Abstract

We numerically investigate the influence of high-order dispersion (HOD) on temporal and spectral characteristics of microresonator-based optical frequency combs. Theoretical analysis based on the moment method associated with numerical simulations are utilized to study the comb evolution dynamics, showing that temporal shifts of steady-state intracavity solitons are induced by high-odd-order dispersion rather than high-even-order dispersion. The role of HOD on comb spectral envelopes is also elucidated through analyzing the intracavity dispersive wave generations. We further demonstrate that the spectral envelope of a broadband optical frequency comb can be engineered by using a cavity dispersion profile with multiple zero dispersion wavelengths.

© 2014 Optical Society of America

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  1. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature 450, 1214 (2007).
    [CrossRef]
  2. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Science 332, 555 (2011).
    [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, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2845 (2011).
    [CrossRef]
  5. M. R. E. Lamont, Y. Okawachi, and A. L. Gaeta, Opt. Lett. 38, 3478 (2013).
    [CrossRef]
  6. 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]
  7. A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 86, 013838 (2012).
    [CrossRef]
  8. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2006).
  9. A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Lett. 37, 43 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. J. Santhanama and G. P. Agrawal, Opt. Commun. 222, 413 (2003).
    [CrossRef]
  19. A. B. Matsko, W. Liang, A. A. Savchenkov, and L. Maleki, Opt. Lett. 38, 525 (2013).
    [CrossRef]
  20. S. Coen and M. Erkintalo, Opt. Lett. 38, 1790 (2013).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. S. Roy, S. K. Bhadra, and G. P. Agrawal, Opt. Lett. 34, 2072 (2009).
    [CrossRef]
  24. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
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    [CrossRef]
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2014 (1)

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[CrossRef]

2013 (8)

2012 (4)

A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Lett. 37, 43 (2012).
[CrossRef]

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

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 86, 013838 (2012).
[CrossRef]

2011 (3)

2009 (1)

2007 (3)

E. N. Tsoy and C. M. de Sterke, Phys. Rev. A 76, 043804 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

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

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

2003 (1)

J. Santhanama and G. P. Agrawal, Opt. Commun. 222, 413 (2003).
[CrossRef]

1999 (1)

1995 (1)

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef]

1992 (1)

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

Agarwal, A. M.

Agrawal, G. P.

S. Roy, S. K. Bhadra, and G. P. Agrawal, Opt. Lett. 34, 2072 (2009).
[CrossRef]

J. Santhanama and G. P. Agrawal, Opt. Commun. 222, 413 (2003).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2006).

Akhmediev, N.

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef]

Arcizet, O.

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

Bache, M.

H. R. Guo, S. F. Wang, X. L. Zeng, and M. Bache, IEEE Photon. Technol. Lett. 25, 1928 (2013).
[CrossRef]

Bao, C. Y.

Bhadra, S. K.

Brasch, V.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[CrossRef]

Chembo, Y. K.

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

Christodoulides, D. N.

Coen, S.

de Sterke, C. M.

E. N. Tsoy and C. M. de Sterke, Phys. Rev. A 76, 043804 (2007).
[CrossRef]

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]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Erkintalo, M.

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.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Gorodetsky, M. L.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[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]

Grigoryan, V. S.

Guo, H. R.

H. R. Guo, S. F. Wang, X. L. Zeng, and M. Bache, IEEE Photon. Technol. Lett. 25, 1928 (2013).
[CrossRef]

S. F. Wang, J. G. Hu, H. R. Guo, and X. L. Zeng, Opt. Express 21, 3067 (2013).
[CrossRef]

Haelterman, M.

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

Henry Wen, Y.

Herr, T.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[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]

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]

Hu, J. G.

Ilchenko, V. S.

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 86, 013838 (2012).
[CrossRef]

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, Nat. Photonics 8, 145 (2014).
[CrossRef]

Karlsson, M.

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef]

Kimerling, L. C.

Kippenberg, T. J.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[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]

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]

Kondratiev, N. M.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[CrossRef]

Lamont, M. R. E.

Levy, J. S.

Liang, W.

Lipson, M.

Maleki, L.

A. B. Matsko, W. Liang, A. A. Savchenkov, and L. Maleki, Opt. Lett. 38, 525 (2013).
[CrossRef]

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 86, 013838 (2012).
[CrossRef]

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, and L. Maleki, Opt. Lett. 37, 43 (2012).
[CrossRef]

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

Matsko, A. B.

A. B. Matsko, W. Liang, A. A. Savchenkov, and L. Maleki, Opt. Lett. 38, 525 (2013).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Lett. 37, 43 (2012).
[CrossRef]

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

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 86, 013838 (2012).
[CrossRef]

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

Menyuk, C. R.

Michel, J.

Mu, J. W.

Mu, R. M.

Okawachi, Y.

Randle, H. G.

