Abstract

Abstract: Recent investigations of microcavity frequency combs based on cascaded four-wave mixing have revealed a link between the evolution of the optical spectrum and the observed temporal coherence. Here we study a silicon nitride microresonator for which the initial four-wave mixing sidebands are spaced by multiple free spectral ranges (FSRs) from the pump. Additional lines then fill in to yield a comb with single FSR spacing, resulting in partial coherence. By using a pulse shaper to select and manipulate the phase of various subsets of spectral lines, we are able to probe the structure of the coherence within the partially coherent comb. Our data demonstrate strong variation in the degree of mutual coherence between different groups of lines and provide support for a simple model of partially coherent comb formation.

© 2012 OSA

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  1. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450(7173), 1214–1217 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett.107(6), 063901 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2012 (2)

T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics6(7), 480–487 (2012).
[CrossRef]

A. R. Johnson, Y. Okawachi, J. S. Levy, J. Cardenas, K. Saha, M. Lipson, and A. L. Gaeta, “Chip-based frequency combs with sub-100 GHz repetition rates,” Opt. Lett.37(5), 875–877 (2012).
[CrossRef] [PubMed]

2011 (6)

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. Photonics5(12), 770–776 (2011).
[CrossRef]

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a MgF₂ whispering gallery mode resonator,” Opt. Lett.36(12), 2290–2292 (2011).
[CrossRef] [PubMed]

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-Based Monolithic Optical Frequency Comb Source,” Opt. Express19(15), 14233–14239 (2011).
[CrossRef] [PubMed]

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett.36(17), 3398–3400 (2011).
[CrossRef] [PubMed]

S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz microresonator optical frequency comb,” Phys. Rev. A84(5), 053833 (2011).
[CrossRef]

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett.107(6), 063901 (2011).
[CrossRef] [PubMed]

2010 (2)

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. Photonics4(1), 37–40 (2010).
[CrossRef]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Cmos compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4(1), 41–45 (2010).
[CrossRef]

2009 (1)

2008 (1)

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett.101(5), 053903 (2008).
[CrossRef] [PubMed]

2007 (2)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q Silica microspheres,” Phys. Rev. A76(4), 043837 (2007).
[CrossRef]

2000 (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
[CrossRef]

Agha, I. H.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q Silica microspheres,” Phys. Rev. A76(4), 043837 (2007).
[CrossRef]

Arcizet, O.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett.101(5), 053903 (2008).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Cardenas, J.

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. Photonics5(12), 770–776 (2011).
[CrossRef]

Chu, S.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Cmos compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4(1), 41–45 (2010).
[CrossRef]

Del’Haye, P.

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett.107(6), 063901 (2011).
[CrossRef] [PubMed]

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett.101(5), 053903 (2008).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Diddams, S. A.

S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz microresonator optical frequency comb,” Phys. Rev. A84(5), 053833 (2011).
[CrossRef]

Duchesne, D.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Cmos compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4(1), 41–45 (2010).
[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. Photonics5(12), 770–776 (2011).
[CrossRef]

Ferrera, M.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Cmos compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4(1), 41–45 (2010).
[CrossRef]

Foster, M. A.

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-Based Monolithic Optical Frequency Comb Source,” Opt. Express19(15), 14233–14239 (2011).
[CrossRef] [PubMed]

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. Photonics4(1), 37–40 (2010).
[CrossRef]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q Silica microspheres,” Phys. Rev. A76(4), 043837 (2007).
[CrossRef]

Gaeta, A. L.

A. R. Johnson, Y. Okawachi, J. S. Levy, J. Cardenas, K. Saha, M. Lipson, and A. L. Gaeta, “Chip-based frequency combs with sub-100 GHz repetition rates,” Opt. Lett.37(5), 875–877 (2012).
[CrossRef] [PubMed]

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “Silicon-Based Monolithic Optical Frequency Comb Source,” Opt. Express19(15), 14233–14239 (2011).
[CrossRef] [PubMed]

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett.36(17), 3398–3400 (2011).
[CrossRef] [PubMed]

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. Photonics4(1), 37–40 (2010).
[CrossRef]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q Silica microspheres,” Phys. Rev. A76(4), 043837 (2007).
[CrossRef]

Gavartin, E.

