Abstract

Microcomb generation with simultaneous χ(2) and χ(3) nonlinearities brings new possibilities for ultrabroadband and potentially self-referenced integrated comb sources. However, the evolution of the intracavity field involving multiple nonlinear processes shows complex dynamics that are still poorly understood. Here, we report on strong soliton regulation induced by fundamental–second-harmonic (FD-SH) mode coupling. The formation of solitons from chaos is extensively investigated based on coupled Lugiato–Lefever equations. The soliton generation shows more deterministic behaviors in the presence of FD-SH mode interaction, which is in sharp contrast with the usual cases where the soliton number and relative locations are stochastic. Deterministic single soliton transition, soliton binding, and prohibition are observed, depending on the phase-matching condition and coupling coefficient between the fundamental and second-harmonic waves. Our finding provides important new insights into the soliton dynamics in microcavities with simultaneous χ(2) and χ(3) nonlinearities and can be immediate guidance for broadband soliton comb generation with such platforms.

© 2018 Chinese Laser Press

Full Article  |  PDF Article
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References

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2018 (5)

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
[Crossref]

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

M.-G. Suh and K. J. Vahala, “Soliton microcomb range measurement,” Science 359, 884–887 (2018).
[Crossref]

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[Crossref]

X. Xue, Y. Xuan, C. Bao, S. Li, X. Zheng, B. Zhou, M. Qi, and A. M. Weiner, “Microcomb-based true-time-delay network for microwave beamforming with arbitrary beam pattern control,” J. Lightwave Technol. 36, 2312–2321 (2018).
[Crossref]

2017 (14)

Y. Wang, F. Leo, J. Fatome, M. Erkintalo, S. G. Murdoch, and S. Coen, “Universal mechanism for the binding of temporal cavity solitons,” Optica 4, 855–863 (2017).
[Crossref]

C. Bao, Y. Xuan, D. E. Leaird, S. Wabnitz, M. Qi, and A. M. Weiner, “Spatial mode-interaction induced single soliton generation in microresonators,” Optica 4, 1011–1015 (2017).
[Crossref]

S. Diallo and Y. K. Chembo, “Optimization of primary Kerr optical frequency combs for tunable microwave generation,” Opt. Lett. 42, 3522–3525 (2017).
[Crossref]

X. Xue, X. Zheng, and A. M. Weiner, “Soliton trapping and comb self-referencing in a single microresonator with χ(2) and χ(3) nonlinearities,” Opt. Lett. 42, 4147–4150 (2017).
[Crossref]

A. Fülöp, M. Mazur, A. Lorences-Riesgo, T. A. Eriksson, P.-H. Wang, Y. Xuan, D. E. Leaird, M. Qi, P. A. Andrekson, A. M. Weiner, and V. Torres-Company, “Long-haul coherent communications using microresonator-based frequency combs,” Opt. Express 25, 26678–26688 (2017).
[Crossref]

S. Fujii, A. Hori, T. Kato, R. Suzuki, Y. Okabe, W. Yoshiki, A. C. Jinnai, and T. Tanabe, “Effect on Kerr comb generation in a clockwise and counter-clockwise mode coupled microcavity,” Opt. Express 25, 28969–28982 (2017).
[Crossref]

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photon. 2, 096104 (2017).
[Crossref]

S.-W. Huang, J. Yang, S.-H. Yang, M. Yu, D.-L. Kwong, T. Zelevinsky, M. Jarrahi, and C. W. Wong, “Globally stable microresonator Turing pattern formation for coherent high-power THz radiation on-chip,” Phys. Rev. X 7, 041002 (2017).
[Crossref]

X. Yi, Q.-F. Yang, X. Zhang, K. Y. Yang, X. Li, and K. Vahala, “Single-mode dispersive waves and soliton microcomb dynamics,” Nat. Commun. 8, 14869 (2017).
[Crossref]

