Abstract

Optical whispering gallery mode (WGM) resonators have been very attracting platforms for versatile Kerr frequency comb generations. We report a systematic study on the material dispersion of various optical materials that are capable of supporting quality factors above 109. Using an analytical approximation of WGM resonant frequencies in disk resonators, we investigate the effect of the geometry and transverse mode order on the total group-velocity dispersion (GVD). We demonstrate that the major radii and the radial mode indices play an important role in tailoring the GVD of WGM resonators. In particular, our study shows that in WGM disk-resonators, the polar families of modes have very similar GVD, while the radial families of modes feature dispersion values that can differ by up to several orders of magnitude. The effect of these giant dispersion shifts are experimentally evidenced in Kerr comb generation with magnesium fluoride. From a more general perspective, this critical feature enables to push the zero-dispersion wavelength of fluorite crystals towards the mid-infrared (mid-IR) range, thereby allowing for efficient Kerr comb generation in that spectral range. We show that barium fluoride is the most interesting crystal in this regard, due to its zero dispersion wavelength (ZDW) at 1.93 μm and an optimal dispersion profile in the mid-IR regime. We expect our results to facilitate the design of different platforms for Kerr frequency comb generations in both telecommunication and mid-IR spectral ranges.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
  6. S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. 38, 37–39 (2013).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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2014 (8)

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. 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. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref] [PubMed]

G. Lin, S. Diallo, R. Henriet, M. Jacquot, and Y. K. Chembo, “Barium fluoride whispering-gallery mode disk-resonator with one billion quality-factor,” Opt. Lett. 39, 6009–6012 (2014).
[Crossref] [PubMed]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Generation of Kerr frequency combs in a sapphire whispering gallery mode microresonator,” Opt. Eng. 53, 122607 (2014).
[Crossref]

G. Lin and N. Yu, “Continuous tuning of double resonance-enhanced second harmonic generation in a dispersive dielectric resonator,” Opt. Express 22, 557–562 (2014).
[Crossref] [PubMed]

D. Ristić, M. Mazzola, A. Chiappini, A. Rasoloniaina, P. Féron, R. Ramponi, G. C. Righini, G. Cibiel, M. Ivanda, and M. Ferrari, “Tailoring of the free spectral range and geometrical cavity dispersion of a microsphere by a coating layer,” Opt. Lett. 39, 5173–5176 (2014).
[Crossref]

G. Schunk, J. U. Frst, M. Frtsch, D. V. Strekalov, U. Vogl, F. Sedlmeir, H. G. L. Schwefel, G. Leuchs, and C. Marquardt, “Identifying modes of large whispering-gallery mode resonators from the spectrum and emission pattern,” Opt. Express 22, 30795–30806 (2014).
[Crossref]

2013 (9)

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

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. 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. Wang, T. Herr, P. DelHaye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref]

I. Breunig, B. Sturman, F. Sedlmeir, H. G. L. Schwefel, and K. Buse, “Whispering gallery modes at the rim of an axisymmetric optical resonator: Analytical versus numerical description and comparison with experiment,” Opt. Express 21, 30683–30692 (2013).
[Crossref]

Y. A. Demchenko and M. L. Gorodetsky, “Analytical estimates of eigenfrequencies, dispersion, and field distribution in whispering gallery resonators,” J. Opt. Soc. Am. B 30, 3056–3063 (2013).
[Crossref]

A. A. Savchenkov, D. Eliyahu, W. Liang, V. S. Ilchenko, J. Byrd, A. B. Matsko, D. Seidel, and L. Maleki, “Stabilization of a Kerr frequency comb oscillator,” Opt. Lett. 38, 2636–2639 (2013).
[Crossref] [PubMed]

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

Y. K. Chembo and C. R. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87, 053852 (2013).
[Crossref]

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

2012 (4)

2011 (2)

A. Savchenkov, A. Matsko, W. Liang, V. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
[Crossref]

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

2010 (5)

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] [PubMed]

Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (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]

G. Lin, B. Qian, F. Oručević, Y. Candela, J.-B. Jager, Z. Cai, V. Lefèvre-Seguin, and J. Hare, “Excitation mapping of whispering gallery modes in silica microcavities,” Opt. Lett. 35, 583–585 (2010).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett. 35, 2822–2824 (2010).
[Crossref] [PubMed]

2008 (1)

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

2007 (1)

P. DelHaye, 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)

1999 (1)

1991 (1)

S. Schiller and R. L. Byer, “High-resolution spectroscopy of whispering gallery modes in large dielectric spheres,” Opt. Lett. 16, 11381140 (1991).
[Crossref]

1977 (1)

D. Milam, M. J. Weber, and A. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31, 822–825 (1977).
[Crossref]

Arcizet, O.

