1. Introduction

Optical frequency combs are coherent light sources characterized by evenly spaced frequency components. While many implementations are based on ultrafast passively mode-locked lasers, in recent years, efforts has been directed to the miniaturization of such bulk sources by taking advantage of progress made in integrated photonics and maturity of nanofabrication. Such novel class of sources, also known as Kerr microcombs [1], rely on the parametric gain provided by the third-order nonlinearity $\chi ^{(3)}$ of a microresonator material. They therefore feature a wide gain bandwidth which can exceed the octave, high comb line spacing (ranging from THz to tens of GHz) and may achieve extremely low oscillation threshold owing to the high quality factor (Q) and low mode volume of the microresonator. Furthermore, a careful balance between group velocity dispersion (GVD) and nonlinearity allows achieving dissipative Kerr soliton (DKS) states, which display high coherence across the entire comb spectrum. This coherence is crucial for a wide range of applications, including but not limited to telecommunications [2], metrology [3], astrocombs [4], light detection and ranging (LiDAR) [5] and spectroscopy [6,7]. Such Kerr microcombs have been so far demonstrated on several integrated photonic platforms, including Si$_3$N$_4$ [8], silica [9], AlN [10], AlGaAs [11], silicon on insulator [12], thin film lithium niobate (TFLN) [13] and SiC [14].

With specific focus on spectroscopy, microcomb sources at mid-infrared (mid-IR) wavelengths (2–20 µm) would be particularly beneficial for the identification of many molecular species with strong absorption lines in this wavelength range [15], with practical impact in applications such as trace gas sensing, chemical analysis, or medical diagnostics, especially in combination with techniques such as dual-comb spectroscopy [16]. However the vast majority of Kerr microcombs reported so far has been based on pumping at telecom wavelengths, either in the C/L band ($\sim$ 1550 nm) or in the O band ($\sim$ 1310 nm), taking advantage of the availability of equipment and pump sources necessary to drive and characterize the integrated devices as well as the initial influence of telecommunication on integrated photonics. The mid-IR wavelength range can be still accessed on chip while pumping with short pulse sources by frequency conversion processes such as difference frequency generation in a $\chi ^{(2)}$ medium [17], supercontinuum generation, or by parametric conversion through four-wave mixing [18]. However, such approaches typically have low repetition rate and are not well suited if repetition rates in the 10’s of GHz are targeted. There is therefore interest in developing Kerr microcombs directly generated closer to the target absorption lines, wherein pumping can be achieved by commercial-grade thulium lasers and amplifiers or narrowband diode sources. Fine tuning techniques could be further implemented to improve the resolution in spectroscopy applications [6].

Reports of Kerr frequency combs in this wavelength range using integrated photonics are relatively few. A comb at 2.5 µm, spanning 200 nm with 100 GHz repetition rate was demonstrated in a crystalline microresonator, hence difficult to integrate [19]. Mid-IR comb generation in silicon photonics was also reported, pumped at 3.07 µm, [12] but the single soliton state could not be accessed. A soliton microcomb spanning 330 nm was generated by pumping near 2 µm in a TFLN microresonator [20]. However, the dispersion engineering as well as fabrication of TFLN integrated devices is still at the moment very challenging, and the power handling is generally limited by the emergence of photorefractive effect [21]. A possible alternative to these solutions is to use silicon nitride (Si$_3$N$_4$) photonics platform. With a widely accessible commercial-grade fabrication process, a wide transparency window, eliminating parasitic nonlinear absorption, ultra-low loss and high power handling capability, such material platform has become widely used for high efficiency and ultrabroad microcomb generation at telecom and visible wavelengths. Given its excellent properties in the mid-IR up to at least 4 µm as confirmed by work on supercontinuum generation [22], it appears as a potential candidate for Kerr comb generation at long wavelength.

In this work, we show for the first time to the best of our knowledge, soliton Kerr comb generation in a 143 GHz free spectral range (FSR) Si$_3$N$_4$ microring resonators, with a pump wavelength close to 2 µm. Several comb state can be easily accessed including the low-noise single soliton state with a spectrum spanning 422 nm (31 THz), limited by the generation of a dispersive wave near 2.2 µm. Further optimization of dispersion should allow pushing the operation deeper in the mid-IR. Our work extends Si$_3$N$_4$ Kerr combs towards the mid-IR, adding new opportunities for the silicon nitride photonics platform.

