1. Introduction

In the past two decades, the optical frequency comb comes to its era since the discovery of the self-referenced carrier-envelope offset phase-locking technique. The direct and accurate link between optical and microwave frequency becomes feasible. As one of the most prospective branches, Kerr frequency combs on microresonators have attracted significant interest [1–6]. Pumping a high-Q microresonator with a single monochromatic laser, hundreds of frequency teeth with identical frequency spacing can be simultaneously excited through cascaded four-wave mixing. Especially as the dissipative Kerr soliton state is obtained [7], the soliton microcombs yield low noise, phase coherence, and broad bandwidth, potentially reaching an octave-spanning. The high-Q property significantly extends the intracavity photon lifetime so that only a few milliwatts of pump power is large enough to trigger the parametric process. So far, power-efficient generation of soliton microcombs has been achieved on platforms such as silicon nitride (Si₃N₄) [8], magnesium fluoride (MgF₂) [7], highly doped silica glass [9], aluminum nitride (AlN) [10], thin-film lithium niobate on insulator (LNOI) [11,12], etc. These platforms simultaneously possess broadband transparency, high nonlinearity, and excellent dispersion engineering ability. Especially, platforms such as AlN and LNOI show both χ⁽²⁾ and χ⁽³⁾ nonlinearities so that self-reference can be achieved on a single chip [13,14].

The conventional method for the generation of soliton microcombs is to artificially scan either the pump frequency or the cavity resonance, thus shifts the pump frequency from an initial blue-detuned region to an effectively red-detuned region [7]. Although the frequency scanning method is maturely developed and widely adopted, it would be more attractive to achieve soliton microcombs in a turnkey manner. Turnkey generation of soliton microcombs does not require a high-performance tunable laser and complex feedback control, thus reduces system complexity and cost. In addition, the one-button self-started operation allows the comb source to enable field-deployable applications. Despite these apparent advantages, research of the turnkey generation of soliton microcombs is still in its infancy. Shen et al. proposed and experimentally demonstrated a fully integrated turnkey generation of soliton microcombs using Rayleigh backscattering assisted self-injection locking [15]. However, since the locking range and the laser linewidth are associated with the intensity of the Rayleigh backscattering [16], the Q-factor should be very high (>10⁷ in this work) to guarantee strong enough scattering intensity. Also, the intensity of the Rayleigh backscattering is random, so that the pump-to-chip coupling distance should be carefully adjusted. Theoretically, Zhang et al. studied the turnkey generation of soliton microcombs on an organically coated microresonator, which has a net negative thermo-optic coefficient (TOC) [17]. Under the negative TOC concept, Lobanov et al. studied the generation of platicon on normal dispersion microresonators and showed that turnkey operation is possible at ultra-high Q-factor (5×10⁹) conditions [18]. However, there is still no experimental evidence that such a multi-layer hybrid platform with negative TOC could simultaneously possess the Q-factor, dispersion, and nonlinear characteristics that the soliton microcombs require, especially for semiconductor microring resonators.

