Abstract

Optical frequency combs based on solitons in nonlinear microresonators open up new regimes for optical metrology and signal processing across a range of expanding and emerging applications. In this work, we advance these combs toward applications by demonstrating protected single-soliton formation and operation in a Kerr-nonlinear microresonator using a phase-modulated pump laser. Phase modulation gives rise to spatially/temporally varying effective loss and detuning parameters, leading to an operation regime in which multi-soliton degeneracy is lifted and a single soliton is the only observable behavior. We achieve direct, on-demand excitation of single solitons as indicated by reversal of the characteristic “soliton step.” Phase modulation also enables precise, high bandwidth control of the soliton pulse train’s properties, and we measure dynamics that agree closely with simulations. We show that the technique can be extended to high-repetition-frequency Kerr solitons through subharmonic phase modulation. These results will facilitate straightforward generation and control of Kerr-soliton microcombs for integrated photonics systems.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (4)

B. Yao, S. W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D. L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
[Crossref]

J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A. Diddams, and S. B. Papp, “Thermal and nonlinear dissipative-soliton dynamics in Kerr-microresonator frequency combs,” Phys. Rev. Lett. 121, 063902 (2018).
[Crossref]

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. 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, 81–85 (2018).
[Crossref]

T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, K. Srinivasan, S. A. Diddams, and S. B. Papp, “Interlocking Kerr-microresonator frequency combs for microwave to optical synthesis,” Opt. Lett. 43, 2933–2936 (2018).
[Crossref]

2017 (3)

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” Nat. Photonics 11, 671–676 (2017).
[Crossref]

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys. 13, 94–102 (2017).
[Crossref]

E. Obrzud, S. Lecomte, and T. Herr, “Temporal solitons in microresonators driven by optical pulses,” Nat. Photonics 11, 600–607 (2017).
[Crossref]

2016 (4)

2015 (6)

K. Luo, J. K. Jang, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous creation and annihilation of temporal cavity solitons in a coherently driven passive fiber resonator,” Opt. Lett. 40, 3735–3738 (2015).
[Crossref]

J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Writing and erasing of temporal cavity solitons by direct phase modulation of the cavity driving field,” Opt. Lett. 40, 4755–4758 (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]

H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photon. J. 7, 2200309 (2015).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

2014 (3)

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]

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. J. Vahala, and S. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1, 10–14 (2014).
[Crossref]

2013 (4)

2012 (1)

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[Crossref]

2009 (1)

2007 (1)

2004 (1)

Adibi, A.

H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photon. J. 7, 2200309 (2015).
[Crossref]

Balakireva, I. V.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

Beha, K.

Beha, K. M.

D. C. Cole, K. M. Beha, S. A. Diddams, and S. B. Papp, “Octave-spanning supercontinuum generation via microwave frequency multiplication,” J. Phys. Conf. Ser. 723, 012035 (2016).
[Crossref]

Bluestone, A.

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. 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, 81–85 (2018).
[Crossref]

Bowers, J. E.

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. 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, 81–85 (2018).
[Crossref]

Brasch, V.

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys. 13, 94–102 (2017).
[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]

Briles, T. C.

J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A. Diddams, and S. B. Papp, “Thermal and nonlinear dissipative-soliton dynamics in Kerr-microresonator frequency combs,” Phys. Rev. Lett. 121, 063902 (2018).
[Crossref]

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. 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, 81–85 (2018).
[Crossref]

T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, K. Srinivasan, S. A. Diddams, and S. B. Papp, “Interlocking Kerr-microresonator frequency combs for microwave to optical synthesis,” Opt. Lett. 43, 2933–2936 (2018).
[Crossref]

Carlson, D. R.

J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A. Diddams, and S. B. Papp, “Thermal and nonlinear dissipative-soliton dynamics in Kerr-microresonator frequency combs,” Phys. Rev. Lett. 121, 063902 (2018).
[Crossref]

Carmon, T.

Chang, L.

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. 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, 81–85 (2018).
[Crossref]

Chembo, Y. K.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[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]

Chen, S.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

Chen, T.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[Crossref]

Cherenkov, A. V.

