Abstract

Kerr frequency combs generated from microresonators are the subject of intense study for potential applications ranging from short pulse generation to frequency metrology to radiofrequency signal processing. Most research employs microresonators with anomalous dispersion, for which modulation instability is believed to play a key role in initiation of the comb. Comb generation in normal-dispersion microresonators has also been reported but is less well understood. Here, we report a detailed investigation of few-moded, normal-dispersion silicon nitride microresonators, showing that mode coupling can strongly modify the local dispersion, even changing its sign. We demonstrate a link between mode coupling and initiation of comb generation by showing experimentally the pinning of one of the initial comb sidebands near a mode-crossing frequency. Associated with this route to comb formation, we observe direct generation of coherent, bandwidth-limited pulses at repetition rates down to 75 GHz, without the need to first pass through a chaotic state. Our results with normal-dispersion devices highlight mode interactions as a beneficial tool for comb initiation and pulse formation.

© 2014 Optical Society of America

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    [CrossRef]
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  58. C. Godey, I. Balakireva, A. Coillet, Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv:1308.2539v1 (2013).
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2014 (2)

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

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

2013 (12)

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

S. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R. Johnson, M. A. Foster, M. R. E. Lamont, M. Lipson, A. L. Gaeta, “Mode locking and femtosecond pulse generation in chip-based frequency combs,” Opt. Express 21, 1335–1343 (2013).
[CrossRef]

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

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

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

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

P. Wang, Y. Xuan, L. Fan, L. T. Varghese, J. Wang, Y. Liu, X. Xue, D. E. Leaird, M. Qi, A. M. Weiner, “Drop-port study of microresonator frequency combs: power transfer, spectra and time-domain characterization,” Opt. Express 21, 22441–22452 (2013) and erratum, Opt. Express 22, 12148 (2014).
[CrossRef]

I. S. Grudinin, L. Baumgartel, N. Yu, “Impact of cavity spectrum on span in microresonator frequency combs,” Opt. Express 21, 26929–26935 (2013).
[CrossRef]

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, Y. K. Chembo, “Azimuthal turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[CrossRef]

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

T. Hansson, D. Modotto, S. Wabnitz, “Dynamics of the modulational instability in microresonator frequency combs,” Phys. Rev. A 88, 023819 (2013).
[CrossRef]

2012 (9)

A. R. Johnson, Y. Okawachi, J. S. Levy, J. Cardenas, K. Saha, M. Lispon, A. L. Gaeta, “Chip-based frequency combs with sub-100  GHz repetition rates,” Opt. Express 37, 875–877 (2012).

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A 85, 023830 (2012).
[CrossRef]

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

A. B. Matsko, A. A. Savchenkov, L. Maleki, “Normal group-velocity dispersion Kerr frequency comb,” Opt. Lett. 37, 43–45 (2012).
[CrossRef]

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

F. Ferdous, H. Miao, P.-H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, A. M. Weiner, “Probing coherence in microcavity frequency combs via optical pulse shaping,” Opt. Express 20, 21033–21043 (2012).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Kerr frequency comb generation in overmoded resonators,” Opt. Express 20, 27290–27298 (2012).
[CrossRef]

A. Matsko, A. Savchenkov, L. Maleki, “On excitation of breather solitons in an optical microresonator,” Opt. Lett. 37, 4856–4858 (2012).
[CrossRef]

P.-H. Wang, F. Ferdous, H. Miao, J. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, A. M. Weiner, “Observation of correlation between route to formation, coherence, noise, and communication performance of Kerr combs,” Opt. Express 20, 29284–29295 (2012).
[CrossRef]

2011 (9)

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[CrossRef]

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011).
[CrossRef]

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

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36, 3398–3400 (2011).
[CrossRef]

S. B. Papp, S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A 84, 053833 (2011).
[CrossRef]

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

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

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

G. Anetsberger, E. M. Weig, J. P. Kotthaus, T. J. Kippenberg, “Cavity optomechanics and cooling nanomechanical oscillators using microresonator enhanced evanescent near-field coupling,” C. R. Phys. 12, 800–816 (2011).

