Programmable access to microresonator solitons with modulational sideband heating

Dissipative Kerr solitons formed in high-Q optical microresonators^1,2 constitute miniaturized optical frequency combs with broad bandwidths and repetition rates in the microwave to millimeter-wave domain. Commonly referred to as “soliton microcombs,” they have already been used in many system-level information and metrology applications, such as coherent telecommunication,^3–5 ultrafast ranging,^6,7 astronomical spectrometer calibration,^8,9 dual-comb spectroscopy,^10,11 low-noise microwave generation,^12,13 photonic neural networks,^14,15 datacenter circuit switches,¹⁶ microwave photonics,^17,18 frequency synthesizers,¹⁹ and optical atomic clocks.²⁰ Critical to the rapid progress of soliton microcomb technology is the development and continuous optimization of various photonic integrated platforms, including silica,^21,22 silicon nitride (Si₃N₄),^23,24 high-index doped silica (Hydex),^25,26 aluminum nitride (AlN),^27,28 lithium niobate (LiNbO₃),^29,30 tantala pentaoxide (Ta₂O₅),³¹ silicon carbide (SiC),^32,33 chalcogenide,³⁴ aluminum gallium arsenide (AlGaAs),^35,36 and gallium phosphide (GaP).³⁷ In addition, the introduction and successful implementation of hybrid and heterogeneous integration^38–44 further enable complex control schemes, extra nonlinearity, and efficient amplification for integrated soliton microcombs.

Despite these advances, one issue that currently prevents a wider deployment of soliton microcombs is how to deterministically access and control the soliton state. This issue is caused by the photo-thermal effect, arising from light absorption, and the thermal-optic effect in optical microresonators,^45,46 particularly those built on integrated platforms. When the continuous-wave (CW) pump’s frequency is scanned through a microresonator resonance, from the blue-detuned side to the red-detuned side, a self-organized pulse waveform (i.e., a soliton state) is formed.¹ However, the photo-thermal effect leads to serious thermal instability that often annihilates the soliton state immediately. Therefore, sophisticated techniques to manage this effect have been developed, such as power kicking,^47,48 single-sideband suppressed-carrier frequency shifters,⁴⁹ dual-laser pumps,^50–54 pump modulation,^55–59 pulse pumping,⁶⁰ or laser self-cooling.^61,62 In addition, cryogenic operations can be helpful.³⁶ In addition, instead of the single-soliton state, efforts have also been made to employ multi-soliton states for reconfigurable photonic microwave filters¹⁸ and the synthesis of terahertz frequencies.⁶³ For frequency metrology applications, the local comb line power enhancement in the multi-soliton state further facilitates the realization of self-referencing.⁶⁴ 

Here, we demonstrate an approach to manage the photo-thermal effect, which enables automatic and deterministic access to a soliton state. This method, employing single-sideband heating, overcomes the photo-thermal effect in integrated microresonators. We apply this method to demonstrate that N-soliton states of 19.97 GHz repetition rate can be deterministically generated for any assigned value of N ≤ 5.

The principle to excite a soliton state in a high-Q optical microresonator with a single continuous-wave (CW) pump laser is shown in Fig. 1(a) top. As the pump laser scans through a resonance from its blue-detuned to the red-detuned side, the resonance is distorted from a Lorentzian to a triangular profile.⁶⁵ This change is due to the increasing intra-cavity power, which, via the photo-thermal effect, levitates the microresonator’s temperature and extends its total optical length. Therefore, the “hot” resonance shifts following the direction of laser scanning. In this case, solitons can form on the red-detuned side of the effective resonance. A signature indicating soliton states is a series of step features (“soliton step”) in the intra-cavity power,⁶⁶ as shown in Fig. 1(a). However, once a soliton state is reached, the intra-cavity power, as well as the microresonator temperature, drops suddenly. This leads to a sudden blue-shift of the resonance, which in turn increases the effective soliton-pump detuning. Therefore, this transition often compromises the soliton stability, causes extremely short or even negligible soliton steps, and often annihilates solitons immediately.