Choi, C.

B. Yao, S. W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D. L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
[Crossref]

Coen, S.

Coillet, A.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

Cole, D. C.

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” Nat. Photonics 11, 671–676 (2017).
[Crossref]

D. C. Cole, K. M. Beha, S. A. Diddams, and S. B. Papp, “Octave-spanning supercontinuum generation via microwave frequency multiplication,” J. Phys. Conf. Ser. 723, 012035 (2016).
[Crossref]

Del’Haye, P.

Diddams, S. A.

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. 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, 81–85 (2018).
[Crossref]

J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A. Diddams, and S. B. Papp, “Thermal and nonlinear dissipative-soliton dynamics in Kerr-microresonator frequency combs,” Phys. Rev. Lett. 121, 063902 (2018).
[Crossref]

T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, K. Srinivasan, S. A. Diddams, and S. B. Papp, “Interlocking Kerr-microresonator frequency combs for microwave to optical synthesis,” Opt. Lett. 43, 2933–2936 (2018).
[Crossref]

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” Nat. Photonics 11, 671–676 (2017).
[Crossref]

D. C. Cole, K. M. Beha, S. A. Diddams, and S. B. Papp, “Octave-spanning supercontinuum generation via microwave frequency multiplication,” J. Phys. Conf. Ser. 723, 012035 (2016).
[Crossref]

S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. J. Vahala, and S. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1, 10–14 (2014).
[Crossref]

S. B. Papp, P. Del’Haye, and S. A. Diddams, “Parametric seeding of a microresonator optical frequency comb,” Opt. Express 21, 17615–17624 (2013).
[Crossref]

Drake, T.

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. 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, 81–85 (2018).
[Crossref]

Drake, T. E.

J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A. Diddams, and S. B. Papp, “Thermal and nonlinear dissipative-soliton dynamics in Kerr-microresonator frequency combs,” Phys. Rev. Lett. 121, 063902 (2018).
[Crossref]

T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, K. Srinivasan, S. A. Diddams, and S. B. Papp, “Interlocking Kerr-microresonator frequency combs for microwave to optical synthesis,” Opt. Lett. 43, 2933–2936 (2018).
[Crossref]

Duan, X.

B. Yao, S. W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D. L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
[Crossref]

Eftekhar, A. A.

H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photon. J. 7, 2200309 (2015).
[Crossref]

Erkintalo, M.

Feng, Z.

B. Yao, S. W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D. L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
[Crossref]

Fredrick, C.

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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. 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, 81–85 (2018).
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Komljenovic, T.

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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. 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, 81–85 (2018).
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T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, K. Srinivasan, S. A. Diddams, and S. B. Papp, “Interlocking Kerr-microresonator frequency combs for microwave to optical synthesis,” Opt. Lett. 43, 2933–2936 (2018).
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E. Obrzud, S. Lecomte, and T. Herr, “Temporal solitons in microresonators driven by optical pulses,” Nat. Photonics 11, 600–607 (2017).
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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. 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, 81–85 (2018).
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Painter, O.

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
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J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A. Diddams, and S. B. Papp, “Thermal and nonlinear dissipative-soliton dynamics in Kerr-microresonator frequency combs,” Phys. Rev. Lett. 121, 063902 (2018).
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T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, K. Srinivasan, S. A. Diddams, and S. B. Papp, “Interlocking Kerr-microresonator frequency combs for microwave to optical synthesis,” Opt. Lett. 43, 2933–2936 (2018).
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D. C. Cole, K. M. Beha, S. A. Diddams, and S. B. Papp, “Octave-spanning supercontinuum generation via microwave frequency multiplication,” J. Phys. Conf. Ser. 723, 012035 (2016).
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S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. J. Vahala, and S. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1, 10–14 (2014).
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S. B. Papp, P. Del’Haye, and S. A. Diddams, “Parametric seeding of a microresonator optical frequency comb,” Opt. Express 21, 17615–17624 (2013).
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Pfeiffer, M. H. P.