P. DelHaye, 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]

O. Arcizet, A. Schliesser, P. DelHaye, R. Holzwarth, and T. J. Kippenberg, “Optical Frequency Comb Generation in Monolithic Microresonators,” in Practical Applications of Microresonators in Optics and Photonics, ed. A. B. Matsko, ed. (CRC, 2009), Ch. 11.

Balakireva, I.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. 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]

Balakireva, I. V.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

Baumgartel, L.

Brasch, V.

T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. 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. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref] [PubMed]

Breunig, I.

Buse, K.

Byer, R. L.

S. Schiller and R. L. Byer, “High-resolution spectroscopy of whispering gallery modes in large dielectric spheres,” Opt. Lett. 16, 11381140 (1991).
[Crossref]

Byrd, J.

Cai, Z.

Candela, Y.

Chembo, Y.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. 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]

Chembo, Y. K.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

G. Lin, S. Diallo, R. Henriet, M. Jacquot, and Y. K. Chembo, “Barium fluoride whispering-gallery mode disk-resonator with one billion quality-factor,” Opt. Lett. 39, 6009–6012 (2014).
[Crossref] [PubMed]

Y. K. Chembo and C. R. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87, 053852 (2013).
[Crossref]

Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (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] [PubMed]

Chen, T.

J. Li, H. Lee, T. Chen, and K. J. Vahala, “Low-pump-power, low-phase-noise, and microwave to millimeter-wave repetition rate operation in microcombs,” Phys. Rev. Lett. 109, 233901 (2012).
[Crossref]

Chiappini, A.

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]

Cibiel, G.

Coen, S.

Coillet, A.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. 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]

DelHaye, P.

C. Wang, T. Herr, P. DelHaye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
[Crossref]

P. DelHaye, 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]

O. Arcizet, A. Schliesser, P. DelHaye, R. Holzwarth, and T. J. Kippenberg, “Optical Frequency Comb Generation in Monolithic Microresonators,” in Practical Applications of Microresonators in Optics and Photonics, ed. A. B. Matsko, ed. (CRC, 2009), Ch. 11.

Demchenko, Y. A.

Diallo, S.

Duchesne, 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).
[Crossref]

Dudley, J.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. 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]

Eliyahu, D.

Erkintalo, M.

Féron, P.

Ferrari, M.

Ferrera, M.

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]

Foster, M. A.

Freude, W.

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. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
[Crossref] [PubMed]

Frst, J. U.

Frtsch, M.

Gaeta, A. L.

Glass, A.

D. Milam, M. J. Weber, and A. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31, 822–825 (1977).
[Crossref]

Godey, C.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

Gorodetsky, M.

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T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
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C. Wang, T. Herr, P. DelHaye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
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T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
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C. Wang, T. Herr, P. DelHaye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
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P. DelHaye, 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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C. Wang, T. Herr, P. DelHaye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
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C. Wang, T. Herr, P. DelHaye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
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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. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
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Yu, N.

G. Lin and N. Yu, “Continuous tuning of double resonance-enhanced second harmonic generation in a dispersive dielectric resonator,” Opt. Express 22, 557–562 (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. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
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Appl. Phys. Lett. (1)

D. Milam, M. J. Weber, and A. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31, 822–825 (1977).
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IEEE Photon. J. (1)

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. Chembo, “Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators,” IEEE Photon. J. 5, 6100409 (2013).
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J. Opt. Soc. Am. B (2)

Nat. Commun. (1)

C. Wang, T. Herr, P. DelHaye, A. Schliesser, J. Hofer, R. Holzwarth, T. Hänsch, N. Picqué, and T. Kippenberg, “Mid-infrared optical frequency combs at 2.5 μm based on crystalline microresonators,” Nat. Commun. 4, 1345 (2013).
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Nat. Photonics (4)

A. Savchenkov, A. Matsko, W. Liang, V. Ilchenko, D. Seidel, and L. Maleki, “Kerr combs with selectable central frequency,” Nat. Photonics 5, 293–296 (2011).
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T. Herr, V. Brasch, J. Jost, C. Wang, N. Kondratiev, M. Gorodetsky, and T. 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. J. Kippenberg, and C. Koos, “Coherent terabit communications with microresonator Kerr frequency combs,” Nat. Photonics 8, 375–380 (2014).
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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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Nature (1)

