Dissipative Kerr soliton (DKS) combs^[1-4] are broadband spectra consisting of equally spaced frequency components with a stable phase relationship, which can connect optical frequency and microwave frequency^[3] and greatly promote the development of spectroscopy and precision measurement^[5], such as coherent optical communication^[6,7], quantum optics^[8], spectroscopy^[9,10], and ultrafast precision ranging and imaging^[11-13].

The generation of DKS combs mainly depends on the Kerr effect in the microresonator^[14,15]. The material platforms that generate DKSs mainly include Si3N4^[16-18], SiO2^[19,20], LiNbO3^[21,22], and MgF2^[23,24]. In order to overcome the instability of the pump laser in the red detuning caused by the above-mentioned positive thermal coefficient materials^[25], scientists have investigated various schemes to achieve stable generation of DKSs, such as power-kicking^[26,27], the fast scanning method^[1,28], and the auxiliary laser heating method^[17,20,29]. In the auxiliary laser heating method, soliton generation is demanding on the auxiliary laser detuning, which needs to be precisely tuned.

Traditionally, when the pump laser is tuned from the high-power chaotic state into the red detuned region, due to thermal instability, there will be an almost invisible soliton existence region, then the pump will rapidly red-shift out of resonance, and the power will be reduced to a minimum. Therefore, to generate DKSs, the laser can only be tuned again from the blue to the red detuned region, i.e., this system is not reversible. To date, there have been few reports of the pump being moved out of resonance from the red detuned region and then tuned back to the red detuned region to stably trigger soliton generation, e.g.,  in 2021, Surya et al. presented a technique for circumventing photorefractive related instabilities in a lithium niobate microcavity with the assistance of an auxiliary laser to achieve cavity stabilization^[30]. This reversibility is achieved by the characteristics of the Si3N4 material and the setting of the initial detuning and polarization state after introducing an auxiliary laser.

In this Letter, based on the auxiliary laser heating method and combined with the double resonance characteristics, a backward tuning scheme for the reversible generation of DKSs is proposed by further studying the dynamic process of soliton generation. Different from the bi-directional switching on the soliton step^[20], the scheme proposed in this paper is that after the forward tuned soliton of the pump laser is annihilated, only the fundamental noise remains in the cavity, and the reversible generation of the soliton is realized by backward tuning. The soliton step range is further extended, the survival time of the soliton becomes longer, and the cavity dynamics has a more complete evolution. Finally, the number of solitons decreases to form a single DKS. Moreover, the switching of the soliton state is achieved by manipulating the detuning of the auxiliary laser, further enhancing the versatility and controllability of the proposed scheme.

The principle of conventional single-pump forward tuning is shown in Fig. 1(a). Due to the thermal effect in the cavity, cavity stability is poor, resulting in an almost invisible region of solitons in the intracavity power curve. Introducing an auxiliary laser with the opposite direction of pump propagation for intracavity thermal tuning, as shown in Fig. 1(b), enables a steady switch of intracavity power from the high-power MI state to the lower power soliton state. The soliton generation mode in this paper is an enhancement of the previous two ways, as shown in the red dashed box in Fig. 1. From the perspective of the scanning direction, after the forward tuning pump laser leaves the resonance from the red detuning side, we change the scanning direction and start backward tuning to reversibly generate solitons. Regarding the change in intracavity power, the output power during backward tuning abruptly rises from base noise to the low-power soliton state. By reasonably setting the auxiliary laser wavelength, the power and temperature in the microresonator are stable during DKS generation. Even after the pump leaves the resonance region from the red detuning side, it can re-enter in the red detuning region through backward tuning, reversibly generating DKS combs, with longer soliton steps, as shown in Fig. 1(e).

The principle of generating DKSs by tuning the dual-laser is demonstrated in Fig. 1(d). The positions of the pump laser and auxiliary laser are represented by the blue and red dashed lines, respectively. The resonant position changes with the power in the microresonator and is red-shifted and blue-shifted accordingly. First, the pump laser and the auxiliary laser are set in the non-resonant region, and the frequency of auxiliary laser is adjusted to stabilize the auxiliary output in chaotic comb state, as shown in State 1, Fig. 1(d). Second, the wavelength of the pump laser is gradually increased to shift it from the blue detuning region to the resonance region. At this time, the intracavity power is increased, the cavity is heated, and the overall resonance wavelength is red-shifted. As a result, the auxiliary laser is shifted away from the resonance center to attain thermal stabilization in the cavity, as shown in State 2, Fig. 1(d). Third, forward tuning increases the wavelength of pump, allowing it to enter the red detuning region, thereby generating solitons in the pump output. At this time, the intracavity power drops sharply, which makes the overall resonant blue-shift, and the auxiliary laser re-enters the resonant region, achieving thermal stabilization. With the wavelength increase, the pump laser moves out of the resonance region, causing a further reduction in intracavity power. The auxiliary laser returns to the resonance center region, reaching the chaotic comb state again, as shown in State 3, Fig. 1(d). Then, the pump laser wavelength is backward tuned to re-enter the red detuning region, resulting in reversible generation of a soliton in the microresonator. The double-resonant characteristic is related to the soliton-induced effect of the continuous wave (CW) laser^[20,31], forming a longer soliton step, as shown in State 4, Fig. 1(d). Finally, in addition to continuous backward tuning of the pump laser wavelength, it is possible to deterministically generate varying numbers of solitons by tuning the auxiliary laser wavelength, as shown in State 5, Fig. 1(d).