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. 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, 81–85 (2018).
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H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys. 13, 94–102 (2017).
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Qi, M.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
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Randle, H. G.

Rao, Y.

B. Yao, S. W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D. L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
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Sinclair, L. C.

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. 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, 81–85 (2018).
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Spencer, D. T.

J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A. Diddams, and S. B. Papp, “Thermal and nonlinear dissipative-soliton dynamics in Kerr-microresonator frequency combs,” Phys. Rev. Lett. 121, 063902 (2018).
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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. 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, 81–85 (2018).
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T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, K. Srinivasan, S. A. Diddams, and S. B. Papp, “Interlocking Kerr-microresonator frequency combs for microwave to optical synthesis,” Opt. Lett. 43, 2933–2936 (2018).
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Srinivasan, K.

T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, K. Srinivasan, S. A. Diddams, and S. B. Papp, “Interlocking Kerr-microresonator frequency combs for microwave to optical synthesis,” Opt. Lett. 43, 2933–2936 (2018).
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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. 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, 81–85 (2018).
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Stone, J.

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. 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, 81–85 (2018).
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Stone, J. R.

J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A. Diddams, and S. B. Papp, “Thermal and nonlinear dissipative-soliton dynamics in Kerr-microresonator frequency combs,” Phys. Rev. Lett. 121, 063902 (2018).
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T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, K. Srinivasan, S. A. Diddams, and S. B. Papp, “Interlocking Kerr-microresonator frequency combs for microwave to optical synthesis,” Opt. Lett. 43, 2933–2936 (2018).
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Suh, M.

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. 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, 81–85 (2018).
[Crossref]

Suh, M.-G.

Sylvestre, T.

Taheri, H.

H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photon. J. 7, 2200309 (2015).
[Crossref]

Theogarajan, L.

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. 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, 81–85 (2018).
[Crossref]

Vahala, K.

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. 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, 81–85 (2018).
[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]

Vahala, K. J.

Vinod, A. K.

B. Yao, S. W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D. L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
[Crossref]

Volet, N.

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. 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, 81–85 (2018).
[Crossref]

Wang, C. Y.

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]

Wang, J.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

Wang, P.-H.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

Weiner, A. M.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

Westly, D.

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. 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, 81–85 (2018).
[Crossref]

T. C. Briles, J. R. Stone, T. E. Drake, D. T. Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, K. Srinivasan, S. A. Diddams, and S. B. Papp, “Interlocking Kerr-microresonator frequency combs for microwave to optical synthesis,” Opt. Lett. 43, 2933–2936 (2018).
[Crossref]

Wiesenfeld, K.

H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photon. J. 7, 2200309 (2015).
[Crossref]

Wong, C. W.

B. Yao, S. W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D. L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
[Crossref]

Xuan, Y.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

Xue, X.

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

Yang, K. Y.

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. 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, 81–85 (2018).
[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]

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[Crossref]

Yang, L.

Yang, Q.-F.

Yao, B.

B. Yao, S. W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D. L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
[Crossref]

Yi, X.

Yu, M.

B. Yao, S. W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D. L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
[Crossref]

IEEE Photon. J. (1)

H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photon. J. 7, 2200309 (2015).
[Crossref]

J. Lightwave Technol. (2)

J. Phys. Conf. Ser. (1)

D. C. Cole, K. M. Beha, S. A. Diddams, and S. B. Papp, “Octave-spanning supercontinuum generation via microwave frequency multiplication,” J. Phys. Conf. Ser. 723, 012035 (2016).
[Crossref]

Nat. Commun. (1)

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]

Nat. Photonics (5)

E. Obrzud, S. Lecomte, and T. Herr, “Temporal solitons in microresonators driven by optical pulses,” Nat. Photonics 11, 600–607 (2017).
[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]

D. C. Cole, E. S. Lamb, P. Del’Haye, S. A. Diddams, and S. B. Papp, “Soliton crystals in Kerr resonators,” Nat. Photonics 11, 671–676 (2017).
[Crossref]

