Abstract

We experimentally demonstrate the generation of highly coherent Type-II micro-combs based on a micro-resonator nested in a fiber cavity loop, known as the filter-driven four wave mixing (FD-FWM) laser scheme. In this system, the frequency spacing of the comb can be adjusted to integer multiples of the free-spectral range (FSR) of the nested micro-resonator by properly tuning the fiber cavity length. Sub-comb lines with single FSR spacing around the primary comb lines can be generated. Such a spectral emission is known as a “Type-II comb.” Our system achieves a fully coherent output. This behavior is verified by numerical simulations. This study represents an important step forward in controlling and manipulating the dynamics of an FD-FWM laser.

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References

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2018 (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]

2017 (8)

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. 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]

M. Kues, C. Reimer, P. Roztocki, L. Romero Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. 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]

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]

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]

C. Bao, P. Liao, A. Kordts, L. Zhang, M. Karpov, M. Pfeiffer, Y. Cao, Y. Yan, A. Almaiman, G. Xie, A. Mohajerin-Ariaei, L. Li, M. Ziyadi, S. Wilkinson, M. Tur, T. Kippenberg, and A. Willner, “Dual-pump generation of high-coherence primary Kerr combs with multiple sub-lines,” Opt. Lett. 42, 595–598 (2017).
[Crossref]

W. Q. Wang, W. F. Zhang, S. T. Chu, B. E. Little, Q. H. Yang, L. R. Wang, X. H. Hu, L. Wang, G. X. Wang, Y. H. Wang, and W. Zhao, “Repetition rate multiplication pulsed laser source based on a micro-ring resonator,” ACS Photon. 4, 1677–1683 (2017).
[Crossref]

L. Di Lauro, J. Li, D. J. Moss, R. Morandotti, S. T. Chu, M. Peccianti, and A. Pasquazi, “Parametric control of thermal self-pulsation in micro-cavities,” Opt. Lett. 42, 3407–3410 (2017).
[Crossref]

2016 (10)

M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica 3, 854–860 (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]

W. Q. Wang, S. T. Chu, B. E. Little, A. Pasquazi, Y. S. Wang, L. R. Wang, W. F. Zhang, L. Wang, X. H. Hu, G. X. Wang, H. Hu, Y. L. Su, F. T. Li, Y. S. Liu, and W. Zhao, “Dual-pump Kerr micro-cavity optical frequency comb with varying FSR spacing,” Sci. Rep. 6, 28501 (2016).
[Crossref]

C. Bao, J. A. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in an optical microresonator,” Phys. Rev. Lett. 117, 163901 (2016).
[Crossref]

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

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10, 316–320 (2016).
[Crossref]

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (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]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (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]

2015 (4)

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]

S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
[Crossref]

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

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

2014 (6)

A. Coillet and Y. K. Chembo, “Routes to spatiotemporal chaos in Kerr optical frequency combs,” Chaos 24, 013113 (2014).
[Crossref]

Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, S. Chen, A. J. Metcalf, J. Wang, D. E. Leaird, M. Qi, and A. M. Weiner, “Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation,” Optica 1, 137–144 (2014).
[Crossref]

P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112, 043905 (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]

J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (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 (7)

2012 (4)

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref]

A. Pasquazi, M. Peccianti, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Stable, dual mode, high repetition rate mode-locked laser based on a microring resonator,” Opt. Express 20, 27355–27362 (2012).
[Crossref]

I. S. Grudinin, L. Baumgartel, and N. Yu, “Frequency comb from a microresonator with engineered spectrum,” Opt. Express 20, 6604–6609 (2012).
[Crossref]

T. Herr, K. Hartinger, J. Riemensberger, C. Wang, E. Gavartin, R. Holzwarth, M. Gorodetsky, and T. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics 6, 480–487 (2012).
[Crossref]

2011 (3)

P. Del’Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[Crossref]

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
[Crossref]

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

2010 (4)

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]

Y. K. Chembo, D. V. Strekalov, and N. Yu, “Spectrum and dynamics of optical frequency combs generated with monolithic whispering gallery mode resonators,” Phys. Rev. Lett. 104, 103902 (2010).
[Crossref]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

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

2009 (2)

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3, 529–533 (2009).
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J. Schröder, T. D. Vo, and B. J. Eggleton, “Repetition-rate-selective, wavelength-tunable mode-locked laser at up to 640 GHz,” Opt. Lett. 34, 3902–3904 (2009).
[Crossref]

2008 (1)

2007 (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

2006 (1)

I. S. Grudinin, V. S. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A 74, 063806 (2006).
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1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
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1992 (1)

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

Almaiman, A.

Anderson, M. H.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. 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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Arcizet, O.

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3, 529–533 (2009).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
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Azaña, J.

M. Kues, C. Reimer, P. Roztocki, L. Romero Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
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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).
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Bao, C.

