K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901(2017).

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip–based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).

[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate,” Nat. Photonics 10, 321–326 (2016).

[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, and K. Vahala, “Active capture and stabilization of temporal solitons in microresonators,” Opt. Lett. 41, 2037–2040 (2016).

[Crossref]

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, 2565–2568 (2016).

[Crossref]

J. K. Jang, M. Erkintalo, J. Schröder, B. J. Eggleton, S. G. Murdoch, and S. Coen, “All-optical buffer based on temporal cavity solitons operating at 10 Gb/s,” Opt. Lett. 41, 4526–4529 (2016).

[Crossref]

K. E. Webb, M. Erkintalo, S. Coen, and S. G. Murdoch, “Experimental observation of coherent cavity soliton frequency combs in silica microspheres,” Opt. Lett. 41, 4613–4616 (2016).

[Crossref]

K. Luo, Y. Xu, M. Erkintalo, and S. G. Murdoch, “Resonant radiation in synchronously pumped passive Kerr cavities,” Opt. Lett. 40, 427–430 (2015).

[Crossref]

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, 1078–1085 (2015).

[Crossref]

J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, “Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons,” Nat. Commun. 6, 7370 (2015).

[Crossref]

P. Del’Haye, A. Coillet, W. Loh, K. Beha, S. B. Papp, and S. A. Diddams, “Phase steps and resonator detuning measurements in microresonator frequency combs,” Nat. Commun. 6, 5668 (2015).

[Crossref]

P. Parra-Rivas, D. Gomila, M. A. Matías, S. Coen, and L. Gelens, “Dynamics of localized and patterned structures in the Lugiato–Lefever equation determine the stability and shape of optical frequency combs,” Phys. Rev. A 89, 043813 (2014).

[Crossref]

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, 145–152 (2014).

[Crossref]

T. Herr, V. Brasch, D. Jost, J. I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).

[Crossref]

C. Milián and D. V. Skryabin, “Soliton families and resonant radiation in a micro-ring resonator near zero group-velocity dispersion,” Opt. Express 22, 3732–3739 (2014).

[Crossref]

M. Conforti, A. Mussot, A. Kudlinski, and S. Trillo, “Modulational instability in dispersion oscillating fiber ring cavities,” Opt. Lett. 39, 4200–4203 (2014).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Observation of dispersive wave emission by temporal cavity solitons,” Opt. Lett. 39, 5503–5506 (2014).

[Crossref]

S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato–Lefever model,” Opt. Lett. 38, 37–39 (2013).

[Crossref]

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 9180–9191 (2013).

[Crossref]

A. F. J. Runge, C. Aguergaray, N. G. R. Broderick, and M. Erkintalo, “Coherence and shot-to-shot spectral fluctuations in noise-like ultrafast fiber lasers,” Opt. Lett. 38, 4327–4330 (2013).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7, 657–663 (2013).

[Crossref]

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7, 102–112 (2013).

[Crossref]

Y. K. Chembo and C. R. Menyuk, “Spatiotemporal Lugiato–Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87, 053852 (2013).

[Crossref]

D. Turaev, A. G. Vladimirov, and S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons,” Phys. Rev. Lett. 108, 263906 (2012).

[Crossref]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).

A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Mode-locked Kerr frequency combs,” Opt. Lett. 36, 2845–2847 (2011).

[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).

[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).

[Crossref]

T. Ackemann, W. J. Firth, and G.-L. Oppo, “Fundamentals and applications of spatial dissipative solitons in photonic devices,” Adv. At. Mol. Opt. Phys. 57, 323–421 (2009).

[Crossref]

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E 75, 016613 (2007).

[Crossref]

I. Pérez-Arjona, V. J. Sánchez-Morcillo, G. J. de Valcárcel, and E. Roldán, “Bright cavity solitons in anisotropic vectorial Kerr cavities,” J. Opt. B 3, S118–S123 (2001).

[Crossref]

T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth, “Cavity solitons in semiconductor microresonators: existence, stability, and dynamical properties,” Phys. Rev. E 62, 8726–8739 (2000).

[Crossref]

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, “Interaction of localized structures in an optical pattern-forming system,” Phys. Rev. Lett. 85, 748–751 (2000).

[Crossref]

S. Coen, M. Haelterman, Ph. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, “Experimental investigation of the dynamics of a stabilized nonlinear fiber ring resonator,” J. Opt. Soc. Am. B 15, 2283–2293 (1998).