X. Xue, F. Leo, Y. Xuan, J. A. Jaramillo-Villegas, P.-H. Wang, D. E. Leaird, M. Erkintalo, M. Qi, and A. M. Weiner, “Second-harmonic assisted four-wave mixing in chip-based microresonator frequency comb generation,” Light Sci. Appl. 6, e16253 (2017).
[Crossref]

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

H. Taheri, A. B. Matsko, and L. Maleki, “Optical lattice trap for Kerr solitons,” Eur. Phys. J. D 71, 153 (2017).
[Crossref]

2016 (6)

X. Guo, C.-L. Zou, H. Jung, and H. X. Tang, “On-chip strong coupling and efficient frequency conversion between telecom and visible optical modes,” Phys. Rev. Lett. 117, 123902 (2016).
[Crossref]

T. Hansson, F. Leo, M. Erkintalo, J. Anthony, S. Coen, I. Ricciardi, M. D. Rosa, and S. Wabnitz, “Single envelope equation modeling of multi-octave comb arrays in microresonators with quadratic and cubic nonlinearities,” J. Opt. Soc. Am. B 33, 1207–1215 (2016).
[Crossref]

M. Pu, L. Ottaviano, E. Semenova, and K. Yvind, “Efficient frequency comb generation in AlGaAs-on-insulator,” Optica 3, 823–826 (2016).
[Crossref]

X. Xue and A. M. Weiner, “Microwave photonics connected with microresonator frequency combs,” Front. Optoelectron. 9, 238–248 (2016).
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
[Crossref]

2015 (5)

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]

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
[Crossref]

J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications,” Phys. Rev. Lett. 114, 093902 (2015).
[Crossref]

I. Ricciardi, S. Mosca, M. Parisi, P. Maddaloni, L. Santamaria, P. D. Natale, and M. D. Rosa, “Frequency comb generation in quadratic nonlinear media,” Phys. Rev. A 91, 063839 (2015).
[Crossref]

T. G. Nguyen, M. Shoeiby, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Integrated frequency comb source based Hilbert transformer for wideband microwave photonic phase analysis,” Opt. Express 23, 22087–22097 (2015).
[Crossref]

2014 (9)

A. Kitao, K. Imakita, I. Kawamura, and M. Fujii, “An investigation into second harmonic generation by Si-rich SiNx thin films deposited by RF sputtering over a wide range of Si concentrations,” J. Phys. D 47, 215101 (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]

X. Xue, Y. Xuan, H.-J. Kim, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Programmable single-bandpass photonic RF filter based on Kerr comb from a microring,” J. Lightwave Technol. 32, 3557–3565 (2014).
[Crossref]

S. Miller, K. Luke, Y. Okawachi, J. Cardenas, A. L. Gaeta, and M. Lipson, “On-chip frequency comb generation at visible wavelengths via simultaneous second- and third-order optical nonlinearities,” Opt. Express 22, 26517–26525 (2014).
[Crossref]

C. Bao and C. Yang, “Mode-pulling and phase-matching in broadband Kerr frequency comb generation,” J. Opt. Soc. Am. B 31, 3074–3080 (2014).
[Crossref]

H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, “Green, red, and IR frequency comb line generation from single IR pump in AlN microring resonator,” Optica 1, 396–399 (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]

B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Loňcar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, 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]

2013 (3)

2012 (1)

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100, 161902 (2012).
[Crossref]

2011 (1)

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

2010 (1)

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

2002 (1)

S. Lettieri, S. D. Finizio, P. Maddalena, V. Ballarini, and F. Giorgis, “Second-harmonic generation in amorphous silicon nitride microcavities,” Appl. Phys. Lett. 81, 4706–4708 (2002).
[Crossref]

Anderson, M.

D. J. Wilson, S. Hönl, K. Schneider, M. Anderson, T. J. Kippenberg, and P. Seidler, “Gallium phosphide microresonator frequency combs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SW3A.1.

Anderson, M. H.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Andrekson, P. A.

Anthony, J.

Balakireva, I. V.

J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications,” Phys. Rev. Lett. 114, 093902 (2015).
[Crossref]

Ballarini, V.