2. Results

2.1 Linear characterization

The Si$_3$N$_4$ microring resonator used in this experiment has a nominal waveguide width of 1.7 µm and a height of 0.8 µm. The devices are fabricated through a commercial-grade, multi-project wafer fabrication run at LIGENTEC SA, using the AN800 process. They display a nominal radius of 158 µm, which corresponds to a free spectral range (FSR) of 143 GHz at 1.97 µm.A microscope image of the device is shown in the inset of Fig. 1(a).

 

Fig. 1. (a) Calculated GVD (blue) and integrated dispersion (orange) for pumping at 1.97 µm (arrow). Inset: Microscope image of the Si$_3$N$_4$ microring resonator. (b) Measured dip visibility at 1.97 µm and 1.55 µm as a function of the nominal gap between ring and bus waveguide. (c) Normalized transmission spectrum at low power (center wavelength: 1969.5 nm for 700 nm gap). Blue line: fit of the experimental data.

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In travelling wave resonators, anomalous GVD ($\beta _2=\partial ^2\beta /\partial \omega ^2<0$) is essential to initiate the comb generation process. The calculated GVD profile for the present waveguide is shown in Fig. 1(a) along with the integrated dispersion $\beta _{\rm int}(\omega )$ given by:

We performed transmission measurements at low optical power, using a single frequency laser operating at 1.97 µm (custom BASIK T20 from NKT Photonics), to assess the linear properties of the resonators and coupling behavior at this wavelength. The temperature of the photonic chip was controlled by placing it on a thermally stabilized mount, and the light was edge-coupled using a lensed fiber. Mode matching of the fundamental transverse electric (TE) mode at the chip facet to the one in the fiber was achieved using an inverse taper. The outcoupled light was collected using a convex lens and then coupled to optical fiber after collimation. Overall coupling loss across the resonator was 3 dB. We recorded the outcoupled light using a photodiode and an oscilloscope. After a coarse temperature tuning of the emission wavelength, we swept the laser frequency across the resonance using built-in piezo actuators. To calibrate the measurements, the input field was phase modulated using a fixed RF frequency to generate reference sidebands [23].

The photonic chip tested contains four microresonators with the same nominal dimensions but with varying gap between the bus waveguide and the ring resonator, ranging from 400 nm to 700 nm. In order to assess the coupling conditions at 1.97 µm, we recorded the transmission trace of all four resonators and extracted the visibility of the resonance. The results showing the change in visibility as a function of gap are plotted in Fig. 1(b). We observe a clear ascending trend, suggesting that all resonators operate in the overcoupled regime at this wavelength range. We also carried the same characterization at 1.55 µm, for which an opposite trend is measured: an indication of going to undercoupled regime, as would be expected.

The high-visibility transmission dip of the 700 nm gap device at a 1969.5 nm resonance is shown in Fig. 1(c). By fitting the data to a Lorentzian function, we calculate the linewidth of the target resonance to be 209 MHz, corresponding to a loaded Q-factor of $0.72\times 10 ^{6}$. Based on the high-Q exhibited by the resonator with 700 nm gap and on the nearly critically coupled condition compared to the other devices, we selected it for our experiment.

2.2 Comb generation

Frequency combs are generated in a microresonator due to four-wave mixing, associated with the $\chi ^{(3)}$ nonlinear properties of the optical medium . While coupling light into the resonator, the resonance frequency gets red-shifted due to thermal effects inside the waveguide, namely thermal expansion and thermorefractive effect. Hence, in order to generate frequency combs, we tune the laser across the resonance from the blue side of the resonance to the red side.

In resonators with anomalous dispersion, stable soliton solutions are predicted on the red side of the resonance. However accessing such states is difficult because of the sudden drop in intracavity power associated with the generation of solitons, reducing the thermal load and therefore causes the resonance to blue-shift and lose the state.