X. Xue, Y. Xuan, Y. Liu, P.-H. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Mode-locked dark pulse Kerr combs in normal-dispersion microresonators,” Nat. Photonics 9, 594–600 (2015).
[Crossref]

H. Lee, T. Chen, J. Li, K. Y. Yang, S. Jeon, O. Painter, and K. J. Vahala, “Chemically etched ultrahigh-Q wedge-resonator on a silicon chip,” Nat. Photonics 6, 369–373 (2012).
[Crossref]

Nat. Phys. (1)

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. P. Pfeiffer, V. Brasch, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators,” Nat. Phys. 13, 94–102 (2017).
[Crossref]

Nature (2)

B. Yao, S. W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D. L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
[Crossref]

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. 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, 81–85 (2018).
[Crossref]

Opt. Express (3)

Opt. Lett. (7)

Optica (2)

Phys. Rev. A (2)

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).
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C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
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Phys. Rev. Lett. (1)

J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A. Diddams, and S. B. Papp, “Thermal and nonlinear dissipative-soliton dynamics in Kerr-microresonator frequency combs,” Phys. Rev. Lett. 121, 063902 (2018).
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F. W. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, eds., NIST Handbook of Mathematical Functions (Cambridge University, 2010).

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Figures (6)

Fig. 1.
Fig. 1. (a) Schematic for soliton generation in a PM-pumped resonator, neglecting interference at the output. (b) Simulated energy-level diagrams for the CW- (orange) and PM-pumped (blue, δ PM = π ) resonator for F 2 = 4 , β 2 = 0.0187 . With PM, an interval in α exists for which the single soliton is the only available energy level. This interval is fairly narrow, but we find that it is readily accessible in experiment. We also observe non-stationary states for values of α 2.7 in the PM case (red shading); whether the system exhibits one of these non-stationary states or an N = 2 soliton state is determined by the initial conditions that seed the formation of the soliton ensemble.
Fig. 2.
Fig. 2. (a) Simulated quasi-CW background intensity without (orange) and with PM of depth π / 2 (blue) and 4 π (green), with F 2 = 3 and β 2 = 0.02 , with analytical approximations in black. Here α is slightly larger than α 1 , the critical value for soliton formation. Dashed traces show the simulated phase profile of the field ψ (green) and of the driving term F e i δ PM cos θ (red) with modulation depth 4 π . The phase of the field is very nearly the phase of the drive plus a constant offset. (b) A simulation of spontaneous single-soliton generation using a phase-modulated pump laser with δ PM = π , F 2 = 4 , and β = 0.0187 . Left: α is decreased smoothly as a function of time τ and then held constant after a soliton is generated. Middle: false-color plot of the intensity in the cavity as a function of time, with the final intensity shown above. Right: false-color plot of the comb spectrum on a logarithmic scale as a function of time, assuming a repetition rate of 22 GHz. Final spectrum is shown above. (c) A simulation of the collapse of a soliton ensemble to N = 1 with initial N = 5 for α = 2.8 , F 2 = 4 , and β = 0.0187 . To slow down the initial dynamics for clarity, the modulation depth is initialized at δ PM = 0 , and then linearly ramped to δ PM = π from τ = 50 to τ = 550 . We note that the simulations presented in parts (b) and (c) are similar to simulations presented in Ref. [16]; we present these for clarity without claiming novelty. (d) Plots of approximations (obtained as described in the text, β 2 = 0.0187 ) to the values α 1 and α 2 of detuning at which the first soliton and a second soliton are generated, respectively, with a zoomed plot depicting details in the upper right. Several values of PM depth are plotted: δ PM = 0 (blue), δ PM = π (yellow), and δ PM = 2 π (green). For each the line to the right is α 1 and the line to the left is α 2 ; the single line for δ PM = 0 represents the line at which the bistability of the CW background vanishes everywhere in this case. Horizontal lines indicate the interval α 2 < α < α 1 obtained in the corresponding LLE simulations with F 2 = 5.1 .
