Abstract

We show that when subjected to high gain, delay-line optoelectronic oscillators can display a strongly multimode behavior depending on the feedback bandwidth. We found that this dynamical regime may arise when the bandwidth of the feedback loop spans over several hundreds of ring cavity-modes, and also when the oscillator is switched on abruptly. Such a persistent multimode regime is detrimental to the performances of this system which is normally intended to provide ultra-pure and single-mode microwaves. We experimentally evidence this multimode dynamics and we propose a theory to explain this undesirable feature.

© 2008 Optical Society of America

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References

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  1. X. S. Yao and L. Maleki, "Optoelectronic microwave oscillator," J. Opt. Soc. Am. B 13,1725-1735 (1996).
    [CrossRef]
  2. L. M. Narducci,  et al, "Mode-mode competition and unstable behavior in a homogeneously broadened ring laser," Phys. Rev. A 33,1842-1854 (1986).
    [CrossRef] [PubMed]
  3. K. A. Winick, "Longitudinal mode competition in chirped grating distributed feedback lasers," IEEE J. Quantum Electron. 35,1402-1411 (1999).
    [CrossRef]
  4. A. M. Yacomotti,  et al, "Dynamics of multimode semiconductor lasers," Phys. Rev. A 69, 053816-1-9 (2004).
    [CrossRef]
  5. J. L. Font, R. Vilaseca, F. Prati, and E. Roldán, "Coexistence of single-mode and multi-longitudinal mode emission in the ring laser model," Opt. Commun. 261,336-341 (2006).
    [CrossRef]
  6. T. Voigt,  et al, "Experimental investigation of RiskenNummedalGrahamHaken laser instability in fiber ring lasers," Appl. Phys. B 79,175-183 (2004).
    [CrossRef]
  7. C. Y. Wang,  et al, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802(R)-1-4 (2007).
    [CrossRef]
  8. Y. Kouomou Chembo, L. Larger, H. Tavernier, R. Bendoula, E. Rubiola, and P. Colet, "Dynamic instabilities of microwaves generated with optoelectronic oscillators," Opt. Lett. 32,2571-2573 (2007).
    [CrossRef]
  9. Y. Kouomou Chembo, L. Larger, and P. Colet, "Nonlinear dynamics and spectral stability of optoelectronic microwave oscillators," IEEE J. Quantum Electron. (in press).

2007 (2)

2006 (1)

J. L. Font, R. Vilaseca, F. Prati, and E. Roldán, "Coexistence of single-mode and multi-longitudinal mode emission in the ring laser model," Opt. Commun. 261,336-341 (2006).
[CrossRef]

2004 (2)

T. Voigt,  et al, "Experimental investigation of RiskenNummedalGrahamHaken laser instability in fiber ring lasers," Appl. Phys. B 79,175-183 (2004).
[CrossRef]

A. M. Yacomotti,  et al, "Dynamics of multimode semiconductor lasers," Phys. Rev. A 69, 053816-1-9 (2004).
[CrossRef]

1999 (1)

K. A. Winick, "Longitudinal mode competition in chirped grating distributed feedback lasers," IEEE J. Quantum Electron. 35,1402-1411 (1999).
[CrossRef]

1996 (1)

1986 (1)

L. M. Narducci,  et al, "Mode-mode competition and unstable behavior in a homogeneously broadened ring laser," Phys. Rev. A 33,1842-1854 (1986).
[CrossRef] [PubMed]

Bendoula, R.

Colet, P.

Y. Kouomou Chembo, L. Larger, H. Tavernier, R. Bendoula, E. Rubiola, and P. Colet, "Dynamic instabilities of microwaves generated with optoelectronic oscillators," Opt. Lett. 32,2571-2573 (2007).
[CrossRef]

Y. Kouomou Chembo, L. Larger, and P. Colet, "Nonlinear dynamics and spectral stability of optoelectronic microwave oscillators," IEEE J. Quantum Electron. (in press).

Font, J. L.

J. L. Font, R. Vilaseca, F. Prati, and E. Roldán, "Coexistence of single-mode and multi-longitudinal mode emission in the ring laser model," Opt. Commun. 261,336-341 (2006).
[CrossRef]

Kouomou Chembo, Y.

