Abstract

By using the four-sideband theory, we analyze the gain spectrum in wideband two-pump fiber optical parametric amplifiers and predict gain ripples over the flat gain region. We derive an approximation of their pseudo-periods and discuss methods for reducing their amplitudes.

© 2008 Optical Society of America

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References

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  1. M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge U. Press, 2007).
    [CrossRef]
  2. C. J. McKinstrie, S. Radic, and A. H. Gnauck, Opt. Photon. News 18(3), 34 (2007).
    [CrossRef]
  3. M. C. Ho, M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, J. Lightwave Technol. 20, 469 (2002).
    [CrossRef]
  4. A. Vedadi, A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, Opt. Commun. 267, 244 (2006).
    [CrossRef]
  5. M. E. Marhic, K. K.-Y. Wong, and L. G. Kazovsky, J. Opt. Soc. Am. B 20, 2425 (2003).
    [CrossRef]
  6. M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, Opt. Lett. 21, 1354 (1996).
    [CrossRef] [PubMed]
  7. J. M. Chavez Boggio, J. D. Marconi, S. R. Bickham, and H. L. Fragnito, Opt. Express 15, 5288 (2007).
    [CrossRef] [PubMed]
  8. M. Yu, C. J. McKinstrie, and G. P. Agrawal, Phys. Rev. E 48, 2178 (1993).
    [CrossRef]
  9. L. Provino, H. Maillotte, E. Lantz, T. Sylvestre, and J. M. Dudley, in Conference on Lasers and Electro-Optics Europe, IEEE Conference Digest (IEEE, 2000), paper CtuL4.
  10. C. J. McKinstrie and S. Radic, Opt. Lett. 27, 1138 (2002).
    [CrossRef]
  11. A. Vedadi, E. Lantz, H. Maillotte, and T. Sylvestre, in 2008 IEEE/LEOS Winter Topical Meeting Series (IEEE, 2008), paper TuB 1.2.
  12. M. E. Marhic, A. A. Rieznik, and H. L. Fragnito, J. Opt. Soc. Am. B 25, 22 (2008).
    [CrossRef]

2008 (1)

2007 (2)

2006 (1)

A. Vedadi, A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, Opt. Commun. 267, 244 (2006).
[CrossRef]

2003 (1)

2002 (2)

1996 (1)

1993 (1)

M. Yu, C. J. McKinstrie, and G. P. Agrawal, Phys. Rev. E 48, 2178 (1993).
[CrossRef]

Agrawal, G. P.

M. Yu, C. J. McKinstrie, and G. P. Agrawal, Phys. Rev. E 48, 2178 (1993).
[CrossRef]

Bickham, S. R.

Chavez Boggio, J. M.

Dudley, J. M.

L. Provino, H. Maillotte, E. Lantz, T. Sylvestre, and J. M. Dudley, in Conference on Lasers and Electro-Optics Europe, IEEE Conference Digest (IEEE, 2000), paper CtuL4.

Fragnito, H. L.

Gnauck, A. H.

C. J. McKinstrie, S. Radic, and A. H. Gnauck, Opt. Photon. News 18(3), 34 (2007).
[CrossRef]

Ho, M. C.

Kazovsky, L. G.

Lantz, E.

A. Vedadi, A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, Opt. Commun. 267, 244 (2006).
[CrossRef]

A. Vedadi, E. Lantz, H. Maillotte, and T. Sylvestre, in 2008 IEEE/LEOS Winter Topical Meeting Series (IEEE, 2008), paper TuB 1.2.

L. Provino, H. Maillotte, E. Lantz, T. Sylvestre, and J. M. Dudley, in Conference on Lasers and Electro-Optics Europe, IEEE Conference Digest (IEEE, 2000), paper CtuL4.

Maillotte, H.

A. Vedadi, A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, Opt. Commun. 267, 244 (2006).
[CrossRef]

A. Vedadi, E. Lantz, H. Maillotte, and T. Sylvestre, in 2008 IEEE/LEOS Winter Topical Meeting Series (IEEE, 2008), paper TuB 1.2.

L. Provino, H. Maillotte, E. Lantz, T. Sylvestre, and J. M. Dudley, in Conference on Lasers and Electro-Optics Europe, IEEE Conference Digest (IEEE, 2000), paper CtuL4.

Marconi, J. D.

Marhic, M. E.

McKinstrie, C. J.

C. J. McKinstrie, S. Radic, and A. H. Gnauck, Opt. Photon. News 18(3), 34 (2007).
[CrossRef]

C. J. McKinstrie and S. Radic, Opt. Lett. 27, 1138 (2002).
[CrossRef]

M. Yu, C. J. McKinstrie, and G. P. Agrawal, Phys. Rev. E 48, 2178 (1993).
[CrossRef]

Mussot, A.

A. Vedadi, A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, Opt. Commun. 267, 244 (2006).
[CrossRef]

Park, Y.

Provino, L.

L. Provino, H. Maillotte, E. Lantz, T. Sylvestre, and J. M. Dudley, in Conference on Lasers and Electro-Optics Europe, IEEE Conference Digest (IEEE, 2000), paper CtuL4.

Radic, S.