[Crossref]

I. V. Barashenkov, Y. S. Smirnov, and N. V. Alexeeva, “Bifurcation to multisoliton complexes in the AC-driven, damped nonlinear Schrödinger equation,” Phys. Rev. E 57, 2350–2364 (1998).

[Crossref]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).

[Crossref]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).

[Crossref]

D. Cai, A. R. Bishop, N. Grønbech-Jensen, and B. A. Malomed, “Bound solitons in the AC-driven, damped nonlinear Schrödinger equation,” Phys. Rev. E 49, 1677–1679 (1994).

[Crossref]

B. A. Malomed, “Bound states of envelope solitons,” Phys. Rev. E 47, 2874–2880 (1993).

[Crossref]

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).

[Crossref]

J. P. Gordon, “Dispersive perturbations of solitons of the nonlinear Schrödinger equation,” J. Opt. Soc. Am. B 9, 91–97 (1992).

[Crossref]

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).

[Crossref]

B. A. Malomed, “Bound solitons in the nonlinear Schrödinger–Ginzburg–Landau equation,” Phys. Rev. A 44, 6954–6957 (1991).

[Crossref]

T. Ackemann, W. J. Firth, and G.-L. Oppo, “Fundamentals and applications of spatial dissipative solitons in photonic devices,” Adv. At. Mol. Opt. Phys. 57, 323–421 (2009).

[Crossref]

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, “Interaction of localized structures in an optical pattern-forming system,” Phys. Rev. Lett. 85, 748–751 (2000).

[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2013).

Y. S. Kivshar and G. P. Agrawal, “Vector solitons,” in Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003), Chap. 9, pp. 278–339.

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E 75, 016613 (2007).

[Crossref]

J. M. Soto-Crespo, N. Akhmediev, P. Grelu, and F. Belhache, “Quantized separations of phase-locked soliton pairs in fiber lasers,” Opt. Lett. 28, 1757–1759 (2003).

[Crossref]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).

[Crossref]

N. N. Akhmediev, “General theory of solitons,” in Soliton-Driven Photonics, A. D. Boardman and A. P. Sukhorukov, eds., vol. 31 of NATO Science Series (Springer, 2001), pp. 371–395.

I. V. Barashenkov, Y. S. Smirnov, and N. V. Alexeeva, “Bifurcation to multisoliton complexes in the AC-driven, damped nonlinear Schrödinger equation,” Phys. Rev. E 57, 2350–2364 (1998).

[Crossref]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901(2017).

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).

[Crossref]

I. V. Barashenkov, Y. S. Smirnov, and N. V. Alexeeva, “Bifurcation to multisoliton complexes in the AC-driven, damped nonlinear Schrödinger equation,” Phys. Rev. E 57, 2350–2364 (1998).

[Crossref]

P. Del’Haye, A. Coillet, W. Loh, K. Beha, S. B. Papp, and S. A. Diddams, “Phase steps and resonator detuning measurements in microresonator frequency combs,” Nat. Commun. 6, 5668 (2015).

[Crossref]

D. Cai, A. R. Bishop, N. Grønbech-Jensen, and B. A. Malomed, “Bound solitons in the AC-driven, damped nonlinear Schrödinger equation,” Phys. Rev. E 49, 1677–1679 (1994).

[Crossref]

T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth, “Cavity solitons in semiconductor microresonators: existence, stability, and dynamical properties,” Phys. Rev. E 62, 8726–8739 (2000).

[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip–based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).

[Crossref]

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, 145–152 (2014).

[Crossref]

T. Herr, V. Brasch, D. Jost, J. I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).

[Crossref]

D. Cai, A. R. Bishop, N. Grønbech-Jensen, and B. A. Malomed, “Bound solitons in the AC-driven, damped nonlinear Schrödinger equation,” Phys. Rev. E 49, 1677–1679 (1994).

[Crossref]

Y. K. Chembo and C. R. Menyuk, “Spatiotemporal Lugiato–Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87, 053852 (2013).

[Crossref]

J. K. Jang, M. Erkintalo, J. Schröder, B. J. Eggleton, S. G. Murdoch, and S. Coen, “All-optical buffer based on temporal cavity solitons operating at 10 Gb/s,” Opt. Lett. 41, 4526–4529 (2016).

[Crossref]

K. E. Webb, M. Erkintalo, S. Coen, and S. G. Murdoch, “Experimental observation of coherent cavity soliton frequency combs in silica microspheres,” Opt. Lett. 41, 4613–4616 (2016).