C. Bao, P. Liao, A. Kordts, L. Zhang, M. Karpov, M. Pfeiffer, Y. Cao, Y. Yan, A. Almaiman, G. Xie, A. Mohajerin-Ariaei, L. Li, M. Ziyadi, S. Wilkinson, M. Tur, T. Kippenberg, and A. Willner, “Dual-pump generation of high-coherence primary Kerr combs with multiple sub-lines,” Opt. Lett. 42, 595–598 (2017).
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C. Bao, J. A. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in an optical microresonator,” Phys. Rev. Lett. 117, 163901 (2016).
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Baumgartel, L.

Beha, K.

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10, 316–320 (2016).
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P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

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

P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112, 043905 (2014).
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Brasch, V.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. 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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H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. 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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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).
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V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351, 357–360 (2016).
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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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J. Pfeifle, V. Brasch, M. Lauermann, Y. Yu, D. Wegner, T. Herr, K. Hartinger, P. Schindler, J. Li, D. Hillerkuss, R. Schmogrow, C. Weimann, R. Holzwarth, W. Freude, J. Leuthold, T. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
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Bromberg, Y.

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
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Cao, Y.

Caspani, L.

M. Kues, C. Reimer, P. Roztocki, L. Romero Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
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A. Pasquazi, L. Caspani, M. Peccianti, M. Clerici, M. Ferrera, L. Razzari, D. Duchesne, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Self-locked optical parametric oscillation in a CMOS compatible microring resonator: a route to robust optical frequency comb generation on a chip,” Opt. Express 21, 13333–13341 (2013).
[Crossref]

Chembo, Y. K.

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]

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]

A. Coillet and Y. K. Chembo, “Routes to spatiotemporal chaos in Kerr optical frequency combs,” Chaos 24, 013113 (2014).
[Crossref]

Y. K. Chembo, D. V. Strekalov, and N. Yu, “Spectrum and dynamics of optical frequency combs generated with monolithic whispering gallery mode resonators,” Phys. Rev. Lett. 104, 103902 (2010).
[Crossref]

Chen, L.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
[Crossref]

Chen, S.

Chu, S.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
[Crossref]

Chu, S. T.

W. Q. Wang, W. F. Zhang, S. T. Chu, B. E. Little, Q. H. Yang, L. R. Wang, X. H. Hu, L. Wang, G. X. Wang, Y. H. Wang, and W. Zhao, “Repetition rate multiplication pulsed laser source based on a micro-ring resonator,” ACS Photon. 4, 1677–1683 (2017).
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M. Kues, C. Reimer, P. Roztocki, L. Romero Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

L. Di Lauro, J. Li, D. J. Moss, R. Morandotti, S. T. Chu, M. Peccianti, and A. Pasquazi, “Parametric control of thermal self-pulsation in micro-cavities,” Opt. Lett. 42, 3407–3410 (2017).
[Crossref]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

W. Q. Wang, S. T. Chu, B. E. Little, A. Pasquazi, Y. S. Wang, L. R. Wang, W. F. Zhang, L. Wang, X. H. Hu, G. X. Wang, H. Hu, Y. L. Su, F. T. Li, Y. S. Liu, and W. Zhao, “Dual-pump Kerr micro-cavity optical frequency comb with varying FSR spacing,” Sci. Rep. 6, 28501 (2016).
[Crossref]

A. Pasquazi, L. Caspani, M. Peccianti, M. Clerici, M. Ferrera, L. Razzari, D. Duchesne, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Self-locked optical parametric oscillation in a CMOS compatible microring resonator: a route to robust optical frequency comb generation on a chip,” Opt. Express 21, 13333–13341 (2013).
[Crossref]

A. Pasquazi, M. Peccianti, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Stable, dual mode, high repetition rate mode-locked laser based on a microring resonator,” Opt. Express 20, 27355–27362 (2012).
[Crossref]

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
[Crossref]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Cino, A.

M. Kues, C. Reimer, P. Roztocki, L. Romero Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

Clerici, M.

Coen, S.

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]

S. Coen and M. Erkintalo, “Universal scaling laws of Kerr frequency combs,” Opt. Lett. 38, 1790–1792 (2013).
[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, P. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nat. Photonics 4, 471–476 (2010).
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J. Schröder, D. Alasia, T. Sylvestre, and S. Coen, “Dynamics of an ultrahigh-repetition-rate passively mode-locked Raman fiber laser,” J. Opt. Soc. Am. B 25, 1178–1186 (2008).
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Coillet, A.

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

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

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]

A. Coillet and Y. K. Chembo, “Routes to spatiotemporal chaos in Kerr optical frequency combs,” Chaos 24, 013113 (2014).
[Crossref]

Cole, D. C.

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10, 316–320 (2016).
[Crossref]

Del’Haye, P.

