Udem, T., Holzwarth, R. & Hänsch, T. W. Optical frequency metrology. Nature 416, 233 (2002).
Google Scholar
Hugi, A., Villares, G., Blaser, S., Liu, H. C. & Faist, J. Mid-infrared frequency comb based on a quantum cascade laser. Nature 492, 229 (2012).
Google Scholar
Täschler, P. et al. Femtosecond pulses from a mid-infrared quantum cascade laser. Nat. Photon. 15, 919 (2021).
Google Scholar
Hillbrand, J., Andrews, A. M., Detz, H., Strasser, G. & Schwarz, B. Coherent injection locking of quantum cascade laser frequency combs. Nat. Photon. 13, 101 (2019).
Google Scholar
Villares, G. et al. On-chip dual-comb based on quantum cascade laser frequency combs. Appl. Phys. Lett. 107, 251104 (2015).
Opačak, N. & Schwarz, B. Theory of frequency-modulated combs in lasers with spatial hole burning, dispersion, and Kerr nonlinearity. Phys. Rev. Lett. https://doi.org/10.1103/physrevlett.123.243902 (2019).
Herr, T. et al. Temporal solitons in optical microresonators. Nat. Photon. 8, 145 (2013).
Google Scholar
Guo, H. et al. Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators. Nat. Phys. 13, 94 (2016).
Xue, X. et al. Mode-locked dark pulse Kerr combs in normal-dispersion microresonators. Nat. Photon. 9, 594 (2015).
Google Scholar
Piccardo, M. et al. Frequency combs induced by phase turbulence. Nature 582, 360 (2020).
Google Scholar
Meng, B. et al. Mid-infrared frequency comb from a ring quantum cascade laser. Optica 7, 162 (2020).
Google Scholar
Aranson, I. S. & Kramer, L. The world of the complex Ginzburg–Landau equation. Rev. Mod. Phys. 74, 99 (2002).
Google Scholar
Bekki, N. & Nozaki, K. Formations of spatial patterns and holes in the generalized Ginzburg–Landau equation. Phys. Lett. A 110, 133 (1985).
Google Scholar
Lega, J. Traveling hole solutions of the complex Ginzburg–Landau equation: a review. Physica D 152–153, 269 (2001).
Google Scholar
Karpov, M. et al. Dynamics of soliton crystals in optical microresonators. Nat. Phys. 15, 1071 (2019).
Google Scholar
Akhmediev, N. & Ankiewicz, A. (eds) Dissipative Solitons: From Optics to Biology and Medicine (Springer, 2008).
Grelu, P. & Akhmediev, N. Dissipative solitons for mode-locked lasers. Nat. Photon. 6, 84 (2012).
Google Scholar
Englebert, N., Arabí, C. M., Parra-Rivas, P., Gorza, S.-P. & Leo, F. Temporal solitons in a coherently driven active resonator. Nat. Photon. 15, 536 (2021).
Google Scholar
Leo, F. et al. Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer. Nat. Photon. 4, 471 (2010).
Google Scholar
Rowley, M. et al. Self-emergence of robust solitons in a microcavity. Nature 608, 303 (2022).
Google Scholar
Zhang, S .et al. Dark-bright soliton bound states in a microresonator. Phys. Rev. Lett. https://doi.org/10.1103/physrevlett.128.033901 (2022).
Marin-Palomo, P. et al. Microresonator-based solitons for massively parallel coherent optical communications. Nature 546, 274 (2017).
Riemensberger, J. et al. Massively parallel coherent laser ranging using a soliton microcomb. Nature 581, 164 (2020).
Google Scholar
Suh, M.-G., Yang, Q.-F., Yang, K. Y., Yi, X. & Vahala, K. J. Microresonator soliton dual-comb spectroscopy. Science 354, 600 (2016).
Google Scholar
Spencer, D. T. et al. An optical-frequency synthesizer using integrated photonics. Nature 557, 81 (2018).
Google Scholar
Yao, Y., Hoffman, A. J. & Gmachl, C. F. Mid-infrared quantum cascade lasers. Nat. Photon. 6, 432 (2012).
Google Scholar
Williams, B. S. Terahertz quantum-cascade lasers. Nat. Photon. 1, 517 (2007).
Google Scholar
Opačak, N., Cin, S. D., Hillbrand, J. & Schwarz, B. Frequency comb generation by Bloch gain induced giant Kerr nonlinearity. Phys. Rev. Lett. https://doi.org/10.1103/physrevlett.127.093902 (2021).
Friedli, P. et al. Four-wave mixing in a quantum cascade laser amplifier. Appl. Phys. Lett. 102, 222104 (2013).