S. Lettieri, S. D. Finizio, P. Maddalena, V. Ballarini, and F. Giorgis, “Second-harmonic generation in amorphous silicon nitride microcavities,” Appl. Phys. Lett. 81, 4706–4708 (2002).
[Crossref]

Bao, C.

Beha, K.

Brasch, V.

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T. Herr, V. Brasch, J. D. Jost, 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).
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H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, “Green, red, and IR frequency comb line generation from single IR pump in AlN microring resonator,” Optica 1, 396–399 (2014).
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X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient visible frequency comb generation via Cherenkov radiation from a Kerr microcomb,” arXiv:1704.04264 (2017).

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Hansson, T.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
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B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Loňcar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
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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).
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T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
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Huang, S.-W.

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A. Kitao, K. Imakita, I. Kawamura, and M. Fujii, “An investigation into second harmonic generation by Si-rich SiNx thin films deposited by RF sputtering over a wide range of Si concentrations,” J. Phys. D 47, 215101 (2014).
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X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient visible frequency comb generation via Cherenkov radiation from a Kerr microcomb,” arXiv:1704.04264 (2017).

Jinnai, A. C.

Joshi, C.

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
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X. Guo, C.-L. Zou, H. Jung, and H. X. Tang, “On-chip strong coupling and efficient frequency conversion between telecom and visible optical modes,” Phys. Rev. Lett. 117, 123902 (2016).
[Crossref]

H. Jung, R. Stoll, X. Guo, D. Fischer, and H. X. Tang, “Green, red, and IR frequency comb line generation from single IR pump in AlN microring resonator,” Optica 1, 396–399 (2014).
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H. Jung, C. Xiong, K. Y. Fong, X. Zhang, and H. X. Tang, “Optical frequency comb generation from aluminum nitride microring resonator,” Opt. Lett. 38, 2810–2813 (2013).
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P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
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Kippenberg, T. J.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
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P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
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T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
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A. Kitao, K. Imakita, I. Kawamura, and M. Fujii, “An investigation into second harmonic generation by Si-rich SiNx thin films deposited by RF sputtering over a wide range of Si concentrations,” J. Phys. D 47, 215101 (2014).
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M.-G. Suh and K. J. Vahala, “Soliton microcomb range measurement,” Science 359, 884–887 (2018).
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M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (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]

Vainio, M.

Venkataraman, V.

B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Loňcar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
[Crossref]

Vijayan, K.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Wabnitz, S.

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]

X. Xue, Y. Xuan, H.-J. Kim, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Programmable single-bandpass photonic RF filter based on Kerr comb from a microring,” J. Lightwave Technol. 32, 3557–3565 (2014).
[Crossref]

Wang, P.-H.

A. Fülöp, M. Mazur, A. Lorences-Riesgo, T. A. Eriksson, P.-H. Wang, Y. Xuan, D. E. Leaird, M. Qi, P. A. Andrekson, A. M. Weiner, and V. Torres-Company, “Long-haul coherent communications using microresonator-based frequency combs,” Opt. Express 25, 26678–26688 (2017).
[Crossref]

X. Xue, F. Leo, Y. Xuan, J. A. Jaramillo-Villegas, P.-H. Wang, D. E. Leaird, M. Erkintalo, M. Qi, and A. M. Weiner, “Second-harmonic assisted four-wave mixing in chip-based microresonator frequency comb generation,” Light Sci. Appl. 6, e16253 (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]

Wang, Y.

