## Abstract

In this work, we demonstrate the generation of breather solitons in an aluminum nitride (AlN) microresonator. Our study shows different techniques for excitation of breather solitons together with stimulated Raman scattering (SRS) by pumping the fundamental transverse electric (TE_{00}) mode. With suitable pump power and laser scan speed, we can eliminate the Raman effect and achieve a single soliton comb (FSR ∼ 374 GHz) beyond 4/5 of an octave-spanning bandwidth (1200–2100 nm). We have also demonstrated the breather and single soliton (FSR ∼ 364** **GHz) states by pumping the first-order TE (TE_{10}) mode using another device with a similar geometry. Our study adds significant development in the dynamics of solitons in the AlN platform.

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## 1. Introduction

Dissipative Kerr solitons (DKSs) are ultrashort, coherent light pulses that retain their shape over time in a nonlinear optical resonator [1]. The prerequisites for temporal self-localized soliton generation are the double balance between the cavity dispersion counterbalanced by the Kerr nonlinearity as well as cavity losses counterbalanced by the nonlinear parametric gain [1,2]. The discovery of the Kerr soliton in microresonators [1] revolutionized the applications in advanced optical communications [3], optical frequency synthesizers [4], dual-comb spectroscopy [5], and ultra-fast distance measurements [6]. In recent years, there have been significant advancement in Kerr soliton generation in a variety of platforms such as MgF_{2} [1], Silica [7], Si_{3}N_{4} [8–10], AlGaAs [11], LiNbO_{3} [12] and AlN [13]. Moreover, various novel soliton states such as the Stokes soliton, soliton molecules, soliton crystals, and breathing solitons have been reported. As opposed to the self-localized stationary soliton states, breather solitons have energy localized in space with temporal oscillations (or vice versa) [14,15]. The imbalance between the dispersion and Kerr nonlinearity along with cavity losses and gain induces intrinsic dynamic instability. Breather solitons are generated due to induced dynamic instability [15] or in the single soliton region, due to the avoided mode crossing (AMX) [16]. Owing to the intrinsic dynamic instability, breather solitons can be accessed between the modulation instability (MI) comb and the soliton state [17]. Breather solitons have a narrow existence window on detuning the cavity resonance, hence making it challenge though vital to characterize them while avoiding instabilities and high noise regimes. To date, novel breather solitons have been demonstrated only in Si, Si_{3}N_{4} and crystalline MgF_{2} platforms [14–16].

Crystalline AlN microresonators have strong Pockels (*χ*^{2}) and Kerr (*χ*^{3}) nonlinearities making them potential candidates for broadband Kerr comb [18] and soliton generation [13,19–21]. In this work, the AlN microresonator we employed can support fundamental transverse-electric (TE_{00}) and first-order TE modes (TE_{10}), with a mode separation of as close as ∼12pm (∼1.5 GHz). Optimal design parameters are vital for generating adjacent resonances with modes that can achieve thermal equilibrium in the microring [10]. A laser scan technique was used to pump the TE_{00} mode while the TE_{10} mode acts as an auxiliary mode to balance the thermo-optic effect and so to allow us to access the soliton states [19]. We achieved the breather solitons accompanied by the stimulated Raman scattering (SRS) at a 250 mW on-chip power and 1nm/s laser scan speed. Moreover, to understand the link between the laser detuning speed and thermal balance, we scanned the pump resonance wavelength at varying speeds to study the breather soliton accessibility. The interplay between the Raman and Kerr effects hinders the process of stable single soliton generation [22,23]. At a relatively high on-chip power of 400 mW and a laser speed of 14 nm/s, we can access the broadband single soliton (beyond 4/5 of octave-spanning) without SRS. Such a broad soliton comb makes the AlN platform a feasible candidate system for an on-chip self-referencing 2*f*−3*f* scheme [24].

## 2. Device characterization

AlN-on-sapphire microring resonators of 60-µm-radius with the free spectral range (FSR) of 374 GHz, fabricated by a standard photolithography method, are utilized in our experiment [25]. A microring with a cross-section of 2.29×1.2 µm^{2} is integrated with a 1.11-µm-wide bus waveguide, with a gap of 0.5 µm.

