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•https://doi.org/10.1364/OPTCON.444775
Breather solitons in AlN microresonators
Adnan Ali Afridi, Haizhong Weng, Jing Li, Jia Liu, Michael McDermott, Qiaoyin Lu, Weihua Guo, and John F. Donegan
Adnan Ali Afridi,1 Haizhong Weng,1,3 Jing Li,1 Jia Liu,2 Michael McDermott,1 Qiaoyin Lu,2 Weihua Guo,2,4 and John F. Donegan1
1School of Physics, CRANN and AMBER, Trinity College Dublin, Dublin 2, Ireland
2Wuhan National Laboratory for Optoelectronics, and School of Optical and Electronic Information, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, China
3haizhong.weng@tcd.ie
4guow@mail.hust.edu.cn
Haizhong Weng https://orcid.org/0000-0002-9424-9645
John F. Donegan https://orcid.org/0000-0002-5240-1434
A Afridi
H Weng
J Li
J Liu
M McDermott
Q Lu
W Guo
J Donegan
Adnan Ali Afridi, Haizhong Weng, Jing Li, Jia Liu, Michael McDermott, Qiaoyin Lu, Weihua Guo, and John F. Donegan, "Breather solitons in AlN microresonators," Opt. Continuum 1, 42-50 (2022)
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Nonlinear Optics
Dissipative solitons
Raman scattering
Solitons
Stimulated Raman scattering
Stimulated scattering
Temporal solitons
Original Manuscript: September 30, 2021
Manuscript Accepted: December 6, 2021
Article Outline
Device characterization
Breather soliton and solitons for TE mode
Breather solitons in TE modes
Equations (1)
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 (TE00) 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 (TE10) 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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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 MgF2 [1], Silica [7], Si3N4 [8–10], AlGaAs [11], LiNbO3 [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, Si3N4 and crystalline MgF2 platforms [14–16].
Crystalline AlN microresonators have strong Pockels (χ2) and Kerr (χ3) 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 (TE00) and first-order TE modes (TE10), 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 TE00 mode while the TE10 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 2f−3f 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 µm2 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.
Fig. 1. Components used in experimental setup for generation, and characterization of soliton. CW: Continuous wave tunable laser (Santec TSL-710), FPC: fiber polarization controller, EDFA: erbium doped fiber amplifier, OSA: optical spectrum analyzer, FBG: fiber Bragg grating, PD: photodiode, ESA: electrical spectrum analyzer.
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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 TE00 (pump mode) and TE10 (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 (TE00) and first order TE modes (TE10), 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 (QL) of the pump and auxiliary modes are 5.9×105 and 5.5×105, respectively. As shown in Fig. 2(c), the FSRs of the TE00 and TE10 modes are measured to be ∼374 and ∼364 GHz, while the two QL approach each other near 1556.68 nm, indicating a weak mode coupling between the two transverse modes. The intrinsic quality factor (Qint) of the TE00 mode resonance at 1550.66 nm without mode coupling is calculated to be 1.1×106, with a slightly over-coupling condition, corresponding to a propagation loss of 0.33 dB/cm.
Fig. 2. (a) Transmission spectrum of the device at TE modes polarization with a ∼40 µW input power. (b) Two fitted close TE00 and TE10 modes with a separation of ∼12 pm around 1556.68 nm. (c) Measured FSRs and calculated QL for TE resonances in a 20 nm range.
3. Breather soliton and solitons for TE00 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 TE00 and TE10 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 TE10 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].
Fig. 3. (a) Measured pump transmission at 250 mW power, with different shadings correspond to the comb states from (i)-(v). (b) Microcomb evolution map at certain stop wavelengths. (c) Evolution of comb spectra at 250 mW on-chip power with certain detuning stop positions generating (i) primary comb, (ii) MI comb, (iii) breather soliton, (iv) breather solitons with SRS, inset shows zoomed-in image of SRS and breather comb lines (v) SRS with weak anti-Stokes lines emission. (d) RF spectra corresponding to different evolution states in (c).