[Crossref]

J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, “Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons,” Nat. Commun. 6, 7370 (2015).

[Crossref]

P. Parra-Rivas, D. Gomila, M. A. Matías, S. Coen, and L. Gelens, “Dynamics of localized and patterned structures in the Lugiato–Lefever equation determine the stability and shape of optical frequency combs,” Phys. Rev. A 89, 043813 (2014).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Observation of dispersive wave emission by temporal cavity solitons,” Opt. Lett. 39, 5503–5506 (2014).

[Crossref]

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 9180–9191 (2013).

[Crossref]

S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato–Lefever model,” Opt. Lett. 38, 37–39 (2013).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7, 657–663 (2013).

[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).

[Crossref]

S. Coen, M. Haelterman, Ph. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, “Experimental investigation of the dynamics of a stabilized nonlinear fiber ring resonator,” J. Opt. Soc. Am. B 15, 2283–2293 (1998).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Bound states of temporal cavity solitons,” in Nonlinear Photonics, NP’2014, Barcelona, Spain, July27–31, 2014 (Optical Society of America, 2014), paper JM5A.59.

P. Del’Haye, A. Coillet, W. Loh, K. Beha, S. B. Papp, and S. A. Diddams, “Phase steps and resonator detuning measurements in microresonator frequency combs,” Nat. Commun. 6, 5668 (2015).

[Crossref]

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” arXiv:1610.00080 (2016).

P. Parra-Rivas, D. Gomila, P. Colet, and L. Gelens, “Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation,” arXiv:1705.02619 (2017).

I. Pérez-Arjona, V. J. Sánchez-Morcillo, G. J. de Valcárcel, and E. Roldán, “Bright cavity solitons in anisotropic vectorial Kerr cavities,” J. Opt. B 3, S118–S123 (2001).

[Crossref]

P. Del’Haye, A. Coillet, W. Loh, K. Beha, S. B. Papp, and S. A. Diddams, “Phase steps and resonator detuning measurements in microresonator frequency combs,” Nat. Commun. 6, 5668 (2015).

[Crossref]

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” arXiv:1610.00080 (2016).

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E 75, 016613 (2007).

[Crossref]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).

P. Del’Haye, A. Coillet, W. Loh, K. Beha, S. B. Papp, and S. A. Diddams, “Phase steps and resonator detuning measurements in microresonator frequency combs,” Nat. Commun. 6, 5668 (2015).

[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).

[Crossref]

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” arXiv:1610.00080 (2016).

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 9180–9191 (2013).

[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).

[Crossref]

S. Coen, M. Haelterman, Ph. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, “Experimental investigation of the dynamics of a stabilized nonlinear fiber ring resonator,” J. Opt. Soc. Am. B 15, 2283–2293 (1998).

[Crossref]

K. E. Webb, M. Erkintalo, S. Coen, and S. G. Murdoch, “Experimental observation of coherent cavity soliton frequency combs in silica microspheres,” Opt. Lett. 41, 4613–4616 (2016).

[Crossref]

J. K. Jang, M. Erkintalo, J. Schröder, B. J. Eggleton, S. G. Murdoch, and S. Coen, “All-optical buffer based on temporal cavity solitons operating at 10 Gb/s,” Opt. Lett. 41, 4526–4529 (2016).

[Crossref]

K. Luo, Y. Xu, M. Erkintalo, and S. G. Murdoch, “Resonant radiation in synchronously pumped passive Kerr cavities,” Opt. Lett. 40, 427–430 (2015).

[Crossref]

J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, “Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons,” Nat. Commun. 6, 7370 (2015).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Observation of dispersive wave emission by temporal cavity solitons,” Opt. Lett. 39, 5503–5506 (2014).

[Crossref]

S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato–Lefever model,” Opt. Lett. 38, 37–39 (2013).

[Crossref]

A. F. J. Runge, C. Aguergaray, N. G. R. Broderick, and M. Erkintalo, “Coherence and shot-to-shot spectral fluctuations in noise-like ultrafast fiber lasers,” Opt. Lett. 38, 4327–4330 (2013).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7, 657–663 (2013).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Bound states of temporal cavity solitons,” in Nonlinear Photonics, NP’2014, Barcelona, Spain, July27–31, 2014 (Optical Society of America, 2014), paper JM5A.59.