Figure 2 is a schematic diagram of the DKS comb generation experiment. Two lasers are respectively emitted by tunable lasers and coupled into the microresonator from opposite directions. The blue line represents the pump path, and the red line represents the auxiliary path. The evolution of the optical field in the microresonator is observed at the pump output by an optical spectrum analyzer (OSA) and an electrical spectrum analyzer (ESA), and the real-time intracavity power changes in the pump path and the auxiliary path are monitored by an oscilloscope (OSC). The microresonator chip is adsorbed on the coupling platform, and the fiber array (FA) is clamped on a motorized platform with six degrees of freedom. Multiple coupling experiments show that the coupling loss between the chip and FA is <2dB on each side. The experimental image of the coupling between the FA and the chip is shown in Fig. S1(a) in the Supplementary Material, where the microresonator used in experiment is in the yellow box. Considering that the chip is easily affected by the temperature change of the external environment and the thermal effect caused by the high-power laser, the metal layer on the chip is used to control the temperature. The heating layer is connected to the temperature controller through the pad, and a PT1000 platinum resistance is fixed on the chip to measure the temperature of the chip in real time. The proportional integral derivative (PID) feedback algorithm is used to control the temperature of the chip at 50°C±0.02°C.

In the experiments, the powers of pump and auxiliary lasers are set at 1.2 W and 1.4 W, respectively, and the corresponding wavelengths are set at ∼1562.5nm and ∼1560.9nm, respectively. The linewidth of the two lasers is <100kHz. Adjust the two FPCs to maximize the output power of pump and auxiliary, and ensure that the two lasers in the microresonator are TM00 mode. It is necessary to fine-tune the auxiliary laser in the initial stage to make it as close as possible to the center of resonance and generate a chaotic comb, as shown in Fig. 3(b). Subsequently, the detuning of the auxiliary laser is kept constant, and the intracavity dynamics process is studied by the forward and backward tuning of the pump laser. Forward tuning and backward tuning of the pump laser are set in the same wavelength range, and the scanning speed is 1 nm/s. The electric field signal change in the microresonator is shown in Fig. 3(a), where the left and right sides of the orange line are the forward tuning and backward tuning of the pump laser, respectively.

The soliton steps exist in both tuning directions, and the soliton steps are significantly longer in the backward tuning. The ranges of soliton steps are 2.0 pm for forward tuning and 24.1 pm for backward tuning. The range is expanded more than 10 times, which can generate solitons in a larger pump detuning range. And the inset in Fig. 3(a) shows the 10 superimposed experimental traces of reversible generation of solitons of backward tuning with the same pump power and tuning speed, where solitons exist in the range of up to 35.3 pm. The experimental results are in agreement with the numerical simulations (in the Supplementary Material), and both demonstrate that the pump laser can generate solitons reversibly in backward tuning. Due to the ability to alleviate the thermal relaxation process during the backward tuning, which improves the stability of the soliton, the range of soliton steps is larger compared to forward tuning. Experiments have shown that solitons can be accessed from different detuning directions and that this property can be used to recover the solitons.

During forward tuning, after the phase matching conditions required for four-wave mixing (FWM) are satisfied, the output comb goes through the primary combs, secondary combs, and chaotic combs in turn, and the spectral evolution of the generated DKSs is shown in Figs. 3(c)–3(e). The pump laser wavelength is slowly and continuously increased based on the generation of chaotic combs, at which time the pump enters the red detuned region, as shown in Fig. 3(f), and the generation of DKSs can be observed with some probability. The wavelength of the pump laser continues forward tuning and leaves resonance from the red detuning region, and the intracavity power decreases. The auxiliary laser located in the blue detuning region passively approaches the resonance center, which in turn heats the microresonator. The stability of the temperature and power in the cavity is maintained, the further drift of the resonance wavelength is prevented, and the auxiliary output returns to the initial chaotic combs, as shown in Fig. 3(g).