2010 (1)

L. Novotny, “Strong coupling, energy splitting, and level crossings: a classical perspective,” Am. J. Phys. 78, 1199–1202 (2010).
[CrossRef]

2009 (6)

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

S. Gröblacher, K. Hammerer, M. R. Vanner, M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[CrossRef]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2009).
[CrossRef]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, D. J. Moss, “CMOS-compatible integrated optical hyperparametric oscillator,” Nat. Photonics 4, 41–45 (2009).
[CrossRef]

I. S. Grudinin, N. Yu, L. Maleki, “Generation of optical frequency combs with a CaF2 resonator,” Opt. Lett. 34, 878–880 (2009).
[CrossRef]

I. H. Agha, Y. Okawachi, A. L. Gaeta, “Theoretical and experimental investigation of broadband cascaded four-wave mixing in high-Q microspheres,” Opt. Express 17, 16209–16215 (2009).
[CrossRef]

2008 (3)

A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, L. Maleki, “Phase noise of whispering gallery photonic hyper-parametric microwave oscillators,” Opt. Express 16, 4130–4144 (2008).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[CrossRef]

2007 (1)

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

2006 (1)

J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006).
[CrossRef]

2005 (2)

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: threshold and phase diffusion,” Phys. Rev. A 71, 033804 (2005).
[CrossRef]

T. Klaassen, J. de Jong, M. van Exter, J. P. Woerdman, “Transverse mode coupling in an optical resonator,” Opt. Lett. 30, 1959–1961 (2005).
[CrossRef]

1992 (1)

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

1991 (1)

H. A. Haus, W. Huang, “Coupled-mode theory,” Proc. IEEE 79, 1505–1518 (1991).
[CrossRef]

1990 (1)

J. C. Tully, “Molecular dynamics with electronic transitions,” J. Chem. Phys. 93, 1061–1071 (1990).
[CrossRef]

1971 (1)

J. C. Tully, R. K. Preston, “Trajectory surface hopping approach to nonadiabatic molecular collisions: the reaction of H+ with D2,” J. Chem. Phys. 55, 562–572 (1971).
[CrossRef]

Agha, I. H.

Aksyuk, V.

Anetsberger, G.

G. Anetsberger, E. M. Weig, J. P. Kotthaus, T. J. Kippenberg, “Cavity optomechanics and cooling nanomechanical oscillators using microresonator enhanced evanescent near-field coupling,” C. R. Phys. 12, 800–816 (2011).

Arcizet, O.

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, 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, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

Aspelmeyer, M.

S. Gröblacher, K. Hammerer, M. R. Vanner, M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[CrossRef]

Balakireva, I.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, Y. K. Chembo, “Azimuthal turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

C. Godey, I. Balakireva, A. Coillet, Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv:1308.2539v1 (2013).

I. Balakireva, A. Coillet, C. Godey, Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part II: case of anomalous dispersion,” arXiv:1308.2542v1 (2013).

Baumgartel, L.

Brasch, V.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[CrossRef]

T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodestky, T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” arXiv:1311.1716 (2013).

Cardenas, J.

A. R. Johnson, Y. Okawachi, J. S. Levy, J. Cardenas, K. Saha, M. Lispon, A. L. Gaeta, “Chip-based frequency combs with sub-100  GHz repetition rates,” Opt. Express 37, 875–877 (2012).

Carmon, T.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100, 103905 (2008).
[CrossRef]

Chembo, Y. K.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, Y. K. Chembo, “Azimuthal turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

C. Godey, I. Balakireva, A. Coillet, Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv:1308.2539v1 (2013).

I. Balakireva, A. Coillet, C. Godey, Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part II: case of anomalous dispersion,” arXiv:1308.2542v1 (2013).

Chen, L.

Chen, S.

X. Xue, Y. Xuan, Y. Liu, P. Wang, S. Chen, J. Wang, D. E. Leaird, M. Qi, A. M. Weiner, “Mode interaction aided soft excitation of dark solitons in normal dispersion microresonators and offset-frequency tunable Kerr combs,” arXiv:1404.2865 (2014).

A brief report on these observations is given in Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, A. J. Metcalf, S. Chen, M. Qi, A. M. Weiner, “Investigation of mode interaction in optical microresonators for Kerr frequency comb generation,” to appear in CLEO: 2014, paper FW1D.2; also see arXiv:1402.5686 (2014).

Chu, S.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, D. J. Moss, “CMOS-compatible integrated optical hyperparametric oscillator,” Nat. Photonics 4, 41–45 (2009).
[CrossRef]

Clemmen, S.

