Deterministic generation and switching of dissipative Kerr soliton in a thermally controlled micro-resonator

Dissipative Kerr solitons (DKSs) in the high-Q micro-resonator corresponds to self-organized short pulse in time domain via double balance between dispersion and Kerr nonlinearity, as well as cavity loss and parametric gain. In this paper, we first experimentally demonstrate deterministic generation and switching of DKSs in a thermally controlled micro-ring resonator based on high-index doped silica glass platform. In our scheme, an auxiliary laser is introduced to timely balance the intra-cavity heat fluctuation. By decreasing the operating temperature through a thermo-electric cooler, soliton crystal is firstly generated, then increasing the temperature, DKSs switching and single soliton are robustly accessed, which is independent of the tuning speed. During the switching process, varieties of DKSs are identified by tens of featured discrete soliton-steps, which is favorable for study of on-chip soliton interactions and nonlinear applications.

Micro-resonator-based dissipative Kerr solitons (DKSs) via parametric four-wave mixing (FWM) have drawn considerable interests in the last decade for its possibility of broad bandwidth, low power consumption and miniaturization operation. 1,2 DKSs have been successfully demonstrated in MgF 2 , Si 3 N 4 , Si, silica and AlN platforms, [3][4][5][6][7] among which the spectra cover from visible to mid-infrared window and the repetition rate ranges from several gigahertz (GHz) to terahertz (THz). 8 Up to now, DKSs have revolutionized the fields of dual-comb spectroscopy, 9,10 chip-scale distance-ranging, 11,12 low-noise microwave generation, 13 optical coherent communication system, 14,15 and astrocomb-based optical calibration. 16,17 To realize practical applications, stably and deterministically accessing single-soliton state is the fundamental issue. While the generation of DKSs in a high-Q micro-cavity requires keeping the pump at effective red-detuned regime where the system suffers from thermal instability. 18 Therefore, complicated techniques are developed to enable DKSs formation, such as rapid frequency tuning or two-protocol "power kicking" scheme, 3,6 as well as rapid thermaltuning method. 19 However, the number of soliton formed in the AIP Advances 9, 025314 (2019); doi: 10.1063/1.5080128 9, 025314-1 ARTICLE scitation.org/journal/adv resonator is relatively stochastic. 20 Recently, H. Guo, et al. introduced a backward frequency tuning scheme to deterministically achieve single soliton state. 21 Regrettably, this scheme relies on wavelength tunable laser which suffers from relatively high noise and broader linewidth typically on the order of ∼100kHz. Recently, an auxiliary-laser-heating method is proposed to access and stabilize the DKS state. 22 Within this scheme, an auxiliary laser is introduced to balance the thermal fluctuation inside the resonator. The intra-cavity heat reduction accompanying with the soliton state switching is compensated by the auxiliary laser which locates at the blue-detuned regime. Thus, the thermal instability is effectively alleviated and arbitrary laser detuning is allowed for the pump. However, in this scheme, the auxiliary and pump laser are in the same polarization state, thus the subsequent spectra-separation remains challenging, which restricts practical applications to some degree. Furthermore, the tunable laser is still required.
In this paper, we demonstrate deterministic DKSs generation and switching in a high-index doped silica glass micro-ring resonator (MRR) 23 using a thermo-electric cooler (TEC), which has been used to realize robust soliton crystal as presented in our previous work, 24 however, transition to single soliton is prohibited using single pump in our follow-up attempts. Here we introduce an auxiliary laser which is counter-coupled into the four-port MRR and orthogonally polarized compared with the pump. By sequentially decreasing and increasing the operation temperature, the DKS switching and annihilation could be clearly recognized from the optical spectra and characteristic discrete steps, which may help to research the intra-cavity soliton dynamics. 25 Additionally, it is convenient to separate the DKS from reflected auxiliary comb components using a polarization beam splitter (PBS), which could enable DKS-based applications and has been successfully used in quantum key distribution. 26 In a further proof experiment, we demonstrate that by setting the DKS-formed temperature, the center wavelength of dispersive waves (DW) could be easily tuned within a broadband range, and avoided mode-crossing free soliton comb can be obtained once the operation temperature is higher than 63.5 ○ C. Figure 1 shows the experimental set up for DKSs generation and switching, as well as spectra-separation. The monolithic integrated four-port high-Q MRR is packaged in a butterfly-package with a thermo-electric cooler (TEC), as shown in the inset, where a Chinese 1 dime is for scaling. The ring radius is ∼592.1µm, corresponding to the free spectral range (FSR) of ∼49 GHz. 24,27 The cross-sections of the ring and bus waveguides are both 2µm × 3µm. The MRR exhibits anomalous dispersion in communication band. 28 The Q factors of TM 00 mode (pump) and TE 00 mode (auxiliary) are 2.05×10 6 and 1.69×10 6 , respectively. 28 The MRR is pigtailed with a standard fiber array with coupling loss of ∼2.5dB per facet 24 and insert loss from other passive optical devices of ∼1dB. The operation temperature of the MRR can be precisely tuned through an external TEC controller. The pump laser (TM 00 , ECDL #1) for soliton is a narrow-linewidth laser whose wavelength is 1561.792nm in our experiment while the auxiliary laser (TE 00 , ECDL #2) is wavelength-tunable, allowing at least 1×FSR tuning range (0.4nm for this device). The two lasers are boosted to a similar power level (on-chip power of 31∼33dBm) using two commercial high-power erbium doped fiber amplifiers (EDFAs). Two fiber polarization controllers (FPCs) are used to control the polarization states of the two lasers. The circulators inhibit the strong light from transmitting to the EDFAs. The generated DKSs coupled out from the drop port are measured using two optical spectrum analyzers (OSAs), electrical spectrum analyzer (ESA) and oscilloscope (OSC).