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]

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10, 316–320 (2016).
[Crossref]

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

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

P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112, 043905 (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]

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]

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, and T. J. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref]

P. Del’Haye, T. Herr, E. Gavartin, M. Gorodetsky, R. Holzwarth, and T. Kippenberg, “Octave spanning tunable frequency comb from a microresonator,” Phys. Rev. Lett. 107, 063901 (2011).
[Crossref]

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3, 529–533 (2009).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Di Lauro, L.

Diddams, S.

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

Diddams, S. A.

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10, 316–320 (2016).
[Crossref]

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

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]

P. Del’Haye, K. Beha, S. B. Papp, and S. A. Diddams, “Self-injection locking and phase-locked states in microresonator-based optical frequency combs,” Phys. Rev. Lett. 112, 043905 (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]

Duchesne, D.

Eggleton, B. J.

Eliyahu, D.

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

Emplit, P.

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

Erkintalo, 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]

S. Coen and M. Erkintalo, “Universal scaling laws of Kerr frequency combs,” Opt. Lett. 38, 1790–1792 (2013).
[Crossref]

Ferdous, F.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
[Crossref]

Ferrera, M.

Fong, K. Y.

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Fortier, T.

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
[Crossref]

Foster, M. A.

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]

Freude, W.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. 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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[Crossref]

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

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion,” Nat. Photonics 3, 529–533 (2009).
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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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Koos, C.

P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. 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]

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M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica 3, 854–860 (2016).
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M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
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Liu, Y. S.

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S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
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W. Liang, D. Eliyahu, V. Ilchenko, A. Savchenkov, A. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
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McMillan, J. F.

S.-W. Huang, H. Zhou, J. Yang, J. F. McMillan, A. Matsko, M. Yu, D.-L. Kwong, L. Maleki, and C. W. Wong, “Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators,” Phys. Rev. Lett. 114, 053901 (2015).
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Miao, H.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics 5, 770–776 (2011).
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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).
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Mohajerin-Ariaei, A.

Morandotti, R.

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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M. Kues, C. Reimer, P. Roztocki, L. Romero Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
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L. Di Lauro, J. Li, D. J. Moss, R. Morandotti, S. T. Chu, M. Peccianti, and A. Pasquazi, “Parametric control of thermal self-pulsation in micro-cavities,” Opt. Lett. 42, 3407–3410 (2017).
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C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
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D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7, 597–607 (2013).
[Crossref]

A. Pasquazi, L. Caspani, M. Peccianti, M. Clerici, M. Ferrera, L. Razzari, D. Duchesne, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Self-locked optical parametric oscillation in a CMOS compatible microring resonator: a route to robust optical frequency comb generation on a chip,” Opt. Express 21, 13333–13341 (2013).
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A. Pasquazi, M. Peccianti, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Stable, dual mode, high repetition rate mode-locked laser based on a microring resonator,” Opt. Express 20, 27355–27362 (2012).
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M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
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L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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Moss, D.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics 4, 41–45 (2010).
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Moss, D. J.

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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M. Kues, C. Reimer, P. Roztocki, L. Romero Cortés, S. Sciara, B. Wetzel, Y. Zhang, A. Cino, S. T. Chu, B. E. Little, D. J. Moss, L. Caspani, J. Azaña, and R. Morandotti, “On-chip generation of high-dimensional entangled quantum states and their coherent control,” Nature 546, 622–626 (2017).
[Crossref]

L. Di Lauro, J. Li, D. J. Moss, R. Morandotti, S. T. Chu, M. Peccianti, and A. Pasquazi, “Parametric control of thermal self-pulsation in micro-cavities,” Opt. Lett. 42, 3407–3410 (2017).
[Crossref]

C. Reimer, M. Kues, P. Roztocki, B. Wetzel, F. Grazioso, B. E. Little, S. T. Chu, T. Johnston, Y. Bromberg, L. Caspani, D. J. Moss, and R. Morandotti, “Generation of multiphoton entangled quantum states by means of integrated frequency combs,” Science 351, 1176–1180 (2016).
[Crossref]

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics 7, 597–607 (2013).
[Crossref]

A. Pasquazi, L. Caspani, M. Peccianti, M. Clerici, M. Ferrera, L. Razzari, D. Duchesne, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Self-locked optical parametric oscillation in a CMOS compatible microring resonator: a route to robust optical frequency comb generation on a chip,” Opt. Express 21, 13333–13341 (2013).
[Crossref]

A. Pasquazi, M. Peccianti, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Stable, dual mode, high repetition rate mode-locked laser based on a microring resonator,” Opt. Express 20, 27355–27362 (2012).
[Crossref]

M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, “Demonstration of a stable ultrafast laser based on a nonlinear microcavity,” Nat. Commun. 3, 765 (2012).
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Oh, D. Y.

