Abstract

We theoretically investigate the phase locking phenomena between the spectral components of Kerr optical frequency combs in the dynamical regime of Turing patterns. We show that these Turing patterns display a particularly strong and robust phase locking, originating from a cascade of phase locked triplets which asymptotically lead to a global phase locking between the modes. The local and global phase locking relationships defining the shape of the comb are analytically determined. Our analysis also shows that solitons display a much weaker phase locking that can be destroyed more easily than in the Turing pattern regime. Our results indicate that Turing patterns are generally the most suitable for applications requiring the highest stability. Experimental generation of such combs is also discussed in detail, and is in excellent agreement with the numerical simulations.

© 2014 Optical Society of America

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  1. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
    [CrossRef]
  2. P. Del’Haye, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 109, 263901 (2012).
    [CrossRef]
  3. J. Li, H. Lee, T. Chen, and K. Vahala, Phys. Rev. Lett. 109, 233901 (2012).
    [CrossRef]
  4. A. B. Matsko and L. Maleki, Opt. Express 21, 28862 (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. Y. K. Chembo and C. R. Menyuk, Phys. Rev. A 87, 053852 (2013).
    [CrossRef]
  7. S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, Opt. Lett. 38, 37 (2013).
    [CrossRef]
  8. I. Balakireva, A. Coillet, C. Godey, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part II: case of anomalous dispersion,” arXiv:1308.2542 (2013).
  9. C. Godey, I. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv:1308.2539 (2013).
  10. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Phys. Rev. Lett. 93, 083904 (2004).
    [CrossRef]
  11. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
    [CrossRef]
  12. Y. K. Chembo, D. V. Strekalov, and N. Yu, Phys. Rev. Lett. 104, 103902 (2010).
    [CrossRef]
  13. Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010).
    [CrossRef]
  14. A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
    [CrossRef]
  15. A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804 (2005).
    [CrossRef]
  16. T. Hansson, D. Modotto, and S. Wabnitz, Phys. Rev. A 88, 023819 (2013).
    [CrossRef]
  17. M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, Opt. Lett. 38, 3478 (2013).
    [CrossRef]

2013 (6)

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

T. Hansson, D. Modotto, and S. Wabnitz, Phys. Rev. A 88, 023819 (2013).
[CrossRef]

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

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

M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, Opt. Lett. 38, 3478 (2013).
[CrossRef]

A. B. Matsko and L. Maleki, Opt. Express 21, 28862 (2013).
[CrossRef]

2012 (2)

P. Del’Haye, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 109, 263901 (2012).
[CrossRef]

J. Li, H. Lee, T. Chen, and K. Vahala, Phys. Rev. Lett. 109, 233901 (2012).
[CrossRef]

2011 (2)

2010 (2)

Y. K. Chembo, D. V. Strekalov, and N. Yu, Phys. Rev. Lett. 104, 103902 (2010).
[CrossRef]

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

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]

2005 (1)

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

2004 (1)

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

Balakireva, I.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

I. Balakireva, A. Coillet, C. Godey, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part II: case of anomalous dispersion,” arXiv:1308.2542 (2013).

C. Godey, I. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv:1308.2539 (2013).

Chembo, Y. K.

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

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

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

Y. K. Chembo, D. V. Strekalov, and N. Yu, Phys. Rev. Lett. 104, 103902 (2010).
[CrossRef]

I. Balakireva, A. Coillet, C. Godey, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part II: case of anomalous dispersion,” arXiv:1308.2542 (2013).

C. Godey, I. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv:1308.2539 (2013).

Chen, T.

J. Li, H. Lee, T. Chen, and K. Vahala, Phys. Rev. Lett. 109, 233901 (2012).
[CrossRef]

Coen, S.

Coillet, A.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

I. Balakireva, A. Coillet, C. Godey, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part II: case of anomalous dispersion,” arXiv:1308.2542 (2013).

