Abstract

Integrated microresonator-based mid-infrared frequency combs based on III-V semiconductors exhibit pronounced higher-order group velocity dispersion that can make it difficult to achieve stable output. One way to stabilize multiple solitons and their repetition rate is to pump simultaneously at two nearby comb lines. Two-color (or bichromatic) pumping also promises to boost the relatively low conversion efficiencies of single-soliton combs. We present simulations showing that, for a realistic InGaAs/InP ridge waveguide, the stabilization effect occurs over only a limited range of pump power and detuning parameters. We map out the parameter ranges for various regimes of operation in terms of the pump power and detuning and determine that the regimes converge quickly as the dispersion is truncated to progressively higher orders.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]

2018 (3)

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref] [PubMed]

areI. Hendry, W. Chen, Y. Wang, B. Garbin, J. Javaloyes, G.-L. Oppo, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude-modulated driving fields,” Phys. Rev. A (Coll. Park) 97(5), 053834 (2018).
[Crossref]

A. Roy, R. Haldar, and S. K. Varshney, “Robust, Synchronous Optical Buffer and Logic Operation in Dual-pump Kerr Micro-Resonator,” J. Lit. Technol. 36(24), 5807–5814 (2018), doi:.
[Crossref]

2017 (4)

T. Jahnke, M. Mikl, and R. Schnaubelt, “Strang splitting for a semilinear Schrodinger eqaution with damping and forcing,” J. Math. Anal. Appl. 455(2), 1051–1071 (2017).
[Crossref]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” Nat. Commun. 8, 14569 (2017).
[Crossref] [PubMed]

C. Bao, H. Taheri, L. Zhang, A. Matsko, Y. Yan, P. Liao, L. Maleki, and A. E. Willner, “High-order dispersion in Kerr comb oscillators,” J. Opt. Soc. Am. B 34(4), 715–725 (2017).
[Crossref]

H. Taheri, A. B. Matsko, and L. Maleki, “Optical Lattice Trap for Kerr Solitons,” Eur. Phys. J. D 71(6), 153 (2017).
[Crossref]

2016 (2)

2015 (1)

H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photonics J. 7(2), 1–9 (2015).
[Crossref]

2014 (5)

2013 (3)

2012 (1)

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

2009 (1)

D. V. Strekalov and N. Yu, “Generation of optical combs in a whispering gallery mode resonator from a bichromatic pump,” Phys. Rev. A 79(4), 41805 (2009).
[Crossref]

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

2004 (1)

E. V. Zemlyanaya and I. V. Barashenkov, “Traveling solitons in the damped-driven nonlinear schrodinger equation,” SIAM J. Appl. Math. 64(3), 800–818 (2004).
[Crossref]

1994 (1)

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65(2), 147–149 (1994).
[Crossref]

1991 (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

Adibi, A.

H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photonics J. 7(2), 1–9 (2015).
[Crossref]

Agarwal, A. M.

Aitchison, J. S.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65(2), 147–149 (1994).
[Crossref]

Al-hemyari, K.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65(2), 147–149 (1994).
[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(6), 063814 (2014).
[Crossref]

Bao, C.

Barashenkov, I. V.

E. V. Zemlyanaya and I. V. Barashenkov, “Traveling solitons in the damped-driven nonlinear schrodinger equation,” SIAM J. Appl. Math. 64(3), 800–818 (2004).
[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(6), 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(5), 053852 (2013).
[Crossref]

Chen, W.

areI. Hendry, W. Chen, Y. Wang, B. Garbin, J. Javaloyes, G.-L. Oppo, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude-modulated driving fields,” Phys. Rev. A (Coll. Park) 97(5), 053834 (2018).
[Crossref]

Cherenkov, A. V.

Coen, S.

areI. Hendry, W. Chen, Y. Wang, B. Garbin, J. Javaloyes, G.-L. Oppo, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude-modulated driving fields,” Phys. Rev. A (Coll. Park) 97(5), 053834 (2018).
[Crossref]

M. Erkintalo and S. Coen, “Coherence properties of Kerr frequency combs,” Opt. Lett. 39(2), 283–286 (2014).
[Crossref] [PubMed]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

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(6), 063814 (2014).
[Crossref]

Del’Haye, P.