LNOI has gained increasing research interests in recent years due to the broadband transparency (0.4–5 µm), both χ⁽²⁾ and χ⁽³⁾ nonlinearities, tight mode confinement, and rich functionalities built upon multi-physics coupling, e.g. electro-optic, photo-elastic, and piezo-electric effects [19]. Many excellent devices have been reported on LNOI platform, including electro-optic modulators [20,21], acousto-optic modulators [22], rare-earth-ion-doped waveguide amplifiers [23], and Kerr microcombs [11,12]. As an inherent effect of lithium niobate (LN), photorefractive (PR) effect changes the refractive index of LN when it is exposed to an optical field, which is due to the excitation of charge carriers from crystal defect sites. This power-dependent refractive index change is strong and opposite to that of the Kerr effect and thermal effect, thus leads to an equivalent negative TOC condition (but much stronger) for turnkey generation of soliton microcombs. He et al. reported a self-starting and bi-directional switchable generation of soliton microcombs on PR-dominated LNOI microresonators [11]. But, the frequency scanning method was adopted, and whether it can operate in a turnkey manner is not clear. Besides, low noise and widely tunable lasers that can be on-chip integrated still meet difficulty. In this paper, we propose for the first time, to the best of our knowledge, that turnkey soliton microcombs can be achieved on PR-dominated LNOI microresonators. We note that the thermal effect becomes severe in small volume microresonators and might annihilate the soliton states in the effectively red-detuned region. Although the thermal effect is faster and much weaker than the PR effect on LNOI, it will induce competition and consequently periodic oscillation of the cavity resonance [24]. Thermal compensation methods are helpful but will significantly increase the complexity and cost. Due to the thermo-optic birefringence of LN, the TOC is almost zero for ordinary light at room temperature [25]. Thus, we can select polarization along the ordinary axis of LN, i.e. fundamental TM mode of x-cut LNOI or fundamental TE mode of z-cut LNOI, to ignore the thermal effect so that the PR effect becomes dominant. We statistically study the existence region of turnkey soliton microcombs in the parameter space of normalized initial pump-resonator detuning and normalized pump power by using the coupled Lugiato-Lefever equation (LLE) [11,24,26,27]. The effects and variation rules of different parameters, such as the total cavity loss rate and the normalized group velocity dispersion (GVD) parameter, are shown. Moreover, the deterministic and turnkey generation of single soliton microcombs assisted by phase-modulated pump laser is studied and discussed.

2. Principle

Power-dependent change of the refractive index in microresonators leads to bistability. Taking an x-cut LNOI microring as the example, Figs. 1(a)–1(b) show the cold cavity and the laser injected cavity with corresponding cavity resonances. When light is injected into the microresonator, the optical field will excite charge carriers due to the crystal defects. These excited charge carriers move along the optic axis of LN due to the bulk photovoltaic effect and reach a steady spatial distribution, which is shown by the signs of “+”, “−” and dotted arrows in Fig. 1(b). Therefore, the resulting space-charge electric field modifies the refractive index via the electro-optic effect of LN [19] and leads to the blue shift of the resonances. Figure 1(c) schematically shows the comparison of Kerr-bistability (green), thermo-bistability (red), PR-bistability (blue), and cold resonance (gray), respectively. We can see that the bistability regions of the Kerr effect and thermal effect fall into the red-detuned side, while the bistability region of the PR effect is in the opposite direction and falls into the blue-detuned side. The dotted curves indicate the middle branches of the bistability solutions which only exist in theory. Since the change of refractive index given by the PR effect is typically greater than that of the Kerr effect and thermal effect, the bistability curve of the PR effect is more tilted. The soliton microcombs locate in the effectively red-detuned region due to the Kerr bistability. The PR effect can drag the cavity resonance towards the shorter wavelength side, which is equivalent to blue-scanning the cavity resonance, thus makes turnkey generation of soliton microcombs possible.

 

Fig. 1. (a) Cold cavity and (b) Laser injected cavity with corresponding cavity resonances (@x-cut LNOI microring as an example). The axis shows the optic axis of LN, which is labeled by “e”. The signs of “+”, “−” and dotted arrows in (b) represent the space-charge electric field induced by the PR effect. The orientation is along the optic axis of LN. (c) Comparison of the Kerr-bistability, thermo-bistability, PR-bistability, and cold resonance. (d) Schematic diagram of intracavity energy variation profile of PR-induced turnkey operation with three evolution stages. (e) and (f) show the schematic diagrams of the principle of PR-induced turnkey operation when the pump is initially blue-detuned and red-detuned, respectively. The three stages (I)-(III) are corresponding to those in (d).