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, “Interaction of localized structures in an optical pattern-forming system,” Phys. Rev. Lett. 85, 748–751 (2000).

[Crossref]

T. Ackemann, W. J. Firth, and G.-L. Oppo, “Fundamentals and applications of spatial dissipative solitons in photonic devices,” Adv. At. Mol. Opt. Phys. 57, 323–421 (2009).

[Crossref]

T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth, “Cavity solitons in semiconductor microresonators: existence, stability, and dynamical properties,” Phys. Rev. E 62, 8726–8739 (2000).

[Crossref]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).

[Crossref]

W. J. Firth, “Theory of cavity solitons,” in Soliton-Driven Photonics, A. D. Boardman and A. P. Sukhorukov, eds., vol. 31 of NATO Science Series (Springer, 2001), pp. 459–485.

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, 2565–2568 (2016).

[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip–based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).

[Crossref]

P. Parra-Rivas, D. Gomila, M. A. Matías, S. Coen, and L. Gelens, “Dynamics of localized and patterned structures in the Lugiato–Lefever equation determine the stability and shape of optical frequency combs,” Phys. Rev. A 89, 043813 (2014).

[Crossref]

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 9180–9191 (2013).

[Crossref]

P. Parra-Rivas, D. Gomila, P. Colet, and L. Gelens, “Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation,” arXiv:1705.02619 (2017).

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7, 102–112 (2013).

[Crossref]

P. Parra-Rivas, D. Gomila, M. A. Matías, S. Coen, and L. Gelens, “Dynamics of localized and patterned structures in the Lugiato–Lefever equation determine the stability and shape of optical frequency combs,” Phys. Rev. A 89, 043813 (2014).

[Crossref]

P. Parra-Rivas, D. Gomila, P. Colet, and L. Gelens, “Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation,” arXiv:1705.02619 (2017).

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip–based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).

[Crossref]

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, 145–152 (2014).

[Crossref]

T. Herr, V. Brasch, D. Jost, J. I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).

[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).

[Crossref]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901(2017).

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E 75, 016613 (2007).

[Crossref]

J. M. Soto-Crespo, N. Akhmediev, P. Grelu, and F. Belhache, “Quantized separations of phase-locked soliton pairs in fiber lasers,” Opt. Lett. 28, 1757–1759 (2003).

[Crossref]

D. Cai, A. R. Bishop, N. Grønbech-Jensen, and B. A. Malomed, “Bound solitons in the AC-driven, damped nonlinear Schrödinger equation,” Phys. Rev. E 49, 1677–1679 (1994).

[Crossref]

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 9180–9191 (2013).

[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).

[Crossref]

S. Coen, M. Haelterman, Ph. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, “Experimental investigation of the dynamics of a stabilized nonlinear fiber ring resonator,” J. Opt. Soc. Am. B 15, 2283–2293 (1998).

[Crossref]

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).

[Crossref]

T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth, “Cavity solitons in semiconductor microresonators: existence, stability, and dynamical properties,” Phys. Rev. E 62, 8726–8739 (2000).

[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate,” Nat. Photonics 10, 321–326 (2016).

[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip–based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).

[Crossref]

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, 145–152 (2014).

[Crossref]

T. Herr, V. Brasch, D. Jost, J. I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).

[Crossref]

E. Obrzud, S. Lecomte, and T. Herr, “Temporal solitons in microresonators driven by optical pulses,” arXiv:1612.08993 (2016).

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).

[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate,” Nat. Photonics 10, 321–326 (2016).

[Crossref]

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7, 102–112 (2013).

[Crossref]

J. K. Jang, M. Erkintalo, J. Schröder, B. J. Eggleton, S. G. Murdoch, and S. Coen, “All-optical buffer based on temporal cavity solitons operating at 10 Gb/s,” Opt. Lett. 41, 4526–4529 (2016).

[Crossref]

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, 2565–2568 (2016).

[Crossref]

J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, “Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons,” Nat. Commun. 6, 7370 (2015).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Observation of dispersive wave emission by temporal cavity solitons,” Opt. Lett. 39, 5503–5506 (2014).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7, 657–663 (2013).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Bound states of temporal cavity solitons,” in Nonlinear Photonics, NP’2014, Barcelona, Spain, July27–31, 2014 (Optical Society of America, 2014), paper JM5A.59.

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, 2565–2568 (2016).

[Crossref]

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, 2565–2568 (2016).