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 TE00 mode is at the blue- detuned side and TE10 is at red detuned side. However, at resonance modes ∼ 1559.65 (state (ii), green trace) and ∼ 1562.65 nm (state iii, blue trace) the TE00 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 TE00 and TE10 modes at 250 mW. Due to efficient third order Kerr nonlinearity and suitable Q factor, broad combs are generated by pumping the TE00 resonance modes (i-iii) as shown in Fig. 4(b). However, in Fig. 4(c), the laser wavelength was now scanned across the TE10 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 TE10 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 sech2 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 TE10 modes
To further explore the dynamics of the breather soliton, another device with the same cross-sectional parameters (2.29×1.2 µm2) and radius (60µm) is used. In this case, the breather soliton and low noise signal soliton are observed when pumping the higher order TE (TE10) mode with as high as ∼450 mW power. A relatively high Qint of ∼1.05×106 is extracted at resonance of ∼1563.93 nm to trigger these nonlinear processes in the TE10 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.
Fig. 4. (a) Transmission traces for the three set (i-iii) of the same mode family (TE) resonances at an on-chip power of 250 mW. (b) Kerr comb optical spectra generation by pumping the three different TE00 resonance modes corresponding to (a). (c) Optical spectra of few comb lines due to weak FWM and/or SRS generated by pumping the TE10 mode at three different sets of resonance wavelengths.
Fig. 5. (a) Experimental observation of the breather soliton, breather soliton with SRS and coherent single soliton at fixed pump power of 250 mW and laser detuning speeds of 2, 6 and 10 nm/s. (b) Corresponding RF spectra evolution. (c) Optical spectrum of sech2 fitted 4/5 octave-spanning single soliton at 400 mW on-chip power achieved with manual tuning. (d) Low-frequency intensity noise of near octave soliton and the PD floor noise.
Fig. 6. (a) Experimental results showing evolution of typical optical spectra (state i-iv), for (i) primary comb, (ii) MI comb, (iii) breather and (iv) single solitons. The red solid curve line in (iv) is Dint simulation for TE10 mode. (b) Corresponding RF spectra. (c) Simulated spectra of breather soliton (top) and single soliton (bottom) corresponds to red dash lines marked in Fig. 6(d), when pumping TE10 mode at a power of 490 mW. (d) Simulated comb temporal evolution (top) and comb power (bottom) versus the normalized detuning.
We now look at modelling the comb and soliton dynamics in the resonator. The integrated dispersion (Dint) 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, ω0 is pump frequency, D1 is FSR of microresonator around the pump, and D2 is second-order dispersion [2]. The red solid curve plotted in bottom stack [see (iv) in Fig. 6(a)] shows the calculated Dint for TE10 mode with extracted D1/2π of ∼368 GHz. The D2/2π is 37.3 MHz, corresponding to a β2 of −0.31 ps2/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 TE10 modes. The LLE equation can be written as follows [14,30]:
(1)$$\mathop t\nolimits_R \frac{{\partial E(t,\tau )}}{{\partial t}} = \left[ { - \alpha - i\delta + iL\sum\limits_{k \ge 2}^n {\frac{{{\beta_k}}}{{k!}}{{\left( {i\frac{\partial }{{\partial \tau }}} \right)}^k} + i\gamma L\mathop {|E |}\nolimits^2 } } \right]E(t,\tau ) + \sqrt \theta \mathop E\nolimits_{in}$$
where E(t, τ) is slowly varying field envelope, α is cavity loss per roundtrip time tR, 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 n2 as nonlinear refractive index, ω0 is pump frequency, c is speed of light and Aeff is effective modal area obtained using COMSOL finite element modeling. The TE10 mode at resonance wavelength of ∼1563.93 nm has a Qint ∼1.05×106 and simulated nonlinear coefficient γ of 0.72 W−1m−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.
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 2f−3f scheme of self-referenced Kerr microcombs on an AlN chip [24]. Moreover, we demonstrated breather and single soliton states using the TE10 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].