Weimann, C.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications,” Phys. Rev. Lett. 114, 093902 (2015).
[Crossref]

Weiner, A. M.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[Crossref]

X. Xue, Y. Xuan, C. Bao, S. Li, X. Zheng, B. Zhou, M. Qi, and A. M. Weiner, “Microcomb-based true-time-delay network for microwave beamforming with arbitrary beam pattern control,” J. Lightwave Technol. 36, 2312–2321 (2018).
[Crossref]

A. Fülöp, M. Mazur, A. Lorences-Riesgo, T. A. Eriksson, P.-H. Wang, Y. Xuan, D. E. Leaird, M. Qi, P. A. Andrekson, A. M. Weiner, and V. Torres-Company, “Long-haul coherent communications using microresonator-based frequency combs,” Opt. Express 25, 26678–26688 (2017).
[Crossref]

X. Xue, X. Zheng, and A. M. Weiner, “Soliton trapping and comb self-referencing in a single microresonator with χ(2) and χ(3) nonlinearities,” Opt. Lett. 42, 4147–4150 (2017).
[Crossref]

C. Bao, Y. Xuan, D. E. Leaird, S. Wabnitz, M. Qi, and A. M. Weiner, “Spatial mode-interaction induced single soliton generation in microresonators,” Optica 4, 1011–1015 (2017).
[Crossref]

X. Xue, F. Leo, Y. Xuan, J. A. Jaramillo-Villegas, P.-H. Wang, D. E. Leaird, M. Erkintalo, M. Qi, and A. M. Weiner, “Second-harmonic assisted four-wave mixing in chip-based microresonator frequency comb generation,” Light Sci. Appl. 6, e16253 (2017).
[Crossref]

X. Xue and A. M. Weiner, “Microwave photonics connected with microresonator frequency combs,” Front. Optoelectron. 9, 238–248 (2016).
[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]

X. Xue, Y. Xuan, H.-J. Kim, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Programmable single-bandpass photonic RF filter based on Kerr comb from a microring,” J. Lightwave Technol. 32, 3557–3565 (2014).
[Crossref]

Wilson, D. J.

D. J. Wilson, S. Hönl, K. Schneider, M. Anderson, T. J. Kippenberg, and P. Seidler, “Gallium phosphide microresonator frequency combs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SW3A.1.

Wolf, S.

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Wong, C. W.

S.-W. Huang, J. Yang, S.-H. Yang, M. Yu, D.-L. Kwong, T. Zelevinsky, M. Jarrahi, and C. W. Wong, “Globally stable microresonator Turing pattern formation for coherent high-power THz radiation on-chip,” Phys. Rev. X 7, 041002 (2017).
[Crossref]

Wu, J.

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photon. 2, 096104 (2017).
[Crossref]

Xiong, C.

Xu, X.

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photon. 2, 096104 (2017).
[Crossref]

Xuan, Y.

Xue, X.

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[Crossref]

X. Xue, Y. Xuan, C. Bao, S. Li, X. Zheng, B. Zhou, M. Qi, and A. M. Weiner, “Microcomb-based true-time-delay network for microwave beamforming with arbitrary beam pattern control,” J. Lightwave Technol. 36, 2312–2321 (2018).
[Crossref]

X. Xue, X. Zheng, and A. M. Weiner, “Soliton trapping and comb self-referencing in a single microresonator with χ(2) and χ(3) nonlinearities,” Opt. Lett. 42, 4147–4150 (2017).
[Crossref]

X. Xue, F. Leo, Y. Xuan, J. A. Jaramillo-Villegas, P.-H. Wang, D. E. Leaird, M. Erkintalo, M. Qi, and A. M. Weiner, “Second-harmonic assisted four-wave mixing in chip-based microresonator frequency comb generation,” Light Sci. Appl. 6, e16253 (2017).
[Crossref]

X. Xue and A. M. Weiner, “Microwave photonics connected with microresonator frequency combs,” Front. Optoelectron. 9, 238–248 (2016).
[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]

X. Xue, Y. Xuan, H.-J. Kim, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Programmable single-bandpass photonic RF filter based on Kerr comb from a microring,” J. Lightwave Technol. 32, 3557–3565 (2014).
[Crossref]

Yang, C.

Yang, J.

S.-W. Huang, J. Yang, S.-H. Yang, M. Yu, D.-L. Kwong, T. Zelevinsky, M. Jarrahi, and C. W. Wong, “Globally stable microresonator Turing pattern formation for coherent high-power THz radiation on-chip,” Phys. Rev. X 7, 041002 (2017).
[Crossref]

Yang, K. Y.