Diddams, S. A.

Docherty, A.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[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 Photonics J. 7(2), 1–9 (2015).
[Crossref]

Erkintalo, M.

areI. Hendry, W. Chen, Y. Wang, B. Garbin, J. Javaloyes, G.-L. Oppo, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude-modulated driving fields,” Phys. Rev. A (Coll. Park) 97(5), 053834 (2018).
[Crossref]

M. Erkintalo and S. Coen, “Coherence properties of Kerr frequency combs,” Opt. Lett. 39(2), 283–286 (2014).
[Crossref] [PubMed]

Gaeta, A. L.

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref] [PubMed]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” Nat. Commun. 8, 14569 (2017).
[Crossref] [PubMed]

M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, “Route to stabilized ultrabroadband microresonator-based frequency combs,” Opt. Lett. 38(18), 3478–3481 (2013).
[Crossref] [PubMed]

Garbin, B.

areI. Hendry, W. Chen, Y. Wang, B. Garbin, J. Javaloyes, G.-L. Oppo, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude-modulated driving fields,” Phys. Rev. A (Coll. Park) 97(5), 053834 (2018).
[Crossref]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Godey, C.

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(6), 063814 (2014).
[Crossref]

Gorodetsky, M. L.

Griffith, A. G.

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref] [PubMed]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” Nat. Commun. 8, 14569 (2017).
[Crossref] [PubMed]

Hagan, D. J.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

Haldar, R.

A. Roy, R. Haldar, and S. K. Varshney, “Robust, Synchronous Optical Buffer and Logic Operation in Dual-pump Kerr Micro-Resonator,” J. Lit. Technol. 36(24), 5807–5814 (2018), doi:.
[Crossref]

Hänsch, T. W.

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

Hansson, T.

T. Hansson and S. Wabnitz, “Bichromatically pumped microresonator frequency combs,” Phys. Rev. A 90(1), 013811 (2014).
[Crossref]

Hendry, I.

areI. Hendry, W. Chen, Y. Wang, B. Garbin, J. Javaloyes, G.-L. Oppo, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude-modulated driving fields,” Phys. Rev. A (Coll. Park) 97(5), 053834 (2018).
[Crossref]

Hutchings, D. C.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

Ironside, C. N.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65(2), 147–149 (1994).
[Crossref]

Jahnke, T.

T. Jahnke, M. Mikl, and R. Schnaubelt, “Strang splitting for a semilinear Schrodinger eqaution with damping and forcing,” J. Math. Anal. Appl. 455(2), 1051–1071 (2017).
[Crossref]

Jang, J. K.

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” Nat. Commun. 8, 14569 (2017).
[Crossref] [PubMed]

Javaloyes, J.

areI. Hendry, W. Chen, Y. Wang, B. Garbin, J. Javaloyes, G.-L. Oppo, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude-modulated driving fields,” Phys. Rev. A (Coll. Park) 97(5), 053834 (2018).
[Crossref]

Ji, X.

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” Nat. Commun. 8, 14569 (2017).
[Crossref] [PubMed]

Kang, J. U.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65(2), 147–149 (1994).
[Crossref]

Kimerling, L. C.

Kippenberg, T. J.

Lamont, M. R. E.

Liao, P.

Lihachev, G. V.

Lipson, M.

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref] [PubMed]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” Nat. Commun. 8, 14569 (2017).
[Crossref] [PubMed]

Lobanov, V. E.

Luke, K.

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” Nat. Commun. 8, 14569 (2017).
[Crossref] [PubMed]

Maleki, L.

Marks, B. S.

Matsko, A.

Matsko, A. B.

H. Taheri, A. B. Matsko, and L. Maleki, “Optical Lattice Trap for Kerr Solitons,” Eur. Phys. J. D 71(6), 153 (2017).
[Crossref]

Menyuk, C. R.

