Abstract

Parametric amplification of pulses in Bragg gratings is investigated numerically. Gain is observed for a much larger range of parameters than in uniform media. This is explained in terms of grating-assisted phase matching. In contrast to that for cw results, the input signal pulse need not be tuned to a particular frequency. Rather, through cross-phase modulation the signal self-locks to the correct frequency for growth.

© 1996 Optical Society of America

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References

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  1. N. Bloembergen, A. J. Sievers, Appl. Phys. Lett. 17, 483 (1970).
    [CrossRef]
  2. C. L. Tang, P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
    [CrossRef]
  3. J. P. van der Ziel, M. Ilegems, Appl. Phys. Lett. 28, 437 (1976).
    [CrossRef]
  4. V. A. Belyakov, N. V. Shipov, Phys. Lett. A 86, 94 (1981).
    [CrossRef]
  5. P. St. J. Russell, J.-L. Archambault, J. Phys. III (Paris) 4, 2471 (1994).
  6. M. J. Steel, C. M. de Sterke, J. Opt. Soc. Am. B 12, 2445 (1996).
    [CrossRef]
  7. P. Krug, T. Stephens, G. Dhosi, Electron. Lett. 31, 1091 (1995).
    [CrossRef]
  8. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  9. B. J. Eggleton, in Proceedings of the 20th Australian Conference on Optical Fibre Technology (IREE Society, Sydney, 1995), p. 128.

1996

1995

P. Krug, T. Stephens, G. Dhosi, Electron. Lett. 31, 1091 (1995).
[CrossRef]

1994

P. St. J. Russell, J.-L. Archambault, J. Phys. III (Paris) 4, 2471 (1994).

1981

V. A. Belyakov, N. V. Shipov, Phys. Lett. A 86, 94 (1981).
[CrossRef]

1976

J. P. van der Ziel, M. Ilegems, Appl. Phys. Lett. 28, 437 (1976).
[CrossRef]

1973

C. L. Tang, P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
[CrossRef]

1970

N. Bloembergen, A. J. Sievers, Appl. Phys. Lett. 17, 483 (1970).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

Archambault, J.-L.

P. St. J. Russell, J.-L. Archambault, J. Phys. III (Paris) 4, 2471 (1994).

Belyakov, V. A.

V. A. Belyakov, N. V. Shipov, Phys. Lett. A 86, 94 (1981).
[CrossRef]

Bey, P. P.

C. L. Tang, P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
[CrossRef]

Bloembergen, N.

N. Bloembergen, A. J. Sievers, Appl. Phys. Lett. 17, 483 (1970).
[CrossRef]

de Sterke, C. M.

Dhosi, G.

P. Krug, T. Stephens, G. Dhosi, Electron. Lett. 31, 1091 (1995).
[CrossRef]

Eggleton, B. J.

B. J. Eggleton, in Proceedings of the 20th Australian Conference on Optical Fibre Technology (IREE Society, Sydney, 1995), p. 128.

Ilegems, M.

J. P. van der Ziel, M. Ilegems, Appl. Phys. Lett. 28, 437 (1976).
[CrossRef]

Krug, P.

P. Krug, T. Stephens, G. Dhosi, Electron. Lett. 31, 1091 (1995).
[CrossRef]

Russell, P. St. J.

P. St. J. Russell, J.-L. Archambault, J. Phys. III (Paris) 4, 2471 (1994).

Shipov, N. V.

V. A. Belyakov, N. V. Shipov, Phys. Lett. A 86, 94 (1981).
[CrossRef]

Sievers, A. J.

N. Bloembergen, A. J. Sievers, Appl. Phys. Lett. 17, 483 (1970).
[CrossRef]

Steel, M. J.

Stephens, T.

P. Krug, T. Stephens, G. Dhosi, Electron. Lett. 31, 1091 (1995).
[CrossRef]

Tang, C. L.

C. L. Tang, P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
[CrossRef]

van der Ziel, J. P.

J. P. van der Ziel, M. Ilegems, Appl. Phys. Lett. 28, 437 (1976).
[CrossRef]

Appl. Phys. Lett.

N. Bloembergen, A. J. Sievers, Appl. Phys. Lett. 17, 483 (1970).
[CrossRef]

J. P. van der Ziel, M. Ilegems, Appl. Phys. Lett. 28, 437 (1976).
[CrossRef]

Electron. Lett.

P. Krug, T. Stephens, G. Dhosi, Electron. Lett. 31, 1091 (1995).
[CrossRef]

IEEE J. Quantum Electron

C. L. Tang, P. P. Bey, IEEE J. Quantum Electron. QE-9, 9 (1973).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. III

P. St. J. Russell, J.-L. Archambault, J. Phys. III (Paris) 4, 2471 (1994).

Phys. Lett. A

V. A. Belyakov, N. V. Shipov, Phys. Lett. A 86, 94 (1981).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

B. J. Eggleton, in Proceedings of the 20th Australian Conference on Optical Fibre Technology (IREE Society, Sydney, 1995), p. 128.

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Figures (2)

Fig. 1
Fig. 1

Time sequence of pulse evolution for κ = 16 cm−1 and Δ = 8 cm−1 ( = −12 cm−1). Curves show E+ (solid), E (dashed–dotted), I (dashed), and P (dotted). The vertical scale refers to the moduli of the amplitudes of E± and I.

Fig. 2
Fig. 2

Dispersion relation for a Bragg grating (solid curves) superposed upon a uniform medium dispersion relation (dashed curves).

Equations (6)

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

- 4 μ < Δ < 0 ,
+ i E + x + i v E + t + κ E - + Γ [ 2 P 2 E + + exp ( - i Δ x ) P 2 I * ] = 0 ,
- i E - x + i v E - t + κ E + + 2 Γ P 2 E - = 0 ,
+ i I x + i v I t + Γ [ 2 P 2 I + exp ( - i Δ x ) P 2 E + * ] = 0 ,
+ i P x + i v P t + Γ P 2 P = 0 ,
ɛ = - 2 μ max - Δ ,

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