[Crossref]

T. Herr, V. Brasch, D. Jost, J. I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).

[Crossref]

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, 145–152 (2014).

[Crossref]

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).

[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip–based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).

[Crossref]

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, 145–152 (2014).

[Crossref]

T. Herr, V. Brasch, D. Jost, J. I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).

[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).

[Crossref]

Y. S. Kivshar and G. P. Agrawal, “Vector solitons,” in Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003), Chap. 9, pp. 278–339.

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, 2565–2568 (2016).

[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).

[Crossref]

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, 145–152 (2014).

[Crossref]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901(2017).

M. Conforti, A. Mussot, A. Kudlinski, and S. Trillo, “Modulational instability in dispersion oscillating fiber ring cavities,” Opt. Lett. 39, 4200–4203 (2014).

[Crossref]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” arXiv:1610.00080 (2016).

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, “Interaction of localized structures in an optical pattern-forming system,” Phys. Rev. Lett. 85, 748–751 (2000).

[Crossref]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).

E. Obrzud, S. Lecomte, and T. Herr, “Temporal solitons in microresonators driven by optical pulses,” arXiv:1612.08993 (2016).

L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).

[Crossref]

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 9180–9191 (2013).

[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).

[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip–based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).

[Crossref]

T. Herr, V. Brasch, D. Jost, J. I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).

[Crossref]

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, 2565–2568 (2016).

[Crossref]

P. Del’Haye, A. Coillet, W. Loh, K. Beha, S. B. Papp, and S. A. Diddams, “Phase steps and resonator detuning measurements in microresonator frequency combs,” Nat. Commun. 6, 5668 (2015).

[Crossref]

L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).

[Crossref]

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, 2565–2568 (2016).

[Crossref]

T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth, “Cavity solitons in semiconductor microresonators: existence, stability, and dynamical properties,” Phys. Rev. E 62, 8726–8739 (2000).

[Crossref]

D. Cai, A. R. Bishop, N. Grønbech-Jensen, and B. A. Malomed, “Bound solitons in the AC-driven, damped nonlinear Schrödinger equation,” Phys. Rev. E 49, 1677–1679 (1994).

[Crossref]

B. A. Malomed, “Bound states of envelope solitons,” Phys. Rev. E 47, 2874–2880 (1993).

[Crossref]

B. A. Malomed, “Bound solitons in the nonlinear Schrödinger–Ginzburg–Landau equation,” Phys. Rev. A 44, 6954–6957 (1991).

[Crossref]

P. Parra-Rivas, D. Gomila, M. A. Matías, S. Coen, and L. Gelens, “Dynamics of localized and patterned structures in the Lugiato–Lefever equation determine the stability and shape of optical frequency combs,” Phys. Rev. A 89, 043813 (2014).

[Crossref]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).

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, 2565–2568 (2016).

[Crossref]

T. Herr, V. Brasch, D. Jost, J. I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).

[Crossref]

K. E. Webb, M. Erkintalo, S. Coen, and S. G. Murdoch, “Experimental observation of coherent cavity soliton frequency combs in silica microspheres,” Opt. Lett. 41, 4613–4616 (2016).

[Crossref]

J. K. Jang, M. Erkintalo, J. Schröder, B. J. Eggleton, S. G. Murdoch, and S. Coen, “All-optical buffer based on temporal cavity solitons operating at 10 Gb/s,” Opt. Lett. 41, 4526–4529 (2016).

[Crossref]

K. Luo, Y. Xu, M. Erkintalo, and S. G. Murdoch, “Resonant radiation in synchronously pumped passive Kerr cavities,” Opt. Lett. 40, 427–430 (2015).

[Crossref]

J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, “Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons,” Nat. Commun. 6, 7370 (2015).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Observation of dispersive wave emission by temporal cavity solitons,” Opt. Lett. 39, 5503–5506 (2014).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7, 657–663 (2013).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Bound states of temporal cavity solitons,” in Nonlinear Photonics, NP’2014, Barcelona, Spain, July27–31, 2014 (Optical Society of America, 2014), paper JM5A.59.

M. Conforti, A. Mussot, A. Kudlinski, and S. Trillo, “Modulational instability in dispersion oscillating fiber ring cavities,” Opt. Lett. 39, 4200–4203 (2014).

[Crossref]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).

G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems: from Dissipative Structures to Order through Fluctuations (Wiley, 1977).

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901(2017).