S. Wang, A. Docherty, B. S. Marks, and C. R. Menyuk, “Boundary tracking algorithms for determining the stability of mode-locked pulses,” J. Opt. Soc. Am. B 31(11), 2914–2930 (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(5), 053852 (2013).
[Crossref]

Michel, J.

Mikl, M.

T. Jahnke, M. Mikl, and R. Schnaubelt, “Strang splitting for a semilinear Schrodinger eqaution with damping and forcing,” J. Math. Anal. Appl. 455(2), 1051–1071 (2017).
[Crossref]

Miller, S. A.

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” Nat. Commun. 8, 14569 (2017).
[Crossref] [PubMed]

Murdoch, S. G.

areI. Hendry, W. Chen, Y. Wang, B. Garbin, J. Javaloyes, G.-L. Oppo, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude-modulated driving fields,” Phys. Rev. A (Coll. Park) 97(5), 053834 (2018).
[Crossref]

Okawachi, Y.

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref] [PubMed]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” Nat. Commun. 8, 14569 (2017).
[Crossref] [PubMed]

M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, “Route to stabilized ultrabroadband microresonator-based frequency combs,” Opt. Lett. 38(18), 3478–3481 (2013).
[Crossref] [PubMed]

Oppo, G.-L.

areI. Hendry, W. Chen, Y. Wang, B. Garbin, J. Javaloyes, G.-L. Oppo, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude-modulated driving fields,” Phys. Rev. A (Coll. Park) 97(5), 053834 (2018).
[Crossref]

Ottaviano, L.

Papp, S. B.

Pavlov, N. G.

Picqué, N.

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref] [PubMed]

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

Pu, M.

Roy, A.

A. Roy, R. Haldar, and S. K. Varshney, “Robust, Synchronous Optical Buffer and Logic Operation in Dual-pump Kerr Micro-Resonator,” J. Lit. Technol. 36(24), 5807–5814 (2018), doi:.
[Crossref]

Schliesser, A.

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

Schnaubelt, R.

T. Jahnke, M. Mikl, and R. Schnaubelt, “Strang splitting for a semilinear Schrodinger eqaution with damping and forcing,” J. Math. Anal. Appl. 455(2), 1051–1071 (2017).
[Crossref]

Semenova, E.

Sheik-Bahae, M.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65(2), 147–149 (1994).
[Crossref]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

Stegeman, G. I.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65(2), 147–149 (1994).
[Crossref]

Strekalov, D. V.

D. V. Strekalov and N. Yu, “Generation of optical combs in a whispering gallery mode resonator from a bichromatic pump,” Phys. Rev. A 79(4), 41805 (2009).
[Crossref]

Taheri, H.

H. Taheri, A. B. Matsko, and L. Maleki, “Optical Lattice Trap for Kerr Solitons,” Eur. Phys. J. D 71(6), 153 (2017).
[Crossref]

C. Bao, H. Taheri, L. Zhang, A. Matsko, Y. Yan, P. Liao, L. Maleki, and A. E. Willner, “High-order dispersion in Kerr comb oscillators,” J. Opt. Soc. Am. B 34(4), 715–725 (2017).
[Crossref]

H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photonics J. 7(2), 1–9 (2015).
[Crossref]

Van Stryland, E. W.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

Varshney, S. K.

A. Roy, R. Haldar, and S. K. Varshney, “Robust, Synchronous Optical Buffer and Logic Operation in Dual-pump Kerr Micro-Resonator,” J. Lit. Technol. 36(24), 5807–5814 (2018), doi:.
[Crossref]

Villeneuve, A.

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65(2), 147–149 (1994).
[Crossref]

Wabnitz, S.

T. Hansson and S. Wabnitz, “Bichromatically pumped microresonator frequency combs,” Phys. Rev. A 90(1), 013811 (2014).
[Crossref]

Wang, S.