Y. Kouomou Chembo, L. Larger, H. Tavernier, R. Bendoula, E. Rubiola, and P. Colet, "Dynamic instabilities of microwaves generated with optoelectronic oscillators," Opt. Lett. 32,2571-2573 (2007).
[CrossRef]

Y. Kouomou Chembo, L. Larger, and P. Colet, "Nonlinear dynamics and spectral stability of optoelectronic microwave oscillators," IEEE J. Quantum Electron. (in press).

Larger, L.

Y. Kouomou Chembo, L. Larger, H. Tavernier, R. Bendoula, E. Rubiola, and P. Colet, "Dynamic instabilities of microwaves generated with optoelectronic oscillators," Opt. Lett. 32,2571-2573 (2007).
[CrossRef]

Y. Kouomou Chembo, L. Larger, and P. Colet, "Nonlinear dynamics and spectral stability of optoelectronic microwave oscillators," IEEE J. Quantum Electron. (in press).

Maleki, L.

Narducci, L. M.

L. M. Narducci,  et al, "Mode-mode competition and unstable behavior in a homogeneously broadened ring laser," Phys. Rev. A 33,1842-1854 (1986).
[CrossRef] [PubMed]

Prati, F.

J. L. Font, R. Vilaseca, F. Prati, and E. Roldán, "Coexistence of single-mode and multi-longitudinal mode emission in the ring laser model," Opt. Commun. 261,336-341 (2006).
[CrossRef]

Roldán, E.

J. L. Font, R. Vilaseca, F. Prati, and E. Roldán, "Coexistence of single-mode and multi-longitudinal mode emission in the ring laser model," Opt. Commun. 261,336-341 (2006).
[CrossRef]

Rubiola, E.

Tavernier, H.

Vilaseca, R.

J. L. Font, R. Vilaseca, F. Prati, and E. Roldán, "Coexistence of single-mode and multi-longitudinal mode emission in the ring laser model," Opt. Commun. 261,336-341 (2006).
[CrossRef]

Voigt, T.

T. Voigt,  et al, "Experimental investigation of RiskenNummedalGrahamHaken laser instability in fiber ring lasers," Appl. Phys. B 79,175-183 (2004).
[CrossRef]

Wang, C. Y.

C. Y. Wang,  et al, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802(R)-1-4 (2007).
[CrossRef]

Winick, K. A.

K. A. Winick, "Longitudinal mode competition in chirped grating distributed feedback lasers," IEEE J. Quantum Electron. 35,1402-1411 (1999).
[CrossRef]

Yacomotti, A. M.

A. M. Yacomotti,  et al, "Dynamics of multimode semiconductor lasers," Phys. Rev. A 69, 053816-1-9 (2004).
[CrossRef]

Yao, X. S.

Appl. Phys. B (1)

T. Voigt,  et al, "Experimental investigation of RiskenNummedalGrahamHaken laser instability in fiber ring lasers," Appl. Phys. B 79,175-183 (2004).
[CrossRef]

IEEE J. Quantum Electron. (2)

Y. Kouomou Chembo, L. Larger, and P. Colet, "Nonlinear dynamics and spectral stability of optoelectronic microwave oscillators," IEEE J. Quantum Electron. (in press).

K. A. Winick, "Longitudinal mode competition in chirped grating distributed feedback lasers," IEEE J. Quantum Electron. 35,1402-1411 (1999).
[CrossRef]

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

Opt. Commun. (1)

J. L. Font, R. Vilaseca, F. Prati, and E. Roldán, "Coexistence of single-mode and multi-longitudinal mode emission in the ring laser model," Opt. Commun. 261,336-341 (2006).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (3)

C. Y. Wang,  et al, "Coherent instabilities in a semiconductor laser with fast gain recovery," Phys. Rev. A 75, 031802(R)-1-4 (2007).
[CrossRef]

L. M. Narducci,  et al, "Mode-mode competition and unstable behavior in a homogeneously broadened ring laser," Phys. Rev. A 33,1842-1854 (1986).
[CrossRef] [PubMed]

A. M. Yacomotti,  et al, "Dynamics of multimode semiconductor lasers," Phys. Rev. A 69, 053816-1-9 (2004).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setup for the single-loop OEO.