In our system, we employed a dual-pumping technique [24,25,26] to counteract the shifting of the resonance and facilitate soliton generation. This approach uses two lasers, one being the pump laser and the other an auxiliary laser for thermal stabilization. The pump laser is scanned across the resonance of interest for comb generation, while the auxiliary laser is positioned on the blue side of another far detuned resonance to induce a preheating of the cavity. The red-shifting of the resonances induced by the pump laser as it is scanned causes the absorption of the fixed auxiliary laser to be reduced as the resonance moves away. As the pump laser is tuned to the effective red side, the auxiliary resonance recoils, bringing the auxiliary laser back into resonance. This counteractive heating increases the width of the soliton steps during the pump scan making the soliton steps more accessible.

The setup for this experiment is shown in Fig. 2(a). The pump is an NKT single frequency laser at 1.97 µm, amplified with a thulium doped fiber amplifier to reach an on-chip power of 22 dBm. The pump wavelength is tuned using a function generator that controlled the internal piezo of the laser. An external cavity laser operating near 1.55 µm and amplified with an erbium doped amplifier to 29 dBm, operates as an auxiliary laser. The auxiliary resonance in this experiment has a linewidth of 140 MHz with a loaded Q value of $1.4 \times 10^{6}$ (intrinsic $Q_0=1.5 \times 10^{6}$) and belongs to the same mode family as the pump resonance. The two beams are combined using a wavelength division multiplexer (WDM) after a polarization controller and coupled into the microresonator. The output light from the microresonator is collimated and coupled into a fiber. The comb light is separated from the auxiliary laser wavelength by another WDM and measured on an optical spectrum analyser (OSA). A portion of this light is also sent through a fiber Bragg grating (FBG) to filter out the pump wavelength to monitor the converted power on an oscilloscope. The auxiliary laser wavelength is also monitored to track its relative position within the auxiliary resonance.

 

Fig. 2. (a) Setup for soliton generation using dual pumping technique comprising two continuous wave (CW) lasers at 1.55 µm and 1.97 µm. The piezo controller of the 1.97 µm is controlled by a function generator. The two pumps are amplified by erbium- and thulium-doped fiber amplifiers (EDFA, TDFA), respectively, and combined using a wavelength division multiplexer (WDM) before coupling into the Si$_3$N$_4$ microresonator. The output of the microresonator is split into the corresponding wavelengths and a part of the light is sent to optical spectrum analyser (OSA) while the rest is sent through a fiber Bragg grating (FBG) to filter out the 1.97 µm pump and observed on an oscilloscope (Osc) using a photodiode (PD). (b) Converted power trace when the 1.97 µm pump is swept across the resonance. (inset) Detail of soliton steps. (c) Converted power trace when the 1.97 µm laser is swept across the resonance in dual pumping configuration. (d) Oscilloscope traces of converted power and microresonator transmission for various values of on-chip pump power. (e) Relation between peak converted power and on-chip pump power. The black arrow highlights the comb threshold.

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A typical converted power trace with the auxiliary laser turned off is shown in Fig. 2(b). The inset offers a closer look at the falling edge, which corresponds to the red side of the pump resonance. A discontinuous step like pattern can be observed signaling generation of solitons in the system. The soliton step duration in this case is extremely short, measured to be about 2 µs. In the same configuration, by with the auxiliary laser manually tuned into the blue side of its corresponding resonance, we are able to significantly increase the soliton steps duration as shown in Fig. 2(c). We found that the steps duration increases to 1.7 ms, making the soliton steps more accessible. The exact position of the auxiliary laser is then fixed at the wavelength where soliton steps with the longest duration are observed.