Wang, Y.

areI. Hendry, W. Chen, Y. Wang, B. Garbin, J. Javaloyes, G.-L. Oppo, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude-modulated driving fields,” Phys. Rev. A (Coll. Park) 97(5), 053834 (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 Photonics J. 7(2), 1–9 (2015).
[Crossref]

Willner, A. E.

Xie, G.

Yan, Y.

Yu, M.

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref] [PubMed]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” Nat. Commun. 8, 14569 (2017).
[Crossref] [PubMed]

Yu, N.

D. V. Strekalov and N. Yu, “Generation of optical combs in a whispering gallery mode resonator from a bichromatic pump,” Phys. Rev. A 79(4), 41805 (2009).
[Crossref]

Yvind, K.

Zemlyanaya, E. V.

E. V. Zemlyanaya and I. V. Barashenkov, “Traveling solitons in the damped-driven nonlinear schrodinger equation,” SIAM J. Appl. Math. 64(3), 800–818 (2004).
[Crossref]

Zhang, L.

Zhao, Z.

Appl. Phys. Lett. (1)

J. U. Kang, A. Villeneuve, M. Sheik-Bahae, G. I. Stegeman, K. Al-hemyari, J. S. Aitchison, and C. N. Ironside, “Limitation due to three-photon absorption on the useful spectral range for nonlinear optics in AlGaAs below half band gap,” Appl. Phys. Lett. 65(2), 147–149 (1994).
[Crossref]

Eur. Phys. J. D (1)

H. Taheri, A. B. Matsko, and L. Maleki, “Optical Lattice Trap for Kerr Solitons,” Eur. Phys. J. D 71(6), 153 (2017).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27(6), 1296–1309 (1991).
[Crossref]

IEEE Photonics J. (1)

H. Taheri, A. A. Eftekhar, K. Wiesenfeld, and A. Adibi, “Soliton formation in whispering-gallery-mode resonators via input phase modulation,” IEEE Photonics J. 7(2), 1–9 (2015).
[Crossref]

J. Lit. Technol. (1)

A. Roy, R. Haldar, and S. K. Varshney, “Robust, Synchronous Optical Buffer and Logic Operation in Dual-pump Kerr Micro-Resonator,” J. Lit. Technol. 36(24), 5807–5814 (2018), doi:.
[Crossref]

J. Math. Anal. Appl. (1)

T. Jahnke, M. Mikl, and R. Schnaubelt, “Strang splitting for a semilinear Schrodinger eqaution with damping and forcing,” J. Math. Anal. Appl. 455(2), 1051–1071 (2017).
[Crossref]

J. Opt. Soc. Am. B (2)

Nat. Commun. (2)

M. Yu, Y. Okawachi, A. G. Griffith, N. Picqué, M. Lipson, and A. L. Gaeta, “Silicon-chip-based mid-infrared dual-comb spectroscopy,” Nat. Commun. 9(1), 1869 (2018).
[Crossref] [PubMed]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, “Breather soliton dynamics in microresonators,” Nat. Commun. 8, 14569 (2017).
[Crossref] [PubMed]

Nat. Photonics (1)

A. Schliesser, N. Picqué, and T. W. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Optica (1)

Phys. Rev. A (4)

T. Hansson and S. Wabnitz, “Bichromatically pumped microresonator frequency combs,” Phys. Rev. A 90(1), 013811 (2014).
[Crossref]

D. V. Strekalov and N. Yu, “Generation of optical combs in a whispering gallery mode resonator from a bichromatic pump,” Phys. Rev. A 79(4), 41805 (2009).
[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(5), 053852 (2013).
[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(6), 063814 (2014).
[Crossref]

Phys. Rev. A (Coll. Park) (1)

areI. Hendry, W. Chen, Y. Wang, B. Garbin, J. Javaloyes, G.-L. Oppo, S. Coen, S. G. Murdoch, and M. Erkintalo, “Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude-modulated driving fields,” Phys. Rev. A (Coll. Park) 97(5), 053834 (2018).
[Crossref]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

SIAM J. Appl. Math. (1)

