Abstract

We show via numerical simulation that Kerr frequency combs can be generated in a nonlinear resonator characterized with normal group-velocity dispersion. We find the spectral shape of the comb and temporal envelope of the corresponding optical pulses formed in the resonator.

© 2012 Optical Society of America

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References

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  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, 1214 (2007).
    [CrossRef]
  3. I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, Phys. Rev. A 76, 043837 (2007).
    [CrossRef]
  4. I. H. Agha, Y. Okawachi, and A. L. Gaeta, Opt. Express 17, 16209 (2009).
    [CrossRef]
  5. Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010).
    [CrossRef]
  6. M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Lett. 17, 745 (1992).
    [CrossRef]
  7. S. Coen and M. Haelterman, Phys. Rev. Lett. 79, 4139 (1997).
    [CrossRef]
  8. A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, and L. Maleki, Opt. Express 16, 4130 (2008).
    [CrossRef]
  9. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
    [CrossRef]
  10. A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, Phys. Rev. A 71, 033804 (2005).
    [CrossRef]
  11. A. Matsko, A. Savchenkov, W. Liang, V. Ilchenko, D. Seidel, and L. Maleki, in Nonlinear Optics: Materials, Fundamentals and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper NWD2.
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  13. C. C. Lam, P. T. Leung, and K. Young, J. Opt. Soc. Am. B 9, 1585 (1992).
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    [CrossRef]

2011

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

2010

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

2009

2008

A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, and L. Maleki, Opt. Express 16, 4130 (2008).
[CrossRef]

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

2007

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

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, Phys. Rev. A 76, 043837 (2007).
[CrossRef]

2005

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

2003

2002

1997

S. Coen and M. Haelterman, Phys. Rev. Lett. 79, 4139 (1997).
[CrossRef]

1992

Agha, I. H.

I. H. Agha, Y. Okawachi, and A. L. Gaeta, Opt. Express 17, 16209 (2009).
[CrossRef]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Arcizet, O.

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

Chembo, Y. K.

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

Coen, S.

S. Coen and M. Haelterman, Phys. Rev. Lett. 79, 4139 (1997).
[CrossRef]

Daimon, M.

Del’Haye, P.

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]

Foster, M. A.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Gaeta, A. L.

I. H. Agha, Y. Okawachi, and A. L. Gaeta, Opt. Express 17, 16209 (2009).
[CrossRef]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Haelterman, M.

S. Coen and M. Haelterman, Phys. Rev. Lett. 79, 4139 (1997).
[CrossRef]

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Lett. 17, 745 (1992).
[CrossRef]

Holzwarth, R.

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.

A. Matsko, A. Savchenkov, W. Liang, V. Ilchenko, D. Seidel, and L. Maleki, in Nonlinear Optics: Materials, Fundamentals and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper NWD2.

Ilchenko, V. S.

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

A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, and L. Maleki, Opt. Express 16, 4130 (2008).
[CrossRef]

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

A. B. Matsko, V. S. Ilchenko, A. A. Savchenkov, and L. Maleki, J. Opt. Soc. Am. B 20, 2292 (2003).
[CrossRef]

Kippenberg, T. J.

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]

Lam, C. C.

Leung, P. T.

Liang, W.

A. Matsko, A. Savchenkov, W. Liang, V. Ilchenko, D. Seidel, and L. Maleki, in Nonlinear Optics: Materials, Fundamentals and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper NWD2.

Maleki, L.

A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, and L. Maleki, Opt. Express 16, 4130 (2008).
[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. B. Matsko, V. S. Ilchenko, A. A. Savchenkov, and L. Maleki, J. Opt. Soc. Am. B 20, 2292 (2003).
[CrossRef]

A. Matsko, A. Savchenkov, W. Liang, V. Ilchenko, D. Seidel, and L. Maleki, in Nonlinear Optics: Materials, Fundamentals and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper NWD2.

Masumura, A.

Matsko, A.

A. Matsko, A. Savchenkov, W. Liang, V. Ilchenko, D. Seidel, and L. Maleki, in Nonlinear Optics: Materials, Fundamentals and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper NWD2.