Science Foundation Ireland (17/NSFC/4918); National Natural Science Foundation of China (61861136001).
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.
1. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, "Temporal solitons in optical microresonators," Nat. Photonics 8(2), 145–152 (2014). [CrossRef]
2. T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, "Dissipative Kerr solitons in optical microresonators," Science 361(6402), eaan8083 (2018). [CrossRef]
3. A. Fülöp, M. Mazur, A. Lorences-Riesgo, Ó. B. Helgason, P. H. Wang, Y. Xuan, D. E. Leaird, M. Qi, P. A. Andrekson, A. M. Weiner, and V. Torres-Company, "High-order Coherent Communications Using Mode-locked Dark-pulse Kerr Combs from Microresonators," Nat Commun 9(1), 1598 (2018). [CrossRef]
4. D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. H. Lee, D. Y. Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, "An optical-frequency synthesizer using integrated photonics," Nature 557(7703), 81–85 (2018). [CrossRef]
5. M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, "Microresonator soliton dual-comb spectroscopy," Science 354(6312), 600–603 (2016). [CrossRef]
6. P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, "Ultrafast optical ranging using microresonator soliton frequency combs," Science 359(6378), 887–891 (2018). [CrossRef]
7. X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, "Soliton frequency comb at microwave rates in a high-Q silica microresonator," Optica 2(12), 1078–1085 (2015). [CrossRef]
8. C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, "Thermally controlled comb generation and soliton modelocking in microresonators," Opt. Lett. 41(11), 2565–2568 (2016). [CrossRef]
9. M. H. P. Pfeiffer, C. Herkommer, J. Liu, H. Guo, M. Karpov, E. Lucas, M. Zervas, and T. J. Kippenberg, "Octave-spanning dissipative Kerr soliton frequency combs in Si3N4 microresonators," Optica 4(7), 684–691 (2017). [CrossRef]
10. Q. Li, T. C. Briles, D. A. Westly, T. E. Drake, J. R. Stone, B. R. Ilic, S. A. Diddams, S. B. Papp, and K. Srinivasan, "Stably accessing octave-spanning microresonator frequency combs in the soliton regime," Optica 4(2), 193–203 (2017). [CrossRef]
11. G. Moille, L. Chang, W. Xie, A. Rao, X. Lu, M. Davanço, J. E. Bowers, and K. Srinivasan, "Dissipative Kerr Solitons in a III-V Microresonator," Laser & Photonics Rev. 14(8), 2000022 (2020). [CrossRef]
12. Z. Gong, X. Liu, Y. Xu, and H. X. Tang, "Near-octave lithium niobate soliton microcomb," Optica 7(10), 1275–1278 (2020). [CrossRef]
13. Z. Gong, A. Bruch, M. Shen, X. Guo, H. Jung, L. Fan, X. Liu, L. Zhang, J. Wang, J. Li, J. Yan, and H. X. Tang, "High-fidelity cavity soliton generation in crystalline AlN micro-ring resonators," Opt. Lett. 43(18), 4366–4369 (2018). [CrossRef]
14. M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, "Breather soliton dynamics in microresonators," Nat. Commun. 8(1), 14569 (2017). [CrossRef]
15. E. Lucas, M. Karpov, H. Guo, M. L. Gorodetsky, and T. J. Kippenberg, "Breathing dissipative solitons in optical microresonators," Nat. Commun. 8(1), 736 (2017). [CrossRef]
16. H. Guo, E. Lucas, M. H. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, "Intermode breather solitons in optical microresonators," Phys. Rev. X 7(4), 041055 (2017). [CrossRef]
17. W. Wang, L. Wang, and W. Zhang, "Advances in Soliton Microcomb Generation," Adv. Photon. 2(03), 1 (2020). [CrossRef]