E. V. Zemlyanaya and I. V. Barashenkov, “Traveling solitons in the damped-driven nonlinear schrodinger equation,” SIAM J. Appl. Math. 64(3), 800–818 (2004).
[Crossref]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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Figures (26)

Fig. 1
Fig. 1 (a) Dispersion curves for SOD (blue), TOD (orange), sixth-order dispersion (6OD) (yellow), and AOD (violet). The inset (a) shows the resonator cross-section, with InP substrate (green), 3 μm wide x 2 μm tall InGaAs core (blue), in air (gray). The quantity β2(ω) is defined in the text. On the short-wavelength side, the curves for TOD, 6OD, and AOD overlap so closely that they are nearly indistinguishable. (b) A single soliton, generated from noise by increasing the detuning from Δ = 0 to Δ = 31.5, rotating in a system with monochromatic pumping and AOD.
Fig. 2
Fig. 2 (a) A single soliton, generated from noise by increasing the detuning by increasing the detuning from Δ = 0 to Δ = 31.5, at a fixed position in the simulation of a system with bichromatic pumping and AOD. (b) Spectra corresponding to a single, stabilized soliton in a system with δ12 = 1 and P2/P1 = 60% and AOD (blue), 6OD (yellow), and TOD (green).). The inset shows a close-up of the pump region, showing two pumps at adjacent resonator modes with P2/P1 = 60% and δ12 = 1.
Fig. 3
Fig. 3 (a) A single pulse in a resonator at Δ = 31.5 with the second pump turned on at 250 ns and off again at 500 ns. (b) The calculated momentum for the evolution shown in (a).
Fig. 4
Fig. 4 (a) Schematic of multiple solitons (blue) present in a resonator with a pump wave as a function of resonator position. The preferred pulse positions are near, but do not coincide with, the minima of the pump interference pattern in green. (b) Spectra of one (blue), two (green), and three (red) equally spaced solitons. Note the increase in total power (efficiency) owing to the increase in the number of intracavity solitons.
Fig. 5
Fig. 5 (a) Two pulses locked by turning on a second pump two FSRs away (δ12 = 2) at 150 ns and (b) Three pulses locked into place by a second pump with δ12 = 3. In both cases, P2/P1 = 60% and Δ = 31.5.
Fig. 6
Fig. 6 (a) Generation and evolution of a single soliton in a system with δ12 = 1 and P2/P1 = 40%. The detunings of both pumps is increased from Δ = 0 to Δ = 31.5 over 300 ns in steps of Δ = 0.5 every 5 ns and remains constant after 300 ns. (b) Calculated momentum corresponding to the evolution depicted in (a).
Fig. 7
Fig. 7 A single soliton in a system with δ12 = 1 and P2/P1 = 40%, stabilized by instantaneously decreasing the pump detuning from Δ = 31.5 to Δ = 25 at 250 ns.
Fig. 8
Fig. 8 A soliton in a system with δ12 = 1 and P2/P1 = 60% as the detuning is increased from Δ = 31.5 by 0.5 every 10 ns, starting from t = 0 and ending at t = 570 ns. The pulse, whose position is initially unstable, begins to rotate around the simulation window.
Fig. 9
Fig. 9 A system with TOD and P2/P1 = 60% and P1 = 2.5 mW (a) Δ = 31.5, (b) Δ = 20.
Fig. 10
Fig. 10 Evolution of the P2/P1 = 60% TOD steady-state solution for systems with (a) P2/P1 = 70%, (b) P2/P1 = 80%, (c) P2/P1 = 90%, (d) P2/P1 = 95%. For all cases, the detuning is Δ = 31.5.
Fig. 11
Fig. 11 Boundaries above which the pulse is no longer in a stable position (blue) or supported (orange) due to insufficient pump power, for values of P2/P1 where stabilized pulses exist with TOD. The detuning for the stabilized pulses is δ0 = 0.04725 for all points except P2/P1 = 0.4, which uses δ0 = 0.0386. The main pump power, P1, scales linearly with α, starting at P1 = 5 mW for α = 0.0016.