C. J. McKinstrie, S. Radic, and A. H. Gnauck, Opt. Photon. News 18(3), 34 (2007).
[CrossRef]

C. J. McKinstrie and S. Radic, Opt. Lett. 27, 1138 (2002).
[CrossRef]

Rieznik, A. A.

Sylvestre, T.

A. Vedadi, A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, Opt. Commun. 267, 244 (2006).
[CrossRef]

A. Vedadi, E. Lantz, H. Maillotte, and T. Sylvestre, in 2008 IEEE/LEOS Winter Topical Meeting Series (IEEE, 2008), paper TuB 1.2.

L. Provino, H. Maillotte, E. Lantz, T. Sylvestre, and J. M. Dudley, in Conference on Lasers and Electro-Optics Europe, IEEE Conference Digest (IEEE, 2000), paper CtuL4.

Vedadi, A.

A. Vedadi, A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, Opt. Commun. 267, 244 (2006).
[CrossRef]

A. Vedadi, E. Lantz, H. Maillotte, and T. Sylvestre, in 2008 IEEE/LEOS Winter Topical Meeting Series (IEEE, 2008), paper TuB 1.2.

Wong, K. K. Y.

Wong, K. K.-Y.

Yang, F. S.

Yu, M.

M. Yu, C. J. McKinstrie, and G. P. Agrawal, Phys. Rev. E 48, 2178 (1993).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

A. Vedadi, A. Mussot, E. Lantz, H. Maillotte, and T. Sylvestre, Opt. Commun. 267, 244 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Photon. News (1)

C. J. McKinstrie, S. Radic, and A. H. Gnauck, Opt. Photon. News 18(3), 34 (2007).
[CrossRef]

Phys. Rev. E (1)

M. Yu, C. J. McKinstrie, and G. P. Agrawal, Phys. Rev. E 48, 2178 (1993).
[CrossRef]

Other (3)

L. Provino, H. Maillotte, E. Lantz, T. Sylvestre, and J. M. Dudley, in Conference on Lasers and Electro-Optics Europe, IEEE Conference Digest (IEEE, 2000), paper CtuL4.

A. Vedadi, E. Lantz, H. Maillotte, and T. Sylvestre, in 2008 IEEE/LEOS Winter Topical Meeting Series (IEEE, 2008), paper TuB 1.2.

M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge U. Press, 2007).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Four-sideband model with pumps, signal, and three generated idlers.

Fig. 2
Fig. 2

Spectrum of the 2P-FOPA gain. Squares, experimental results; solid curve, 4S analysis; dashed curve, 2S analysis (standard model). The parameters are β 2 = 6.4 × 10 30 s 2 m 1 , β 3 = 0.65 × 10 40 s 3 m 1 , β 4 = 1.6 × 10 55 s 4 m 1 , γ = 8 W 1 m 1 , and Δ ω P = 3.25 × 10 13 rad s .

Fig. 3
Fig. 3

(a), (b) Zoom in on the edges of the flat-gain region. Dashed curve, plot of Eq. (9).

Fig. 4
Fig. 4

(a) Gain spectra of 2P-FOPAs with β 2 = 6.3 × 10 30 s 2 m 1 , β 4 = 1.6 × 10 55 s 4 m 1 (solid curve) and β 2 = 5 × 10 29 s 2 m 1 , β 4 = 1.6 × 10 55 s 4 m 1 (dotted curve). (b) Ripple relative amplitudes associated with the FOPA of Fig. 2 (dashed curve) and the two FOPAs of Fig. 3b with positive β 4 (solid line) and negative β 4 (dotted curve).

Equations (9)

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Y z = j M Y
Δ β i = β ( ω i ) β ( ω g ) = k = 2 ( 1 ) k × i β k k ! ( Δ ω i k Δ ω P k ) ,
Y ( z ) = exp ( j M z ) Y ( 0 ) .
A i = exp { ( 1 ) i j [ γ ( P 2 P 1 ) 2 + ( β 3 6 ) ( Δ ω S 3 Δ ω P 3 ) ] z } × [ cosh ( g z ) j κ 2 g sinh ( g z ) ] ( i = 3 , 4 ) ,
A i ( 1 2 j κ 4 g ) × exp ( { ( 1 ) i j [ γ ( P 2 P 1 ) 2 + ( β 3 6 ) ( Δ ω S 3 Δ ω P 3 ) ] + g } z ) ( i = 3 , 4 ) .
A a exp ( j p 1 z + g 1 z ) + b exp ( j p 2 z + g 2 z ) ,
G ( z ) a 2 e 2 g 1 z + b 2 e 2 g 2 z + 2 a b e ( g 1 + g 2 ) z cos [ ( p 1 p 2 ) z + φ ] ,
( Δ β 3 ( Δ ω S B ) + γ P 1 ) × v 3 ( Δ ω S B ) + γ P 1 × v 5 ( Δ ω S B ) + r × v 6 ( Δ ω S B ) + r × v 4 ( Δ ω S B ) = ( Δ β 5 ( Δ ω S ) + γ P 1 ) × v 3 ( Δ ω S B ) + γ P 1 × v 5 ( Δ ω S B ) + r × v 6 ( Δ ω S B ) + r × v 4 ( Δ ω S B ) .
cos [ ( p 1 p 2 ) z ] cos β 3 Δ ω P ( Δ ω P Δ ω S ) 2 z + γ ( P 2 P 1 ) z .

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