X. Yi, Q.-F. Yang, X. Zhang, K. Y. Yang, X. Li, and K. Vahala, “Single-mode dispersive waves and soliton microcomb dynamics,” Nat. Commun. 8, 14869 (2017).
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

Yang, Q.-F.

X. Yi, Q.-F. Yang, X. Zhang, K. Y. Yang, X. Li, and K. Vahala, “Single-mode dispersive waves and soliton microcomb dynamics,” Nat. Commun. 8, 14869 (2017).
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

Yang, S.-H.

S.-W. Huang, J. Yang, S.-H. Yang, M. Yu, D.-L. Kwong, T. Zelevinsky, M. Jarrahi, and C. W. Wong, “Globally stable microresonator Turing pattern formation for coherent high-power THz radiation on-chip,” Phys. Rev. X 7, 041002 (2017).
[Crossref]

Yi, X.

X. Yi, Q.-F. Yang, X. Zhang, K. Y. Yang, X. Li, and K. Vahala, “Single-mode dispersive waves and soliton microcomb dynamics,” Nat. Commun. 8, 14869 (2017).
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

Yoshiki, W.

Yu, M.

S.-W. Huang, J. Yang, S.-H. Yang, M. Yu, D.-L. Kwong, T. Zelevinsky, M. Jarrahi, and C. W. Wong, “Globally stable microresonator Turing pattern formation for coherent high-power THz radiation on-chip,” Phys. Rev. X 7, 041002 (2017).
[Crossref]

Yvind, K.

Zelevinsky, T.

S.-W. Huang, J. Yang, S.-H. Yang, M. Yu, D.-L. Kwong, T. Zelevinsky, M. Jarrahi, and C. W. Wong, “Globally stable microresonator Turing pattern formation for coherent high-power THz radiation on-chip,” Phys. Rev. X 7, 041002 (2017).
[Crossref]

Zervas, M.

M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
[Crossref]

Zhang, X.

X. Yi, Q.-F. Yang, X. Zhang, K. Y. Yang, X. Li, and K. Vahala, “Single-mode dispersive waves and soliton microcomb dynamics,” Nat. Commun. 8, 14869 (2017).
[Crossref]

H. Jung, C. Xiong, K. Y. Fong, X. Zhang, and H. X. Tang, “Optical frequency comb generation from aluminum nitride microring resonator,” Opt. Lett. 38, 2810–2813 (2013).
[Crossref]

Zheng, X.

Zhou, B.

Zou, C.-L.

X. Guo, C.-L. Zou, H. Jung, and H. X. Tang, “On-chip strong coupling and efficient frequency conversion between telecom and visible optical modes,” Phys. Rev. Lett. 117, 123902 (2016).
[Crossref]

X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient visible frequency comb generation via Cherenkov radiation from a Kerr microcomb,” arXiv:1704.04264 (2017).

APL Photon. (1)

X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, “Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source,” APL Photon. 2, 096104 (2017).
[Crossref]

Appl. Phys. Lett. (2)

S. Lettieri, S. D. Finizio, P. Maddalena, V. Ballarini, and F. Giorgis, “Second-harmonic generation in amorphous silicon nitride microcavities,” Appl. Phys. Lett. 81, 4706–4708 (2002).
[Crossref]

T. Ning, H. Pietarinen, O. Hyvärinen, J. Simonen, G. Genty, and M. Kauranen, “Strong second-harmonic generation in silicon nitride films,” Appl. Phys. Lett. 100, 161902 (2012).
[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, 153 (2017).
[Crossref]

Front. Optoelectron. (1)

X. Xue and A. M. Weiner, “Microwave photonics connected with microresonator frequency combs,” Front. Optoelectron. 9, 238–248 (2016).
[Crossref]

J. Lightwave Technol. (2)

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

J. Phys. D (1)

A. Kitao, K. Imakita, I. Kawamura, and M. Fujii, “An investigation into second harmonic generation by Si-rich SiNx thin films deposited by RF sputtering over a wide range of Si concentrations,” J. Phys. D 47, 215101 (2014).
[Crossref]