P. DelHaye, 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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Opt. Eng. (1)

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Generation of Kerr frequency combs in a sapphire whispering gallery mode microresonator,” Opt. Eng. 53, 122607 (2014).
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Opt. Express (8)

I. S. Grudinin, L. Baumgartel, and N. Yu, “Impact of cavity spectrum on span in microresonator frequency combs,” Opt. Express 21, 26929–26935 (2013).
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G. Lin and N. Yu, “Continuous tuning of double resonance-enhanced second harmonic generation in a dispersive dielectric resonator,” Opt. Express 22, 557–562 (2014).
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Other (2)

O. Arcizet, A. Schliesser, P. DelHaye, R. Holzwarth, and T. J. Kippenberg, “Optical Frequency Comb Generation in Monolithic Microresonators,” in Practical Applications of Microresonators in Optics and Photonics, ed. A. B. Matsko, ed. (CRC, 2009), Ch. 11.

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Figures (6)

Fig. 1
Fig. 1

(a) Geometry of the disk resonator. (b) Schematic of Kerr frequency comb generations in a fiber taper coupled resonator setup. WGMR: WGM resonator. vG is the primary parametric gain peak spacing from the pump frequency v0.

Fig. 2
Fig. 2

Comparison of material dispersion for different optical materials: fused silica (SiO2), sapphire, MgF2, CaF2 and BaF2. Dashed lines designate the corresponding ZDW s: 1.27 μm, 1.31 μm 1.34 μm, 1.55 μm and 1.93 μm, respectively. The vertical blue and brown zones highlight the telecommunication C-band and mid-IR windows. Note that the GVDM profile of MgF2 investigated here is derived for the ordinary ray. The extraordinary one has very similar profile with a slightly different ZDW at 1.57 μm.

Fig. 3
Fig. 3

(a) Calculated geometry dispersion influence on the total GVD for a MgF2 disk with different R and r = 0.1 mm. Dashed line: material GVDM curve. (b) Calculated zero total dispersion wavelengths λ0 for R from 0.5 mm to 5 mm. Inset: distribution of the electric field amplitude for a fundamental WGMs with R = 1 mm and r = 0.1 mm. Note: λ0 is the resonant wavelength that has its total dispersion closest to 0.

Fig. 4
Fig. 4

Calculated total GVD for different transverse WGMs in a MgF2 disk with R = 1 mm and r = 0.1 mm. Top: Electric field amplitude distribution of WGMs; Bottom: GVD as a function of the resonant wavelength. For WGMs with transverse indices of (a) q = 1, 2, 3, p = 0 and (b) p = 0, 1, 2, q = 1. Dashed line: material GVDM curve.

Fig. 5
Fig. 5

Experimental observation of three primary combs showing very different spacing of (a) 4-vFSR, (b) 164-vFSR and (c) 229-vFSR. Three different WGMs were pumped in the same resonator, and the large difference of GVD explains the large difference of primary comb multiplicity.

Fig. 6
Fig. 6

(a) Calculated geometry dispersion influence on the total GVD for a disk BaF2 with different R and r = 0.1 mm. Dashed line: material GVDM curve. (b) Calculated zero total dispersion wavelengths λ0 for R from 0.5 mm to 5 mm. Inset: distribution of the electric field amplitude for a fundamental WGM with R = 1 mm and r = 0.1 mm. (c) Calculated radial mode order influence on the total GVD for a disk BaF2 with R = 1 mm and r = 0.1 mm. WGM indices: q = 1, 2, 3, 4, 5, 6 and p = 0. (d) The corresponding electric field amplitude distribution of WGMs.

Tables (2)

Tables Icon

Table 1 Characteristics of bulk fused silica, Sapphire, MgF2, CaF2, BaF2 at T ≈ 300 K for Kerr comb generationa

Tables Icon

Table 2 Indices of WGMs and zero total dispersion wavelength for MgF2 with R = 1 mm and r = 0.1 mm

Equations (3)

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GVD m = λ c 2 n ( λ ) λ 2
2 π n ( λ ) R λ = m α q ( m 2 ) 1 / 3 + ( p + 1 2 ) ( R r ) 1 / 2
GVD 4 π 2 n ( λ ) 3 R 2 c 2 λ 2 Δ v FSR .

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