T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics6(7), 480–487 (2012).
[CrossRef]

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett.107(6), 063901 (2011).
[CrossRef] [PubMed]

Gondarenko, 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. Photonics4(1), 37–40 (2010).
[CrossRef]

Gorodetsky, M. L.

T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics6(7), 480–487 (2012).
[CrossRef]

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett.107(6), 063901 (2011).
[CrossRef] [PubMed]

Grudinin, I. S.

Hartinger, K.

T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics6(7), 480–487 (2012).
[CrossRef]

Herr, T.

T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics6(7), 480–487 (2012).
[CrossRef]

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett.107(6), 063901 (2011).
[CrossRef] [PubMed]

Holzwarth, R.

T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics6(7), 480–487 (2012).
[CrossRef]

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett.107(6), 063901 (2011).
[CrossRef] [PubMed]

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett.101(5), 053903 (2008).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Ilchenko, V. S.

Johnson, A. R.

Kippenberg, T. J.

T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics6(7), 480–487 (2012).
[CrossRef]

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett.107(6), 063901 (2011).
[CrossRef] [PubMed]

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett.101(5), 053903 (2008).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Kuzucu, O.

Leaird, D. E.

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. Photonics5(12), 770–776 (2011).
[CrossRef]

Levy, J. S.

Liang, W.

Lipson, M.

Little, B. E.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Cmos compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4(1), 41–45 (2010).
[CrossRef]

Maleki, L.

Matsko, A. B.

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. Photonics5(12), 770–776 (2011).
[CrossRef]

Morandotti, R.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Cmos compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4(1), 41–45 (2010).
[CrossRef]

Moss, D. J.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Cmos compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4(1), 41–45 (2010).
[CrossRef]

Okawachi, Y.

Papp, S. B.

S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz microresonator optical frequency comb,” Phys. Rev. A84(5), 053833 (2011).
[CrossRef]

Razzari, L.

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Cmos compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4(1), 41–45 (2010).
[CrossRef]

Riemensberger, J.

T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics6(7), 480–487 (2012).
[CrossRef]

Saha, K.

Savchenkov, A. A.

Schliesser, A.

P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett.101(5), 053903 (2008).
[CrossRef] [PubMed]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Seidel, D.

Sharping, J. E.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q Silica microspheres,” Phys. Rev. A76(4), 043837 (2007).
[CrossRef]

Srinivasan, K.

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. Photonics5(12), 770–776 (2011).
[CrossRef]

Turner-Foster, A. C.

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. Photonics4(1), 37–40 (2010).
[CrossRef]

Varghese, L. T.

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. Photonics5(12), 770–776 (2011).
[CrossRef]

Wang, C.

T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics6(7), 480–487 (2012).
[CrossRef]

Wang, J.

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. Photonics5(12), 770–776 (2011).
[CrossRef]

Weiner, A. M.

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. Photonics5(12), 770–776 (2011).
[CrossRef]

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71(5), 1929–1960 (2000).
[CrossRef]

Wen, Y. H.

Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450(7173), 1214–1217 (2007).
[CrossRef] [PubMed]

Yu, N.

Nat. Photonics (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. Photonics4(1), 37–40 (2010).
[CrossRef]

L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Cmos compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4(1), 41–45 (2010).
[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. Photonics5(12), 770–776 (2011).
[CrossRef]

T. Herr, J. Riemensberger, C. Wang, K. Hartinger, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, “Universal formation dynamics and noise of Kerr-frequency combs in microresonators,” Nat. Photonics6(7), 480–487 (2012).
[CrossRef]

Nature (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450(7173), 1214–1217 (2007).
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Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (2)

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S. B. Papp and S. A. Diddams, “Spectral and temporal characterization of a fused-quartz microresonator optical frequency comb,” Phys. Rev. A84(5), 053833 (2011).
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P. Del’Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, “Full stabilization of a microresonator-based optical frequency comb,” Phys. Rev. Lett.101(5), 053903 (2008).
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P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, “Octave Spanning Tunable Frequency Comb from a Microresonator,” Phys. Rev. Lett.107(6), 063901 (2011).
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Figures (9)