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Figure 1(d) shows the schematic diagram of the intracavity energy variation profile with three evolution stages. Figure 1(e) shows the schematic diagram of the principle of PR-induced turnkey generation of soliton microcombs when the pump is initially blue-detuned. In stage (I), the pump laser is initiated on the blue-detuned side (shorter wavelength) of the microresonator. The cavity resonance will be shifted towards the blue side due to the increase of intracavity energy. In stage (II), the blue shift of the resonance accompanies the accelerated growth of the intracavity power. Thus, the enhancing of the PR effect keeps dragging the resonance across the pump laser. Consequently, the pump laser is passively located to the existence region of soliton (green shaded) on the effectively red-detuned side. The intracavity field experiences modulation instability (MI), chaos, and reaches a soliton state with statistical soliton number. In stage (III), the formation of the soliton state abruptly decreases the intracavity power. This power change alarms the PR effect to stop the blue shift of the cavity resonance but turn to shift the resonance backward to the red side. This backward shift will not be strong so that the change of the intracavity power will converge to calm down the PR effect gradually. Thus, the pump laser and cavity resonance will finally lock with each other in the existence region of soliton. When the pump is initially red-detuned, the turnkey process is similar to that of the initially blue-detuned case, as shown in Fig. 1(f). The difference is that the pump laser is always on the red-detuned side without crossing over the cavity resonance. Moreover, we note that for the case the pump laser is initiated on the red-detuned side, the transition from the stage (I) to (II) is very quick. The gradually increasing of the intracavity energy at the initial stage shown in Fig. 1(d) will no longer exist.

The dynamics of the generation of soliton microcombs inside a microresonator is governed by the LLE,

The dynamics of the space-charge electric field induced by the PR effect is given by an excitation-relaxation process [11,24],

By normalizing Eqs. (1) and (2) we have,

In our simulations, the parameters of PR effect are chosen to Γ_sp = 125 kHz, g_E = 2.55×10⁴ Hz·m/V, η_sp = 3.91×10¹⁰ Hz·V/(m·W) according to the reported works [11]. We note that the parameter η_sp is approximate and is power-dependent actually [11,24]. However, models (2) and (5) still make sense to analyze the PR dynamics qualitatively. An adequate model of the PR effect needs further experimental evidence.

3. Results and discussion

3.1 Turnkey generation of soliton microcombs

We numerically calculate Eqs. (4–6) with split-step Fourier method to study the conditions and dynamics of turnkey generation of soliton microcombs on PR-dominated LNOI microresonators. We assume that the PR-induced detuning has a small change in one round-trip, thus Eq. (4) can be solved by the difference method with the step length of one round-trip time. A natural question for turnkey generation of soliton microcombs is how to initiate a pump laser, including the pump frequency and the power. In the parameter space of normalized initial pump-resonator detuning and normalized pump power, i.e. (ζ₀, p₀), we trace the boundary of the turnkey region at different combinations of κ and d₂. For each given ζ₀ within (−45, 15), we sweep p₀ within (0, 20) to see whether turnkey generation of soliton microcombs is possible. We do 100-run statistical simulations at each (ζ₀, p₀) operating point by seeding the pump with the single-photon quantum noise [28]. If it enters the soliton states and remains stable for a long time at least once in 100 runs, we think that turnkey generation of soliton microcombs can be achieved at this operating point and label this point as “Yes”. If all final states are continuous wave (CW) for all 100 runs, we think that turnkey generation of soliton microcombs can’t be achieved at this operating point and we label this operating point as “No”. Figure 2(a) shows the calculated boundaries of turnkey regions at a fixed total cavity loss rate of κ = 6.0 × 10⁸ s⁻¹ and different normalized GVD parameters of d₂ = 0.008, 0.016, and 0.024, respectively. We note that there exists an upper boundary of the turnkey region for d₂ = 0.008 at higher p₀. However, the physical pump power corresponding to that p₀ is so high (more than 1 W) that it is difficult to be realized for semiconductor lasers and does not meet the expectation of low power consumption. Therefore, our simulations stop at p₀ = 20.

 

Fig. 2. Turnkey regions in the (ζ₀, p₀) parameter space at (a) fixed κ and varied d₂; and (b) fixed d₂ and varied κ. The regions surrounded by and outside the boundary curves correspond to successful and failed turnkey operations, labeled as ‘Yes’ and ‘No’, respectively.