In order to measure the threshold for comb generation, we recorded the converted power trace for various input pump powers as shown in Fig. 2(d). The pump laser was swept across the resonance using a triangular signal with 50 Hz frequency while the auxiliary laser was switched off. We then recorded the transmission of the microresonator along with the corresponding converted power trace on an oscilloscope. The converted power trace was extracted from the resonator transmission by passing a portion of the light through a fiber Bragg grating centered at 1970 nm and then recording the transmission at the throughput port. Fig. 2(d) shows output of the microresonator (orange) and converted power (blue) during the laser sweep, as measured on the oscilloscope. The converted power is observed to be zero for on-chip pump powers less than 50 mW. With increasing pump powers we observe that the resonance shape changes from Lorentzian to triangular owing to the resonance red-shift, while the converted power increases owing to comb generation. Plotting the maximum value of the total converted power for each recorded trace against the on-chip pump power in Fig. 2(e), we infer that the threshold power for comb generation is close to 50 mW, as indicated by the arrow.

2.3 Experimental spectra and soliton formation

With the auxiliary laser providing compensation for thermal effects, the soliton states on the red side of the resonance could then be accessed by tuning the pump wavelength from blue side of the resonance to red. This approach allowed for controlled and reliable access to various comb and soliton states in our microresonator.

Figure 3 illustrates the measured optical spectrum for various stages observed during the comb generation process as the laser is swept across the resonance, alongside simulation results, which will be discussed in detail in the next section. For each of the regimes observed, the generated comb power was retrieved by a fast photodetector (bandwidth: 20 GHz) and recorded by a real-time oscilloscope and the power spectral density (PSD) was calculated through a fast Fourier transform (FFT), thus yielding the intensity noise characteristic for each of the comb states generated.

 

Fig. 3. (a)-(e) Experimental (blue) and simulated (orange) optical spectra at various stages of comb generation, respectively: 1) primary comb, 2) modulation instability (chaotic) comb, 3) multi-soliton state, 4) single soliton state. Insets show the PSD of the recorded intensity, hinting the low-noise character of soliton states. (f)(g) Simulation map of comb evolution and intracavity power.

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The optical spectrum of the pump laser when it operates outside the resonance is depicted in Fig. 3(a), with the converted power PSD as an inset. Since no combs are generated at this stage and consequently no light reaches the photodiode, the inset depicts the noise floor of the photodiode. Moving the pump laser further into the resonance leads to the formation of initial sidebands in the resonator, which emerge from the modulation instability (MI) gain inside the resonator (Fig. 3(b)). The sidebands here display a spacing of 26 FSRs, which can vary slightly depending on the specific pump power and detuning conditions, and constitute the primary comb (Turing pattern) state, characterized by the absence of a fixed phase relation among the comb lines. The corresponding intensity noise PSD, shown in the inset, is quite similar to the case of single pump, proving the high coherence of the generated lines. Deeper into the resonance, but still on the blue side, we are able to access the chaotic MI comb which is shown in 3(c), characterized by high intensity noise at low frequencies as is seen in the inset of this figure.

When the pump laser is tuned to the red side of the pump resonance, soliton steps become accessible. The steps closer to the resonance corresponds to multi-soliton states, associated with more than one pulse circulating inside the cavity and higher overall comb power. The presence of more than one soliton in the ring gives rise to an interference pattern in the optical spectra: as an example, the blue trace in Fig. 3(d) corresponds to the optical spectrum of a multi-soliton state with two pulses circulating inside the cavity. The transition to a soliton state is accompanied by the disappearance of low frequency noise peaks in the intensity noise PSD as shown in the inset of Fig. 3(d).

Finally, we carefully tune the pump laser further into the red side to access the single soliton step, resulting in the smooth spectrum shown in Fig. 3(e), with line spacing of 1 FSR. Such state is expected to correspond to a mode-locked pulse train with repetition rate $f_{\rm rep}= {143}\,\textrm{GHz}$ and transform-limited pulse duration. From a $\mathrm {sech}^2$ fit of the main peak of the envelope we estimate a pulse duration of about 41 fs. The soliton spectrum also displays a secondary peak at 2.2 µm, corresponding to the zero crossing point in the integrated dispersion profile of the resonator (see Fig. 1(a)), and hence the emergence of a dispersive wave, characterized by an oscillatory tail in the temporal domain. The overall −20 dB bandwidth (corresponding to the dynamic range of our spectrometer) of the single soliton comb is about 422 nm.