To circumvent such thermally induced instability, here we develop a blue-detuned sideband heating scheme to balance the sudden cooling of the microresonator during soliton formation. The principle is depicted in Fig. 1(a) at bottom. With proper frequency and power differences between the pump laser and its sideband, wherever the resonance moves, the sideband will drag the resonance back. For example, when the resonance experiences a sudden blue-shift during the transition from modulation instability to a soliton state, more optical power from the sideband enters the resonance, which levitates the microresonator’s temperature to counteract the cooling. In such a way, the microresonator’s intra-cavity power and temperature are locked, and the soliton step is extended, facilitating soliton formation.

Experimentally, we create the sideband by phase-modulation of the carrier pump laser. The experimental setup is shown in Fig. 2(a). The pump laser is an external-cavity diode laser (ECDL, Toptica CTL 1550) with its frequency ν₀ tuned by a piezo, which is actuated by an arbitrary function generator (AFG, Rigol DG4062). A phase modulator (PM, iXblue LPZ-LN-10) creates two sidebands (ν₋ and ν₊) from the carrier pump laser. The modulated laser is then power-amplified by an erbium-doped fiber amplifier (EDFA, KEOPSYS CEFA-C-PB-HP). A band-pass filter is applied to reject amplifier spontaneous emission (ASE) noise from the EDFA. After that, the laser power is coupled into an integrated silicon nitride (Si₃N₄) optical microresonator fabricated using a DUV subtractive process.⁶⁷ The Si₃N₄ microresonator features a 19.97 GHz free spectral range (FSR) and an intrinsic quality factor of Q₀ ≈ 1 × 10⁷, characterized using a vector spectrum analyzer⁶⁸ (see the supplementary material). After the Si₃N₄ microresonator, the pump laser is blocked by two fiber Bragg gratings (FBG), providing 30 dB total attenuation. Finally, the output optical spectrum is monitored by an optical spectrum analyzer (OSA, Yokogawa AQ6370D). The optical power is detected by a photodiode (PD, Thorlabs PDA10CS2) and monitored by an oscilloscope (OSC, Rigol DHO4404).

The wavelength and power of the pump laser without phase modulation are 1555.7 nm and 730 mW, respectively. The pump laser’s frequency scans through resonance from the effectively blue-detuned to the red-detuned side (“forward tuning”¹), with the direction marked by arrows in Fig. 2(b). The light detected by the PD and recorded by the OSC corresponds to the generated light from Kerr parametric oscillation in the microresonator. The soliton step is marked with a red color within the total 1.5 GHz frequency range. Due to the photo-thermal effect in Si₃N₄, the soliton step is so short that it is barely seen, making it challenging to access a soliton state. However, when phase-modulating the pump laser with a modulation frequency of f_m = 374 MHz and RF power applied to the PM of 11 dBm, a pair of sidebands ν_± = ν₀ ± f_m are created. The carrier pump laser’s power is 8.3 times higher than that of one sideband. Only the blue sideband ν₊ is used to counteract the thermal effect,^56,57 while the red sideband ν₋ is idle. Prominent soliton step extension is observed with the phase modulation, as shown in Fig. 2(b). We repeatedly scan the laser through the resonance 150 times and statistically analyze the soliton step length, as shown in Fig. 2(c). The statistical mean values are 5.2 and 42.7 MHz, respectively, corresponding to eight-times extension due to sideband heating. It is worth noting that the on-chip power of the blue sideband is 37 mW, which is sufficient to induce a prominent photo-thermal effect but insufficient to trigger Kerr parametric oscillation. In addition, we have not observed the generation of sub-comb lines due to the cross-phase modulation between the blue sideband and the soliton combines (see the supplementary material for detail).