E. Obrzud, S. Lecomte, and T. Herr, “Temporal solitons in microresonators driven by optical pulses,” arXiv:1612.08993 (2016).

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, 2565–2568 (2016).

[Crossref]

T. Ackemann, W. J. Firth, and G.-L. Oppo, “Fundamentals and applications of spatial dissipative solitons in photonic devices,” Adv. At. Mol. Opt. Phys. 57, 323–421 (2009).

[Crossref]

P. Del’Haye, A. Coillet, W. Loh, K. Beha, S. B. Papp, and S. A. Diddams, “Phase steps and resonator detuning measurements in microresonator frequency combs,” Nat. Commun. 6, 5668 (2015).

[Crossref]

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” arXiv:1610.00080 (2016).

P. Parra-Rivas, D. Gomila, M. A. Matías, S. Coen, and L. Gelens, “Dynamics of localized and patterned structures in the Lugiato–Lefever equation determine the stability and shape of optical frequency combs,” Phys. Rev. A 89, 043813 (2014).

[Crossref]

P. Parra-Rivas, D. Gomila, P. Colet, and L. Gelens, “Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation,” arXiv:1705.02619 (2017).

I. Pérez-Arjona, V. J. Sánchez-Morcillo, G. J. de Valcárcel, and E. Roldán, “Bright cavity solitons in anisotropic vectorial Kerr cavities,” J. Opt. B 3, S118–S123 (2001).

[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip–based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).

[Crossref]

G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems: from Dissipative Structures to Order through Fluctuations (Wiley, 1977).

I. Pérez-Arjona, V. J. Sánchez-Morcillo, G. J. de Valcárcel, and E. Roldán, “Bright cavity solitons in anisotropic vectorial Kerr cavities,” J. Opt. B 3, S118–S123 (2001).

[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate,” Nat. Photonics 10, 321–326 (2016).

[Crossref]

I. Pérez-Arjona, V. J. Sánchez-Morcillo, G. J. de Valcárcel, and E. Roldán, “Bright cavity solitons in anisotropic vectorial Kerr cavities,” J. Opt. B 3, S118–S123 (2001).

[Crossref]

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, “Interaction of localized structures in an optical pattern-forming system,” Phys. Rev. Lett. 85, 748–751 (2000).

[Crossref]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).

[Crossref]

I. V. Barashenkov, Y. S. Smirnov, and N. V. Alexeeva, “Bifurcation to multisoliton complexes in the AC-driven, damped nonlinear Schrödinger equation,” Phys. Rev. E 57, 2350–2364 (1998).

[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate,” Nat. Photonics 10, 321–326 (2016).

[Crossref]

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E 75, 016613 (2007).

[Crossref]

J. M. Soto-Crespo, N. Akhmediev, P. Grelu, and F. Belhache, “Quantized separations of phase-locked soliton pairs in fiber lasers,” Opt. Lett. 28, 1757–1759 (2003).

[Crossref]

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).

[Crossref]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).

S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato–Lefever model,” Opt. Lett. 38, 37–39 (2013).

[Crossref]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901(2017).

M. Conforti, A. Mussot, A. Kudlinski, and S. Trillo, “Modulational instability in dispersion oscillating fiber ring cavities,” Opt. Lett. 39, 4200–4203 (2014).

[Crossref]

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).

[Crossref]

D. Turaev, A. G. Vladimirov, and S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons,” Phys. Rev. Lett. 108, 263906 (2012).

[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, and K. Vahala, “Active capture and stabilization of temporal solitons in microresonators,” Opt. Lett. 41, 2037–2040 (2016).

[Crossref]

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, 1078–1085 (2015).

[Crossref]

D. Turaev, A. G. Vladimirov, and S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons,” Phys. Rev. Lett. 108, 263906 (2012).

[Crossref]

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).

[Crossref]

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, 145–152 (2014).

[Crossref]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).

X. Yi, Q.-F. Yang, K. Y. Yang, and K. Vahala, “Active capture and stabilization of temporal solitons in microresonators,” Opt. Lett. 41, 2037–2040 (2016).

[Crossref]

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, 1078–1085 (2015).

[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, and K. Vahala, “Active capture and stabilization of temporal solitons in microresonators,” Opt. Lett. 41, 2037–2040 (2016).

[Crossref]

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, 1078–1085 (2015).

[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, and K. Vahala, “Active capture and stabilization of temporal solitons in microresonators,” Opt. Lett. 41, 2037–2040 (2016).