To get more insight on the soliton formation dynamics, we investigated the generation of multi-soliton states and soliton crystals in the microresonator. While tuning the laser to the red side of the resonance it is possible to access several different soliton regimes, visualized as steps in the converted power trace (Fig. 2(c)). The manifestation of such states generally occurs in a stochastic fashion, as a consequence of the chaotic MI comb formation that precedes their access. Nevertheless, once a soliton state is accessed, it displays stability over time, making such operation stable.

Several examples of multi-soliton spectra observed are shown in Fig. 4. Figure 4(a) corresponds to a perfect soliton crystal with 7 transform-limited pulses circulating inside the cavity with the same relative angle of separation among them. This is evidenced by a line spacing of 7 FSRs, and complete extinction of all other lines. Figures 4(b)-(d) correspond to multi-soliton states with two solitons circulating inside the cavity and varying relative angle between them, as shown by the different interference feature. The retrieved spectra can be intuitively understood as a beating between two single soliton spectra in the frequency domain, whereas the beating period reveals the relative phase between them, as illustrated in the insets.

 

Fig. 4. Experimental spectra for (a) soliton crystal and (b-d) multi-soliton states generated in the microresonator.

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2.4 Numerical simulations

To confirm our experimental results, we used the split-step Fourier method to solve the Lugiato-Lefever equation (Eq. (2)) in order to numerically reproduce the different behaviors observed. To get a full picture, we included higher order dispersion (HOD) terms and intra-pulse Raman effect.

Here $t_R$ is the round-trip time, $E$ is the electric field envelope, $\tau$ is the slow time, $t$ is the fast-time, $\alpha '$ the total round-trip loss estimated from the measured Q-factor as $\alpha ' = t_R \omega _{\rm {res}} /Q$, $\delta _0$ the pump detuning with respect to the closest resonance position given by $(\beta (\omega _{\rm {res}})-\beta (\omega ))\cdot L$, $L$ the perimeter of the ring, $\beta _k$ the $k^{th}$ HOD coefficient, $f_r$ the Raman fraction of the nonlinear response, $h_r(t)$ the temporal Raman response of Si$_3$N$_4$, $\gamma$ the nonlinear coefficient estimated by $\gamma =\omega _{\rm {res}}n_2/(cA_{\rm {eff}})=0.672$ W$^{-1}$m$^{-1}$, $\kappa$ the coupling coefficient from the bus to the ring given by the coupling Q-factor found experimentally as $\kappa =t_R\omega _{\rm {res}}(1/Q-1/Q_0)$ and $E_{in}$ the pump electric field. $E$ is normalized in a way that $|E|^2$ gives the optical power in W. For the nonlinear index, we used $n_2=2.4 \cdot 10^{-19}$ m$^2$W$^{-1}$ [27]. Since the analytical expression of the Raman function $h_r(t)$ is not known in our case, we approximate it using the same method as in [28], that used the same material as our sample and estimated the Raman coefficients to be $f_r=0.2$ and $T_r=20$ fs.

The detuning of the pump is varied linearly at each round-trip to reproduce the continuous red-shifting applied in the experiment. The comb spectrum at each roundtrip is recorded, corresponding to the intensity map depicted in Fig. 3(f). Additionally, the intracavity energy is plotted in Fig. 3(g) along with the detuning at each roundtrip. The initial condition is seeded by a one-photon-per-mode noise. All the stages of the comb formation obtained by numerical simulation are then labeled from 1 to 4 and the corresponding spectra are superimposed to the experimental ones, as shown in Figs. 3(b)-(e).

All the distinctive features of the experimental comb spectra are well-reproduced, remarkably the primary comb FSR, position of the dispersive wave, comb bandwidth and pump-to-sidebands ratio.

A small discrepancy between numerical prediction and experiments is visible that is likely to come from slight inaccuracies in the calculation of $\beta _2$ as well as HOD terms.

The transition through the different comb states while sweeping the pump wavelength is marked by different patterns identifiable in Fig. 3(g), which represents the numerical counterpart to the measured converted power displayed in Fig. 2(c). Analogous patterns are observed. Most notably, the primary comb (regime 1) is characterized by low noise fluctuation, which shifts to a noisy chaotic MI comb (regime 2). The subsequent regimes represent the soliton steps, which are associated with a drop in the intracavity energy (i.e. converted power) in a step-like fashion, corresponding to the different multi-soliton regimes, and eventually dropping to a two-solitons (regime 3) and finally single soliton state (regime 4) before recovering the linear dynamics.