S. Ramelow, A. Farsi, S. Clemmen, J. S. Levy, A. R. Johnson, Y. Okawachi, M. R. E. Lamont, M. Lipson, A. L. Gaeta, “Strong polarization mode coupling in microresonators,” arXiv:1405.5211 (2014).

Coen, S.

Coillet, A.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, Y. K. Chembo, “Azimuthal turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

C. Godey, I. Balakireva, A. Coillet, Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv:1308.2539v1 (2013).

I. Balakireva, A. Coillet, C. Godey, Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part II: case of anomalous dispersion,” arXiv:1308.2542v1 (2013).

de Jong, J.

Del’Haye, P.

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

C. Y. Wang, T. Herr, P. Del’Haye, A. Schliesser, J. Hofer, R. Holzwarth, T. W. Hänsch, N. Picqué, 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, R. Holzwarth, T. J. 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, 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, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

Diddams, S. A.

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

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

S. B. Papp, S. A. Diddams, “Spectral and temporal characterization of a fused-quartz-microresonator optical frequency comb,” Phys. Rev. A 84, 053833 (2011).
[CrossRef]

Duchesne, D.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, D. J. Moss, “CMOS-compatible integrated optical hyperparametric oscillator,” Nat. Photonics 4, 41–45 (2009).
[CrossRef]

Dudley, J. M.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, Y. K. Chembo, “Azimuthal turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Emplit, P.

Erkintalo, M.

Fan, L.

Farsi, A.

S. Ramelow, A. Farsi, S. Clemmen, J. S. Levy, A. R. Johnson, Y. Okawachi, M. R. E. Lamont, M. Lipson, A. L. Gaeta, “Strong polarization mode coupling in microresonators,” arXiv:1405.5211 (2014).

Ferdous, F.

Ferrera, M.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, D. J. Moss, “CMOS-compatible integrated optical hyperparametric oscillator,” Nat. Photonics 4, 41–45 (2009).
[CrossRef]

Fong, K. Y.

Foster, M. A.

Gaeta, A. L.

S. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R. Johnson, M. A. Foster, M. R. E. Lamont, M. Lipson, A. L. Gaeta, “Mode locking and femtosecond pulse generation in chip-based frequency combs,” Opt. Express 21, 1335–1343 (2013).
[CrossRef]

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

A. R. Johnson, Y. Okawachi, J. S. Levy, J. Cardenas, K. Saha, M. Lispon, A. L. Gaeta, “Chip-based frequency combs with sub-100  GHz repetition rates,” Opt. Express 37, 875–877 (2012).

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. 36, 3398–3400 (2011).
[CrossRef]

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, A. L. Gaeta, “Silicon-based monolithic optical frequency comb source,” Opt. Express 19, 14233–14239 (2011).
[CrossRef]

I. H. Agha, Y. Okawachi, A. L. Gaeta, “Theoretical and experimental investigation of broadband cascaded four-wave mixing in high-Q microspheres,” Opt. Express 17, 16209–16215 (2009).
[CrossRef]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2009).
[CrossRef]

S. Ramelow, A. Farsi, S. Clemmen, J. S. Levy, A. R. Johnson, Y. Okawachi, M. R. E. Lamont, M. Lipson, A. L. Gaeta, “Strong polarization mode coupling in microresonators,” arXiv:1405.5211 (2014).

Gavartin, E.

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

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

Gelens, L.

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

P. Parra-Rivas, D. Gomila, M. A. Matias, S. Coen, L. Gelens, “Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs,” arXiv:1401.6059v1 (2014).

Godey, C.

C. Godey, I. Balakireva, A. Coillet, Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv:1308.2539v1 (2013).

I. Balakireva, A. Coillet, C. Godey, Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part II: case of anomalous dispersion,” arXiv:1308.2542v1 (2013).

Gomila, D.

P. Parra-Rivas, D. Gomila, M. A. Matias, S. Coen, L. Gelens, “Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs,” arXiv:1401.6059v1 (2014).

Gondarenko, A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4, 37–40 (2009).
[CrossRef]

Gorodestky, M. L.

T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodestky, T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” arXiv:1311.1716 (2013).

Gorodetsky, M. L.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[CrossRef]

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

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

Gröblacher, S.

S. Gröblacher, K. Hammerer, M. R. Vanner, M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[CrossRef]

Grudinin, I. S.

Haelterman, M.

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

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

Hammerer, K.

S. Gröblacher, K. Hammerer, M. R. Vanner, M. Aspelmeyer, “Observation of strong coupling between a micromechanical resonator and an optical cavity field,” Nature 460, 724–727 (2009).
[CrossRef]

Hänsch, T. W.

