Abstract

We theoretically investigate mode-locked regimes of optical-frequency combs generated in a nonlinear ring microresonator pumped with continuous-wave light. We find that breather solitons can be formed in the resonator for certain values of frequency and power of the pump. We argue that relatively slow modulation of the comb-frequency harmonics observed in several recent experiments can be attributed to soliton formation.

© 2012 Optical Society of America

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  1. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Phys. Rev. Lett. 93, 083904 (2004).
    [CrossRef]
  2. A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, Phys. Rev. Lett. 93, 243905 (2004).
    [CrossRef]
  3. M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, IEEE J. Quantum Electron. 25, 2045 (1989).
    [CrossRef]
  4. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
    [CrossRef]
  5. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
    [CrossRef]
  6. M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, Opt. Express 19, 14233 (2011).
    [CrossRef]
  7. 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]
  8. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
    [CrossRef]
  9. I. H. Agha, Y. Okawachi, and A. L. Gaeta, Opt. Express 17, 16209 (2009).
    [CrossRef]
  10. Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010).
    [CrossRef]
  11. W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2290 (2011).
    [CrossRef]
  12. 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]
  13. F. Ferdous, H. Miao, P.-H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, Opt. Express 20, 21033 (2012).
    [CrossRef]
  14. I. S. Grudinin, L. Baumgartel, and N. Yu, Opt. Express 20, 6604 (2012).
    [CrossRef]
  15. S. B. Papp and S. A. Diddams, Phys. Rev. A 84, 053833 (2011).
    [CrossRef]
  16. A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2845 (2011).
    [CrossRef]
  17. I. V. Barashenkov and Y. S. Smirnov, Phys. Rev. E 54, 5707 (1996).
    [CrossRef]
  18. A. B. Matsko, A. A. Savchenkov, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 85, 023830 (2012).
    [CrossRef]
  19. E. Kuznetsov, Sov. Phys. Dokl. 22, 507 (1977).
  20. Y. C. Ma, Stud. Appl. Math. 60, 43 (1979).
  21. B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
    [CrossRef]
  22. N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
    [CrossRef]
  23. E. Fermi, J. Pasta, and S. Ulam, Studies of Nonlinear Problems I (Los Alamos report LA-1940, 1955); reprinted in E. Fermi, Collected Papers, Vol. II, E. Segre, ed. (University of Chicago, 1965), p. 978.
  24. G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 87, 033902 (2001).
    [CrossRef]
  25. N. N. Akhmediev, Nature 413, 267 (2001).
    [CrossRef]
  26. J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
    [CrossRef]
  27. A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804(2005).
    [CrossRef]

2012 (5)

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

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

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]

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

F. Ferdous, H. Miao, P.-H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, Opt. Express 20, 21033 (2012).
[CrossRef]

2011 (6)

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2290 (2011).
[CrossRef]

M. A. Foster, J. S. Levy, O. Kuzucu, K. Saha, M. Lipson, and A. L. Gaeta, Opt. Express 19, 14233 (2011).
[CrossRef]

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

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

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]

2010 (1)

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

2009 (2)

2008 (1)

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

2007 (1)

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

2005 (1)

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804(2005).
[CrossRef]

2004 (2)

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

2001 (2)

G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 87, 033902 (2001).
[CrossRef]

N. N. Akhmediev, Nature 413, 267 (2001).
[CrossRef]

1996 (1)

I. V. Barashenkov and Y. S. Smirnov, Phys. Rev. E 54, 5707 (1996).
[CrossRef]

1989 (1)

M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, IEEE J. Quantum Electron. 25, 2045 (1989).
[CrossRef]

1986 (1)

N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
[CrossRef]

1979 (1)

Y. C. Ma, Stud. Appl. Math. 60, 43 (1979).

1977 (1)

E. Kuznetsov, Sov. Phys. Dokl. 22, 507 (1977).

Agha, I. H.

Akhmediev, N.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, Nature 413, 267 (2001).
[CrossRef]

Aksyuk, V.

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 Y. S. Smirnov, Phys. Rev. E 54, 5707 (1996).
[CrossRef]

Baumgartel, L.

Chembo, Y. K.

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

Chen, L.

F. Ferdous, H. Miao, P.-H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, Opt. Express 20, 21033 (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]

Del’Haye, P.

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

Dias, F.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

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.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

Emplit, P.

G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 87, 033902 (2001).
[CrossRef]

Fatome, J.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

Ferdous, F.