It is worth noticing that the soliton regime displays a stochastic phenomenology even in numerical simulations, owing to the chaotic nature of the MI comb states which alters the initial conditions for comb formation even for slight variations of the simulation parameters.

3. Discussion

The system developed showcases the suitability of commercial-grade technologies – most notably Tm-based fiber lasers and amplifiers and foundry-grade silicon nitride photonic chips – for accessing the mid-IR spectral region with soliton microcombs. The availability of thick-film and low-loss silicon nitride waveguides is a key enabling factor, as it grants a wide window of anomalous GVD, yielding in our case dispersive wave condition ($\beta _{\rm int}=0$) at 2.25 µm, and high intrinsic Q-factors ($Q_0 = 2.7 \times 10^6$) corresponding to a propagation loss of about 0.11 dB cm⁻¹ at 1.97 µm, close to the values observed in the telecom band. Such features allow to achieve comb generation with a threshold as small as 50 mW, therefore accessible by standard Tm-doped fiber sources.

Moreover, accessibility to high-Q resonances in the telecom band allows the implementation of a dual-pumping scheme, which addresses the well-known issue of thermal instabilities by increasing the soliton steps duration by almost 3 orders of magnitude (from ${2}\,\mathrm{\mu}\textrm{s}$ to $\sim {2}\,\textrm{ms}$ in the present demonstration), making them more accessible and in a reproducible fashion. Such strategy allows to repeatably access several species of comb states, ranging from Turing rolls, modulation instability (chaotic) combs, and soliton states. The latter states are characterized by low noise (inherited by the narrow-linewidth pumping source), high repetition rate (143 GHz and its multiples), and a broad bandwidth of 422 nm (31 THz), and manifest either as single- and multi-soliton states, or as higher-order soliton crystals. Systematic comparison with simulations shows the reproducibility and predictability of such soliton states, for which we estimate a transform-limited pulse duration as small as 41 fs.

Moreover, the comb spectrum could be further extended in the mid-IR with dispersion engineering. Indeed, setting the zero-dispersion wavelength more distant from the pump on the red side would push the dispersive wave towards longer wavelengths in the normal dispersion region, resulting in an enhanced coverage of the mid-IR spectral region. To this end, the usage of thicker silicon nitride films has been used to demonstrate mid-IR incoherent combs displaying similar bandwidth (45 THz), but spanning longer wavelength ranges [29], and also to generate supercontinuum [30]. In these works, the longer wavelength cut-off was attributed to the onset of silica absorption, around 4 µm, rather than by the position of the dispersive wave. More advanced dispersion techniques can be also adopted for that purpose, for example through the use of concentric resonators [31]. Further improvements to the present demonstration may be therefore enabled by the commercial availability of thicker silicon nitride photonic platforms or by improved photonic circuit design.

Further advances in fabrication capabilities may also lead to a reduction of the propagation loss, making comb generation accessible with milliwatt or sub-milliwatt level threshold, therefore dropping the requirement of an external amplification stage. This would be a crucial improvement in the perspective of accessing soliton microcomb generation through commercially available laser sources, as fiber and diode lasers operating at 2 µm, overcoming the ubiquitous need for bulky and expensive optical parametric oscillators typically used for the generation of Kerr combs in the mid-IR region [12,19,29].

Finally, in a long-term perspective, the aforementioned improvements could be combined with the integration of the pumping source on-chip. This tantalizing objective may be achieved either through hybrid integration of III-V sources with silicon nitride photonics technology [32] or through the inclusion of rare-earth dopants on the silicon nitride platform [33]. Besides an obvious advantage in terms of integration capabilities, the inclusion of an integrated pumping source bears the potential for turn-key operation, i.e. self-starting of the soliton regime [34], and for significant linewidth narrowing through the self-injection locking mechanism [35], opening a pathway towards chip-scale integration of mid-IR spectroscopy.