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

Hansson, T.

T. Hansson, D. Modotto, S. Wabnitz, “Dynamics of the modulational instability in microresonator frequency combs,” Phys. Rev. A 88, 023819 (2013).
[CrossRef]

Hartinger, K.

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

Haus, H. A.

H. A. Haus, W. Huang, “Coupled-mode theory,” Proc. IEEE 79, 1505–1518 (1991).
[CrossRef]

Henriet, R.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, Y. K. Chembo, “Azimuthal turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Herr, T.

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

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[CrossRef]

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

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

T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodestky, T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” arXiv:1311.1716 (2013).

Hofer, J.

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

Holzwarth, R.

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

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

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

P. Del’Haye, T. Herr, E. Gavartin, R. Holzwarth, T. J. 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, 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, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

Huang, S.-W.

S.-W. Huang, J. F. McMillan, J. Yang, A. Matsko, H. Zhou, M. Yu, D.-L. Kwong, L. Maleki, C. W. Wong, “Direct generation of 74-fs mode-locking from on-chip normal dispersion frequency combs,” arXiv:1404.3256 (2014).

Huang, W.

H. A. Haus, W. Huang, “Coupled-mode theory,” Proc. IEEE 79, 1505–1518 (1991).
[CrossRef]

Ilchenko, V.

Ilchenko, V. S.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, L. Maleki, “Hard and soft excitation regimes of Kerr frequency combs,” Phys. Rev. A 85, 023830 (2012).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, L. Maleki, “Kerr frequency comb generation in overmoded resonators,” Opt. Express 20, 27290–27298 (2012).
[CrossRef]

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, L. Maleki, “Generation of near-infrared frequency combs from a MgF2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, L. Maleki, “Phase noise of whispering gallery photonic hyper-parametric microwave oscillators,” Opt. Express 16, 4130–4144 (2008).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, L. Maleki, “Optical hyperparametric oscillations in a whispering-gallery-mode resonator: threshold and phase diffusion,” Phys. Rev. A 71, 033804 (2005).
[CrossRef]

Johnson, A. R.

S. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R. Johnson, M. A. Foster, M. R. E. Lamont, M. Lipson, A. L. Gaeta, “Mode locking and femtosecond pulse generation in chip-based frequency combs,” Opt. Express 21, 1335–1343 (2013).
[CrossRef]

A. R. Johnson, Y. Okawachi, J. S. Levy, J. Cardenas, K. Saha, M. Lispon, A. L. Gaeta, “Chip-based frequency combs with sub-100  GHz repetition rates,” Opt. Express 37, 875–877 (2012).

S. Ramelow, A. Farsi, S. Clemmen, J. S. Levy, A. R. Johnson, Y. Okawachi, M. R. E. Lamont, M. Lipson, A. L. Gaeta, “Strong polarization mode coupling in microresonators,” arXiv:1405.5211 (2014).

Jost, J. D.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[CrossRef]

T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodestky, T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” arXiv:1311.1716 (2013).

Jung, H.

Kippenberg, T. J.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[CrossRef]

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

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

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

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

G. Anetsberger, E. M. Weig, J. P. Kotthaus, T. J. Kippenberg, “Cavity optomechanics and cooling nanomechanical oscillators using microresonator enhanced evanescent near-field coupling,” C. R. Phys. 12, 800–816 (2011).

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, 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, T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[CrossRef]

T. Herr, V. Brasch, J. D. Jost, I. Mirgorodskiy, G. Lihachev, M. L. Gorodestky, T. J. Kippenberg, “Mode spectrum and temporal soliton formation in optical microresonators,” arXiv:1311.1716 (2013).

Klaassen, T.

Kondratiev, N. M.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2013).
[CrossRef]

Kotthaus, J. P.

G. Anetsberger, E. M. Weig, J. P. Kotthaus, T. J. Kippenberg, “Cavity optomechanics and cooling nanomechanical oscillators using microresonator enhanced evanescent near-field coupling,” C. R. Phys. 12, 800–816 (2011).

Kuzucu, O.

Kwong, D.-L.

S.-W. Huang, J. F. McMillan, J. Yang, A. Matsko, H. Zhou, M. Yu, D.-L. Kwong, L. Maleki, C. W. Wong, “Direct generation of 74-fs mode-locking from on-chip normal dispersion frequency combs,” arXiv:1404.3256 (2014).

