Abstract

We show numerically that a synchronously pumped optical parametric oscillator can show giant noise amplification of the order of 109. We use pseudospectra to identify the parameter region for giant noise amplification and to estimate its magnitude.

© 2009 Optical Society of America

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References

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  1. A. J. Scroggie, G.-L. Oppo, and G. D'Alessandro, J. Opt. Soc. Am. B 17, 84 (2000).
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  2. J. D. V. Khaydarov, J. H. Andrews, and K. D. Singer, J. Opt. Soc. Am. B 12, 2199 (1995).
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  3. L. Lefort, K. Puech, S. D. Butterworth, Y. P. Svirko, and D. C. Hanna, Opt. Lett. 24, 28 (1999).
    [CrossRef]
  4. J. Khurgin, J. M. Melkonian, A. Godard, M. Lefebvre, and E. Rosencher, Opt. Express 16, 4804 (2008).
    [CrossRef] [PubMed]
  5. R. Zambrini, S. M. Barnett, P. Colet, and M. San Miguel, Phys. Rev. A 65, 023813 (2002).
    [CrossRef]
  6. L. N. Trefethen and M. Embree, Spectra and Pseudospectra (Princeton U. Press, 2005).
  7. A. Haché, G. R. Allan, and H. M. van Driel, J. Opt. Soc. Am. B 12, 2209 (1995).
    [CrossRef]
  8. F. Papoff, G. D'Alessandro, and G.-L. Oppo, Phys. Rev. Lett. 100, 123905 (2008).
    [CrossRef] [PubMed]
  9. K. Petermann, IEEE J. Quantum Electron. 15, 566 (1979).
    [CrossRef]
  10. W. J. Firth and A. M. Yao, Phys. Rev. Lett. 95, 073903 (2005).
    [CrossRef] [PubMed]
  11. L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, Science 261, 578 (1993).
    [CrossRef] [PubMed]
  12. S. D. Butterworth, V. Pruneri, and D. C. Hanna, Opt. Lett. 21, 1345 (1996).
    [CrossRef] [PubMed]

2008 (2)

2005 (1)

W. J. Firth and A. M. Yao, Phys. Rev. Lett. 95, 073903 (2005).
[CrossRef] [PubMed]

2002 (1)

R. Zambrini, S. M. Barnett, P. Colet, and M. San Miguel, Phys. Rev. A 65, 023813 (2002).
[CrossRef]

2000 (1)

1999 (1)

1996 (1)

1995 (2)

1993 (1)

L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, Science 261, 578 (1993).
[CrossRef] [PubMed]

1979 (1)

K. Petermann, IEEE J. Quantum Electron. 15, 566 (1979).
[CrossRef]

Allan, G. R.

Andrews, J. H.

Barnett, S. M.

R. Zambrini, S. M. Barnett, P. Colet, and M. San Miguel, Phys. Rev. A 65, 023813 (2002).
[CrossRef]

Butterworth, S. D.

Colet, P.

R. Zambrini, S. M. Barnett, P. Colet, and M. San Miguel, Phys. Rev. A 65, 023813 (2002).
[CrossRef]

D'Alessandro, G.

F. Papoff, G. D'Alessandro, and G.-L. Oppo, Phys. Rev. Lett. 100, 123905 (2008).
[CrossRef] [PubMed]

A. J. Scroggie, G.-L. Oppo, and G. D'Alessandro, J. Opt. Soc. Am. B 17, 84 (2000).
[CrossRef]

Driscoll, T. A.

L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, Science 261, 578 (1993).
[CrossRef] [PubMed]

Embree, M.

L. N. Trefethen and M. Embree, Spectra and Pseudospectra (Princeton U. Press, 2005).

Firth, W. J.

W. J. Firth and A. M. Yao, Phys. Rev. Lett. 95, 073903 (2005).
[CrossRef] [PubMed]

Godard, A.

Haché, A.

Hanna, D. C.

Khaydarov, J. D. V.

Khurgin, J.

Lefebvre, M.

Lefort, L.

Melkonian, J. M.

Oppo, G.-L.

F. Papoff, G. D'Alessandro, and G.-L. Oppo, Phys. Rev. Lett. 100, 123905 (2008).
[CrossRef] [PubMed]

A. J. Scroggie, G.-L. Oppo, and G. D'Alessandro, J. Opt. Soc. Am. B 17, 84 (2000).
[CrossRef]

Papoff, F.