We further investigate the optimal value of f_m for maximum soliton step extension, as shown in Fig. 2(d) left. The optimal value under 11 dBm RF power is f_m = 374 MHz. The effect of RF power on soliton step length is also investigated, as shown in Fig. 2(d) right.

Next, we realize the deterministic generation of an N-soliton state using the sideband heating method. Figure 3(a) shows the dynamic PD voltage, i.e., the dynamically generated light power, where the soliton step sits in zone 2. The supplementary material shows that zone 2 covers the full range of detected voltages for all possible soliton steps in 50 time measurements. Zone 1 indicates that the laser frequency is effectively blue-detuned, and zone 3 indicates far red-detuned, neither of which allows soliton existence.

To distinguish the soliton number, we use the backward tuning scheme by increasing the laser frequency.⁶⁶ The soliton power trace probed by the PD is converted to a voltage trace that shows a clear stair feature in Fig. 3(b). Each step in the stair corresponds to a soliton state with a different N. We measure the mean voltage $V̄$ values of each step and classify them into a different soliton number N. Figure 3(c) shows that, after repeating 20 times, a linear relation between the voltage and soliton number is found, i.e., $V̄=a×N+b$⁠, with a = 0.0609 and b = 0.0265.

Previously, program-controlled single-soliton generation was realized with two lasers and integrated microresonators with repetition rates above 49 GHz^26,53,54 that are difficult to detect with normal fast photodetectors. Here, using only one laser and with calibrated zones and (a, b) parameters, we demonstrate a program for deterministic generation of target N-soliton state in our Si₃N₄ microresonator with FSR down to 19.97 GHz, in addition to the single-soliton state. The program logic is shown in Fig. 3(d), which consists of two blocks. The first block (blue) is to land on a soliton step, and the second block (red) is to produce the target N-soliton state. Initially, the laser frequency scans from ν_s to ν_e (ν_s > ν_e) close to the resonance, such that the final PD voltage lands in zone 3, as shown by the lightest blue trace in Fig. 3(a). The scanning window is then translated by Δν, i.e., the laser is re-scanned from ν_s + Δν to ν_e + Δν. After that, if the PD voltage lands in zone 1, meaning that the laser frequency is blue-detuned and the soliton state is missed, then the system is re-initiated. If the PD voltage still lands in zone 3, the laser frequency scanning window is further translated by Δν. The process continues until the PD voltage lands in zone 2, signaling that a soliton state is reached, as the darkest blue trace shows in Fig. 3(a).

When a soliton state is reached, the program’s second block starts. Using (a, b) parameters and the PD voltage, the current soliton number is estimated by (V − b)/a. For a target soliton number N, if (V − b)/a < N − 0.5, the target N-soliton generation fails and the system is re-initiated. If (V − b)/a > N + 0.5, the laser frequency is increased with step Δν′ until (V − b)/a ∈ [N − 0.5, N + 0.5], where the N-soliton state is successfully produced. Parameters (Δν, Δν′) are self-adaptive and modified to accelerate the sequence (see the supplementary material).

We repeatedly apply the program for automatic N-soliton generation 100 times. The soliton number N can be retrieved by inverse Fourier transform on the soliton’s optical spectrum on OSA, as shown in Fig. 4(a). We verify the soliton number of every addressed N = 5, 4, 3, 2, 1-soliton state. The RF power spectrum of the single-soliton repetition rate is shown in the left inset of Fig. 4(a), where the coherence of comb lines is revealed from the pure single RF signal with a signal-to-noise ratio exceeding 50 dB at 1 kHz resolution bandwidth. The statistic charts of time consumption for the N = 3, 2, 1-soliton state addressing are shown in Fig. 4(b). The success rates are 93%, 99%, and 100% for N = 3, 2, 1-soliton production, respectively. In the backward tuning process, the soliton number can be reduced by two or more, especially when the soliton number is large (which is true for microresonators with a small FSR), so that the success rate of multiple solitons is not 100%. Table I summarizes the data of up to 5-soliton production. The maximum N = 9 soliton state can be addressed, while the N > 9-soliton state is challenging to distinguish due to the large power variation. The existence of the N-soliton state is monitored by sampling the PD voltage V at 10 Hz rate.