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We find that the smallest normalized GVD parameter of d₂ = 0.008 leads to the largest turnkey region. When the d₂ is increased, the area of turnkey regions shrinks. Especially, the upper and right boundaries shrink more apparently. We find that in our simulations the peak power of the solitons and the MI comb power have small changes for different d₂. Thus, a smaller d₂ will cause a smaller soliton comb energy, which then leads to a larger energy drop from MI state to soliton state (for the same soliton number). Due to the limitation of the existence region of soliton and the larger energy drop, the PR effect can stop the blue shift of the cavity resonances more easily to avoid shifting the total pump-resonator detuning out of the existence region of soliton. Therefore, a smaller d₂ leads to a broader turnkey region. Besides, it is not the case that the higher pump power is used, the broader turnkey region can be achieved. There is an upper p₀ boundary exceeding which the intracavity energy change, thus the normalized PR-induced detuning change, will be so strong that it will shift ζ out of the existence region of soliton directly. Moreover, we find that the turnkey region in the initial blue-detuned region (ζ₀ < 0) is much broader than that in the initial red-detuned region (ζ₀ > 0). This is because initiated from a red-detuned region, the cavity resonance and the pump move apart from each other from the start. This moving apart scenario accompanies the decrease of intracavity energy. Thus, the pump frequency should be initially located close enough to the cavity resonance so that the intracavity energy can be efficiently enhanced for exciting Kerr bistability. Figure 2(b) shows that the turnkey regions at fixed d₂ and varied κ have a similar variation law compared with that in Fig. 2(a). For a given d₂ = 0.016, the turnkey regions shrink apparently when κ is increased from 2.4×10⁸ s⁻¹, 6.0×10⁸ s⁻¹ to 1.2×10⁹ s⁻¹, which correspond to the physical loaded Q-factors of 5×10⁶, 2×10⁶, and 1×10⁶, respectively. This is because a microresonator with larger κ (lower loaded Q-factor) induces a narrower existence region of soliton. The PR effect shifting out of the normalized total pump-resonator detuning from the existence region of soliton becomes much easier. When κ is as large as 1.2×10⁹ s⁻¹, the turnkey operation becomes impossible at the initially red-detuned pumping condition. Therefore, we conclude that the turnkey generation of soliton microcombs is feasible at both initially blue- and red-detuned pumping conditions. A smaller d₂ and a smaller κ benefit the broad turnkey region.

To show the turnkey dynamics and the statistical characteristic of different states, we arbitrarily select four (ζ₀, p₀) operating points for example. The total cavity loss rate and normalized GVD parameters are fixed at κ = 6.0 × 10⁸ s⁻¹ and d₂ = 0.008, respectively. The four operating points are (ζ₀ = −16.5, p₀ = 10), (ζ₀ = 0, p₀ = 10), (ζ₀ = −3.5, p₀ = 13.2), and (ζ₀ = 3.5, p₀ = 13.2), which correspond to the scenarios of far blue-detuned and low power, zero-detuned and low power, near blue-detuned and high power, and near red-detuned and high power, respectively. Figures 3(a)–3(d) show the normalized intracavity energy variation profiles of 100-run statistical simulations. Zoom-in views of the soliton excitation stages are shown in all four operating points. For each operating point, we can see the soliton steps and the statistical behavior of the final states. Figures 3(e)–3(h) show the percentage for different number of solitons generated corresponding to these four operating points. The number zero indicates a final state of CW. We find that at the low pump power conditions, the percentage for CW state is high, i.e., failure of the generation of soliton microcombs. For example, Figs. 3(e) and 3(f) show that the percentage for CW state at (ζ₀ = −16.5, p₀ = 10) and (ζ₀ = 0, p₀ = 10) are 37% and 62%, respectively. The zero-detuned case (ζ₀ = 0) shows the worst percentage for generation of soliton microcombs because enhancing intracavity energy is so quick that it will shift the normalized total pump-resonator detuning out of the existence region of soliton at the early stage easily. We note that the percentage for CW state can be decreased by increasing the normalized pump power. Figures 3(g) and 3(h) show that the percentage for CW state is remarkably decreased when the normalized pump power is increased to p₀ = 13.2, regardless of the normalized initial pump-resonator detuning. Still, the near red-detuned case (ζ₀ = 3.5) has a higher CW percentage of 10% compared with that of 7% at the near blue-detuned case (ζ₀ = −3.5). We note that the four operating points all show that the 2-soliton state has the highest percentage of 35%, 21%, 43%, and 52%, respectively. But, the 3-soliton state disappears in a zero-detuned case. The results conclude that an operating point in the turnkey region with higher normalized pump power will lead to a better percentage for generation of soliton microcombs.

