Abstract

We perform the first theoretical modeling of the full spectral–temporal dynamics of octave-spanning parametric microresonator comb generation through use of the Lugiato–Lefever model extended to include higher-order dispersion and self-steepening. We show that three distinct stages are necessary to achieve single-pulse modelocking and discuss the dispersion characteristics required for ultrabroadband, stabilized comb generation. Our simulations agree well with previous experimental demonstrations and predict many of the observed features, including multipulse generation, dispersive wave generation, modelocking, and comb stabilization.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
    [CrossRef]
  2. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 12147 (2007).
  3. A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2845 (2011).
    [CrossRef]
  4. F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, Nat. Photonics 5, 770 (2011).
    [CrossRef]
  5. S. B. Papp and S. A. Diddams, Phys. Rev. A 84, 053833 (2011).
    [CrossRef]
  6. M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “A silicon-based monolithic optical frequency comb source,” arXiv:1102.0326 (2008).
  7. K. Saha, Y. Okawachi, B. Shim, J. S. Levy, R. Salem, A. R. Johnson, M. A. Foster, M. R. Lamont, M. Lipson, and A. L. Gaeta, Opt. Express 21, 1335 (2013).
    [CrossRef]
  8. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonator,” arXiv:1211.0733 (2013).
  9. M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
    [CrossRef]
  10. Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010).
    [CrossRef]
  11. S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, Opt. Lett. 38, 37 (2013).
    [CrossRef]
  12. L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
    [CrossRef]
  13. Y. K. Chembo and C. R. Menyuk, Phys. Rev. A 87, 053852 (2013).
    [CrossRef]
  14. J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
    [CrossRef]
  15. O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, J. Lightwave Technol. 21, 61 (2003).
    [CrossRef]
  16. Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, Opt. Lett. 36, 3398 (2011).
    [CrossRef]
  17. A. B. Matsko, W. Liang, A. A. Savchenkov, and L. Maleki, Opt. Lett. 38, 525 (2013).
    [CrossRef]
  18. T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 6, 480 (2012).
    [CrossRef]
  19. M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, Opt. Express 16, 1300 (2008).
    [CrossRef]
  20. S. Coen and M. Erkintalo, Opt. Lett. 38, 1790 (2013).
    [CrossRef]
  21. M. R. E. Lamont, B. T. Kuhlmey, and C. M. de Sterke, Opt. Express 16, 7551 (2008).
    [CrossRef]

2013 (5)

2012 (1)

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 6, 480 (2012).
[CrossRef]

2011 (5)

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[CrossRef]

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, Nat. Photonics 5, 770 (2011).
[CrossRef]

S. B. Papp and S. A. Diddams, Phys. Rev. A 84, 053833 (2011).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2845 (2011).
[CrossRef]

Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, Opt. Lett. 36, 3398 (2011).
[CrossRef]

2010 (1)

Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010).
[CrossRef]

2008 (2)

2007 (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 12147 (2007).

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

2003 (1)

1992 (1)

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

1987 (1)

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef]

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 12147 (2007).

Brasch, V.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonator,” arXiv:1211.0733 (2013).

Chembo, Y. K.

Y. K. Chembo and C. R. Menyuk, Phys. Rev. A 87, 053852 (2013).
[CrossRef]

Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010).
[CrossRef]

Chen, L.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, Nat. Photonics 5, 770 (2011).
[CrossRef]

Coen, S.

de Sterke, C. M.

Del’Haye, P.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 12147 (2007).

Diddams, S. A.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[CrossRef]

S. B. Papp and S. A. Diddams, Phys. Rev. A 84, 053833 (2011).
[CrossRef]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Erkintalo, M.

Ferdous, F.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, Nat. Photonics 5, 770 (2011).
[CrossRef]

Foster, M. A.

Gaeta, A. L.

Gavartin, E.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 6, 480 (2012).
[CrossRef]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Gorodetsky, M. L.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 6, 480 (2012).
[CrossRef]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonator,” arXiv:1211.0733 (2013).

Haelterman, M.

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

Hartinger, K.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 6, 480 (2012).
[CrossRef]

Herr, T.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 6, 480 (2012).
[CrossRef]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonator,” arXiv:1211.0733 (2013).

Holzlohner, R.

Holzwarth, R.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 6, 480 (2012).
[CrossRef]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 12147 (2007).

Ilchenko, V. S.

Johnson, A. R.

Jost, J. D.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonator,” arXiv:1211.0733 (2013).

Kippenberg, T. J.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 6, 480 (2012).
[CrossRef]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 12147 (2007).

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonator,” arXiv:1211.0733 (2013).

Kondratiev, N. M.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonator,” arXiv:1211.0733 (2013).

