Abstract

A technique is presented for narrowing the spectral linewidth of microwave signals generated photonically by heterodyning a pair of vertical-cavity surface-emitting lasers forming an extended optically coupled cavity. The experimentally demonstrated linewidth reduction, by as much as a factor of 104—to less than 10 kHz in microwave frequencies up to a couple of gigahertz—is approximately ten times that expected with conventional line-narrowing techniques such as optical feedback. An interpretation is given in terms of mode locking in pairs of optically coupled lasers as a first demonstration in the frequency domain of lag synchronization of coupled oscillators. The results of theoretical modeling agree well with the experimental results.

© 2005 Optical Society of America

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References

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  1. S. Gevorgian, L. R. Pendrill, and A. Alping, in Microwave Photonics from Components to Applications and Systems, A. Vilcot, B. Cabon, and J. Chazelas, eds. (Kluwer Academic, Boston, Mass., 2003).
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    [CrossRef]
  3. R. W. Tkach and A. R. Chraplyvy, J. Lightwave Technol. LT-4, 1655 (1986).
    [CrossRef]
  4. S. Eriksson and Å. M. Lindberg, J. Opt. B: Quantum Semiclassic. Opt. 4, 149 (2002).
    [CrossRef]
  5. C. Mirasso, M. Kolesik, M. Matus, J. White, and J. Moloney, Phys. Rev. A 65, 013805 (2001).
    [CrossRef]
  6. J. Mulet, C. Mirasso, T. Heil, and I. Fischer, J. Opt. B: Quantum Semiclassic. Opt. 6, 97 (2003).
    [CrossRef]
  7. J. Y. Law and G. P. Agrawal, J. Opt. Soc. Am. B 15, 562 (1997).
    [CrossRef]
  8. N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, Opt. Lett. 28, 1677 (2003).
    [CrossRef] [PubMed]
  9. R. Holwarth, M. Zimmermann, Th. Udem, and T. W. Hänsch, IEEE J. Quantum Electron. 37, 1493 (2001).
    [CrossRef]
  10. K. E. Razavi and P. A. Davies, IEE Proc. Optoelectron. 145, 159 (1998).
    [CrossRef]
  11. X. S. Yao and L. Maleki, Opt. Lett. 22, 1867 (1997).
    [CrossRef]
  12. H.-C. Chang, X. Cao, U. K. Mishra, and R. A. York, IEEE Trans. Microwave Theory Tech. 45, 604 (1997).
    [CrossRef]

2003 (2)

N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, Opt. Lett. 28, 1677 (2003).
[CrossRef] [PubMed]

J. Mulet, C. Mirasso, T. Heil, and I. Fischer, J. Opt. B: Quantum Semiclassic. Opt. 6, 97 (2003).
[CrossRef]

2002 (1)

S. Eriksson and Å. M. Lindberg, J. Opt. B: Quantum Semiclassic. Opt. 4, 149 (2002).
[CrossRef]

2001 (2)

C. Mirasso, M. Kolesik, M. Matus, J. White, and J. Moloney, Phys. Rev. A 65, 013805 (2001).
[CrossRef]

R. Holwarth, M. Zimmermann, Th. Udem, and T. W. Hänsch, IEEE J. Quantum Electron. 37, 1493 (2001).
[CrossRef]

1998 (1)

K. E. Razavi and P. A. Davies, IEE Proc. Optoelectron. 145, 159 (1998).
[CrossRef]

1997 (4)

X. S. Yao and L. Maleki, Opt. Lett. 22, 1867 (1997).
[CrossRef]

H.-C. Chang, X. Cao, U. K. Mishra, and R. A. York, IEEE Trans. Microwave Theory Tech. 45, 604 (1997).
[CrossRef]

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

J. Y. Law and G. P. Agrawal, J. Opt. Soc. Am. B 15, 562 (1997).
[CrossRef]

1986 (1)

R. W. Tkach and A. R. Chraplyvy, J. Lightwave Technol. LT-4, 1655 (1986).
[CrossRef]

Agrawal, G. P.