Fig. 3.
Fig. 3. (a) Frequency-domain depiction of the experiment, with cavity modes shown in blue and laser frequencies shown in red. Modulation of a counter-propagating probe beam at f PDH after shifting by f AOM and subsequent locking of the red PDH sideband to the resonance allows detuning control via ν 0 ν pump = f AOM f PDH , with adjustments implemented by changing f PDH . (b) Schematic depiction of the components of the experiment used for frequency control of the system.
Fig. 4.
Fig. 4. (a) Measurement of a reversed soliton step in the comb power associated with soliton generation from the background. Inset shows qualitatively similar dynamics observed in an LLE-simulated comb-power trace. (b) Measured optical spectrum of the soliton generated with a phase-modulated pump laser. The spectrum of the pump, which contains phase-modulation sidebands, is visible in the center. The soliton’s spectral envelope closely matches the sech 2 envelope that has been overlaid in dashed red. (c) Plot of the out-coupled soliton pulse train’s repetition rate as recorded by a photodetector, exhibiting a characteristically high signal-to-noise ratio. We emphasize that this data is obtained with the phase modulation turned off; otherwise the recorded RF signal is dominated by through-coupled phase-modulation sidebands at f PM f FSR f rep . (d) Histogram of measured offset in detuning from a reference value at which a soliton is generated over 160 successive trials, with a Gaussian fit shown in red. The width of the interval over which solitons are generated is larger than the calculated width of the protected N = 1 level shown in Fig. 1(b), but the model does not include laser fluctuations and other experimental effects.
Fig. 5.
Fig. 5. (a) Measured spectrogram of f rep as f PM is swept over ± 50    kHz , with glitches where the locking range is exceeded. Inset: qualitative agreement with simulations, shown in red, when f PM is outside of the locking bandwidth. As the soliton and the pump phase evolve at different frequencies f rep and f PM , the soliton periodically approaches the maximum of the phase profile. The soliton’s group velocity changes, nearly locking to the phase modulation, before becoming clearly unlocked again. (b) Measured eye diagram of f rep as f PM is switched ± 40    kHz with 10 μs transition time. (c) The same with 60 ns transition time, and an LLE simulation of the dynamics (red) with depth δ PM = 0.9 π and resonator linewidth Δ ν = 1.5    MHz . (d) Simulated switching dynamics for various linewidths and modulation depths. The theory trace from (c) is reproduced in solid red in both panels. Top, solid black: modulation depth 0.9 π as in (c), and Δ ν = 10    MHz (fastest, left), 3 MHz, and 1.4 MHz. Bottom, dashed red: linewidth Δ ν = 1.5    MHz as in (c), with modulation depths of 2 π and 6 π (curves nearly overlap).
Fig. 6.
Fig. 6. (a) Simulated spectra of PM at f FSR with depth 0.15 π (blue) and at f FSR / 21 with depth 8.3 π (red). The relationships between the fields that address resonator modes 1 , 0, and 1 (as indicated by the gray Lorentzian curves) are the same in both cases. (b) LLE simulation of single-soliton generation using the subharmonic phase-modulation spectrum shown in red in panel (a). Only modes n = 0 , ± 21 , ± 42 , of the phase-modulated driving field are coupled into the resonator and affect the LLE dynamics, with modes | n | > 21 having negligible power. As α is decreased from a large initial value, a soliton is spontaneously generated, as in the case of phase modulation near the FSR.

Equations (6)

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ψ τ = ( 1 + i α ) ψ + i | ψ | 2 ψ i β 2 2 2 ψ θ 2 + F e i δ PM cos θ .
F = ( γ ( θ ) + i α eff ( θ ) ) φ i | φ | 2 φ .
γ ( θ ) = 1 + β 2 2 δ PM cos θ ,
α eff ( θ ) = α β 2 2 δ PM 2 sin 2 θ .
ψ = F e i δ PM cos θ γ ( θ ) + i ( α eff ( θ ) ρ ( θ ) ) ,
F 2 = ( γ ( θ ) 2 + ( α eff ( θ ) ρ ( θ ) ) 2 ) ρ ( θ ) .

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