#### 2.1 Experimental setup

Figure 1 depicts the experimental setup for soliton generation and characterization. An external cavity tunable laser (Santec TSL-710) is amplified by an erbium-doped amplifier (EDFA) and pumped into the microresonator via a tapered lensed fiber. The desired input polarization is selected and controlled by a fiber polarization controller (FPC). The comb spectrum at the output is collected using another lensed fiber which is sent further in two paths, one to an optical spectrum analyzer (OSA) to observe the spectrum and second to a fiber Bragg grating (FBG). The band rejection (BR) part of the FBG is used for the radio frequency (RF) noise measurements using an electrical spectrum analyzer (ESA). Transmission and soliton intensity were measured with the Santec multi-port power meter (MPM), connected to the band pass (BP) part of the FBG filter.

#### 2.2 Results

Figure 2(a) shows the transmission spectrum of TE polarized light over a range of 20 nm, which is measured using a CW laser with −14 dBm output power and a synched power meter with 0.1 pm resolution. The total chip insertion loss is ∼6.4 dB, mainly contributed by the coupling loss of about ∼3.2 dB per facet. Figure 2(b) is the zoom-in view of two nearby modes, with fitted curves, with TE_{00} (pump mode) and TE_{10} (auxiliary mode), at resonances of 1556.68 nm and 1556.69 nm respectively. In this work, the AlN microresonator we employed can support fundamental transverse electric (TE_{00}) and first order TE modes (TE_{10}), with a mode separation of as close as ∼12pm (∼1.5 GHz). The two close modes methodology in these resonators differs from our soliton crystal work, reported elsewhere [20], which were caused by avoided mode crossing (AMX). The loaded quality factors (Q_{L}) of the pump and auxiliary modes are 5.9×10^{5} and 5.5×10^{5}, respectively. As shown in Fig. 2(c), the FSRs of the TE_{00} and TE_{10} modes are measured to be ∼374 and ∼364 GHz, while the two Q_{L} approach each other near 1556.68 nm, indicating a weak mode coupling between the two transverse modes. The intrinsic quality factor (Q_{int}) of the TE_{00} mode resonance at 1550.66 nm without mode coupling is calculated to be 1.1×10^{6}, with a slightly over-coupling condition, corresponding to a propagation loss of 0.33 dB/cm.

## 3. Breather soliton and solitons for TE_{00} mode

To experimentally demonstrate the breather soliton, we pump the microresonator at a 250 mW on-chip power and sweep the laser wavelength with 1nm/s speed over the resonances. Figure 3(a) represents the triangular transmission trace with the two discrete steps that are due to the TE_{00} and TE_{10} modes. The colored shadings on the transmission correspond to five different comb states i.e. (i) primary comb, (ii) modulation instability (MI) comb, (iii) breather soliton, (iv) breather soliton with SRS, and (v) SRS. We keep the same pump tuning speed and carefully select different stop wavelengths to access various comb states and the plotted evolution map is shown in Fig. 3(b). At certain detuning positions, change in the spectrum is obvious from the primary comb (dashed line i) to MI comb state (dashed line ii), breather soliton states without and with SRS (dashed line iii & iv). During these measurements, all of the spectra are in steady-state regime and can last for over fifteen minutes. Figures 3(c)–3(d) show the relevant optical and RF spectra at five different states. Explicitly looking into the comb evolution, at a certain threshold, cavity power builds up hence initializing the strong third order Kerr nonlinearity four-wave mixing (FWM), generating the primary comb with few sidebands. The multi-FSR (15×FSR) primary comb lines in the state (i) of Fig. 3(c) are generated at a stop wavelength of ∼1556.77 nm with a low-frequency RF noise spectrum shown in Fig. 3(d) (state i). Further increasing the cavity power by sweeping the laser wavelength at a red-detuned stop wavelength of ∼1556.86 nm, the single-FSR MI comb is produced with a broad RF noise spectrum [in Fig*.* 3(d) state ii]. The breather soliton without and with SRS are accessed and plotted in Fig. 3(c) state (iii) and (iv) respectively, at the stop wavelengths of ∼1556.87 nm and ∼1556.89 nm. The measured spectra range from 1200–2200 nm in states (ii-iv) and extends below 1200 nm, which is beyond our OSA range. Both the RF noise at states iii and iv significantly decreases and series of sharp tones correspond to the soliton breather states [14,15]. Various studies have been done to explore the switching and coexistence between the SRS and FWM Kerr microcomb [26–28]. Here, in state (iv), we noticed the broadening of the RF breather frequency, which we attribute to the coexistence of the breather soliton and SRS. Considering the coherence of the breather soliton, the locking between soliton and the SRS is worth investigating for applications in microwave photonics. We presume that the Stokes line originates from the adjacent TE_{10} mode and belong to the higher order mode considering that the combs near the SRS line has a smaller spacing compared with that of the breather soliton. As shown in state (v) of Fig. 3(c), by sweeping the laser wavelength to ∼1556.9 nm prior to it going off the cavity resonance, we get third order nonlinear SRS line with a shift of 656 cm^{−}, corresponding to the phonon $E_2^{high}$[19,29].