Alping, A.

S. Gevorgian, L. R. Pendrill, and A. Alping, in Microwave Photonics from Components to Applications and Systems, A. Vilcot, B. Cabon, and J. Chazelas, eds. (Kluwer Academic, Boston, Mass., 2003).

Cao, X.

H.-C. Chang, X. Cao, U. K. Mishra, and R. A. York, IEEE Trans. Microwave Theory Tech. 45, 604 (1997).
[CrossRef]

Chang, H.-C.

H.-C. Chang, X. Cao, U. K. Mishra, and R. A. York, IEEE Trans. Microwave Theory Tech. 45, 604 (1997).
[CrossRef]

Chraplyvy, A. R.

R. W. Tkach and A. R. Chraplyvy, J. Lightwave Technol. LT-4, 1655 (1986).
[CrossRef]

Davies, P. A.

K. E. Razavi and P. A. Davies, IEE Proc. Optoelectron. 145, 159 (1998).
[CrossRef]

Eriksson, S.

S. Eriksson and Å. M. Lindberg, J. Opt. B: Quantum Semiclassic. Opt. 4, 149 (2002).
[CrossRef]

Fischer, I.

J. Mulet, C. Mirasso, T. Heil, and I. Fischer, J. Opt. B: Quantum Semiclassic. Opt. 6, 97 (2003).
[CrossRef]

Fujiwara, N.

Gevorgian, S.

S. Gevorgian, L. R. Pendrill, and A. Alping, in Microwave Photonics from Components to Applications and Systems, A. Vilcot, B. Cabon, and J. Chazelas, eds. (Kluwer Academic, Boston, Mass., 2003).

Hänsch, T. W.

R. Holwarth, M. Zimmermann, Th. Udem, and T. W. Hänsch, IEEE J. Quantum Electron. 37, 1493 (2001).
[CrossRef]

Heil, T.

J. Mulet, C. Mirasso, T. Heil, and I. Fischer, J. Opt. B: Quantum Semiclassic. Opt. 6, 97 (2003).
[CrossRef]

Holwarth, R.

R. Holwarth, M. Zimmermann, Th. Udem, and T. W. Hänsch, IEEE J. Quantum Electron. 37, 1493 (2001).
[CrossRef]

Kolesik, M.

C. Mirasso, M. Kolesik, M. Matus, J. White, and J. Moloney, Phys. Rev. A 65, 013805 (2001).
[CrossRef]

Kurths, J.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

Law, J. Y.

Lindberg, Å. M.

S. Eriksson and Å. M. Lindberg, J. Opt. B: Quantum Semiclassic. Opt. 4, 149 (2002).
[CrossRef]

Maleki, L.

Matus, M.

C. Mirasso, M. Kolesik, M. Matus, J. White, and J. Moloney, Phys. Rev. A 65, 013805 (2001).
[CrossRef]

Mirasso, C.

J. Mulet, C. Mirasso, T. Heil, and I. Fischer, J. Opt. B: Quantum Semiclassic. Opt. 6, 97 (2003).
[CrossRef]

C. Mirasso, M. Kolesik, M. Matus, J. White, and J. Moloney, Phys. Rev. A 65, 013805 (2001).
[CrossRef]

Mishra, U. K.

H.-C. Chang, X. Cao, U. K. Mishra, and R. A. York, IEEE Trans. Microwave Theory Tech. 45, 604 (1997).
[CrossRef]

Moloney, J.

C. Mirasso, M. Kolesik, M. Matus, J. White, and J. Moloney, Phys. Rev. A 65, 013805 (2001).
[CrossRef]

Mulet, J.

J. Mulet, C. Mirasso, T. Heil, and I. Fischer, J. Opt. B: Quantum Semiclassic. Opt. 6, 97 (2003).
[CrossRef]

Ohtsubo, J.

Pendrill, L. R.