C. Godey, I. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv:1308.2539 (2013).

Del’Haye, P.

P. Del’Haye, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 109, 263901 (2012).
[CrossRef]

Diddams, S. A.

P. Del’Haye, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 109, 263901 (2012).
[CrossRef]

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

Dudley, J.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Erkintalo, M.

Gaeta, A. L.

Godey, C.

I. Balakireva, A. Coillet, C. Godey, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part II: case of anomalous dispersion,” arXiv:1308.2542 (2013).

C. Godey, I. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv:1308.2539 (2013).

Hansson, T.

T. Hansson, D. Modotto, and S. Wabnitz, Phys. Rev. A 88, 023819 (2013).
[CrossRef]

Henriet, R.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Holzwarth, R.

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

Ilchenko, V. S.

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

Kippenberg, T. J.

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

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

Lamont, M. R. E.

Larger, L.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Lee, H.

J. Li, H. Lee, T. Chen, and K. Vahala, Phys. Rev. Lett. 109, 233901 (2012).
[CrossRef]

Li, J.

J. Li, H. Lee, T. Chen, and K. Vahala, Phys. Rev. Lett. 109, 233901 (2012).
[CrossRef]

Liang, W.

Maleki, L.

A. B. Matsko and L. Maleki, Opt. Express 21, 28862 (2013).
[CrossRef]

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

Matsko, A. B.

A. B. Matsko and L. Maleki, Opt. Express 21, 28862 (2013).
[CrossRef]

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

Menyuk, C.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Menyuk, C. R.

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

Modotto, D.

T. Hansson, D. Modotto, and S. Wabnitz, Phys. Rev. A 88, 023819 (2013).
[CrossRef]

Okawachi, Y.

Papp, S. B.

P. Del’Haye, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 109, 263901 (2012).
[CrossRef]

Randle, H. G.

Saleh, K.

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Savchenkov, A. A.

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

Seidel, D.

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

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]

Strekalov, D.

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

Strekalov, D. V.

Y. K. Chembo, D. V. Strekalov, and N. Yu, Phys. Rev. Lett. 104, 103902 (2010).
[CrossRef]

Sylvestre, T.

Vahala, K.

J. Li, H. Lee, T. Chen, and K. Vahala, Phys. Rev. Lett. 109, 233901 (2012).
[CrossRef]

Vahala, K. J.

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

Wabnitz, S.

T. Hansson, D. Modotto, and S. Wabnitz, Phys. Rev. A 88, 023819 (2013).
[CrossRef]

Yu, N.

Y. K. Chembo, D. V. Strekalov, and N. Yu, Phys. Rev. Lett. 104, 103902 (2010).
[CrossRef]

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

IEEE Photon. J. (1)

A. Coillet, I. Balakireva, R. Henriet, K. Saleh, L. Larger, J. Dudley, C. Menyuk, and Y. K. Chembo, IEEE Photon. J. 5, 6100409 (2013).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (4)

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]

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

T. Hansson, D. Modotto, and S. Wabnitz, Phys. Rev. A 88, 023819 (2013).
[CrossRef]

Phys. Rev. Lett. (5)

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

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

Y. K. Chembo, D. V. Strekalov, and N. Yu, Phys. Rev. Lett. 104, 103902 (2010).
[CrossRef]

P. Del’Haye, S. B. Papp, and S. A. Diddams, Phys. Rev. Lett. 109, 263901 (2012).
[CrossRef]

J. Li, H. Lee, T. Chen, and K. Vahala, Phys. Rev. Lett. 109, 233901 (2012).
[CrossRef]

Science (1)

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

Other (2)

I. Balakireva, A. Coillet, C. Godey, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part II: case of anomalous dispersion,” arXiv:1308.2542 (2013).

C. Godey, I. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the Lugiato-Lefever model for Kerr optical frequency combs. Part I: case of normal dispersion,” arXiv:1308.2539 (2013).

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