to approximately the width of a single MRR resonance linewidth. The upper limit of the step size for the laser scan is set similarly, while the lower limit is set to the laser step resolution, yielding a final range of 0.0001 nm - 0.005 nm. The limits on the dwell time are set based on those of the laser itself when in scan mode, from 0.1 s to 0.5 s. Finally, the EDFA current is limited to within its specification range, between 0.1 A and 4.2 A.

Our laser allows for two different scan modes, discrete and continuous. We performed our experiment using discrete scan steps according to the specified values for step size, span, and dwell time. The choice of discrete over continuous sweeping was motivated by the lower range in the scan speed provided by the laser in the continuous scan mode. In principle, with better equipment, continuous scanning can also be incorporated into our approach.

Choice of the fitness function

To characterize the quality of each individual, we have to specify a fitness function. The choice of the fitness function is an open problem in the field of evolutionary algorithms, with the definition of the function depending on the specific targets of the optimization problem. Our fitness function for the microcomb generation and tailoring process, defined in Eq. (2), is characterized by some or all the following objectives, which specify the target spectrum criteria:

Target line spacing between microcomb lines

We tailor the line spacing of the microcomb by defining it as some multiple of the device’s FSR (although an explicit value can also be specified). We measure the distance between consecutive intensity peaks in the spectral trace, average these measurements, and then apply a normalized Euclidean norm. This yields a value that indicates proximity to the target line spacing, as retrieved using the following formula:

$$\frac{\left|{s}_{{target}}-s\right|}{{s}_{{target}}},$$
(6)

where starget is the target line spacing and s is the measured average line spacing of the microcomb.

Uniformity of the microcomb line separation

This metric is implemented as a (normalized) standard deviation using the following relation:

$$\max \left(\frac{\sigma }{\mu },C\right),$$
(7)

where µ is mean spacing, σ is the standard deviation of the measured distances between adjacent comb lines, and C is an empirically defined ceiling value (to keep the value within bounds).

We collect the spectral traces with the OSA set to maximum hold mode, at the end of each laser scan, while the OSA is scanning during the microcomb generation procedure. The max-hold trace illustrates the comb shape achieved even if the laser steps too far and overshoots the microcomb state (e.g., the sweep span parameter is too wide). In such a way, combined with the power trace criterion (see below), we monitor the microcomb shapes achieved even when they are overshot.

Envelope general uniformity and proximity to a defined shape

The peaks of each line are interpolated together, then a Euclidian norm is applied to find the distance from the target shape, analogous to Eq. (6). If no target shape is defined, then the score is based on the standard deviation of adjacent peak heights, analogous to Eq. (7), to target a smooth intensity transition between adjacent microcomb lines. This latter metric avoids general chaotic states, whereas the former targets specific shapes. An explicit definition of a target shape is a stricter criterion and requires knowledge of the possible microcomb states, whereas the uniformity criterion is better suited for a simple exploration of non-chaotic regimes. In this way, we indirectly impose an intensity-related objective without setting a large number of targets for each microcomb line.

Power trace

We track the microcomb evolution through the power trace – for example, the MRR exhibits a threshold intracavity power level for comb formation, while a distinct drop in power is measured when the comb state is lost (i.e., the comb is unstable or overshot). Furthermore, some microcomb states (e.g., SCs) are associated with distinct features in the power trace corresponding to the dynamical regime in which they form62,67,85. We assign a penalty function associated with the power trace: a sudden, very large, drop signifies a lost state and, thus, we assign a penalty whose value is related to where the drop occurs. In the case of distinct features with respect to the power trace, the penalty is assigned if the desired features are not found in the trace. The penalty is then added to the overall fitness score. If the desired power criterion is not met, the overall fitness score is worse, thus encouraging the algorithm to find regimes that fulfill this criterion.

Thus, for any single realization of the GA, a combination of the above four criteria is used to specify the type of microcomb desired as the target. Since we define the total fitness function as a weighted sum of multiple objectives, skewing the weightings allows for favoring specific objectives (or, by implication, microcomb features) over others depending on the use case. If an objective is not relevant – that is, no constraint on that specific criterion is needed for the intended microcomb – a zero-weight assignment to said objective allows us to eliminate it. In this way, we ensure maximum reconfigurability in our algorithm.

We also account for auxiliary restrictions that need to be considered. For example, a ‘death penalty’ is assigned to individuals that are deemed as infeasible solutions – that is, the case of finding a single pump line at the end of the laser scan implies no microcomb formation occurred, and thus receives an extremely poor score to ensure it is not selected for the next generation and is quickly removed. We set boundaries on the values of the possible genes as dictated by equipment specifications and our understanding of the parameter space of the system (e.g., minimum required power for nonlinear processes to occur vs maximum input power allowed into the MRR).