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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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [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

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

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

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

2008

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

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

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]

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]

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]

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

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

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

Opt. Lett.

Phys. Rev. A

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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).
[CrossRef]

Phys. Rev. Lett.

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, 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]

Rev. Sci. Instrum.

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Other

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A. M. Weiner, Ultrafast Optics (Wiley, 2009), Chap. 3.

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 based on Crystalline Microresonators,” http://arxiv.org/PS_cache/arxiv/pdf/1109/1109.2716v1.pdf

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, “Transient Regime of Kerr Frequency Comb Formation,” http://arxiv.org/pdf/1111.3922.pdf

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