S. Gevorgian, L. R. Pendrill, and A. Alping, in Microwave Photonics from Components to Applications and Systems, A. Vilcot, B. Cabon, and J. Chazelas, eds. (Kluwer Academic, Boston, Mass., 2003).

Pikovsky, A. S.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

Razavi, K. E.

K. E. Razavi and P. A. Davies, IEE Proc. Optoelectron. 145, 159 (1998).
[CrossRef]

Rosenblum, M. G.

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

Takiguchi, Y.

Tkach, R. W.

R. W. Tkach and A. R. Chraplyvy, J. Lightwave Technol. LT-4, 1655 (1986).
[CrossRef]

Udem, Th.

R. Holwarth, M. Zimmermann, Th. Udem, and T. W. Hänsch, IEEE J. Quantum Electron. 37, 1493 (2001).
[CrossRef]

White, J.

C. Mirasso, M. Kolesik, M. Matus, J. White, and J. Moloney, Phys. Rev. A 65, 013805 (2001).
[CrossRef]

Yao, X. S.

York, R. A.

H.-C. Chang, X. Cao, U. K. Mishra, and R. A. York, IEEE Trans. Microwave Theory Tech. 45, 604 (1997).
[CrossRef]

Zimmermann, M.

R. Holwarth, M. Zimmermann, Th. Udem, and T. W. Hänsch, IEEE J. Quantum Electron. 37, 1493 (2001).
[CrossRef]

IEE Proc. Optoelectron. (1)

K. E. Razavi and P. A. Davies, IEE Proc. Optoelectron. 145, 159 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. Holwarth, M. Zimmermann, Th. Udem, and T. W. Hänsch, IEEE J. Quantum Electron. 37, 1493 (2001).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

H.-C. Chang, X. Cao, U. K. Mishra, and R. A. York, IEEE Trans. Microwave Theory Tech. 45, 604 (1997).
[CrossRef]

J. Lightwave Technol. (1)

R. W. Tkach and A. R. Chraplyvy, J. Lightwave Technol. LT-4, 1655 (1986).
[CrossRef]

J. Opt. B: Quantum Semiclassic. Opt. (2)

S. Eriksson and Å. M. Lindberg, J. Opt. B: Quantum Semiclassic. Opt. 4, 149 (2002).
[CrossRef]

J. Mulet, C. Mirasso, T. Heil, and I. Fischer, J. Opt. B: Quantum Semiclassic. Opt. 6, 97 (2003).
[CrossRef]

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

Opt. Lett. (2)

Phys. Rev. A (1)

C. Mirasso, M. Kolesik, M. Matus, J. White, and J. Moloney, Phys. Rev. A 65, 013805 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997).
[CrossRef]

Other (1)

S. Gevorgian, L. R. Pendrill, and A. Alping, in Microwave Photonics from Components to Applications and Systems, A. Vilcot, B. Cabon, and J. Chazelas, eds. (Kluwer Academic, Boston, Mass., 2003).

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Figures (2)

Fig. 1
Fig. 1

Experimental setup for optical line narrowing of mutually coupled VCSELs: AC, alternating current; FSR, free spectral range.

Fig. 2
Fig. 2

Heterodyne spectra of a pair of optically coupled VCSELs: (a) theory (coupling rate of κ=0.5/ns, injection current of I1.2ITH, frequency resolution of 880 kHz) and (b) experiment (resolution bandwidth of 1 MHz, sweep time of 50 ms, single sweep).

Equations (1)

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I1,2t=G1,2-γI1,2t+2κI1,2tI2,1t-τ1/2×cosϕ2,1t-τ-ϕ1,2t+ϕ0+RSP+FIt,ϕ1,2t=α2G1,2-γ+κI2,1t-τI1,2t1/2×cosϕ2,1t-τ-ϕ1,2t+ϕ0+FΦt,dn1,2dt=J1,2q-ntτe-G1,2I1,2t+Fnt,

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