Abstract

A mode-locked solid-state laser containing a birefringent element is shown to emit synchronously two frequency combs associated to the two polarization eigenstates of the cavity. An analytical model predicts the polarization evolution of the pulse train, which is determined by the adjustable intracavity birefringence. Experiments realized with a Nd:YAG laser passively mode locked by a semiconductor saturable absorber mirror are in perfect agreement with the model. Locking between the two combs arises for particular values of their frequency difference, e.g., half the repetition rate, and the pulse train polarization sequence is then governed by the relative overall phase offset of the two combs.

© 2012 Optical Society of America

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M. Brunel and M. Vallet, Opt. Lett. 33, 2524 (2008).
[CrossRef]

M. Yamaki, K. Hoki, H. Kono, and Y. Fujimura, Chem. Phys. 347, 272 (2008).
[CrossRef]

2006 (2)

K. Hartinger and R. A. Bartels, Opt. Lett. 31, 3526 (2006).
[CrossRef]

J. Javaloyes, J. Mulet, and S. Balle, Phys. Rev. Lett. 97, 163902 (2006).
[CrossRef]

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Q. Yang, Opt. Commun. 238, 329 (2004).
[CrossRef]

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U. Keller, Nature 424, 831 (2003).
[CrossRef]

2001 (1)

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, IEEE Photon. Technol. Lett. 13, 367 (2001).
[CrossRef]

2000 (2)

1998 (1)

1997 (3)

M. Vallet, M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 56, 5121 (1997).
[CrossRef]

S. T. Cundiff, B. C. Collings, and W. H. Knox, Opt. Express 1, 12 (1997).
[CrossRef]

M. Brunel, M. Vallet, G. Ropars, A. Le Floch, F. Bretenaker, G. Joulié, and J. C. Keromnes, Phys. Rev. A 55, 1391 (1997).
[CrossRef]

1996 (1)

G. W. Baxter, J. M. Dawes, P. Decker, and D. S. Knowles, IEEE Photon. Technol. Lett. 8, 1015 (1996).
[CrossRef]

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W. H. Loh, Y. Ozeki, and C. L. Tang, Appl. Phys. Lett. 56, 2613 (1990).
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1973 (1)

A. Le Floch and G. Stephan, C. R. Acad. Sci. B 277, 265 (1973).

1965 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

Akhmediev, N. N.

Alouini, M.

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, IEEE Photon. Technol. Lett. 13, 367 (2001).
[CrossRef]

Balle, S.

J. Javaloyes, J. Mulet, and S. Balle, Phys. Rev. Lett. 97, 163902 (2006).
[CrossRef]

Bartels, R. A.

Baxter, G. W.

G. W. Baxter, J. M. Dawes, P. Decker, and D. S. Knowles, IEEE Photon. Technol. Lett. 8, 1015 (1996).
[CrossRef]

Benazet, B.

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, IEEE Photon. Technol. Lett. 13, 367 (2001).
[CrossRef]

Bergman, K.

Bretenaker, F.

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, IEEE Photon. Technol. Lett. 13, 367 (2001).
[CrossRef]

M. Brunel, M. Vallet, G. Ropars, A. Le Floch, F. Bretenaker, G. Joulié, and J. C. Keromnes, Phys. Rev. A 55, 1391 (1997).
[CrossRef]

M. Vallet, M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 56, 5121 (1997).
[CrossRef]

Brunel, M.

M. Brunel and M. Vallet, Opt. Lett. 33, 2524 (2008).
[CrossRef]

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, IEEE Photon. Technol. Lett. 13, 367 (2001).
[CrossRef]

M. Brunel, M. Vallet, G. Ropars, A. Le Floch, F. Bretenaker, G. Joulié, and J. C. Keromnes, Phys. Rev. A 55, 1391 (1997).
[CrossRef]

M. Vallet, M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 56, 5121 (1997).
[CrossRef]

Buccafusca, O.

Chen, X.

Collings, B.

Collings, B. C.

Cundiff, S. T.

Dawes, J. M.

G. W. Baxter, J. M. Dawes, P. Decker, and D. S. Knowles, IEEE Photon. Technol. Lett. 8, 1015 (1996).
[CrossRef]

Decker, P.

G. W. Baxter, J. M. Dawes, P. Decker, and D. S. Knowles, IEEE Photon. Technol. Lett. 8, 1015 (1996).
[CrossRef]

Di Bin, P.

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, IEEE Photon. Technol. Lett. 13, 367 (2001).
[CrossRef]

Evtuhov, V.

Fujimura, Y.

M. Yamaki, K. Hoki, H. Kono, and Y. Fujimura, Chem. Phys. 347, 272 (2008).
[CrossRef]

Hartinger, K.

Haus, H. A.

H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

Hoki, K.

M. Yamaki, K. Hoki, H. Kono, and Y. Fujimura, Chem. Phys. 347, 272 (2008).
[CrossRef]

Javaloyes, J.

J. Javaloyes, J. Mulet, and S. Balle, Phys. Rev. Lett. 97, 163902 (2006).
[CrossRef]

Joulié, G.

M. Brunel, M. Vallet, G. Ropars, A. Le Floch, F. Bretenaker, G. Joulié, and J. C. Keromnes, Phys. Rev. A 55, 1391 (1997).
[CrossRef]

Keller, U.

U. Keller, Nature 424, 831 (2003).
[CrossRef]

Keromnes, J. C.

M. Brunel, M. Vallet, G. Ropars, A. Le Floch, F. Bretenaker, G. Joulié, and J. C. Keromnes, Phys. Rev. A 55, 1391 (1997).
[CrossRef]

Knowles, D. S.