[Crossref]

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, 1078–1085 (2015).

[Crossref]

D. Turaev, A. G. Vladimirov, and S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons,” Phys. Rev. Lett. 108, 263906 (2012).

[Crossref]

T. Ackemann, W. J. Firth, and G.-L. Oppo, “Fundamentals and applications of spatial dissipative solitons in photonic devices,” Adv. At. Mol. Opt. Phys. 57, 323–421 (2009).

[Crossref]

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).

[Crossref]

I. Pérez-Arjona, V. J. Sánchez-Morcillo, G. J. de Valcárcel, and E. Roldán, “Bright cavity solitons in anisotropic vectorial Kerr cavities,” J. Opt. B 3, S118–S123 (2001).

[Crossref]

J. P. Gordon, “Dispersive perturbations of solitons of the nonlinear Schrödinger equation,” J. Opt. Soc. Am. B 9, 91–97 (1992).

[Crossref]

S. Coen, M. Haelterman, Ph. Emplit, L. Delage, L. M. Simohamed, and F. Reynaud, “Experimental investigation of the dynamics of a stabilized nonlinear fiber ring resonator,” J. Opt. Soc. Am. B 15, 2283–2293 (1998).

[Crossref]

L. Socci and M. Romagnoli, “Long-range soliton interactions in periodically amplified fiber links,” J. Opt. Soc. Am. B 16, 12–17 (1999).

[Crossref]

P. Del’Haye, A. Coillet, W. Loh, K. Beha, S. B. Papp, and S. A. Diddams, “Phase steps and resonator detuning measurements in microresonator frequency combs,” Nat. Commun. 6, 5668 (2015).

[Crossref]

J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, “Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons,” Nat. Commun. 6, 7370 (2015).

[Crossref]

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, 145–152 (2014).

[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).

[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. R. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90 MHz frame rate,” Nat. Photonics 10, 321–326 (2016).

[Crossref]

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7, 102–112 (2013).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Ultraweak long-range interactions of solitons observed over astronomical distances,” Nat. Photonics 7, 657–663 (2013).

[Crossref]

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Commun. 91, 401–407 (1992).

[Crossref]

C. Milián and D. V. Skryabin, “Soliton families and resonant radiation in a micro-ring resonator near zero group-velocity dispersion,” Opt. Express 22, 3732–3739 (2014).

[Crossref]

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 9180–9191 (2013).

[Crossref]

A. F. J. Runge, C. Aguergaray, N. G. R. Broderick, and M. Erkintalo, “Coherence and shot-to-shot spectral fluctuations in noise-like ultrafast fiber lasers,” Opt. Lett. 38, 4327–4330 (2013).

[Crossref]

X. Yi, Q.-F. Yang, K. Y. Yang, and K. Vahala, “Active capture and stabilization of temporal solitons in microresonators,” Opt. Lett. 41, 2037–2040 (2016).

[Crossref]

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, 2565–2568 (2016).

[Crossref]

J. K. Jang, M. Erkintalo, J. Schröder, B. J. Eggleton, S. G. Murdoch, and S. Coen, “All-optical buffer based on temporal cavity solitons operating at 10 Gb/s,” Opt. Lett. 41, 4526–4529 (2016).

[Crossref]

K. E. Webb, M. Erkintalo, S. Coen, and S. G. Murdoch, “Experimental observation of coherent cavity soliton frequency combs in silica microspheres,” Opt. Lett. 41, 4613–4616 (2016).

[Crossref]

M. Conforti, A. Mussot, A. Kudlinski, and S. Trillo, “Modulational instability in dispersion oscillating fiber ring cavities,” Opt. Lett. 39, 4200–4203 (2014).

[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Observation of dispersive wave emission by temporal cavity solitons,” Opt. Lett. 39, 5503–5506 (2014).

[Crossref]

K. Luo, Y. Xu, M. Erkintalo, and S. G. Murdoch, “Resonant radiation in synchronously pumped passive Kerr cavities,” Opt. Lett. 40, 427–430 (2015).

[Crossref]

J. M. Soto-Crespo, N. Akhmediev, P. Grelu, and F. Belhache, “Quantized separations of phase-locked soliton pairs in fiber lasers,” Opt. Lett. 28, 1757–1759 (2003).

[Crossref]

A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Mode-locked Kerr frequency combs,” Opt. Lett. 36, 2845–2847 (2011).