Light Sci. Appl. (1)

X. Xue, F. Leo, Y. Xuan, J. A. Jaramillo-Villegas, P.-H. Wang, D. E. Leaird, M. Erkintalo, M. Qi, and A. M. Weiner, “Second-harmonic assisted four-wave mixing in chip-based microresonator frequency comb generation,” Light Sci. Appl. 6, e16253 (2017).
[Crossref]

Nat. Commun. (2)

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
[Crossref]

X. Yi, Q.-F. Yang, X. Zhang, K. Y. Yang, X. Li, and K. Vahala, “Single-mode dispersive waves and soliton microcomb dynamics,” Nat. Commun. 8, 14869 (2017).
[Crossref]

Nat. Photonics (6)

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]

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]

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]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2010).
[Crossref]

B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Loňcar, “Diamond nonlinear photonics,” Nat. Photonics 8, 369–374 (2014).
[Crossref]

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

Nature (1)

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Optica (5)

Phys. Rep. (1)

A. Pasquazi, M. Peccianti, L. Razzari, D. J. Moss, S. Coen, M. Erkintalo, Y. K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, A. M. Weiner, and R. Morandotti, “Micro-combs: a novel generation of optical sources,” Phys. Rep. 729, 1–81 (2018).
[Crossref]

Phys. Rev. A (1)

I. Ricciardi, S. Mosca, M. Parisi, P. Maddaloni, L. Santamaria, P. D. Natale, and M. D. Rosa, “Frequency comb generation in quadratic nonlinear media,” Phys. Rev. A 91, 063839 (2015).
[Crossref]

Phys. Rev. Lett. (4)

X. Guo, C.-L. Zou, H. Jung, and H. X. Tang, “On-chip strong coupling and efficient frequency conversion between telecom and visible optical modes,” Phys. Rev. Lett. 117, 123902 (2016).
[Crossref]

M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. P. Pfeiffer, M. Zervas, M. Geiselmann, and T. J. Kippenberg, “Raman self-frequency shift of dissipative Kerr solitons in an optical microresonator,” Phys. Rev. Lett. 116, 103902 (2016).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, 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]

J. Pfeifle, A. Coillet, R. Henriet, K. Saleh, P. Schindler, C. Weimann, W. Freude, I. V. Balakireva, L. Larger, C. Koos, and Y. K. Chembo, “Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications,” Phys. Rev. Lett. 114, 093902 (2015).
[Crossref]

Phys. Rev. X (1)

S.-W. Huang, J. Yang, S.-H. Yang, M. Yu, D.-L. Kwong, T. Zelevinsky, M. Jarrahi, and C. W. Wong, “Globally stable microresonator Turing pattern formation for coherent high-power THz radiation on-chip,” Phys. Rev. X 7, 041002 (2017).
[Crossref]

Sci. Adv. (1)

A. Dutt, C. Joshi, X. Ji, J. Cardenas, Y. Okawachi, K. Luke, A. L. Gaeta, and M. Lipson, “On-chip dual-comb source for spectroscopy,” Sci. Adv. 4, e1701858 (2018).
[Crossref]

Science (4)

P. Trocha, M. Karpov, D. Ganin, M. H. P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T. J. Kippenberg, and C. Koos, “Ultrafast optical ranging using microresonator soliton frequency combs,” Science 359, 887–891 (2018).
[Crossref]

M.-G. Suh and K. J. Vahala, “Soliton microcomb range measurement,” Science 359, 884–887 (2018).
[Crossref]

M.-G. Suh, Q.-F. Yang, K. Y. Yang, X. Yi, and K. J. Vahala, “Microresonator soliton dual-comb spectroscopy,” Science 354, 600–603 (2016).
[Crossref]

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

Other (2)

X. Guo, C.-L. Zou, H. Jung, Z. Gong, A. Bruch, L. Jiang, and H. X. Tang, “Efficient visible frequency comb generation via Cherenkov radiation from a Kerr microcomb,” arXiv:1704.04264 (2017).