18. H. Weng, J. Liu, A. A. Afridi, J. Li, J. Dai, X. Ma, Y. Zhang, Q. Lu, J. F. Donegan, and W. Guo, "Octave-spanning Kerr frequency comb generation with stimulated Raman scattering in an AlN microresonator," Opt. Lett. 46(3), 540–543 (2021). [CrossRef]
19. H. Weng, J. Liu, A. A. Afridi, J. Li, J. Dai, X. Ma, H. Long, Y. Zhang, Q. Lu, J. F. Donegan, and W. Guo, "Directly accessing octave-spanning dissipative Kerr soliton frequency combs in an AlN microring resonator," Photonics Res. 9(7), 1351–1357 (2021). [CrossRef]
20. H. Weng, A. A. Afridi, J. Liu, J. Li, J. Dai, X. Ma, Y. Zhang, Q. Lu, W. Guo, and J. F. Donegan, "Near octave-spanning breathing soliton crystal in an AlN microresonator," Opt. Lett. 46(14), 3436–3439 (2021). [CrossRef]
21. X. Liu, Z. Gong, A. W. Bruch, J. B. Surya, J. Lu, and H. X. Tang, "Aluminum nitride nanophotonics for beyond-octave soliton microcomb generation and self-referencing," Nat. Commun. 12(1), 5428 (2021). [CrossRef]
22. M. Yu, Y. Okawachi, R. Cheng, C. Wang, M. Zhang, A. L. Gaeta, and M. Lončar, "Raman Lasing and Soliton Mode-locking in Lithium Niobate Microresonators," Light: Sci. Appl. 9(1), 9 (2020). [CrossRef]
23. C. Bao, L. Zhang, C. L. Kimerling, J. Michel, and C. Yang, "Soliton Breathing Induced by Stimulated Raman Scattering and Self-steepening in Octave-spanning Kerr Frequency Comb Generation," Opt. Express 23(14), 18665–8670 (2015). [CrossRef]
24. V. Brasch, E. Lucas, J. D. Jost, M. Geiselmann, and T. J. Kippenberg, "Self-referenced photonic chip soliton Kerr frequency comb," Light: Sci. Appl. 6(1), e16202 (2017). [CrossRef]
25. J. Liu, H. Weng, A. A. Afridi, J. Li, J. Dai, X. Ma, H. Long, Y. Zhang, Q. Lu, J. F. Donegan, and W. Guo, "Photolithography allows high-Q AlN microresonators for near octave-spanning frequency comb and harmonic generation," Opt. Express 28(13), 19270–19280 (2020). [CrossRef]
26. X. Liu, C. Sun, B. Xiong, L. Wang, J. Wang, Y. Han, Z. Hao, H. Li, Y. Luo, J. Yan, T. Wei, Y. Zhang, and J. Wang, "Integrated High-Q Crystalline AlN Microresonators for Broadband Kerr and Raman Frequency Combs," ACS Photonics 5(5), 1943–1950 (2018). [CrossRef]
27. Y. Okawachi, M. Yu, V. Venkataraman, P. M. Latawiec, A. G. Griffith, M. Lipson, M. Loncar, and A. L. Gaeta, "Competition between Raman and Kerr effects in microresonator comb generation," Opt. Lett. 42(14), 2786 (2017). [CrossRef]
28. S. Fujii, T. Kato, R. Suzuki, A. Hori, and T. Tanabe, "Transition between Kerr comb and stimulated Raman comb in a silica whispering gallery mode microcavity," J. Opt. Soc. Am. B 35(1), 100 (2018). [CrossRef]
29. M. Bickermann, B. M. Epelbaum, P. Heimann, Z. G. Herro, and A. Winnacker, "Orientation-dependent phonon observation in single-crystalline aluminum nitride," Appl. Phys. Lett. 86(13), 131904 (2005). [CrossRef]
30. G. Moille, Q. Li, X. Lu, and K. Srinivasan, "pyLLE: A fast and user friendly Lugiato-Lefever equation solver," J Res. Natl. Inst. Stand. Technol. 124, 124012 (2019). [CrossRef]
31. S. Wan, R. Niu, Z.-Y. Wang, J.-L. Peng, M. Li, J. Li, G.-C. Guo, C.-L. Zou, and C.-H. Dong, "Frequency stabilization and tuning of breathing solitons in Si3N4 microresonators," Photonics Res. 8(8), 1342–1349 (2020). [CrossRef]
32. W. Weng, R. Bouchand, E. Lucas, E. Obrzud, T. Herr, and T. J. Kippenberg, "Heteronuclear soliton molecules in optical microresonators," Nat. Commun. 11(1), 2402 (2020). [CrossRef]
Article Order
T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, "Temporal solitons in optical microresonators," Nat. Photonics 8(2), 145–152 (2014).