To further validate the absence of nonlinear competition between these two close modes, we pump the adjacent three groups of TE resonances at 250 mW power and plot their transmissions in Fig. 4(a). In Fig. 4(a), the TE resonance modes at ∼ 1553.65 nm (state i, orange trace) the TE_{00} mode is at the blue- detuned side and TE_{10} is at red detuned side. However, at resonance modes ∼ 1559.65 (state (ii), green trace) and ∼ 1562.65 nm (state iii, blue trace) the TE_{00} is at red detuned side which exhibits good agreement with measured transmission at low power [see Fig. 3(a)]. Figures 4(b) and 4(c) summarize the comb spectra when pumping different TE_{00} and TE_{10} modes at 250 mW. Due to efficient third order Kerr nonlinearity and suitable Q factor, broad combs are generated by pumping the TE_{00} resonance modes (i-iii) as shown in Fig. 4(b). However, in Fig. 4(c), the laser wavelength was now scanned across the TE_{10} resonance modes of the specific groups (i-iii). We observe few comb lines (primary comb) and/or SRS lines which can confirm the SRS line in Fig. 3(c) states (iv) and (v) is also from the TE_{10} mode.

The non-linear microresonator heats up due to the thermo-optic effect when pumped with the CW light. To access the coherent single soliton state, the thermal equilibrium in the cavity is vital. This can be achieved by the three key parameters such as threshold power, laser scan speed over the resonance and Q-factor [1,15]. We scan the laser wavelength over the resonance mode at different detuning stop positions, which are 1556.865, 1556.845 and 1556.805 nm, with continuous sweep speeds of 2, 6 and 10 nm/s, respectively. We can stably and repeatedly access breather soliton and single soliton spectra [see Fig. 5(a)] and their corresponding RF spectra are shown in Fig. 5(b). Finally, by increasing the on-chip power to 400 mW, we can access the single soliton microcomb beyond 4/5 of an octave span with a relatively fast sweeping speed of 14 nm/s. We are using a relatively slow sweeping speed compared with the thermal relaxation in the cavity owing to the presence of the auxiliary mode, while the scan speed also needs to be optimized to reach the thermal equilibrium for the single soliton generation [1]. Figure 5(c) shows the generated single soliton microcomb spectrum ranges from 1200 to 2100 nm (total span of 108 THz), with a 3 dB bandwidth of 9 THz according to the fitted sech^{2} envelope (black dashed line). The low noise RF spectrum equivalent to the photodetector floor noise level as shown in the Fig. 5(d), corresponds to phase-locked coherent single soliton state.

## 4. Breather solitons in TE_{10} modes

To further explore the dynamics of the breather soliton, another device with the same cross-sectional parameters (2.29×1.2 µm^{2}) and radius (60µm) is used. In this case, the breather soliton and low noise signal soliton are observed when pumping the higher order TE (TE_{10}) mode with as high as ∼450 mW power. A relatively high Q_{int} of ∼1.05×10^{6} is extracted at resonance of ∼1563.93 nm to trigger these nonlinear processes in the TE_{10} mode. In addition, in this microresonator, there is no Raman effect to suppress the microcomb generation. By careful manually increasing the laser wavelength to 1564, 1564.06, 1564.08, and 1564.11 nm, respectively, we observed (i) primary comb, (ii) MI comb, (iii) breather and (iv) single soliton (ranging from ∼ 1425–1750nm) successively, as shown in Fig. 6(a). Corresponding RF spectra are shown in Fig. 6(b), where the high noise level is observed at state (ii), which drastically reduces to narrow and sharp RF beat note at comb state (iii). The low noise RF beat note spectrum in Fig. 6(b) without any sharp peaks corresponds to the state (iv) single soliton comb.