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]

Roy, S.

Saha, K.

Santhanama, J.

J. Santhanama and G. P. Agrawal, Opt. Commun. 222, 413 (2003).
[CrossRef]

Savchenkov, A. A.

A. B. Matsko, W. Liang, A. A. Savchenkov, and L. Maleki, Opt. Lett. 38, 525 (2013).
[CrossRef]

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

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 86, 013838 (2012).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, and L. Maleki, Opt. Lett. 37, 43 (2012).
[CrossRef]

A. B. Matsko, A. A. Savchenkov, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Opt. Lett. 36, 2845 (2011).
[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, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 86, 013838 (2012).
[CrossRef]

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]

Singh, V.

Siviloglou, G. A.

Sylvestre, T.

Trillo, S.

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

Tsoy, E. N.

E. N. Tsoy and C. M. de Sterke, Phys. Rev. A 76, 043804 (2007).
[CrossRef]

Wabnitz, S.

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, Nat. Photonics 8, 145 (2014).
[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]

Wang, S. F.

H. R. Guo, S. F. Wang, X. L. Zeng, and M. Bache, IEEE Photon. Technol. Lett. 25, 1928 (2013).
[CrossRef]

S. F. Wang, J. G. Hu, H. R. Guo, and X. L. Zeng, Opt. Express 21, 3067 (2013).
[CrossRef]

Wilken, T.

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

Yang, C. X.

Zeng, X. L.

S. F. Wang, J. G. Hu, H. R. Guo, and X. L. Zeng, Opt. Express 21, 3067 (2013).
[CrossRef]

H. R. Guo, S. F. Wang, X. L. Zeng, and M. Bache, IEEE Photon. Technol. Lett. 25, 1928 (2013).
[CrossRef]

Zhang, L.

IEEE Photon. Technol. Lett. (1)

H. R. Guo, S. F. Wang, X. L. Zeng, and M. Bache, IEEE Photon. Technol. Lett. 25, 1928 (2013).
[CrossRef]

J. Lightwave Technol. (1)

Nat. Photonics (2)

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. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[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. (2)

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

J. Santhanama and G. P. Agrawal, Opt. Commun. 222, 413 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (10)

Phys. Rev. A (5)

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

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

A. A. Savchenkov, A. B. Matsko, W. Liang, V. S. Ilchenko, D. Seidel, and L. Maleki, Phys. Rev. A 86, 013838 (2012).
[CrossRef]

N. Akhmediev and M. Karlsson, Phys. Rev. A 51, 2602 (1995).
[CrossRef]

E. N. Tsoy and C. M. de Sterke, Phys. Rev. A 76, 043804 (2007).
[CrossRef]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Science (1)

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

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2006).

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Figures (4)

Fig. 1.
Fig. 1.

Temporal evolution dynamics of intracavity solitons: (a) only β2 (2×102ps2/m). (b) β2 and β3 (4×104ps3/m). (c) β2 and β4 (16×106ps4/m). (d) β2 and β5 (8×108ps5/m). In all cases, Ein=1.0W, γ=1W1m1, tR=4.4ps, L=628μm, α=θ=0.009.

Fig. 2.
Fig. 2.

PM curves in different HOD region (β3, β4). The gray line in the inset denotes the boundary of different PM features. β2 is 2×102ps2/m; |β3|, |β4| are 4×104ps3/m and 8×106ps4/m, respectively. A, B, D, and E locate in (β3, β4) with different signs, and C is (β3, 0). All PM lines in different colors correspond with the colors of A, B, C, D, E in the inset.

Fig. 3.
Fig. 3.

Final steady-state (a) temporal and (b) spectral envelopes calculated based on same-color dispersion curves shown in Fig. 2.

Fig. 4.
Fig. 4.

Engineering the spectra of broadband frequency combs by tuning the dispersion profiles with (a) three and (b) four ZDWs. The corresponding group velocity profiles are (c) and (d) as well as the PM conditions in (e) and (f), respectively. (g) and (h) are the resultant comb spectra.

Equations (9)

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

tRE(t,τ)t=[αiδ0+iLk2βkk!(iτ)k+iγL|E|2]E(t,τ)+θEin,
Ep=+|E|2dτ,Tp=1Ep+τ|E|2dτ,
Ωp=i2Ep+(E*EτEE*τ)dτ.
dEpdt=0,dΩpdt=0,
dTpdt=k1(+Lβ2k+1(2k+1)!|kEτk|2dτ)+k1(+iLβ2k(2k)!(Θk(t,τ))dτ),
Θk(t,τ)=k1E*τk1kEτkk1Eτk1kE*τk.
F[kE(t,τ)τk]=(iω)kE˜(t,ω),k=1,2,3,,
[(iω)kE˜(t,ω)]t=0,
dTpdt=k1(+Lβ2k+1(2k+1)!|kEτk|2dτ).

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