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10, 316–320 (2016).
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Okawachi, Y.

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).
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M. Yu, Y. Okawachi, A. G. Griffith, M. Lipson, and A. L. Gaeta, “Mode-locked mid-infrared frequency combs in a silicon microresonator,” Optica 3, 854–860 (2016).
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Ottaviano, L.

Papp, S. B.

P. Del’Haye, A. Coillet, T. Fortier, K. Beha, D. C. Cole, K. Y. Yang, H. Lee, K. J. Vahala, S. B. Papp, and S. A. Diddams, “Phase-coherent microwave-to-optical link with a self-referenced microcomb,” Nat. Photonics 10, 516–520 (2016).
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K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10, 316–320 (2016).
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P. Del’Haye, A. Coillet, W. Loh, K. Beha, S. B. Papp, and S. A. Diddams, “Phase steps and resonator detuning measurements in microresonator frequency combs,” Nat. Commun. 6, 5668 (2015).
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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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Figures (7)

Fig. 1.
Fig. 1. (a) Experimental setup of the FD-FWM laser. In the setup, a nonlinear high-Q micro-ring resonator is nested in a fiber ring cavity, which contains an optical amplifier (EYDFA), a free-space delay line (DL), a tunable passband filter (TBF), a Faraday isolator (IS), and a polarization controller (PC). (b) Frequency-comb-assisted spectroscopy scheme, which consists of a tunable external cavity diode laser (ECDL) and a reference comb. A scanning CW laser was split into two signals, which are labeled S1 and S2, to perform frequency calibration and the spectroscopy of the micro-ring resonance, respectively. The beating of the tunable laser and the reference comb is extracted with a photodiode (PD) and radio frequency bandpass filter (RFBF). (c) A typical spectroscopy measurement of the micro-cavity resonances and (d) zoom in view. A Lorentzian-shaped resonance (red) combined with the beat note between the probe laser and the oscillating comb line (blue and green). The micro-comb line can be determined by assessing the position where an abrupt phase change takes place, reported in (d), by pink arrow.
Fig. 2.
Fig. 2. (a)–(c) Experimental optical spectra and (d)–(f) autocorrelation traces of the laser output for frequency spacings at (a), (d) a single FSR, and (b), (e) multiple FSRs, for the primary comb. (c) and (d) report a Type-II comb.
Fig. 3.
Fig. 3. Experimental optical spectra of the Type-II micro-comb laser output. A mode-locking state at 300  GHz repetition rate (6 times the fundamental repetition rate of the micro-resonator) is overlaid as a red dotted line. The subgroups of Type-II combs around the primary comb lines 1, 7, 13, and 19 are highlighted in black, blue, green, and magenta, respectively.
Fig. 4.
Fig. 4. (a)–(d) Resonance profiles of the primary combs, as numbered in Fig. 3, and (e)–(h) one set of sub-combs around the primary comb line 13.
Fig. 5.
Fig. 5. (a) Frequency line position versus mode number. Dots are measurements related to the subset around the primary lines 1, 7, 13, and 19 (as highlighted in Fig. 3 and plotted in black, blue, green, and magenta, respectively). Error bars are within the marker size. The results are fitted with a straight line with angular coefficient 48.952  GHz±3  MHz, which takes into account the error of the measured frequencies due to the accuracy of our frequency-comb-assisted spectroscopy system. (b) Residual plot. Error bars are within the marker size. It shows clearly that all the sub-combs have, within our accuracy, the same FSR but are detuned of 4 times the main-cavity FSR (293  MHz).
Fig. 6.
Fig. 6. (a)–(c) Simulated optical spectra and (d)–(f) AC of the laser output with frequency spacing at 1, 4, and 8 FSR. The saturation power ratios are 1, 40, and 100, respectively. The cavity-period detunings (δ, see text) are 0, 0.25, and 0.125 for (a) and (d), (b) and (e), and (c) and (f), respectively.
Fig. 7.
Fig. 7. (a)–(d) Simulated optical spectra, (e)–(h) AC (blue) and normalized temporal evolution of the intensity (red) of 8 FSR primary combs and Type-II combs. Here, the saturation powers are in a ratio 1, 2, 2.5, 3.5 for (a) and (e), (b) and (f), (c) and (g), and (d) and (h), respectively.

Equations (7)

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Tr(tA+τA)iLrβr2ττA+iγLr|A|2A=0,
Tf(tB+τB)iLfβf2ττBgLf(1+ττΩg2)B=0.
g=g01+0Tf|B|2PsatdτTf,
A(t,0)=κB(t,Tf)eiϕf1κ2A(t,0)eiϕr,
A(t,Tr2)=1κ2A(t,Tr2)eiϕr,
B(t,0)=κA(t,Tr2)eiϕr,
Tf=(N+δ)Tr,

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