D. J. Wilson, S. Hönl, K. Schneider, M. Anderson, T. J. Kippenberg, and P. Seidler, “Gallium phosphide microresonator frequency combs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2018), paper SW3A.1.

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Figures (6)

Fig. 1.
Fig. 1. (a) Scheme of Kerr comb generation in a microcavity with simultaneous χ(2) and χ(3) nonlinearities. (b) Illustration of mode coupling between the fundamental and second-harmonic waves through sum (SFG) and difference (DFG) frequency generation.
Fig. 2.
Fig. 2. (a) Fifth second-harmonic mode power and the absolute phase mismatch (|Δϕ|) versus ΔkL. The vertical dash line indicates the calculated ΔkL for perfect phase matching. (b) Spectra and (c) waveforms of the fundamental (FD) and second-harmonic (SH) waves when ΔkL=3.544 (perfect phase matching). (d) Spectra and (e) waveforms when ΔkL=3.5 (not perfect phase matching).
Fig. 3.
Fig. 3. Soliton transitions in a cavity with only third-order Kerr nonlinearity (κ=0). (a) Intracavity power versus pump detuning. 100 traces are overlaid. The number of traces corresponding to two, three, and four solitons is 21, 73, and 6, respectively. (b)–(d) Overlaid comb spectra for two, three, and four solitons.
Fig. 4.
Fig. 4. Deterministic single soliton formation assisted by FD-SH mode coupling when κ=3  W1/2·m1 and ΔkL=3.515. (a) Intracavity fundamental power versus pump detuning. 100 traces are overlaid. The white dash line shows the absolute phase mismatch calculated according to Eq. (3). The full vertical scale corresponds to 00.1  rad. (b) Intracavity second-harmonic power versus pump detuning. (c) Spectra of the fundamental (FD) and second-harmonic (SH) waves when δ0=0.025. (d) Zoom-in spectra of the fundamental comb lines around the pump, showing weak amplitude and phase perturbations at the fifth mode (marked with a dashed circle). Circle (°): κ=0; triangle (Δ): κ=3  W1/2·m1.
Fig. 5.
Fig. 5. Soliton binding due to FD-SH mode coupling when κ=3  W1/2·m1 and ΔkL=3.505. (a) Intracavity fundamental power versus pump detuning. 100 traces are overlaid. The absolute phase mismatch calculated according to Eq. (3) is also plotted as in Fig. 4(a). (b) Intracavity second-harmonic power versus pump detuning. (c) Overlaid spectra of the fundamental comb when δ0=0.045. Two patterns can be observed. (d) Time-domain waveforms of the two patterns, showing that the soliton is trapped by the oscillations induced by FD-SH mode coupling. The time offset is adjusted such that one soliton is aligned for the two patterns.
Fig. 6.
Fig. 6. Soliton prohibition caused by strong FD-SH mode coupling when κ=6  W1/2·m1 and ΔkL=3.515. (a) Intracavity fundamental power versus pump detuning. 100 traces are overlaid. The absolute phase mismatch calculated according to Eq. (3) is also plotted as in Fig. 4(a). (b) Intracavity second-harmonic power versus pump detuning.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E1z=(α1iδ1ik122τ2+iγ1|E1|2+i2γ12|E2|2)E1+iκE2E1*+η1Ein,
E2z=(α2i2δ1iΔkΔkτik222τ2+iγ2|E2|2+i2γ21|E1|2)E2+iκ*E12.
Δϕ=ϕSH(2ωp+NΔω)ϕFD(ωp)ϕFD(ωp+NΔω)=ΔkL+ΔkLNΔω+k2L2(NΔω)2+2γ21|E1|2L2δ0,
E1|z=0=E10+eiϕ02δ0γ1Lsech[2δ0|k1|L(τtR2)],
ϕ0=arccos(1π8δ0α12Pinγ1η12L).

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