Abstract

We demonstrate a novel split-step solution for analyzing nonlinear fiber Bragg gratings. The solution is used for designing nonlinear fiber Bragg gratings with a low reflectivity. The structure of the grating is designed according to the profiles of the incident and reflected pulses. We demonstrate our method for nonlinear compression of a pulse reflected from a fiber Bragg grating. The method allows us to obtain compressed pulses with a very low wing intensity.

© 2006 Optical Society of America

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  1. B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, J. Opt. Soc. Am. B 16, 587 (1999).
    [CrossRef]
  2. A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
    [CrossRef]
  3. J. T. Mok, I. M. Littler, E. Tsoy, and B. J. Eggleton, Opt. Lett. 30, 2457 (2005).
    [CrossRef] [PubMed]
  4. A. Rosenthal and M. Horowitz, IEEE J. Quantum Electron. 39, 1018 (2003).
    [CrossRef]
  5. C. M. de Sterke, K. R. Jackson, and B. D. Robert, J. Opt. Soc. Am. B 8, 403 (1991).
    [CrossRef]
  6. C. M. de Sterke and J. E. Sipe, Phys. Rev. A 42, 2858 (1990).
    [CrossRef] [PubMed]
  7. G. H. Golub, P. C. Hansen, and D. P. O'Leary, SIAM J. Matrix Anal. Appl. 21, 185 (1999).
    [CrossRef]

2005

2003

A. Rosenthal and M. Horowitz, IEEE J. Quantum Electron. 39, 1018 (2003).
[CrossRef]

1999

G. H. Golub, P. C. Hansen, and D. P. O'Leary, SIAM J. Matrix Anal. Appl. 21, 185 (1999).
[CrossRef]

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, J. Opt. Soc. Am. B 16, 587 (1999).
[CrossRef]

1991

1990

C. M. de Sterke and J. E. Sipe, Phys. Rev. A 42, 2858 (1990).
[CrossRef] [PubMed]

1989

A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

Aceves, A. B.

A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

de Sterke, C. M.

Eggleton, B. J.

Golub, G. H.

G. H. Golub, P. C. Hansen, and D. P. O'Leary, SIAM J. Matrix Anal. Appl. 21, 185 (1999).
[CrossRef]

Hansen, P. C.

G. H. Golub, P. C. Hansen, and D. P. O'Leary, SIAM J. Matrix Anal. Appl. 21, 185 (1999).
[CrossRef]

Horowitz, M.

A. Rosenthal and M. Horowitz, IEEE J. Quantum Electron. 39, 1018 (2003).
[CrossRef]

Jackson, K. R.

Littler, I. M.

Mok, J. T.

O'Leary, D. P.

G. H. Golub, P. C. Hansen, and D. P. O'Leary, SIAM J. Matrix Anal. Appl. 21, 185 (1999).
[CrossRef]

Robert, B. D.

Rosenthal, A.

A. Rosenthal and M. Horowitz, IEEE J. Quantum Electron. 39, 1018 (2003).
[CrossRef]

Sipe, J. E.

C. M. de Sterke and J. E. Sipe, Phys. Rev. A 42, 2858 (1990).
[CrossRef] [PubMed]

Slusher, R. E.

Tsoy, E.

Wabnitz, S.

A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

IEEE J. Quantum Electron.

A. Rosenthal and M. Horowitz, IEEE J. Quantum Electron. 39, 1018 (2003).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Lett. A

A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

Phys. Rev. A

C. M. de Sterke and J. E. Sipe, Phys. Rev. A 42, 2858 (1990).
[CrossRef] [PubMed]

SIAM J. Matrix Anal. Appl.

G. H. Golub, P. C. Hansen, and D. P. O'Leary, SIAM J. Matrix Anal. Appl. 21, 185 (1999).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Intensity of a gap soliton after propagating 16 cm , calculated numerically by using the split-step solution (solid curve) and analytically (Ref. [2]) (dashed curve)

Fig. 2
Fig. 2

Schematic description of optical pulse compression geometry.

Fig. 3
Fig. 3

(a) Amplitude and (b) phase of the designed grating with α = 200 (solid curve), α = 2000 (dashed curve), and α = 20,000 (short-dashed curve).

Fig. 4
Fig. 4

Desired reflected field (dashed curve) compared with the reflected field, calculated by using a grating designed with α = 200 (dashed curve), α = 2000 (short-dashed curve), and α = 20,000 (dotted curve). The inset shows the wing intensity, normalized to the maximum power of the desired reflected field.

Equations (12)

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d d τ [ u ( τ , z ) v ( τ , z ) ] = ( A + B ) [ u ( τ , z ) v ( τ , z ) ] ,
A = [ A 1 0 0 A 2 ] , B = [ 0 q ( z ) * q ( z ) 0 ] ,
A 1 = d d z + i Γ [ u ( r , z ) 2 + 2 v ( τ , z ) 2 ] ,
A 2 = d d z + i Γ [ v ( τ , z ) 2 + 2 u ( τ , z ) 2 ] ,
ρ n = sin ( q ( n Δ ) Δ ) q ( n Δ ) q ( n Δ ) q ( n Δ ) Δ .
exp ( A Δ ) [ u n ( τ m ) v n ( τ m ) ] = [ exp [ i Γ Δ ( u n 1 ( τ m ) 2 + 2 v n ( τ m ) 2 ) ] u n 1 ( τ m ) exp [ i Γ Δ ( v n + 1 ( τ m ) 2 + 2 u n ( τ m ) 2 ) ] v n + 1 ( τ m ) ]
exp ( B Δ ) [ u n ( τ m ) v n ( τ m ) ] = [ 1 ρ n 2 ρ n * ρ n 1 ρ n 2 ] [ u n ( τ m ) v n ( τ m ) ] .
u n ( τ m + 1 ) = 1 ρ n 2 u n 1 ( τ m ) exp [ i Γ Δ ( u n 1 ( τ m ) 2 + 2 v n ( τ m ) 2 ) ] + ρ n * v n + 1 ( τ m ) exp [ i Γ Δ ( v n + 1 ( τ m ) 2 + 2 u n ( τ m ) 2 ) ] ,
v n ( τ m + 1 ) = 1 ρ n 2 v n + 1 ( τ m ) exp [ i Γ Δ ( v n + 1 ( τ m ) 2 + 2 u n ( τ m ) 2 ) ] ρ n u n 1 ( τ m ) exp [ i Γ Δ ( u n 1 ( τ m ) 2 + 2 v n ( τ m ) 2 ) ] .
max n ( ρ n ) , 2 Γ max n , m [ v n ( τ m ) 2 + u n ( τ m ) 2 ] Δ 1 .
v 1 ( τ 2 n 1 ) = m = 1 n d n m ρ m , n = 1 , 2 , 3 , , N ,
d n m = u 0 ( τ 2 n 2 m ) exp [ i m Δ Γ u 0 ( τ 2 n 2 m ) 2 ] w = 1 m 1 exp [ 2 i Δ Γ u 0 ( τ 2 n 2 w 1 ) 2 ] .

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