F. Papoff, G. D'Alessandro, and G.-L. Oppo, Phys. Rev. Lett. 100, 123905 (2008).
[CrossRef] [PubMed]

Petermann, K.

K. Petermann, IEEE J. Quantum Electron. 15, 566 (1979).
[CrossRef]

Pruneri, V.

Puech, K.

Reddy, S. C.

L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, Science 261, 578 (1993).
[CrossRef] [PubMed]

Rosencher, E.

San Miguel, M.

R. Zambrini, S. M. Barnett, P. Colet, and M. San Miguel, Phys. Rev. A 65, 023813 (2002).
[CrossRef]

Scroggie, A. J.

Singer, K. D.

Svirko, Y. P.

Trefethen, A. E.

L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, Science 261, 578 (1993).
[CrossRef] [PubMed]

Trefethen, L. N.

L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, Science 261, 578 (1993).
[CrossRef] [PubMed]

L. N. Trefethen and M. Embree, Spectra and Pseudospectra (Princeton U. Press, 2005).

van Driel, H. M.

Yao, A. M.

W. J. Firth and A. M. Yao, Phys. Rev. Lett. 95, 073903 (2005).
[CrossRef] [PubMed]

Zambrini, R.

R. Zambrini, S. M. Barnett, P. Colet, and M. San Miguel, Phys. Rev. A 65, 023813 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Petermann, IEEE J. Quantum Electron. 15, 566 (1979).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (1)

R. Zambrini, S. M. Barnett, P. Colet, and M. San Miguel, Phys. Rev. A 65, 023813 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

F. Papoff, G. D'Alessandro, and G.-L. Oppo, Phys. Rev. Lett. 100, 123905 (2008).
[CrossRef] [PubMed]

W. J. Firth and A. M. Yao, Phys. Rev. Lett. 95, 073903 (2005).
[CrossRef] [PubMed]

Science (1)

L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, Science 261, 578 (1993).
[CrossRef] [PubMed]

Other (1)

L. N. Trefethen and M. Embree, Spectra and Pseudospectra (Princeton U. Press, 2005).

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Figures (2)

Fig. 1
Fig. 1

Noisy leading edge of the signal pulse (dashed curve) arrives at the crystal when the pump pulse (solid curve) is very large and is amplified together with the idler (dotted-dashed curve). Losses during propagation quench the nonamplified tail of the signal pulse.

Fig. 2
Fig. 2

Numerical pseudospectra of L and corresponding evolution of the signal field for two values of the pump amplitude P a and detuning τ c . (A) and (B) Eigenvalues of L (dots), the unit circle (thick circle), and boundaries of Λ ϵ ( L ) for ϵ = { 10 0 , , 10 10 } in the complex plane. (C) and (D) Corresponding signal amplitude, obtained by numerically integrating Eq. (1), as a function of round trip and τ. The (dimensionless) parameter values correspond to those for lithium niobate [1, 3]; v j 1 = { 1.0166 , 1 , 1.0049 } , β j = { 1.29 , 0.343 , 1.47 } × 10 7 , ρ j = { 0 , 0 , 0 } , Δ k = 0 , θ = 0 , R = 0.37 , and τ p = 0.0244 . A δ-correlated noise with amplitude A j = 10 8 was added to the equations. One unit of dimensionless time is equivalent to 137 ps , and the length of the crystal is 20 mm .

Tables (1)

Tables Icon

Table 1 Estimate of Kreiss Constant for the Two Examples Shown in Fig. 2

Equations (7)

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z E 1 = υ 1 1 t E 1 ( ρ 1 i Δ k ) E 1 + i β 1 t t E 1 E 2 E 3 ,
z E 2 = υ 2 1 t E 2 ρ 2 E 2 + i β 2 t t E 2 + E 1 E ¯ 3 ,
z E 3 = υ 3 1 t E 3 ρ 3 E 3 + i β 3 t t E 3 + E 1 E ¯ 2 ,
E 1 ( 0 , t ) = P ( t ) , E 3 ( 0 , t ) = 0 ,
E 2 ( 0 , t ) = exp ( i θ ) R E 2 ( 1 , t T c + 1 ) ,
Λ ϵ ( L ) = { z C : ( z L ) 1 ϵ 1 } .
K = sup ϵ > 0 K ϵ , with K ϵ ρ ϵ ( L ) 1 ϵ ,

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