In our experiments, the auxiliary and the pump laser are coupled into the orthogonal modes of the MRR simultaneously through carefully tuning the wavelength of the auxiliary laser, such as 1558.26nm in one of our tests. The pump laser is slightly closer to the corresponding resonance compared to the auxiliary laser while both of them are blue-detuned relative to each resonance. Fig. 2(a) sketches the complete evolution process of the intra-cavity optical spectra. Decreasing the operation temperature through the TEC, the pump first reaches the threshold of optical parametric oscillation (OPO). The primary and modulation instability (MI) combs are successively generated while the auxiliary laser keeps approaching the resonance but under the OPO threshold value (state (i) and (ii) of Fig. 2(a)). The corresponding experimental optical and electrical spectra are presented in state (i) and (ii) of Fig. 2(b), respectively. Further decreasing the temperature, the resonance climbs over the pump and the red-detuned regime is achieved, the corresponding optical spectrum exhibits soliton crystal feature (state (iii) of Figs 2(a) and (b)). 24,29 During this process, the resulting power drop of pump comb inside the MRR is effectively compensated by the power increment of auxiliary laser which locates at blue-detuned regime. This is clearly proved by the complementary steps of power traces shown in Figs. 3(a) and (b), which are monitored via the drop-and add-port of the MRR. Further decreasing the temperature (forward tuning), the frequency combs will vanish as illustrated in Fig. 3(a). In contrast, increasing the temperature from this stage (backward tuning), the soliton switching could be stably accessed. This behavior is indicated in Fig. 3(b) where the number of solitons in the MRR is reduced step by step until single soliton state is achieved. State (iv) of Fig. 2 (b) shows the single soliton spectrum, where the sech 2 fitting (red) suggests 114fs pulse width and 4.4nm (11×FSR) frequency shift induced by Raman self-frequency shift (RSFS) and soliton recoil. 30 The RF spectra show ∼48.97 GHz of repetition rate. Meanwhile, the discrete spikes comb lines reveals that the primary comb is stimulated simultaneously by the auxiliary laser. It should be noted that the state of the auxiliary comb is determined by the relative position of the pump and auxiliary lasers. These two combs are easily separated using a PBS in subsequent experiments.

FIG. 3.
The power trace under forward (a) and forward-backward tuning (b) schemes, the discrete steps suggest different soliton states, such as three-(i) and four-(ii) soliton state, whose spectra are shown as (i) and (ii) of (c), respectively.
It is intriguing that when the operation temperature is forward and backward tuned, the intra-cavity optical field exhibits entirely different feature. Such distinct observation is attributed to thermal nonlinearity in the MRR. 21 Specifically, to maintain the soliton states, the frequency of the pump should keep in the soliton existence range (SER) (δ L <δ<δ H ), where δ L and δ H are the lower and upper boundaries of the SER, respectively. The upper boundary δ H is degenerate with respect to the number of solitons. 21 Therefore, DKSs switching can't be realized by increasing the effective detuning of the pump, which corresponds to decreasing the operation temperature in our scheme. On the contrary, the lower boundary of the SER is nondegenerate with respect to the number of solitons which benefits from the thermal nonlinearity 21 of the high-Q MRR. Therefore, the staircase patterned power trace can be expected when the pump sweeps backward, equivalent to increasing the temperature in our experiments. Each step corresponds to a specific soliton state, as an example, the markers in Fig. 3 (b) are three-and four-soliton states whose spectra are shown as (i) and (ii) in Fig. 3(c), respectively.