Fig. 12
Fig. 12 A single, stabilized soliton generated from noise by increasing the detuning from Δ = 0 to Δ = 31.5, in a system with TOD, δ12 = −1 and P2/P1 = 60%.
Fig. 13
Fig. 13 Real components of the intracavity field profile for a TOD system with bichromatic pumping with P2/P1 = 60% and δ12 = 1 (red) and δ12 = −1 (blue).
Fig. 14
Fig. 14 (a) Single pulse generation and evolution in a TOD system with high- and low-frequency secondary pumps with P2/P1 = P3/P1 = 20%. In (a), initially the normalized detuning is increased by Δ = 1 every 10 ns, up to a maximum of Δ = 25. The detuning is instantaneously increased to Δ = 28 at 380 ns, which delocalizes the pulse. (b) The steady-state solution from (a) in a TOD system with high- and low-frequency secondary pumps with P2/P1 = P3/P1 = 50% and Δ = 28.
Fig. 15
Fig. 15 Stability boundaries for TOD and δ12 = 1: in Region I the pulse position is stable, in Region II the pulse rotates because the detuning is too high, in Region III the single pulse solution goes back to a chaotic multipulse state, and in Region IV the pulse disappears, and the system transitions to a low-power CW solution.
Fig. 16
Fig. 16 Stability boundaries for 6OD and δ12 = 1. The meanings of Regions I-IV are the same as in Fig. 15, while in Region V the pulse breathes in amplitude and width as it rotates.
Fig. 17
Fig. 17 Single pulse generation and evolution in a system with SOD and bichromatic pumping with P2/P1 = 60%, Δ = 31.5, and δ12 = 1.
Fig. 18
Fig. 18 Histogram of the number of pulses created in simulations of a system with TOD, δ12 = 1, and P2/P1 = 60% over 1100 runs. N(0) = 548, N(1) = 552. Simulations are carried out from noise by increasing the detuning as shown by Fig. 19.
Fig. 19
Fig. 19 Generation and annihilation of two solitons in a system with TOD, P2/P1 = 60%, and δ12 = 1. Detuning increases from Δ = 0 to Δ = 30 at a rate of 1 every 5 ns.
Fig. 20
Fig. 20 Decreasing the detuning in a stabilized system with a single soliton with TOD, P2/P1 = 60%, and δ12 = 1. (a) The detuning is decreased from Δ = 30 to 21.5. (b) The detuning is decreased further from Δ = 21.5 to 14.5.
Fig. 21
Fig. 21 Pulse evolution with main pump detuning Δ1 = 31.5 and second pump detuning Δ2 = 25.5 with δ12 = 1.
Fig. 22
Fig. 22 Evolution of the P2/P1 = 60% TOD δ12 = 1 steady-state solution for a system with P2/P1 = 98%.
Fig. 23
Fig. 23 Pulse evolution for the shifted steady-state solution from Fig. 12 in a system with TOD, δ12 = −1, and P2/P1 = 70%.
Fig. 24
Fig. 24 Soliton creation and evolution in a system with SOD and monochromatic pumping. The detuning is increased from Δ = 0 to Δ = 75 at a rate of 0.5 per 5 ns.
Fig. 25
Fig. 25 (a) Evolution of the steady-state solution from Fig. 16 in a SOD system with P2/P1 = 86% and δ12 = 1. (b) Evolution of the steady-state solution from Fig. 16 in a SOD system with P2/P1 = 87% and δ12 = 1.
Fig. 26
Fig. 26 Evolution of the shifted steady-state solution from Fig. B1 in a SOD system with P2/P1 = 70% and δ12 = 1.

Tables (1)

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Table 1 Dispersion Coefficients

Equations (2)

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t R E(t,τ) t =[ αi δ 0 +iL k2 β k k! ( i τ ) k +iγL | E | 2 ]E+ θ ( E in (1) + E in (2) e iφ )
P= 1 2 t R /2 t R /2 dτ E * ( i τ )E+c.c.

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