G. W. Baxter, J. M. Dawes, P. Decker, and D. S. Knowles, IEEE Photon. Technol. Lett. 8, 1015 (1996).
[CrossRef]

Knox, W. H.

Kono, H.

M. Yamaki, K. Hoki, H. Kono, and Y. Fujimura, Chem. Phys. 347, 272 (2008).
[CrossRef]

Le Floch, A.

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, IEEE Photon. Technol. Lett. 13, 367 (2001).
[CrossRef]

M. Vallet, M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 56, 5121 (1997).
[CrossRef]

M. Brunel, M. Vallet, G. Ropars, A. Le Floch, F. Bretenaker, G. Joulié, and J. C. Keromnes, Phys. Rev. A 55, 1391 (1997).
[CrossRef]

A. Le Floch and G. Stephan, C. R. Acad. Sci. B 277, 265 (1973).

Loh, W. H.

W. H. Loh, Y. Ozeki, and C. L. Tang, Appl. Phys. Lett. 56, 2613 (1990).
[CrossRef]

Mulet, J.

J. Javaloyes, J. Mulet, and S. Balle, Phys. Rev. Lett. 97, 163902 (2006).
[CrossRef]

Ozeki, Y.

W. H. Loh, Y. Ozeki, and C. L. Tang, Appl. Phys. Lett. 56, 2613 (1990).
[CrossRef]

Ropars, G.

M. Brunel, M. Vallet, G. Ropars, A. Le Floch, F. Bretenaker, G. Joulié, and J. C. Keromnes, Phys. Rev. A 55, 1391 (1997).
[CrossRef]

M. Vallet, M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 56, 5121 (1997).
[CrossRef]

Siegman, A. E.

Smirl, A. L.

Soto-Crespo, J. M.

Stephan, G.

A. Le Floch and G. Stephan, C. R. Acad. Sci. B 277, 265 (1973).

Tam, H. Y.

Tang, C. L.

W. H. Loh, Y. Ozeki, and C. L. Tang, Appl. Phys. Lett. 56, 2613 (1990).
[CrossRef]

Tang, D. Y.

Thony, P.

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, IEEE Photon. Technol. Lett. 13, 367 (2001).
[CrossRef]

Vallet, M.

M. Brunel and M. Vallet, Opt. Lett. 33, 2524 (2008).
[CrossRef]

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, IEEE Photon. Technol. Lett. 13, 367 (2001).
[CrossRef]

M. Brunel, M. Vallet, G. Ropars, A. Le Floch, F. Bretenaker, G. Joulié, and J. C. Keromnes, Phys. Rev. A 55, 1391 (1997).
[CrossRef]

M. Vallet, M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 56, 5121 (1997).
[CrossRef]

Wu, X.

Yamaki, M.

M. Yamaki, K. Hoki, H. Kono, and Y. Fujimura, Chem. Phys. 347, 272 (2008).
[CrossRef]

Yang, Q.

Q. Yang, Opt. Commun. 238, 329 (2004).
[CrossRef]

Zhang, H.

Zhao, L. M.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

W. H. Loh, Y. Ozeki, and C. L. Tang, Appl. Phys. Lett. 56, 2613 (1990).
[CrossRef]

C. R. Acad. Sci. B (1)

A. Le Floch and G. Stephan, C. R. Acad. Sci. B 277, 265 (1973).

Chem. Phys. (1)

M. Yamaki, K. Hoki, H. Kono, and Y. Fujimura, Chem. Phys. 347, 272 (2008).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

G. W. Baxter, J. M. Dawes, P. Decker, and D. S. Knowles, IEEE Photon. Technol. Lett. 8, 1015 (1996).
[CrossRef]

M. Alouini, B. Benazet, M. Vallet, M. Brunel, P. Di Bin, F. Bretenaker, A. Le Floch, and P. Thony, IEEE Photon. Technol. Lett. 13, 367 (2001).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (1)

U. Keller, Nature 424, 831 (2003).
[CrossRef]

Opt. Commun. (1)

Q. Yang, Opt. Commun. 238, 329 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (2)

M. Vallet, M. Brunel, G. Ropars, A. Le Floch, and F. Bretenaker, Phys. Rev. A 56, 5121 (1997).
[CrossRef]

M. Brunel, M. Vallet, G. Ropars, A. Le Floch, F. Bretenaker, G. Joulié, and J. C. Keromnes, Phys. Rev. A 55, 1391 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

J. Javaloyes, J. Mulet, and S. Balle, Phys. Rev. Lett. 97, 163902 (2006).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Experimental laser and detection setup. (b) Schematic frequency combs. (c) Schematic polarization sequences emitted when δν=frep/2 and δν=frep/8.

Fig. 2.
Fig. 2.

Experimental eigenstate beats Ex+Ey2 (red), and ExEy2 (blue) for (a) δν0, (b) δν=frep/4, and (c) δν=7/15frep.

Fig. 3.
Fig. 3.

Experimental FFT spectrum of the laser output, when δνfrep/2. (a) δν outside the locking range, (b) δν inside the locking range, and (c) resulting frep/2-periodic spectrum.

Fig. 4.
Fig. 4.

Experimental eigenstate beats Ex+Ey2 (red), and ExEy2 (blue), when the comb frequency shift δν is locked at frep/2. (a) Ψ=0 and (b) Ψ=0.39rad.

Equations (3)

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

[Ex(t)Ey(t)]=ei2πνxt[1ei(2πδνt+ψ)]pA(tpfrep).
J⃗p=12[1exp(i(2πpδνfrep+ψ))].
J⃗p=12[1(1)pexp(iψ)].

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