Lamont, M. R. E.

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, 3rd ed. (Butterworth-Heinemann, 2003).

Larger, L.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. M. Dudley, C. R. Menyuk, Y. K. Chembo, “Azimuthal turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Leaird, D. E.

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A brief report on these observations is given in Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, A. J. Metcalf, S. Chen, M. Qi, A. M. Weiner, “Investigation of mode interaction in optical microresonators for Kerr frequency comb generation,” to appear in CLEO: 2014, paper FW1D.2; also see arXiv:1402.5686 (2014).

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A brief report on these observations is given in Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, A. J. Metcalf, S. Chen, M. Qi, A. M. Weiner, “Investigation of mode interaction in optical microresonators for Kerr frequency comb generation,” to appear in CLEO: 2014, paper FW1D.2; also see arXiv:1402.5686 (2014).

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A brief report on these observations is given in Y. Liu, Y. Xuan, X. Xue, P.-H. Wang, A. J. Metcalf, S. Chen, M. Qi, A. M. Weiner, “Investigation of mode interaction in optical microresonators for Kerr frequency comb generation,” to appear in CLEO: 2014, paper FW1D.2; also see arXiv:1402.5686 (2014).

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Yu, N.

Zhang, X.

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Figures (9)

Fig. 1.
Fig. 1.

Numerical investigation of mode-coupling effect when the resonances of the two modes get close and cross each other: (a) no mode coupling and (b) with mode coupling.

Fig. 2.
Fig. 2.

(a) Microscope image of the silicon nitride resonator with path length of 5.92 mm. (b) Measured transmission spectrum of the resonator. Inset is the zoom-in transmission spectrum showing resonances from different transverse-mode families.

Fig. 3.
Fig. 3.

(a) Measured FSR versus optical wavelength for two TE modes plotted in red circles and blue triangles and fitted with D156ps/nm·km and D160ps/nm·km, respectively. (b)–(d) Aligned resonances with fixed increment showing the mode coupling with different coupling strength. (b) Strong coupling case centered at 1542 nm with clear avoided crossings. (c) Weak coupling case centered at 1552 nm. (d) Zoomed-in view of the weak coupling case. (e) Zoom-in view and fitted FSR spectrum in a mode-crossing area. (f) Calculated D and corresponding D2 value of mode 1 and mode 2 plotted in red and blue, respectively.

Fig. 4.
Fig. 4.

Comb generation at different pump wavelength with one of the first sidebands kept at an approximately constant location (a) around 1560 nm and (b) around 1550 nm.

Fig. 5.
Fig. 5.

(a) Microscope image of the silicon nitride resonator with path length of 1.97 mm. (b) Aligned resonances centered at 1563 nm with fixed increment showing the mode coupling. (c) Comb generation at different pump wavelength; one of the first sidebands remains close to 1563 nm.

Fig. 6.
Fig. 6.

Generation of coherent mode-locked Type I comb due to the mode coupling. (a) Generated comb spectrum at the drop port. (b) Fifteen lines are selected, amplified, and filtered for time domain characterization. (c) Autocorrelation of time domain pulse compared with that of theoretical bandwidth-limited pulse, showing good coherence and mode-locking behavior. (d) Intensity noise compared with the measurement system noise floor.

Fig. 7.
Fig. 7.

(a) Simulated comb generation pumping at different resonances in normal-dispersion microresonator with mode coupling. (b) and (c) Simulated mode coupling initialized Type I comb spectrum and its intracavity intensity, respectively.

Fig. 8.
Fig. 8.

Observation of “Pinned” first sidebands for the resonator with passively mode locked “Type I” comb as discussed in Ref. [20].

Fig. 9.
Fig. 9.

Asymmetric comb spectra. (a) and (b) Comb generation using resonators with 25GHz FSR with “pinned” sideband close to 1551 nm, (c) and (d) comb generation using resonators with 75GHz FSR with “pinned” sideband close to 1563 nm.

Tables (1)

Tables Icon

Table 1. Estimated Coupling Strength for Four Mode-Crossing Areas Shown in Fig. 3(a)

Equations (3)

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

dE1dt=(1τo11τe1jδ1)E1+jκ12E2+2τe1E0,
dE2dt=(1τo21τe2jδ2)E2+jκ21E1+2τe2E0.
D22π=λ2·neff·FSR2·D.

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