Kuhlmey, B. T.

Kuzucu, O.

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “A silicon-based monolithic optical frequency comb source,” arXiv:1102.0326 (2008).

Lamont, M. R.

Lamont, M. R. E.

Leaird, D. E.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, Nat. Photonics 5, 770 (2011).
[CrossRef]

Lefever, R.

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef]

Levy, J. S.

Liang, W.

Lipson, M.

Lugiato, L. A.

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef]

Maleki, L.

Matsko, A. B.

Menyuk, C. R.

Miao, H.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, Nat. Photonics 5, 770 (2011).
[CrossRef]

Okawachi, Y.

Papp, S. B.

S. B. Papp and S. A. Diddams, Phys. Rev. A 84, 053833 (2011).
[CrossRef]

Randle, H. G.

Riemensberger, J.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 6, 480 (2012).
[CrossRef]

Saha, K.

Salem, R.

Savchenkov, A. A.

Schliesser, A.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 12147 (2007).

Seidel, D.

Shim, B.

Sinkin, O. V.

Srinivasan, K.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, Nat. Photonics 5, 770 (2011).
[CrossRef]

Sylvestre, T.

Trillo, S.

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

Turner, A. C.

Varghese, L. T.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, Nat. Photonics 5, 770 (2011).
[CrossRef]

Wabnitz, S.

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

Wang, C. Y.

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 6, 480 (2012).
[CrossRef]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonator,” arXiv:1211.0733 (2013).

Wang, J.

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, Nat. Photonics 5, 770 (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, Nat. Photonics 5, 770 (2011).
[CrossRef]

Wen, Y. H.

Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 12147 (2007).

Yu, N.

Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010).
[CrossRef]

Zweck, J.

J. Lightwave Technol. (1)

Nat. Photonics (2)

T. Herr, K. Hartinger, J. Riemensberger, C. Y. Wang, E. Gavartin, R. Holzwarth, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 6, 480 (2012).
[CrossRef]

F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, Nat. Photonics 5, 770 (2011).
[CrossRef]

Nature (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 12147 (2007).

Opt. Commun. (1)

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[CrossRef]

Opt. Express (3)

Opt. Lett. (5)

Phys. Rev. A (3)

Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010).
[CrossRef]

Y. K. Chembo and C. R. Menyuk, Phys. Rev. A 87, 053852 (2013).
[CrossRef]

S. B. Papp and S. A. Diddams, Phys. Rev. A 84, 053833 (2011).
[CrossRef]

Phys. Rev. Lett. (1)

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Science (1)

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
[CrossRef]

Other (2)

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, “A silicon-based monolithic optical frequency comb source,” arXiv:1102.0326 (2008).

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonator,” arXiv:1211.0733 (2013).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Evolution of single-pulse modelocking within a 226 GHz monolithic Si3N4 ring resonator. Each of the four stages (bottom to top) represents an increase in pump detuning from on-resonance to δ0=0.02, 0.04, 0.05642 at simulated times t=25, 50, 75 ns. The pump power, |Ein|2, is kept constant at 1.5 W. Column 1 is the temporal evolution, with power plotted on identical linear scales, and τ spanning a single roundtrip time. Column 2 is the spectral evolution, with spectral power plotted on the same 100 dB-scale. Columns 3 and 4 show the temporal and spectral power, respectively, at the end of Stages I–IV.

Fig. 2.
Fig. 2.

Processes involved in initial comb formation. (a) Anomalous GVD allows for MI from pump. (b) Cascaded FWM from further power build-up. (c) Minicomb formation due to MI/FWM. (d) FWM mirroring with central pumped mode.

Fig. 3.
Fig. 3.

(a) Spectrogram of the single-pulse modelocked frequency comb, plotted on a 100 dB scale. (b) Comparison of the theoretical (top) and experimental (bottom) frequency comb spectra. Data is from Okawachi et al. [16].

Fig. 4.
Fig. 4.

Temporal and spectral evolution with the same parameters used in Fig. 1. For this case δ0 is kept at 0.015 and the pump power is set at 0.5 W for 30 ns, then increased to 1 W for 0.5 ns, and dropped to 0.376 W for the last 30 ns, demonstrating a different route to single-pulse modelocking.

Fig. 5.
Fig. 5.

Frequency comb spectra (blue area) of waveguide with varying widths pumped at λp=1550nm. All other materials and dimensions are the same. The GVD for each waveguide geometry is shown by the red (solid) line.

Equations (1)

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

TRE(t,τ)t=κEin+[α2κ2iδ0+iLk2βkk!(iτ)k+iγL(1+iω0τ)|E(t,τ)|2]E(t,τ),

Metrics