Abstract

Using the known solutions of the Lugiato–Lefever equation, we derive universal trends of Kerr frequency combs. In particular, normalized properties of temporal cavity soliton solutions lead us to a simple analytic estimate of the maximum attainable bandwidth for given pump resonator parameters. The result is validated via comparison with past experiments encompassing a diverse range of resonator configurations and parameters.

© 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. Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010).
    [CrossRef]
  3. A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 85, 023830 (2012).
    [CrossRef]
  4. A. B. Matsko, W. Liang, A. A. Savchenkov, and L. Maleki, Opt. Lett. 38, 525 (2013).
    [CrossRef]
  5. A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2845 (2011).
    [CrossRef]
  6. S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, Opt. Lett. 38, 37 (2013).
    [CrossRef]
  7. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, arXiv:1211.0733.
  8. F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
    [CrossRef]
  9. M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
    [CrossRef]
  10. I. V. Barashenkov and Yu. S. Smirnov, Phys. Rev. E 54, 5707 (1996).
  11. A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Lett. 37, 4856 (2012).
    [CrossRef]
  12. F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, Opt. Express 21, 9180 (2013).
    [CrossRef]
  13. S. Wabnitz, Opt. Lett. 18, 601 (1993).
    [CrossRef]
  14. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
    [CrossRef]
  15. Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, Opt. Lett. 36, 3398 (2011).
    [CrossRef]
  16. I. S. Grudinin, L. Baumgartel, and N. Yu, Opt. Express 20, 6604 (2012).
    [CrossRef]
  17. P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Phys. Rev. Lett. 107, 063901 (2011).
    [CrossRef]
  18. M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 109, 223904 (2012).
    [CrossRef]
  19. F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
    [CrossRef]

2013 (4)

2012 (4)

A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Lett. 37, 4856 (2012).
[CrossRef]

I. S. Grudinin, L. Baumgartel, and N. Yu, Opt. Express 20, 6604 (2012).
[CrossRef]

M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 109, 223904 (2012).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 85, 023830 (2012).
[CrossRef]

2011 (4)

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

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

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

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

2010 (2)

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

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

2007 (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

1996 (1)

I. V. Barashenkov and Yu. S. Smirnov, Phys. Rev. E 54, 5707 (1996).

1993 (1)

1992 (1)

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

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Barashenkov, I. V.

I. V. Barashenkov and Yu. S. Smirnov, Phys. Rev. E 54, 5707 (1996).

Baumgartel, L.

Brasch, V.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, arXiv:1211.0733.

Chembo, Y. K.

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

Coen, S.

Del’Haye, P.

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Diddams, S. A.

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

Dudley, J. M.

M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 109, 223904 (2012).
[CrossRef]

Emplit, Ph.

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, Opt. Express 21, 9180 (2013).
[CrossRef]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

Erkintalo, M.

S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, Opt. Lett. 38, 37 (2013).
[CrossRef]

M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 109, 223904 (2012).
[CrossRef]

Gaeta, A. L.

Gavartin, E.

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

Gelens, L.

Genty, G.

M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 109, 223904 (2012).
[CrossRef]

Gorodetsky, M. L.

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, arXiv:1211.0733.

Gorza, S.-P.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

Grudinin, I. S.

Haelterman, M.

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, Opt. Express 21, 9180 (2013).
[CrossRef]

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

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

Herr, T.

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, arXiv:1211.0733.

Holzwarth, R.

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

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Ilchenko, V. S.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 85, 023830 (2012).
[CrossRef]

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

Jost, J. D.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, arXiv:1211.0733.

Kippenberg, T. J.

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

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, arXiv:1211.0733.

Kockaert, P.

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

Kondratiev, N. M.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, arXiv:1211.0733.

Leo, F.

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, Opt. Express 21, 9180 (2013).
[CrossRef]

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

Levy, J. S.

Liang, W.

Lipson, M.

Maleki, L.

Matsko, A. B.

Murdoch, S. G.

M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 109, 223904 (2012).
[CrossRef]

Mussot, A.

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

Okawachi, Y.

Randle, H. G.

Saha, K.

Savchenkov, A. A.

Schliesser, A.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Seidel, D.

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 85, 023830 (2012).
[CrossRef]

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

Smirnov, Yu. S.

I. V. Barashenkov and Yu. S. Smirnov, Phys. Rev. E 54, 5707 (1996).

Sylvestre, T.

Taki, M.

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

Trillo, S.

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

Wabnitz, S.

S. Wabnitz, Opt. Lett. 18, 601 (1993).
[CrossRef]

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

Wang, C. Y.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, arXiv:1211.0733.

Wen, Y. H.

Wilken, T.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Xu, Y. Q.

M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 109, 223904 (2012).
[CrossRef]

Yu, N.

Nat. Photonics (1)

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[CrossRef]

Nature (1)

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
[CrossRef]

Opt. Commun. (1)

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

Opt. Express (2)

Opt. Lett. (6)

Phys. Rev. A (2)

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

A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 85, 023830 (2012).
[CrossRef]

Phys. Rev. E (1)

I. V. Barashenkov and Yu. S. Smirnov, Phys. Rev. E 54, 5707 (1996).

Phys. Rev. Lett. (3)

P. Del’Haye, T. Herr, E. Gavartin, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Phys. Rev. Lett. 107, 063901 (2011).
[CrossRef]

M. Erkintalo, Y. Q. Xu, S. G. Murdoch, J. M. Dudley, and G. Genty, Phys. Rev. Lett. 109, 223904 (2012).
[CrossRef]

F. Leo, A. Mussot, P. Kockaert, Ph. Emplit, M. Haelterman, and M. Taki, Phys. Rev. Lett. 110, 104103 (2013).
[CrossRef]

Science (1)

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

Other (1)

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, arXiv:1211.0733.

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 (3)

Fig. 1.
Fig. 1.

(a) Intracavity peak power versus detuning for the cw (black), MI (green), and CS (blue) branches. Dashed and dotted lines indicate unstable solutions as described in the text. The temporal and spectral intensity profiles of particular MI and CS solutions (crosses) are illustrated in (b), (c) and (d), (e), respectively.

Fig. 2.
Fig. 2.

(a) Normalized CS duration (left axis) and peak power (right axis) versus Δ/X for various pump levels (dashed: oscillatory CSs; other unstable CSs are omitted for clarity). (b) Examples of numerical CS temporal intensity profiles for parameters corresponding to the dots in (a). In both panels, the numerical results are compared with analytic approximations (grey circles).

Fig. 3.
Fig. 3.

Theoretical Kerr comb bandwidth calculated from Eq. (3) versus 2nd order GVD for varying values of γPinF (solid lines) and upper limit (dotted line). The black diamonds are the theoretical estimates for the references listed in Table 1 with the corresponding experimental bandwidths shown as green dots.

Tables (1)

Tables Icon

Table 1. Comparison of Experimental 3 dB Comb Bandwidths (Δfexp) with Analytical Predictions (Δftheo)

Equations (3)

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

E(t,τ)t=[1+i(|E|2Δ)iη2τ2]E+S.
X=Y32ΔY2+(Δ2+1)Y,
Δftheo=0.3151.7632γPinQλpFSRπc|β2|=0.3151.7632γPinFπ|β2|,

Metrics