 

Fig. 3. The normalized intracavity energy variation profiles at κ = 6.0 × 10⁸ s⁻¹ and d₂ = 0.008 in the cases of (a) ζ₀ = −16.5, p₀ = 10, (b) ζ₀ = 0, p₀ = 10, (c) ζ₀ = −3.5, p₀ = 13.2 and (d) ζ₀ = 3.5, p₀ = 13.2. The inset shows the zoom-in view of the soliton excitation stages. Percentage for different number of solitons excited at κ = 6.0 × 10⁸ s⁻¹ and d₂ = 0.008 in the cases of (e) ζ₀ = −16.5, p₀ = 10, (f) ζ₀ = 0, p₀ = 10, (g) ζ₀ = −3.5, p₀ = 13.2, and (h) ζ₀ = 3.5, p₀ = 13.2.

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We study the dynamics of turnkey generation of soliton microcombs at the operating point of (ζ₀ = −16.5, p₀ = 10) at κ = 6.0 × 10⁸ s⁻¹ and d₂ = 0.008. Taking a case of generation of single soliton microcombs as an example, Figs. 4(a) and 4(b) show the variation profiles of the normalized intracavity energy and the normalized total pump-resonator detuning. Figure 4(c) shows the corresponding temporal evolution profile. We see that after the pump laser is switched on from the blue-detuned region of ζ₀ = −16.5, the intracavity field experiences, in turn, the states of MI, chaos, 4 solitons, and finally single soliton. The intracavity energy self-starts to be enhanced in the early stage and drops apparently due to the transition from the chaotic state to the soliton state. The featured soliton steps of 4-soliton and single soliton states are clearly shown in Figs. 4(a) and 4(c). Accordingly, the normalized total pump-resonator detuning ζ also self-starts and routes to the effectively red-detuned region during the MI and chaotic states. The abrupt crossing from blue- to the red-detuned region around τ = 0.1×10⁴ is attributed to the trigger of PR-bistability. When the intracavity field reaches the 4-soliton state, the blue shift induced by the PR effect becomes slow due to the drop of intracavity energy. This process manifests as a slow-down of the increasing of ζ. When the intracavity field further reaches the single soliton state, the intracavity energy drops again. Consequently, ζ cannot increase anymore but turn to decrease at τ= 0.4×10⁴ and finally converges to ζ = 16 in the existence region of a single soliton. The stable ζ is accompanied by the invariant of normalized intracavity energy, thus the cavity reaches balance and the single soliton state becomes stable.

 

Fig. 4. (a) Normalized intracavity energy variation profile, (b) Normalized total pump-resonator detuning variation profile, (c) Temporal evolution profile and (d) Normalized net MI gain evolution profile (unstable CW solution is used). (e) Instantaneous temporal profile (blue) and instantaneous spectral profile (purple) of the states of MI, chaos, 4 solitons, and single soliton.

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The most important step for soliton microcombs formation would be the appearance of primary combs through MI. To gain more physical insight, we have done the linear stability analysis of the CW solution Ψ₀ against periodic perturbations [29]. The perturbed ansatz is given by,

Substituting Eq. (7) into Eq. (4) and with first-order approximation, we can obtain the eigenvalues σ as,