Then the pump laser wavelength is backward tuned, and the pump laser re-enters the resonance from the red detuned region, and the multiple DKSs are reversibly generated, as shown in Fig. 3(h). The pump laser is continuously backward tuned, and the solitons gradually annihilate, forming a single DKS with a spectral envelope that matches the sech2 curve, as shown in Fig. 3(i). The single DKS spectrum has a comb spacing of 94.3 GHz, and the pump wavelength and auxiliary wavelength are 1562.5362 nm and 1560.9968 nm, respectively. The inset in Fig. 3(i) shows the pulse time of the single DKS measured by the APE autocorrelator, which is 10.6 ps. After the various DKS states have been formed, the radio frequency (RF) noise is relatively low and is basically in the state of the noise floor, as shown in Fig. 3(j). The whole tuning process does not depend on the fast scanning of the pump laser, and the length of the soliton step is also effectively extended, which is more convenient for the adjustment of the various DKSs. After several experiments, the above backward tuning scheme can stably generate a wide soliton step as long as the auxiliary laser is in the chaotic state at the initial time. The number of generated solitons depends on the initial detuning of the auxiliary laser, and the DKS can be generated deterministically by adjusting the detuning of the auxiliary laser.

With the conventional use of auxiliary laser tuning to generate DKS, the wavelength of the auxiliary laser is usually kept essentially unchanged. After the introduction of pump backward tuning, the detuning requirements for the auxiliary lasers are relaxed, and the thermal balance in the cavity is easier to achieve. Even if the initial detuning of the auxiliary laser is not accurately set, solitons could not be generated during the forward tuning but could still be reversibly generated during the backward tuning, as shown in Fig. 4.

When generating DKSs, the intracavity power is constant. In the dual-laser system, the intracavity power can be adjusted simultaneously in two dimensions, i.e., the intracavity power can be adjusted by tuning the auxiliary laser wavelength in addition to changing the pump wavelength, which changes the longitudinal power position of the soliton steps during the pump laser scan, allowing a larger number of solitons to be deterministically switched.

Under constant power and polarization conditions for the two lasers, the auxiliary laser is tuned, and the OSA records the change of the spectrum during the tuning process. As shown in Fig. 5, it reflects the process of changing the DKS state by increasing the auxiliary laser wavelength when the pump laser wavelength is fixed around 1562.529 nm. As the frequency of the auxiliary laser slowly approaches the resonance center, the cavity power increases, leading to microresonator reheating and causing the resonance in the cavity to red-shift. The detuned state of the pump laser relative to the resonance region moves toward reduced energy. Therefore, when the auxiliary laser is slowly tuned from 1560.9702 nm to 1560.9754 nm, the number of solitons generated in the cavity gradually decreases. The spectrum changes from 5 solitons to 2 solitons one by one, as shown in Fig. 5. The detuning of the auxiliary laser continues to be adjusted to reach a single soliton similar to state VIII in Fig. 3(b), and finally the soliton collapses. The corresponding schematic diagram of the soliton distribution in the microresonator is shown in the upper right corner of each spectrogram. The envelopes of a single soliton, two solitons, and three solitons are relatively regular and easy to distinguish. By determining the intracavity power position of a single soliton, we can infer the number of solitons at other powers. This method of fine-tuning the multiple solitons generated in the microresonator by tuning the auxiliary laser realizes the deterministic control of the soliton number during the generation process, and the stable switching of solitons is realized, which enriches the dynamic process in the cavity.

We have demonstrated a backward tuning scheme for reversible DKS generation, which uses thermal stabilization of the auxiliary laser and backward tuning of the pump laser to achieve reversible generation and deterministic switching of the soliton. Furthermore, the backward tuning scheme increases the length of the soliton steps and allows the soliton to be generated over a larger pump detuning range (24.1 pm), compared to traditional schemes^[20], which can only generate solitons within a few pm of pump detuning. In addition, this scheme reduces the stringent requirements for the auxiliary laser detuning so that, even if the initial detuning of the auxiliary laser is not accurately set, solitons could not be generated during the forward tuning, but could still be reversibly generated during the backward tuning. The experimental results show that the step length of the soliton generated by backward tuning is 10 times larger than that of forward tuning. Eventually, a low-noise DKS with a spectral range greater than 150 nm is generated in the microresonator, which proves the reversibility of soliton generation. And by adjusting the detuning of the auxiliary laser, precise control of the soliton number is realized. Notably, our scheme’s practicality and robustness stem from its relaxed requirements for auxiliary laser wavelength, making it applicable to microresonators with strong thermal effects. Additionally, the ability to reverse the pump laser tuning direction for soliton regeneration distinguishes our approach, highlighting the recoverability of solitons after collapse. This feature is of great significance for sustaining DKSs over extended periods, representing a crucial advancement for practical DKS applications.