F. Ferdous, H. Miao, P.-H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, Opt. Express 20, 21033 (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]

Fermi, E.

E. Fermi, J. Pasta, and S. Ulam, Studies of Nonlinear Problems I (Los Alamos report LA-1940, 1955); reprinted in E. Fermi, Collected Papers, Vol. II, E. Segre, ed. (University of Chicago, 1965), p. 978.

Finot, C.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[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.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[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]

Grudinin, I. S.

Haelterman, M.

G. Van Simaeys, P. Emplit, and M. Haelterman, Phys. Rev. Lett. 87, 033902 (2001).
[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]

Haus, H. A.

M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, IEEE J. Quantum Electron. 25, 2045 (1989).
[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]

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, 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]

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2290 (2011).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804(2005).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

Kibler, B.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

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, 1214 (2007).
[CrossRef]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

Korneev, V. I.

N. Akhmediev and V. I. Korneev, Theor. Math. Phys. 69, 1089 (1986).
[CrossRef]

Kubota, H.

M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, IEEE J. Quantum Electron. 25, 2045 (1989).
[CrossRef]

Kuznetsov, E.

E. Kuznetsov, Sov. Phys. Dokl. 22, 507 (1977).

Kuzucu, O.

Leaird, D. E.

F. Ferdous, H. Miao, P.-H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, Opt. Express 20, 21033 (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]

Levy, J. S.

Liang, W.

Lipson, M.

Ma, Y. C.

Y. C. Ma, Stud. Appl. Math. 60, 43 (1979).

Maleki, L.

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]

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2290 (2011).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804(2005).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

Matsko, A. B.

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]

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2290 (2011).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804(2005).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

Miao, H.

F. Ferdous, H. Miao, P.-H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, Opt. Express 20, 21033 (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]

Millot, G.

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, Sci. Rep. 2, 463 (2012).
[CrossRef]

Mohageg, M.

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

Nakazawa, M.

M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, IEEE J. Quantum Electron. 25, 2045 (1989).
[CrossRef]

Okawachi, Y.

Papp, S. B.

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

Pasta, J.

E. Fermi, J. Pasta, and S. Ulam, Studies of Nonlinear Problems I (Los Alamos report LA-1940, 1955); reprinted in E. Fermi, Collected Papers, Vol. II, E. Segre, ed. (University of Chicago, 1965), p. 978.

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.

Savchenkov, A. A.

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]

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2290 (2011).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804(2005).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, Phys. Rev. Lett. 93, 243905 (2004).
[CrossRef]

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]

W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2290 (2011).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

Smirnov, Y. S.

I. V. Barashenkov and Y. S. Smirnov, Phys. Rev. E 54, 5707 (1996).
[CrossRef]

Solomatine, I.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

Spillane, S. M.

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Phys. Rev. Lett. 93, 083904 (2004).
[CrossRef]

Srinivasan, K.

F. Ferdous, H. Miao, P.-H. Wang, D. E. Leaird, K. Srinivasan, L. Chen, V. Aksyuk, and A. M. Weiner, Opt. Express 20, 21033 (2012).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Density plot of time evolution of the frequency comb spectrum generated inside a nonlinear microresonator pumped with cw light of fixed power. The envelope of the spectrum experiences slow temporal oscillation. The frequency and contrast of the oscillation depend on the pump power as well as relative detuning of the optical pump and the corresponding resonator mode. The dependence on the detuning is illustrated in (a)–(c). The spectrum shown in plot (a) is calculated for ωω0=6.25γ0, (b) 7γ0, and (c) 7.75γ0. The amplitude of the electric field presented in the pictures is normalized as e=(g/γ0)1/2e^.

Fig. 2.
Fig. 2.

Spectrum of amplitudes of optical harmonics of the frequency comb generated in the microresonator for ωω0=7.75γ0 [Fig. 1(c)]. The narrowest and widest spectra are presented in (a) and (b).

Fig. 3.
Fig. 3.

The shortest (red solid curve) and longest (blue dashed curve) optical pulses generated in the resonator for the spectra shown in Fig. 2.

Fig. 4.
Fig. 4.

Normalized power and phase of the RF signal generated by the Kerr frequency comb on a fast photodiode at FSR frequency. The solution is found for specific pump detuning ωω0=7γ0, where RF modulation has maximal contrast.

Equations (2)

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V^=g2(e^)2e^2,
a^.j=(γ0+iωj)a^j+i[V^,a^j]+F0eiωtδj0,j,

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