The square root term in Eq. (8) describes the MI gain. The real part of σ_± describes the net MI gain, which is positive when the MI gain overcomes the loss. Therefore, we just consider σ₊. To investigate when the net MI gain will become positive during the turnkey process, we calculate σ₊ at a range of µ along the turnkey process. Figure 4(d) shows the normalized net MI gain evolution profile during the turnkey process. We see that the normalized net MI gain starts becoming positive at τ= 0.07×10⁴, corresponding to the normalized total pump-resonator detuning of ζ = −1.44. The frequency location is found to be µ ≈ ±50, which is shown by the horizontal dashed lines. There are some differences for the net MI gain evolution profile between the proposed turnkey method and the conventional frequency scanning method. For the conventional frequency scanning method, the pump frequency is usually scanned unidirectional, that is, scanning the pump frequency from the initially blue-detuned region to the effectively red-detuned region. Therefore, the value and the range of µ for the positive net MI gain will increase during the frequency scanning process. Moreover, the position of the peak positive net MI gain would locate at a larger µ. However, in our turnkey method, artificial frequency scanning is not needed. The PR-induced detuning is equivalent to automatically scanning the total pump-resonator detuning. Due to the negative power-dependent behavior compared to the Kerr effect, the PR-induced detuning will increase first and then decrease. Therefore, the behavior of the net MI gain evolution profile will be first broadened, which is similar to that of the frequency scanning method. Then, the net MI gain will experience a reverse process of shrinking, as shown in Fig. 4(d).

Figure 4(e) shows the instantaneous temporal profile (blue) and instantaneous spectral profile (purple) of the states of MI, chaos, 4 solitons, and single soliton during the evolution. For the state of MI, the temporal profile is modulated periodically, and primary sidebands appear at µ ≈ ±50 in the spectrum, which is coincident with the position of the initial positive net MI gain shown in Fig. 4(d). As for the chaotic state, the temporal and spectral profiles are both noisy, but more comb lines appear in the spectrum. When the 4-soliton state is reached, the temporal profile shows 4 solitons with random temporal locations. The spectral profile shows modulated sech² envelope. When the single soliton state is reached finally, a smooth sech² envelope is obtained in the spectrum. We also study the cases that the pump laser was not switched on instantaneously, but with the energy rise time less than, comparable to, and larger than the relaxation time of the PR effect (τ_PR = 1/Γ_sp = 8 µs). We find that the non-instantaneous switching on of the pump laser will not invalidate the turnkey generation of the soliton microcombs. Considering that the typical switch-on time of semiconductor lasers is microseconds scale or even less [15], our method is practically feasible. Even though a pump laser with a slow switch-on speed is required, one can consider integrating an electro-optic switch before the microresonator on the same LNOI chip, which is feasible with current techniques and would not add too much complexity.

3.2 Deterministic and turnkey generation of single soliton microcombs

We have shown that turnkey generation of soliton microcombs on PR-dominated LNOI microresonators is statistical. The experience of chaotic state results in the stochastic soliton numbers in the final states [7]. For practical applications, turnkey microcombs with deterministic single soliton state are more desirable. There have been some methods reported on the deterministic generation of single soliton microcombs, including joint forward and backward pump scanning [30], pump amplitude or phase modulation [31–34], and pulse trigger [35,36]. Benefitting from the excellent electro-optic characteristic, LNOI platform shows unique advantages in high-speed phase and intensity modulators with impressive 3-dB bandwidth beyond 100 GHz [20,37,38]. Therefore, combining the phase modulator and the microresonator on the same LNOI platform makes deterministic and turnkey generation of single soliton microcombs feasible.

Considering a sinusoidal response phase modulation, the normalized pump field is now given by,

By using the phase-modulated pump laser, Figs. 5(a)–5(d) show the temporal evolution profile, spectral evolution profile, normalized intracavity energy variation profile, normalized total pump-resonator detuning variation profile, respectively, during the turnkey generation of single soliton microcombs. The main parameters are κ = 6.0 × 10⁸ s⁻¹, d₂ = 0.016, ζ₀ = −3.5, p₀ = 7.2 and M = π/2. We can see that after a certain evolution time, the normalized intracavity energy becomes unchanged, and the normalized total pump-resonator detuning converges. The temporal profile finally evolves into a single soliton state and the spectral profile does not oscillate anymore. Figure 5(e) shows the zoom-in view of the soliton excitation stage in Fig. 5(a). We find that although the intracavity field experiences chaos and stochastic multi-soliton states, the final state can evolve into a single soliton. In the multi-soliton stage, the solitons assemble to the potential well established by phase modulation, which locates at the maximum phase modulation point, i.e., ϕ = π/2. During the assembling process, the solitons collide with each other and annihilate. Only one soliton survives and is locked at the temporal position of ϕ = π/2. Figure 5(f) shows the zoom-in view of the normalized intracavity energy, which represents clear soliton steps during the evolution. We note that the duration of the soliton step is non-uniform because the occurrence time of soliton colliding and annihilation is random. Figure 5(g) shows the instantaneous temporal profile at τ = 1×10⁴, where a single soliton with a temporal width of 1/210 of 2π is obtained. Figure 5(h) shows the corresponding instantaneous spectral profile. We find that most power of the central pump line is transferred to the adjacent sidebands due to phase modulation.