Fig. 1
Fig. 1

Possible routes to comb formation. The optical frequency axis is portrayed in free spectral range (FSR) units. Arrows are drawn in an attempt to represent the approximate order in which new comb lines are generated; no attempt is made to indicate all the couplings involved in the four wave mixing process. (a) Case where initial comb lines are spaced by one FSR from the pump line, with subsequent comb lines, generated through cascaded four wave mixing, spreading out from the center. (b) Case where initial comb lines are spaced from the pump line by N FSRs, where N>1 is an integer. Here N = 3 is assumed. (c) When the pump laser is tuned closer into resonance, additional lines are observed to fill in, resulting in spectral lines spaced by nominally 1 FSR.

Fig. 2
Fig. 2

Schematic of the experimental setup for line-by-line pulse shaping of a frequency comb from a silicon nitride microring. CW: continuous-wave; EDFA: erbium doped fiber amplifier; FPC: fiber polarization controller; µring: silicon nitride microring; OSA: optical spectrum analyzer. The autocorrelator is constructed in a background-free, noncollinear geometry.

Fig. 3
Fig. 3

(a) Spectrum of the generated 3 FSR spacing comb after the pulse shaper and applied phase profile . (b) Autocorrelation traces corresponding to (a). (c) Spectrum of the generated 1 FSR spacing comb after the pulse shaper and applied phase profile. Here we tune the CW laser 53 pm further towards the red compared to (a). (d) Autocorrelation traces corresponding to (c). The pump line is attenuated by 15 dB by the pulse shaper. Blue and red traces are experimental traces before and after phase compensation respectively. Black traces are calculated by taking the OSA spectrums and assuming flat spectral phase.

Fig. 4
Fig. 4

Spectra and autocorrelation traces for 3 subfamilies of comb lines with 3 FSR spacing selected from the spectrum shown in Fig. 3(c). Blue and red traces are experimental traces before and after phase compensation respectively. Black traces are calculated by taking the OSA spectrums and assuming flat spectral phase.

Fig. 5
Fig. 5

Spectra and autocorrelation traces for 2 subfamilies of comb lines with 2 FSR spacing selected from the spectrum shown in Fig. 3(c). Blue and red traces are experimental traces before and after phase compensation respectively. Black traces are calculated by taking the OSA spectrums and assuming flat spectral phase.

Fig. 6
Fig. 6

Autocorrelation traces for 3 line experiments for different ∆Φ for lines {-3, 0, 3}, for which high coherence is observed. Here colored lines are the experimental traces and black lines are the simulated traces.

Fig. 7
Fig. 7

Autocorrelation traces for 3 line experiments for different ∆Φ for lines {-2, 1, 4}, for which low coherence is observed. Here colored lines are the experimental traces and black lines are the simulated traces.

Fig. 8
Fig. 8

Visibility traces of (a) three subfamilies of 3 FSRs, (b) two subfamilies of 2 FSRs, and (c) two subfamilies of 1 FSR. Here in the visibility curves, red, green and black lines are the experimental data; blue lines are ideal theoretical curves calculated assuming full coherence based on the power spectra corresponding to the respective red line visibility curves. Numbers in curly braces indicate the 3 lines that are used in the experiments. Error bars (shown for representative curves) and shaded areas represent the mean ± one standard deviation.

Fig. 9
Fig. 9

Proposed model for type II comb formation. (a) First: generation of a cascade of sidebands spaced by N FSRs (Nδω) from the pump. Here N = 6 is illustrated. (b)-(c) The 2nd event is an independent four-wave mixing process, which creates new sidebands spaced by a different amount, ± nδω' (n = 1,2 or 3....for different lines), from each of the lines in the previous step. Due to dispersion, it is very unlikely that the new frequency spacings will be exact submultiples of the original N FSR spacing; i.e., δω' ≠ δω.

Equations (1)

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V( ΔΦ )= | p( τ p )p( τ p +T/2) | | p( τ p )+p( τ p +T/2) |

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