We now look at modelling the comb and soliton dynamics in the resonator. The integrated dispersion (D_{int}) derived from the Taylor expansion of resonance frequencies around pump can be written as, ${D_{int}}(\mu )= {\omega _\mu } - ({{\omega_0} + {D_1} \cdot \mu + 1/2!{D_2} \cdot {\mu^2} +{\cdot}{\cdot} \cdot{\cdot} \cdot{\cdot} \cdot{\cdot} } ),$ where *µ* is relative mode number, *ω _{0}* is pump frequency

*, D*is FSR of microresonator around the pump, and

_{1}*D*is second-order dispersion [2]. The red solid curve plotted in bottom stack [see (iv) in Fig. 6(a)] shows the calculated D

_{2}_{int}for TE

_{10}mode with extracted D

_{1}/2π of ∼368 GHz. The D

_{2}/2π is 37.3 MHz, corresponding to a β

_{2}of −0.31 ps

^{2}/m through $\; {D_2} ={-} c/nD_1^2{\beta _2}$, indicating pump is in the anomalous dispersion regime.

We use the Lugiato-Lefever equation (LLE) to simulate comb dynamics when pumping the TE_{10} modes. The LLE equation can be written as follows [14,30]:

*E(t, τ)*is slowly varying field envelope,

*α*is cavity loss per roundtrip time

*t*,

_{R}*δ*is pump cavity detuning, L is cavity length, ${\beta _k}$ is kth order dispersion coefficient and $\gamma = {n_2}{\omega _0}/c{A_{eff}}$ is nonlinear coefficient with n

_{2}as nonlinear refractive index,

*ω*

_{0}is pump frequency,

*c*is speed of light and

*A*

_{eff}is effective modal area obtained using COMSOL finite element modeling. The TE

_{10}mode at resonance wavelength of ∼1563.93 nm has a Q

_{int}∼1.05×10

^{6}and simulated nonlinear coefficient

*γ*of 0.72 W

^{−1}m

^{−1}in this case. Using the simulated dispersion [see red line in iv of Fig. 6(a)], nonlinear coefficient

*γ*value and extracted Q factors single soliton is obtained at a relatively high power of 490 mW. Figure 6(c) plots the breather and single soliton spectra, which agree with measurement results shown in Fig. 6(a). In Fig. 6(d), the top and bottom are temporal comb evolution and comb power versus pump detuning. The red dashed lines iii and iv indicates breather soliton and single soliton states at detuning position.

## 5. Conclusion

In conclusion, with a relatively slow forward sweeping (1nm/s) technique, we have experimentally demonstrated the breather soliton together with SRS by pumping the two nearby TE modes in an AlN microresonator. Further work will be performed on our device for the control and stabilization of the breather frequency using an injection-locking technique [31]. A relatively high forward sweeping speed has been shown to help avoid the SRS. A near octave-spanning (beyond 4/5) single soliton was realized at a pumping speed of 14 nm/s and power of 400 mW, which can be potentially utilized with in the integrated 2*f*−3*f* scheme of self-referenced Kerr microcombs on an AlN chip [24]. Moreover, we demonstrated breather and single soliton states using the TE_{10} mode in another device with similar dimensions. Our study using AlN microresonators is a significant addition in the study of soliton dynamics. Furthermore, considering that both TE modes can be used for soliton generation, soliton molecules are expected to be achieved in a single resonator for broadening the applications in a dual-comb spectrometer [32].

## Funding

Science Foundation Ireland (17/NSFC/4918); National Natural Science Foundation of China (61861136001).

## Disclosures

The authors declare no conflicts of interest.

## Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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