 

Fig. 5. (a) Temporal evolution profile, (b) Spectral evolution profile, (c) Normalized intracavity energy variation profile, and (d) Normalized total pump-resonator detuning variation profile during the turnkey generation of single soliton microcombs assisted by phase modulation. The main parameters are κ = 6.0 × 10⁸ s⁻¹, d₂ = 0.016, ζ₀ = −3.5, p₀ = 7.2 and M = π/2. (e) Zoom-in view of the soliton excitation stage in (a). (f) Zoom-in view of the normalized intracavity energy in (c). (g) Instantaneous temporal and (h) Instantaneous spectral profile of the single soliton microcombs at τ = 1×10⁴. (i) Percentage for the single soliton state at different modulation depths. (j) Temporal evolution profile during the deterministic and turnkey generation of single soliton microcombs at M = 18. Other parameters are kept unchanged. (k) Zoom-in view of (j).

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We note that the soliton colliding leads to soliton annihilation for the selected modulation depth in Figs. 5(a)–5(h), which means that the final result will be different for different multi-solitons states reached with even and odd soliton numbers. Thus, the percentage for single soliton generation is not 100%. By increasing the modulation depth to a certain threshold, soliton annihilation can transfer to soliton merging, which will let two solitons merge to one soliton and guarantee a 100% single soliton generation [31]. By doing 100-run statistical simulations at different modulation depths, Fig. 5(i) shows the percentage for the single soliton generation as a function of M. We find that the threshold of M is about M_thre = 16. For M < M_thre, the interaction of solitons is soliton annihilation, which makes the percentage less than 100%. When M ≥ M_thre, the percentage becomes 100% because the soliton merging replaces the soliton annihilation. Figures 5(j) and 5(k) show the temporal evolution profile of single soliton microcombs generation at M = 18 and the zoom-in view of the soliton merging stage. The other parameters are kept unchanged. Compared to that in Fig. 5(e) at M = π/2, Fig. 5(k) shows that all solitons in the multi-solitons state can collide and finally merge into a single soliton.

4. Summary

In summary, we propose and numerically demonstrate that turnkey generation of soliton microcombs can be achieved on PR effect dominated LNOI microresonators. Without artificial frequency scanning, the turnkey generation of soliton microcombs can be realized for either blue-detuned or red-detuned pumping conditions. Furthermore, using a phase-modulated pump laser, we demonstrate that deterministic and turnkey generation of single soliton microcombs can be achieved. In experiments, we can first characterize the microresonators to determine the resonance frequencies through a low-intensity frequency-scanning probe, thus determine which wavelength is desired to locate the pump laser. Then, we can either order the corresponding frequency-fixed pump lasers or the microresonators whose resonances can satisfy the available frequency-fixed pump lasers. To maintain the precise pump-resonance frequency detuning, the frequency-fixed laser should have a frequency stabilization unit. Besides, the turnkey region shown in our manuscript shows a broad range for the initial pump-resonance detuning, which reduces the restriction of the pump laser and practical operation.

Since the LNOI platform possesses multiple nonlinear characteristics, the influences of stimulated Raman scattering and nonlinear coupling between χ⁽²⁾ and χ⁽³⁾ nonlinearities on the turnkey generation of soliton microcombs will be investigated in further work. It might also be interesting whether the turnkey operation still works when the PR and thermal effects coexist. Our work proposes a competitive candidate for turnkey generation of soliton microcombs, which shows useful guidance to the experimentalists and paves the way for practical implementation of microcombs sources out of the lab.