[Crossref]
T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, "Dissipative Kerr solitons in optical microresonators," Science 361(6402), eaan8083 (2018).
A. Fülöp, M. Mazur, A. Lorences-Riesgo, Ó. B. Helgason, P. H. Wang, Y. Xuan, D. E. Leaird, M. Qi, P. A. Andrekson, A. M. Weiner, and V. Torres-Company, "High-order Coherent Communications Using Mode-locked Dark-pulse Kerr Combs from Microresonators," Nat Commun 9(1), 1598 (2018).
D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. H. Lee, D. Y. Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, "An optical-frequency synthesizer using integrated photonics," Nature 557(7703), 81–85 (2018).
M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, "Microresonator soliton dual-comb spectroscopy," Science 354(6312), 600–603 (2016).
P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, "Ultrafast optical ranging using microresonator soliton frequency combs," Science 359(6378), 887–891 (2018).
X. Yi, Q.-F. Yang, K. Y. Yang, M.-G. Suh, and K. Vahala, "Soliton frequency comb at microwave rates in a high-Q silica microresonator," Optica 2(12), 1078–1085 (2015).
C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, "Thermally controlled comb generation and soliton modelocking in microresonators," Opt. Lett. 41(11), 2565–2568 (2016).
M. H. P. Pfeiffer, C. Herkommer, J. Liu, H. Guo, M. Karpov, E. Lucas, M. Zervas, and T. J. Kippenberg, "Octave-spanning dissipative Kerr soliton frequency combs in Si3N4 microresonators," Optica 4(7), 684–691 (2017).
Q. Li, T. C. Briles, D. A. Westly, T. E. Drake, J. R. Stone, B. R. Ilic, S. A. Diddams, S. B. Papp, and K. Srinivasan, "Stably accessing octave-spanning microresonator frequency combs in the soliton regime," Optica 4(2), 193–203 (2017).
G. Moille, L. Chang, W. Xie, A. Rao, X. Lu, M. Davanço, J. E. Bowers, and K. Srinivasan, "Dissipative Kerr Solitons in a III-V Microresonator," Laser & Photonics Rev. 14(8), 2000022 (2020).
Z. Gong, X. Liu, Y. Xu, and H. X. Tang, "Near-octave lithium niobate soliton microcomb," Optica 7(10), 1275–1278 (2020).
Z. Gong, A. Bruch, M. Shen, X. Guo, H. Jung, L. Fan, X. Liu, L. Zhang, J. Wang, J. Li, J. Yan, and H. X. Tang, "High-fidelity cavity soliton generation in crystalline AlN micro-ring resonators," Opt. Lett. 43(18), 4366–4369 (2018).
M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, "Breather soliton dynamics in microresonators," Nat. Commun. 8(1), 14569 (2017).
E. Lucas, M. Karpov, H. Guo, M. L. Gorodetsky, and T. J. Kippenberg, "Breathing dissipative solitons in optical microresonators," Nat. Commun. 8(1), 736 (2017).
H. Guo, E. Lucas, M. H. Pfeiffer, M. Karpov, M. Anderson, J. Liu, M. Geiselmann, J. D. Jost, and T. J. Kippenberg, "Intermode breather solitons in optical microresonators," Phys. Rev. X 7(4), 041055 (2017).
