Abstract

Octave-spanning optical frequency combs are especially interesting in optical metrology owing to the ability of self-referencing. We report a theoretical study on the generation of octave-spanning combs in the whispering gallery modes of a microresonator. Through a modal expansion model simulation in a calcium fluoride microcavity, we show that a combination of suitable pump power, Kerr nonlinearity, and dispersion profile can lead to stable and robust octave-spanning optical frequency combs.

© 2010 Optical Society of America

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  1. S. T. Cundiff and J. Ye, Rev. Mod. Phys. 75, 325 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  5. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, Phys. Rev. Lett. 101, 093902 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. B. R. Johnson, J. Opt. Soc. Am. A 10, 343 (1993).
  10. S. Schiller, Appl. Opt. 32, 2181 (1993).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. M. Daimon and A. Masumura, Appl. Opt. 41, 5275 (2002).
    [CrossRef] [PubMed]
  13. Y. K. Chembo, D. V. Strekalov, and N. Yu, Phys. Rev. Lett. 104, 103902 (2010).
    [CrossRef] [PubMed]

2010 (1)

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

2009 (3)

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] [PubMed]

2007 (1)

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

2006 (2)

J. L. Hall, Rev. Mod. Phys. 78, 1279 (2006).
[CrossRef]

T. W. Hänsch, Rev. Mod. Phys. 78, 1297 (2006).
[CrossRef]

2003 (1)

S. T. Cundiff and J. Ye, Rev. Mod. Phys. 75, 325 (2003).
[CrossRef]

2002 (1)

1993 (2)

B. R. Johnson, J. Opt. Soc. Am. A 10, 343 (1993).

S. Schiller, Appl. Opt. 32, 2181 (1993).
[CrossRef] [PubMed]

A, J. Opt. Soc.

B. R. Johnson, J. Opt. Soc. Am. A 10, 343 (1993).

Agha, I. H.

Arcizet, O.

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Nat. Photon. 3, 529 (2009).
[CrossRef]

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

Chembo, Y. K.

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

Cundiff, S. T.

S. T. Cundiff and J. Ye, Rev. Mod. Phys. 75, 325 (2003).
[CrossRef]

Daimon, M.

Del’Haye, P.

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Nat. Photon. 3, 529 (2009).
[CrossRef]

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

P. Del’Haye, T. Herr, E. Gavartin, R. Holzwarth, and T. J. Kippenberg, “Octave spanning frequency comb on a chip,” arXiv:0912.4890v1 (2009).

Gaeta, A. L.

Gavartin, E.

P. Del’Haye, T. Herr, E. Gavartin, R. Holzwarth, and T. J. Kippenberg, “Octave spanning frequency comb on a chip,” arXiv:0912.4890v1 (2009).

Gorodetsky, M. L.

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Nat. Photon. 3, 529 (2009).
[CrossRef]

Grudinin, I. S.

Hall, J. L.

J. L. Hall, Rev. Mod. Phys. 78, 1279 (2006).
[CrossRef]

Hänsch, T. W.

T. W. Hänsch, Rev. Mod. Phys. 78, 1297 (2006).
[CrossRef]

Herr, T.

P. Del’Haye, T. Herr, E. Gavartin, R. Holzwarth, and T. J. Kippenberg, “Octave spanning frequency comb on a chip,” arXiv:0912.4890v1 (2009).

Holzwarth, R.

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Nat. Photon. 3, 529 (2009).
[CrossRef]

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

P. Del’Haye, T. Herr, E. Gavartin, R. Holzwarth, and T. J. Kippenberg, “Octave spanning frequency comb on a chip,” arXiv:0912.4890v1 (2009).

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] [PubMed]

Johnson, B. R.

B. R. Johnson, J. Opt. Soc. Am. A 10, 343 (1993).

Kippenberg, T. J.

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Nat. Photon. 3, 529 (2009).
[CrossRef]

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

P. Del’Haye, T. Herr, E. Gavartin, R. Holzwarth, and T. J. Kippenberg, “Octave spanning frequency comb on a chip,” arXiv:0912.4890v1 (2009).

Maleki, L.

I. S. Grudinin, N. Yu, and L. Maleki, Opt. Lett. 34, 878 (2009).
[CrossRef] [PubMed]

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

Masumura, A.

Matsko, A. B.

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

Okawachi, Y.

Savchenkov, A. A.

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

Schiller, S.

Schliesser, A.

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

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] [PubMed]

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] [PubMed]

Strekalov, D. V.

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

Wilken, T.

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

Ye, J.

S. T. Cundiff and J. Ye, Rev. Mod. Phys. 75, 325 (2003).
[CrossRef]

Yu, N.

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

I. S. Grudinin, N. Yu, and L. Maleki, Opt. Lett. 34, 878 (2009).
[CrossRef] [PubMed]

Appl. Opt. (2)

Nat. Photon. (1)

P. Del’Haye, O. Arcizet, M. L. Gorodetsky, R. Holzwarth, and T. J. Kippenberg, Nat. Photon. 3, 529 (2009).
[CrossRef]

Nature (1)

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

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (2)

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

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

Rev. Mod. Phys. (3)

S. T. Cundiff and J. Ye, Rev. Mod. Phys. 75, 325 (2003).
[CrossRef]

J. L. Hall, Rev. Mod. Phys. 78, 1279 (2006).
[CrossRef]

T. W. Hänsch, Rev. Mod. Phys. 78, 1297 (2006).
[CrossRef]

Other (2)

P. Del’Haye, T. Herr, E. Gavartin, R. Holzwarth, and T. J. Kippenberg, “Octave spanning frequency comb on a chip,” arXiv:0912.4890v1 (2009).

B. R. Johnson, J. Opt. Soc. Am. A 10, 343 (1993).

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Figures (2)

Fig. 1
Fig. 1

Lateral view of the microdisk resonator, and two-dimensional representation of the WGM 0 = 192 (TE).

Fig. 2
Fig. 2

Numerical simulation of an octave- spanning optical frequency comb. The intracavity power values are (a) | A in | 2 = 3 | A th | 2 and (b) | A in | 2 = 4 | A th | 2 .

Equations (4)

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ϒ p ( r , θ , ϕ ) = ( 1 ) 1 4 2 1 2 π 3 4 S p ( r ) e 1 2 ( θ π 2 ) 2 e i ϕ 0 + S p 2 ( r ) r 2 d r ,
ω p = c n ( ω p ) a { [ + 1 2 ] + ξ 1 [ + 1 2 2 ] 1 3 p n 0 2 1 + 3 20 ξ 1 2 [ + 1 2 2 ] 1 3 + O [ + 1 2 ] 2 3 } ,
A ˙ η = 1 2 Δ ω η A η + 1 2 Δ ω η δ η 0 F 0 e i σ t i g 0 α , β , μ Λ η α β μ A α A β * A μ e i ϖ α β μ η t .
Λ η α β μ = ω μ 2 ω 0 2 ω α ω β ω μ ω η 3 V [ ϒ η * · ϒ μ ] [ ϒ β * · ϒ α ] d V V ϒ 0 4 d V

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