Matsko, A. B.

A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, and L. Maleki, Opt. Express 16, 4130 (2008).
[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. B. Matsko, V. S. Ilchenko, A. A. Savchenkov, and L. Maleki, J. Opt. Soc. Am. B 20, 2292 (2003).
[CrossRef]

Okawachi, Y.

I. H. Agha, Y. Okawachi, and A. L. Gaeta, Opt. Express 17, 16209 (2009).
[CrossRef]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Rubiola, E.

Savchenkov, A.

A. Matsko, A. Savchenkov, W. Liang, V. Ilchenko, D. Seidel, and L. Maleki, in Nonlinear Optics: Materials, Fundamentals and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper NWD2.

Savchenkov, A. A.

A. A. Savchenkov, E. Rubiola, A. B. Matsko, V. S. Ilchenko, and L. Maleki, Opt. Express 16, 4130 (2008).
[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. B. Matsko, V. S. Ilchenko, A. A. Savchenkov, and L. Maleki, J. Opt. Soc. Am. B 20, 2292 (2003).
[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. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
[CrossRef]

A. Matsko, A. Savchenkov, W. Liang, V. Ilchenko, D. Seidel, and L. Maleki, in Nonlinear Optics: Materials, Fundamentals and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper NWD2.

Sharping, J. E.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, Phys. Rev. A 76, 043837 (2007).
[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]

Strekalov, D.

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

Trillo, S.

Wabnitz, S.

Wilken, T.

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

Young, K.

Yu, N.

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

Appl. Opt.

J. Opt. Soc. Am. B

Nature

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

Opt. Express

Opt. Lett.

Phys. Rev. A

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

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, Phys. Rev. A 76, 043837 (2007).
[CrossRef]

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

Phys. Rev. Lett.

S. Coen and M. Haelterman, Phys. Rev. Lett. 79, 4139 (1997).
[CrossRef]

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

Science

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

Other

A. Matsko, A. Savchenkov, W. Liang, V. Ilchenko, D. Seidel, and L. Maleki, in Nonlinear Optics: Materials, Fundamentals and Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper NWD2.

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Figures (4)

Fig. 1.
Fig. 1.

Normalized slow amplitude [|A11|(g/2πγ0)1/2] and phase of the intracavity field of the pumped mode versus normalized detuning [(ωω11)/2πγ0]. The region of the maximum field accumulation is shifted to smaller frequencies due to the self-phase modulation effect (the effective index of refraction increases with intensity of light circulating in the mode). The pump power is fixed, f=(F0/2πγ0)(g/2πγ0)1/2=2.244. The stable solutions of the set Eq. (1) that do not reveal the Kerr comb generation are shown by blue lines. The stable solution that reveals the comb generation is shown by the red line. The solution is localized in both amplitude and frequency spaces. The insets show the region of parameters where the comb is generated.

Fig. 2.
Fig. 2.

Normalized slow amplitude [|A11|(g/2πγ0)1/2] and phase of the intracavity field of the pumped mode versus the normalized amplitude of the external pump [f=(F0/2πγ0)(g/2πγ0)1/2]. The frequency detuning is fixed (ωω11)/2πγ0=4. Stable solutions of the set Eq. (1) that do not reveal Kerr comb generation are shown by blue lines. The stable solution that reveals comb generation is shown by the red line. The solution is localized. The inset shows the region of parameters where the comb is generated.

Fig. 3.
Fig. 3.

Normalized slow amplitude [|A10|(g/2πγ0)1/2 and |A12|(g/2πγ0)1/2 are the same] of the first sidebands of the pump mode for the same parameters of the system as used in Figs. 1and 2.

Fig. 4.
Fig. 4.

Normalized slow amplitude [(g|e^e^|/2πγ0)1/2] of the intracavity field versus time, and the corresponding optical comb found for a fixed pump power f=2.244 and frequency detuning of the pump light from the selected mode (ωω11)/2πγ0=4. The 100GHz FSR of the resonator is expected.

Equations (1)

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

a^.j=(γ0+iωj)a^j+i[V^,a^j]+F0eiωtδ11,j,

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