[Crossref]

S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato–Lefever model,” Opt. Lett. 38, 37–39 (2013).

[Crossref]

C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes,” Opt. Lett. 12, 614–616 (1987).

[Crossref]

B. A. Malomed, “Bound solitons in the nonlinear Schrödinger–Ginzburg–Landau equation,” Phys. Rev. A 44, 6954–6957 (1991).

[Crossref]

Y. K. Chembo and C. R. Menyuk, “Spatiotemporal Lugiato–Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87, 053852 (2013).

[Crossref]

P. Parra-Rivas, D. Gomila, M. A. Matías, S. Coen, and L. Gelens, “Dynamics of localized and patterned structures in the Lugiato–Lefever equation determine the stability and shape of optical frequency combs,” Phys. Rev. A 89, 043813 (2014).

[Crossref]

J. M. Soto-Crespo, P. Grelu, N. Akhmediev, and N. Devine, “Soliton complexes in dissipative systems: vibrating, shaking, and mixed soliton pairs,” Phys. Rev. E 75, 016613 (2007).

[Crossref]

B. A. Malomed, “Bound states of envelope solitons,” Phys. Rev. E 47, 2874–2880 (1993).

[Crossref]

T. Maggipinto, M. Brambilla, G. K. Harkness, and W. J. Firth, “Cavity solitons in semiconductor microresonators: existence, stability, and dynamical properties,” Phys. Rev. E 62, 8726–8739 (2000).

[Crossref]

D. Cai, A. R. Bishop, N. Grønbech-Jensen, and B. A. Malomed, “Bound solitons in the AC-driven, damped nonlinear Schrödinger equation,” Phys. Rev. E 49, 1677–1679 (1994).

[Crossref]

I. V. Barashenkov, Y. S. Smirnov, and N. V. Alexeeva, “Bifurcation to multisoliton complexes in the AC-driven, damped nonlinear Schrödinger equation,” Phys. Rev. E 57, 2350–2364 (1998).

[Crossref]

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, “Interaction of localized structures in an optical pattern-forming system,” Phys. Rev. Lett. 85, 748–751 (2000).

[Crossref]

T. Herr, V. Brasch, D. Jost, J. I. Mirgorodskiy, G. Lihachev, M. L. Gorodetsky, and T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” Phys. Rev. Lett. 113, 123901 (2014).

[Crossref]

K. Krupa, K. Nithyanandan, U. Andral, P. Tchofo-Dinda, and P. Grelu, “Real-time observation of internal motion within ultrafast dissipative optical soliton molecules,” Phys. Rev. Lett. 118, 243901(2017).

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Multisoliton solutions of the complex Ginzburg–Landau equation,” Phys. Rev. Lett. 79, 4047–4051 (1997).

[Crossref]

L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).

[Crossref]

D. Turaev, A. G. Vladimirov, and S. Zelik, “Long-range interaction and synchronization of oscillating dissipative solitons,” Phys. Rev. Lett. 108, 263906 (2012).

[Crossref]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).

[Crossref]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, “Real-time full bandwidth measurement of spectral noise in supercontinuum generation,” Sci. Rep. 2, 882 (2012).

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip–based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).

[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).

[Crossref]

P. Parra-Rivas, D. Gomila, P. Colet, and L. Gelens, “Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation,” arXiv:1705.02619 (2017).

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Bound states of temporal cavity solitons,” in Nonlinear Photonics, NP’2014, Barcelona, Spain, July27–31, 2014 (Optical Society of America, 2014), paper JM5A.59.

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” arXiv:1610.00080 (2016).

E. Obrzud, S. Lecomte, and T. Herr, “Temporal solitons in microresonators driven by optical pulses,” arXiv:1612.08993 (2016).

G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems: from Dissipative Structures to Order through Fluctuations (Wiley, 1977).

N. N. Akhmediev, “General theory of solitons,” in Soliton-Driven Photonics, A. D. Boardman and A. P. Sukhorukov, eds., vol. 31 of NATO Science Series (Springer, 2001), pp. 371–395.

W. J. Firth, “Theory of cavity solitons,” in Soliton-Driven Photonics, A. D. Boardman and A. P. Sukhorukov, eds., vol. 31 of NATO Science Series (Springer, 2001), pp. 459–485.

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2013).

Y. S. Kivshar and G. P. Agrawal, “Vector solitons,” in Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003), Chap. 9, pp. 278–339.