In conclusion, we have demonstrated a novel experimental approach to manage the photo-thermal effect commonly encountered in the generation of dissipative Kerr solitons in optical microresonators. The approach is based on phase-modulation of the CW pump, where the generated blue sideband synergizes with the carrier pump and thermally stabilizes the microresonator. The sideband provides immediate heating when the intra-cavity power transits to a soliton state and the microresonator experiences a sudden cooling. Using a 19.97-GHz-FSR Si₃N₄ microresonator, we successfully demonstrated soliton step extension by more than eight times with the sideband heating. Furthermore, we have developed a program to automatically, deterministically, and quickly address to target N-soliton state, including the single-soliton state. We show a near 100% success rate and as short as 10 s time consumption for N-soliton state addressing.

While demonstrated on Si₃N₄, our method is also useful for soliton generation in other platforms suffering from stronger photo-thermal effects. Experimentally, one can choose a proper power level of the blue sideband (which is sufficient to induce a photo-thermal effect but insufficient to trigger Kerr parametric oscillation) and then manually search for the ideal modulation frequency on the CW pump to generate the blue sideband. With few iterations, the ideal combination of modulational power and frequency is acquired. The program-controlled automatic addressing of the N-soliton state can be critical for several applications in microwave photonics and frequency comb metrology. Together, our method facilitates a wider range of applications of soliton microcomb systems outside of laboratory environments.

See the supplementary material for details on the simulation, chip characterization, determination of zone 2, sequence acceleration for N-soliton state addressing, and nonlinear effect of the blue sideband.

We thank Yuan Chen, Sanli Huang, and Zhongkai Wang for their assistance in the experiment, Suwan Sun for his assistance in the simulation, and Jijun He for the fruitful discussion. J. Liu acknowledges the support from the National Natural Science Foundation of China (Grant No. 12261131503), the Shenzhen-Hong Kong Cooperation Zone for Technology and Innovation (Grant No. HZQB-KCZYB2020050), and the Guangdong Provincial Key Laboratory (Grant No. 2019B121203002). Y.-H.L. acknowledges the support from the China Postdoctoral Science Foundation (Grant No. 2022M721482). Hairun Guo acknowledges the support from the National Natural Science Foundation of China (Grant No. 11974234). Silicon nitride chips were fabricated by Qaleido Photonics.

W. S., J. Long and J. Liu filed a patent application related to this work. Others declare no conflicts of interest.

Huamin Zheng: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (supporting); Writing – review & editing (equal). Wei Sun: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (lead); Writing – original draft (equal); Writing – review & editing (equal). Xingxing Ding: Software (equal); Visualization (supporting); Writing – review & editing (equal). Haoran Wen: Data curation (equal); Formal analysis (equal); Investigation (supporting); Visualization (supporting); Writing – review & editing (equal). Ruiyang Chen: Software (supporting); Visualization (supporting); Writing – review & editing (equal). Baoqi Shi: Investigation (supporting); Visualization (supporting); Writing – review & editing (equal). Yi-Han Luo: Funding acquisition (supporting); Software (supporting); Visualization (supporting); Writing – review & editing (equal). Jinbao Long: Investigation (equal). Chen Shen: Resources (equal). Shan Meng: Investigation (supporting). Hairun Guo: Funding acquisition (supporting); Software (equal); Writing – review & editing (equal). Junqiu Liu: Conceptualization (equal); Formal analysis (equal); Funding acquisition (lead); Methodology (equal); Project administration (lead); Resources (equal); Supervision (lead); Validation (equal); Visualization (supporting); Writing – original draft (equal); Writing – review & editing (equal).

The code and data that support the findings of this study are openly available in Zenodo (https://doi.org/10.5281/zenodo.10158216).