Abstract

It is shown that the energy of a weak probe, copropagating with a strong pump pulse through a fiber grating, can be made to heap up on the pump’s leading edge.

© 1992 Optical Society of America

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References

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  1. See, e.g., W. J. Tomlinson, R. H. Stolen, C. V. Shank, J. Opt. Soc. Am. B 1, 139 (1984).
    [CrossRef]
  2. D. Schadt, B. Jaskorzynska, Electron. Lett. 23, 1090 (1987).
    [CrossRef]
  3. B. Jaskorzynska, D. Schadt, IEEE J. Quantum Electron. 24, 2117 (1988).
    [CrossRef]
  4. J. E. Rothenberg, Opt. Lett. 15, 495 (1990).
    [CrossRef] [PubMed]
  5. Q. Z. Wang, P. P. Ho, R. R. Alfano, Opt. Lett. 15, 1023 (1990).
    [CrossRef] [PubMed]
  6. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  7. P. L. Baldeck, P. P. Ho, R. R. Alfano, in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), p. 117.
  8. H. G. Winful, Appl. Phys. Lett. 40, 527 (1985).
    [CrossRef]
  9. G. Meltz, W. W. Morey, W. H. Glenn, Opt. Lett. 14, 823 (1989).
    [CrossRef] [PubMed]
  10. C. M. de Sterke, K. R. Jackson, B. D. Robert, J. Opt. Soc. Am. B 8, 403 (1991).
    [CrossRef]
  11. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

1991 (1)

1990 (2)

1989 (1)

1988 (1)

B. Jaskorzynska, D. Schadt, IEEE J. Quantum Electron. 24, 2117 (1988).
[CrossRef]

1987 (1)

D. Schadt, B. Jaskorzynska, Electron. Lett. 23, 1090 (1987).
[CrossRef]

1985 (1)

H. G. Winful, Appl. Phys. Lett. 40, 527 (1985).
[CrossRef]

1984 (1)

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Agrawal, G. P.

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

Alfano, R. R.

Q. Z. Wang, P. P. Ho, R. R. Alfano, Opt. Lett. 15, 1023 (1990).
[CrossRef] [PubMed]

P. L. Baldeck, P. P. Ho, R. R. Alfano, in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), p. 117.

Baldeck, P. L.

P. L. Baldeck, P. P. Ho, R. R. Alfano, in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), p. 117.

de Sterke, C. M.

Glenn, W. H.

Ho, P. P.

Q. Z. Wang, P. P. Ho, R. R. Alfano, Opt. Lett. 15, 1023 (1990).
[CrossRef] [PubMed]

P. L. Baldeck, P. P. Ho, R. R. Alfano, in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), p. 117.

Jackson, K. R.

Jaskorzynska, B.

B. Jaskorzynska, D. Schadt, IEEE J. Quantum Electron. 24, 2117 (1988).
[CrossRef]

D. Schadt, B. Jaskorzynska, Electron. Lett. 23, 1090 (1987).
[CrossRef]

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Meltz, G.

Morey, W. W.

Robert, B. D.

Rothenberg, J. E.

Schadt, D.

B. Jaskorzynska, D. Schadt, IEEE J. Quantum Electron. 24, 2117 (1988).
[CrossRef]

D. Schadt, B. Jaskorzynska, Electron. Lett. 23, 1090 (1987).
[CrossRef]

Shank, C. V.

Stolen, R. H.

Tomlinson, W. J.

Wang, Q. Z.

Winful, H. G.

H. G. Winful, Appl. Phys. Lett. 40, 527 (1985).
[CrossRef]

Appl. Phys. Lett. (1)

H. G. Winful, Appl. Phys. Lett. 40, 527 (1985).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Electron. Lett. (1)

D. Schadt, B. Jaskorzynska, Electron. Lett. 23, 1090 (1987).
[CrossRef]

IEEE J. Quantum Electron. (1)

B. Jaskorzynska, D. Schadt, IEEE J. Quantum Electron. 24, 2117 (1988).
[CrossRef]

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

Opt. Lett. (3)

Other (2)

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

P. L. Baldeck, P. P. Ho, R. R. Alfano, in The Supercontinuum Laser Source, R. R. Alfano, ed. (Springer-Verlag, New York, 1989), p. 117.

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Figures (3)

Fig. 1
Fig. 1

Dispersion relation of an idealized fiber with (solid curves) and without (dashed lines) a grating. The grating introduces a photonic band gap, which for the example in the text has a width of 3.2 GHz. The center of the gap, the Bragg resonance, is denoted k0, ω0. Since vg is given by the slope of the dispersion curve, signals with frequencies close to the gap are slowed down. The probe’s initial frequency and wave number for the example in the text are indicated by the crosses. Note that since at k = k0, vg vanishes, the dispersion d2k/dω2 there diverges.

Fig. 2
Fig. 2

(a) Probe intensity (solid curve) versus the position inside the grating just after the arrival of the pump (dashed curve). The incoming intensity of the probe is 1 unit. Note that the scales for the pump and probe differ significantly. The vertical scale refers to the probe intensity. The pump’s peak power is 5 kW (b) Same as (a) but just before the pump leaves the grating. Note that the probe energy is swept away by the pump edge.

Fig. 3
Fig. 3

Probe (solid curve) and pump (dashed curve) intensity as a function of time just behind the fiber grating. The incoming probe intensity is 1 unit, while the vertical scale refers to the probe intensity. The origin of time is taken to be when the pump leaves the grating.

Equations (7)

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n ( x ) = n + Δ n cos ( 2 π x / d ) + n ( 2 ) I ,
E ( x , t ) = [ F + ( x , t ) exp ( + i k 0 x ) + F - ( x , t ) × exp ( - i k 0 x ) ] exp ( - i ω 0 t ) + c . c . ,
+ i F + x + i n c F + t + κ F - + Γ F + 2 F + + 2 Γ F - 2 F + = 0 , - i F - x + i n c F + t + κ F + + Γ F - 2 F - + 2 Γ F + 2 F - = 0 ,
κ = k 0 Δ n 2 n
F + ( x , t ) = E p ( x - c t / n ) exp ( - i Ω p t ) + E + ( x , t ) exp ( - i Ω 0 t ) , F - ( x , t ) = E - ( x , t ) exp ( - i Ω 0 t ) ,
+ i E + x + i n c E + t + κ E - + δ ( x , t ) E + = 0 , - i E - x + i n c E - t + κ E + + δ ( x , t ) E - = 0 ,
δ ( x , t ) = δ 0 + 2 Γ E p ( x - c t / n ) 2 ,

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