Google Scholar
Gaeta, A. L., Lipson, M. & Kippenberg, T. J. Photonic-chip-based frequency combs. Nat. Photon. 13, 158 (2019).
Google Scholar
Jaidl, M. et al. Comb operation in terahertz quantum cascade ring lasers. Optica 8, 780 (2021).
Google Scholar
Paolo Micheletti et al. Terahertz optical solitons from dispersion-compensated antenna-coupled planarized ring quantum cascade lasers. Sci. Adv. 9, eadf9426 (2023).
Meng, B. et al. Dissipative Kerr solitons in semiconductor ring lasers. Nat. Photon. 16, 142 (2021).
Google Scholar
Columbo, L. et al. Unifying frequency combs in active and passive cavities: temporal solitons in externally driven ring lasers. Phys. Rev. Lett. https://doi.org/10.1103/physrevlett.126.173903 (2021).
Prati, F. et al. Soliton dynamics of ring quantum cascade lasers with injected signal. Nanophotonics 10, 195 (2020).
Henry, C. Theory of the linewidth of semiconductor lasers. IEEE J. Quantum Electron. 18, 259 (1982).
Google Scholar
Opačak, N. et al. Spectrally resolved linewidth enhancement factor of a semiconductor frequency comb. Optica 8, 1227 (2021).
Google Scholar
Efremidis, N., Hizanidis, K., Nistazakis, H. E., Frantzeskakis, D. J. & Malomed, B. A. Stabilization of dark solitons in the cubic Ginzburg–Landau equation. Phys. Rev. E 62, 7410 (2000).
Google Scholar
Perraud, J.-J. et al. One-dimensional “spirals”: novel asynchronous chemical wave sources. Phys. Rev. Lett. 71, 1272 (1993).
Google Scholar
Burguete, J., Chaté, H., Daviaud, F. & Mukolobwiez, N. Bekki–Nozaki amplitude holes in hydrothermal nonlinear waves. Phys. Rev. Lett. 82, 3252 (1999).
Google Scholar
Slepneva, S. et al. Convective Nozaki–Bekki holes in a long cavity OCT laser. Opt. Express 27, 16395 (2019).
Google Scholar
Gowda, U. et al. Turbulent coherent structures in a long cavity semiconductor laser near the lasing threshold. Opt. Lett. 45, 4903 (2020).
Google Scholar
Popp, S., Stiller, O., Aranson, I., Weber, A. & Kramer, L. Localized hole solutions and spatiotemporal chaos in the 1D complex Ginzburg–Landau equation. Phys. Rev. Lett. 70, 3880 (1993).
Google Scholar
Popp, S., Stiller, O., Aranson, I. & Kramer, L. Hole solutions in the 1D complex Ginzburg–Landau equation. Physica D 84, 398 (1995).
Google Scholar
Kazakov, D. et al. Active mid-infrared ring resonators. Nat. Commun. https://doi.org/10.1038/s41467-023-44628-7 (2024).
Burghoff, D. et al. Evaluating the coherence and time-domain profile of quantum cascade laser frequency combs. Opt. Express 23, 1190 (2015).
Google Scholar
Jang, J. K., Erkintalo, M., Murdoch, S. G. & Coen, S. Observation of dispersive wave emission by temporal cavity solitons. Opt. Lett. 39, 5503 (2014).
Google Scholar
Anderson, M. H. et al. Zero dispersion Kerr solitons in optical microresonators. Nat. Commun. https://doi.org/10.1038/s41467-022-31916-x (2022).
Obrzud, E., Lecomte, S. & Herr, T. Temporal solitons in microresonators driven by optical pulses. Nat. Photon. 11, 600 (2017).
Google Scholar
Liu, D., Zhang, L., Tan, Y. & Dai, D. High-order adiabatic elliptical-microring filter with an ultra-large free-spectral-range. J. Lightw. Technol. 39, 5910 (2021).
Google Scholar
Mansuripur, T. S. et al. Single-mode instability in standing-wave lasers: the quantum cascade laser as a self-pumped parametric oscillator. Phys. Rev. https://doi.org/10.1103/physreva.94.063807 (2016).
White, A. D. et al. Integrated passive nonlinear optical isolators. Nat. Photon. 17, 143–149 (2022).
Google Scholar
Xiang, C. et al. 3D integration enables ultralow-noise isolator-free lasers in silicon photonics. Nature 620, 78–85 (2023).
Google Scholar
Villares, G., Hugi, A., Blaser, S. & Faist, J. Dual-comb spectroscopy based on quantum-cascade-laser frequency combs. Nat. Commun. https://doi.org/10.1038/ncomms6192 (2014).