W. Wang, L. Wang, and W. Zhang, "Advances in Soliton Microcomb Generation," Adv. Photon. 2(03), 1 (2020).
H. Weng, J. Liu, A. A. Afridi, J. Li, J. Dai, X. Ma, Y. Zhang, Q. Lu, J. F. Donegan, and W. Guo, "Octave-spanning Kerr frequency comb generation with stimulated Raman scattering in an AlN microresonator," Opt. Lett. 46(3), 540–543 (2021).
H. Weng, J. Liu, A. A. Afridi, J. Li, J. Dai, X. Ma, H. Long, Y. Zhang, Q. Lu, J. F. Donegan, and W. Guo, "Directly accessing octave-spanning dissipative Kerr soliton frequency combs in an AlN microring resonator," Photonics Res. 9(7), 1351–1357 (2021).
H. Weng, A. A. Afridi, J. Liu, J. Li, J. Dai, X. Ma, Y. Zhang, Q. Lu, W. Guo, and J. F. Donegan, "Near octave-spanning breathing soliton crystal in an AlN microresonator," Opt. Lett. 46(14), 3436–3439 (2021).
X. Liu, Z. Gong, A. W. Bruch, J. B. Surya, J. Lu, and H. X. Tang, "Aluminum nitride nanophotonics for beyond-octave soliton microcomb generation and self-referencing," Nat. Commun. 12(1), 5428 (2021).
M. Yu, Y. Okawachi, R. Cheng, C. Wang, M. Zhang, A. L. Gaeta, and M. Lončar, "Raman Lasing and Soliton Mode-locking in Lithium Niobate Microresonators," Light: Sci. Appl. 9(1), 9 (2020).
C. Bao, L. Zhang, C. L. Kimerling, J. Michel, and C. Yang, "Soliton Breathing Induced by Stimulated Raman Scattering and Self-steepening in Octave-spanning Kerr Frequency Comb Generation," Opt. Express 23(14), 18665–8670 (2015).
V. Brasch, E. Lucas, J. D. Jost, M. Geiselmann, and T. J. Kippenberg, "Self-referenced photonic chip soliton Kerr frequency comb," Light: Sci. Appl. 6(1), e16202 (2017).
J. Liu, H. Weng, A. A. Afridi, J. Li, J. Dai, X. Ma, H. Long, Y. Zhang, Q. Lu, J. F. Donegan, and W. Guo, "Photolithography allows high-Q AlN microresonators for near octave-spanning frequency comb and harmonic generation," Opt. Express 28(13), 19270–19280 (2020).
X. Liu, C. Sun, B. Xiong, L. Wang, J. Wang, Y. Han, Z. Hao, H. Li, Y. Luo, J. Yan, T. Wei, Y. Zhang, and J. Wang, "Integrated High-Q Crystalline AlN Microresonators for Broadband Kerr and Raman Frequency Combs," ACS Photonics 5(5), 1943–1950 (2018).
Y. Okawachi, M. Yu, V. Venkataraman, P. M. Latawiec, A. G. Griffith, M. Lipson, M. Loncar, and A. L. Gaeta, "Competition between Raman and Kerr effects in microresonator comb generation," Opt. Lett. 42(14), 2786 (2017).
S. Fujii, T. Kato, R. Suzuki, A. Hori, and T. Tanabe, "Transition between Kerr comb and stimulated Raman comb in a silica whispering gallery mode microcavity," J. Opt. Soc. Am. B 35(1), 100 (2018).
M. Bickermann, B. M. Epelbaum, P. Heimann, Z. G. Herro, and A. Winnacker, "Orientation-dependent phonon observation in single-crystalline aluminum nitride," Appl. Phys. Lett. 86(13), 131904 (2005).
G. Moille, Q. Li, X. Lu, and K. Srinivasan, "pyLLE: A fast and user friendly Lugiato-Lefever equation solver," J Res. Natl. Inst. Stand. Technol. 124, 124012 (2019).