In the optical spectrum of single soliton shown in Figs. 2(b), dispersive waves (DWs) 31 are clearly observed at the wavelength of ∼1490nm. We characterize the DW using a PBS, the pumpand reflected auxiliary-comb spectra are presented in Figs. 4(a) and (b), respectively. It is clearly seen that the components of the DWs are almost in the same polarization with the auxiliary comb (TE mode). To investigate this situation, further integrated dispersion calculations are performed and shown in Fig. 4(c), where unperturbed (dashed line, no mode crossing) and perturbed (solid line, mode crossing) dispersion curves are both presented for comparison. During the calculation, the thermal-optic effect is considered and the coupling factor G is assumed to be 2π×500MHz. 31 The good match between calculation and experiment reveals that the TE 01 mode is involved as interacting mode and strong modeinteraction 32 between TE 01 and TM 00 mode occurred inside the MRR, which leads to an avoided mode crossing on the mode dispersion curve (dashed line) that induces the DWs and mode hybridizations. 31 Therefore the DW components in our device are expected to be in TE 01 mode.
To determine the Raman property as well as characterizing the temporal profile of different soliton states, we performed the simulation using the damped, driven Lugiato-Lefever equation (LLE) with simplified Raman term in first order of Taylor expansion, 33,34 which is valid in our case because the pulse width of 114fs of our device is larger than 100fs: [34][35][36] (tR ∂ ∂t where E(t, τ) is the complex slowly varying amplitude of the intracavity electric field, t and τ are slow and fast time of the system. α and κ corresponds to the loss and coupling parameter, β 2 is the GVD value and β 3 is third order dispersion. L is the total MRR length. δ and γ are detuning and nonlinear parameters, respectively. First term on right hand side is Kerr nonlinearity while another contributes to the Raman interactions, where τ R is the Raman shock time which is partly responsible for self-frequency shift. 34,37 During the simulation, τ R is 2.7 fs 34 and other material-related parameters are calculated with a finite element solver. 34 The β 3 and δ values are used to delicately adjust the global dispersion curve. The calculation is realized through fourth-order Runge-Kutta method. 38 The simulated spectrum (red envelope) in Fig. 4(d) is in good agreement with the experimental results (midnight blue) and the inset is the expected soliton pulse inside the MRR. Theoretically, the DKS could be achieved at any operation temperature provided that the wavelength, detuning and polarization of pump and auxiliary laser are appropriately chosen. The change of temperature could help us to control the center wavelength of DW. Fig. 5 shows the experimental results of four 2-soliton state under ∼44.6 ○ C, ∼48.5 ○ C, ∼55.5 ○ C and ∼63.5 ○ C, respectively. The DW is shifted significantly to shorter wavelength with increasing temperature. Remarkably, when the temperature is ∼63.5 ○ C, the mode-crossing point is tuned out of threshold and no obvious DW is observed, the corresponding spectrum exhibits perfect smooth envelope without any local defects. Our scheme provides a viable and easy way to manipulate the spatial-mode induced DW.
Right now, the number of soliton is not strictly reduced one by one in our experiments (N, N-1⋅⋅⋅1), 21 this is attributed to the fact that manually temperature-tuning through a variable-resistor in our current configuration is not precise. We believe that deterministically one-by-one soliton annihilation can be realized once the temperature is tuned at a precision of ∼0.02 ○ C, which is one order more precise than the SER. This can be realized using programmable digital-to-analog converter to adjust the TEC temperature instead of inexactly manual tuning, besides, an on-chip microheater could also be a considerable choice for strict deterministic DKSs switching.
In conclusion, we experimentally demonstrate deterministic generation and switching of DKSs in a thermally controlled highindex doped silica MRR with a wavelength-fixed pump. Our scheme is absolutely tuning-speed independent which attributes to the fact that the intra-cavity heat fluctuation is timely balanced by an orthogonally polarized auxiliary laser. Varieties of DKSs and their switching processes are obtained, which is insightful to research the soliton dynamics. Furthermore, the auxiliary laser could be completely filtered out simply using a PBS. By simply determining the DKSformed temperature, the center wavelength of DW could be broadly tuned. Our scheme is expected to provide high-performance DKSs in practical applications.
We would like to draw the readers' attention that during the submission of this work, dissipative Kerr soliton generation using an auxiliary laser has recently been demonstrated within silica rod platform independently. 39,40