Fig. 2.
Fig. 2.

Experimental radio-frequency spectrum of the OEO after 30 seconds (dashed line) and after 2 hours (continuous line), in a 10 MHz window. The modal competition can be considered in this case as permanent.

Fig. 3.
Fig. 3.

Numerical simulation of the radio-frequency spectrum of the OEO after 1 s, in a 10 MHz window. The thin line represents the result of the simulation, while the thick line represents an averaging of the spectrum with a 125 kHz resolution, in order to facilitate comparison with the oscilloscope display of Fig. 2.

Equations (22)

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x + 1 ΔΩ dx dt + Ω 0 2 ΔΩ t 0 t x ( s ) ds = β cos 2 [ x ( t T ) + ϕ ] ,
𝒜 . = μ 𝒜 + 2 μ γ J c 1 [ 2 𝒜 T ] 𝒜 T ,
x ( t ) = k = 0 3 ε k x k ( T 0 , T 1 , T 2 , T 3 ) + 𝒪 ( ε 4 ) ,
𝒜 ( t ) = k = 0 3 ε k 𝒜 k ( T 0 , T 1 , T 2 , T 3 ) + 𝒪 ( ε 4 ) ,
D 0 2 u 0 + Ω 0 2 u 0 = 0
D 0 2 u 1 + Ω 0 2 u 1 = 2 D 0 D 1 u 0 2 μ ̂ D 0 u 0
+ 2 μ ̂ γ J 1 [ 2 𝒜 0 T ] × cos [ Ω 0 T 0 + ψ T ]
D 0 2 u 2 + Ω 0 2 u 2 = 2 D 0 D 1 u 1 ( D 1 2 + 2 D 0 D 2 ) u 0 2 μ ̂ ( D 0 u 1 + D 1 u 0 )
+ 2 μ ̂ γ { 2 𝒜 1 T J 1 [ 2 𝒜 0 T ] } × cos [ Ω 0 T 0 + ψ T ]
D 0 2 u 3 + Ω 0 2 u 3 = 2 D 0 D 1 u 2 ( D 1 2 + 2 D 0 D 2 ) u 1
2 ( D 0 D 3 + D 1 D 2 ) u 0 2 μ ̂ ( D 0 u 2 + D 1 u 1 + D 2 u 0 )
+ 2 μ ̂ γ { 2 𝒜 2 T J 1 [ 2 𝒜 0 T ] + 2 𝒜 1 T 2 J 1 [ 2 𝒜 0 T ] }
× cos [ Ω 0 T 0 + ψ T ]
x 0 = 1 2 𝒜 ( T 1 , T 2 , T 3 ) e i Ω 0 T 0 + 1 2 𝒜 * ( T 1 , T 2 , T 3 ) e i Ω 0 T 0 ,
𝒜 ( T 1 , T 2 , T 3 ) = A ( T 1 ) n = N N a n ( T 3 ) e in Ω ̂ T T 2 ,
𝒜 0 = Ω 0 A N N a n e in Ω ̂ T T 2
𝒜 1 = 1 2 A i ( A * T 1 A A * A T 1 ) N N a n e i n Ω ̂ T T 2
𝒜 2 = 1 2 Ω 0 A A T 1 2 N N a n e in Ω ̂ T T 2 + 1 2 Ω ̂ T A
× [ N N a n e in Ω ̂ T T 2 N N n a n * e in Ω ̂ T T 2 + c . c . ] [ N N a n e in Ω ̂ T T 2 ] ,
A T 1 = μ ̂ A + 2 μ ̂ γ J 1 [ 2 𝒜 0 T ] [ 2 𝒜 0 T ] A T .
a n T 3 = in Ω ̂ T Ω 0 { μ ̂ + 1 A A T 1 } a n
+ 2 μ ̂ γ A T A a n × { 2 𝒜 2 T J 1 [ 2 𝒜 0 T ] + 2 𝒜 1 T 2 J 1 [ 2 𝒜 0 T ] } [ 2 A T · N N a n e in Ω ̂ T T 2 ] ,

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