S. Wan, R. Niu, Z.-Y. Wang, J.-L. Peng, M. Li, J. Li, G.-C. Guo, C.-L. Zou, and C.-H. Dong, "Frequency stabilization and tuning of breathing solitons in Si3N4 microresonators," Photonics Res. 8(8), 1342–1349 (2020).
W. Weng, R. Bouchand, E. Lucas, E. Obrzud, T. Herr, and T. J. Kippenberg, "Heteronuclear soliton molecules in optical microresonators," Nat. Commun. 11(1), 2402 (2020).
Afridi, A. A.
Anderson, M.
Andrekson, P. A.
Bao, C.
Bickermann, M.
Bluestone, A.
Bouchand, R.
Bowers, J. E.
Brasch, V.
Briles, T. C.
Bruch, A.
Bruch, A. W.
Chang, L.
Cheng, R.
Dai, J.
Davanço, M.
Diddams, S. A.
Donegan, J. F.
Dong, C.-H.
Drake, T.
Drake, T. E.
Epelbaum, B. M.
Fan, L.
Fredrick, C.
Freude, W.
Fujii, S.
Fülöp, A.
Gaeta, A. L.
Ganin, D.
Geiselmann, M.
Gong, Z.
Gorodetsky, M. L.
Griffith, A. G.
Guo, G.-C.
Guo, H.
Guo, W.
Guo, X.
Han, Y.
Hao, Z.
Heimann, P.
Helgason, Ó. B.
Herkommer, C.
Herr, T.
Herro, Z. G.
Hori, A.
Ilic, B. R.
Jang, J. K.
Joshi, C.
Jost, J. D.
Jung, H.
Karpov, M.
Kato, T.
Kimerling, C. L.
Kippenberg, T. J.
Klenner, A.
Komljenovic, T.
Kondratiev, N. M.
Koos, C.
Kordts, A.
Krockenberger, J.
Latawiec, P. M.
Leaird, D. E.
Lee, S. H.
Li, H.
Li, J.
Li, M.
Li, Q.
Lipson, M.
Liu, J.
Liu, X.
Loncar, M.
Long, H.
Lorences-Riesgo, A.
Lu, J.
Lu, Q.
Lu, X.
Lucas, E.
Luke, K.
Luo, Y.
Ma, X.
Marin-Palomo, P.
Mazur, M.
Michel, J.
Miller, S. A.
Moille, G.
Newbury, N. R.
Niu, R.
Norberg, E.
Obrzud, E.
Oh, D. Y.
Okawachi, Y.
Papp, S. B.
Peng, J.-L.
Pfeiffer, M. H.
Pfeiffer, M. H. P.
Qi, M.
Randel, S.
Rao, A.
Shen, M.
Sinclair, L. C.
Spencer, D. T.
Srinivasan, K.
Stone, J.
Stone, J. R.
Suh, M.-G.
Sun, C.
Surya, J. B.
Suzuki, R.
Tanabe, T.
Tang, H. X.
Theogarajan, L.
Torres-Company, V.
Trocha, P.
Vahala, K.
Vahala, K. J.
Venkataraman, V.
Volet, N.
Wan, S.
Wang, C.
Wang, C. Y.
Wang, J.
Wang, L.
Wang, P. H.
Wang, W.
Wang, Z.-Y.
Wei, T.
Weimann, C.
Weiner, A. M.
Weng, H.
Weng, W.
Westly, D.
Westly, D. A.
Winnacker, A.
Wolf, S.
Xie, W.
Xiong, B.
Xu, Y.
Xuan, Y.
Yan, J.
Yang, K. Y.
Yang, Q.-F.
Yi, X.
Yu, M.
Zervas, M.
Zhang, M.
Zhang, W.
Zhang, Y.
Zou, C.-L.
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(1) t R ⁡ ∂ E ( t , τ ) ∂ t = [ − α − i δ + i L ∑ k ≥ 2 n β k k ! ( i ∂ ∂ τ ) k + i γ L | E | 2 ] E ( t , τ ) + θ E i n
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