Abstract

It is demonstrated that a single, uniform long-period fiber grating (LPFG) working in the linear regime inherently behaves as an ultrafast optical temporal differentiator. Specifically, we show that the output temporal waveform in the core mode of a LPFG providing full energy coupling into the cladding mode is proportional to the first derivative of the optical temporal signal (e.g., optical pulse) launched at the input of the LPFG. Moreover, a LPFG providing full energy recoupling back from the cladding mode into the core mode inherently implements second-order temporal differentiation. Our numerical results have confirmed the feasibility of this simple, all-fiber approach to processing optical signals with temporal features in the picosecond and subpicosecond ranges.

© 2005 Optical Society of America

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References

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  1. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
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  2. M. Kulishov and J. Azaña, J. Opt. Soc. Am. A 22, 1319 (2005).
    [CrossRef]
  3. N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
    [CrossRef]

2005

2004

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
[CrossRef]

1996

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Azaña, J.

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Erdogan, T.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Kam, C. H.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
[CrossRef]

Kulishov, M.

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Ngo, N. Q.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
[CrossRef]

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Tjin, S. C.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
[CrossRef]

Vengsarkar, A. M.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Yu, S. F.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
[CrossRef]

J. Lightwave Technol.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

N. Q. Ngo, S. F. Yu, S. C. Tjin, and C. H. Kam, Opt. Commun. 230, 115 (2004).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Amplitude of the spectral transmission function corresponding to the core mode of a 5 cm long uniform LPFG with κ L = π 2 (solid curve) and to an ideal first-order optical differentiator (dashed–dotted curve). (b) Amplitude of the spectral transmission function corresponding to the cladding mode of a 5 cm long uniform LPFG with κ L = π (solid curve) and to an ideal second-order optical differentiator (dashed–dotted curve).

Fig. 2
Fig. 2

Dashed curves, temporal waveform corresponding to the 3 ps super-Gaussian optical pulse launched at the input of the simulated LPFGs. Solid curves, output temporal waveforms (top) in the core of a 5 cm long uniform LPFG with κ L = π 2 [spectrum in Fig. 1(a)] and (bottom) in the cladding of a 5 cm long uniform LPFG with κ L = π [spectrum in Fig. 1(b)]. Dotted curves, ideal (analytical) first (top) and second (bottom) time derivatives of the input pulse.

Fig. 3
Fig. 3

Maximum signal bandwidth (FWHM bandwidth of input Gaussian pulse) that can be processed with a uniform LPFG operated as a first-order differentiator (solid curve with open squares) and as a second-order differentiator (dashed curve with open diamonds) to keep the processing error lower than 1%, evaluated for different grating lengths: eff, efficiency.

Equations (4)

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H co ( ω opt ) = [ cos ( γ L ) + j σ γ sin ( γ L ) ] exp [ j ( β co σ ) L ] ,
H cl ( ω opt ) = j κ γ sin ( γ L ) exp [ j ( β cl + σ ) L ] ,
H co ( ω opt ) [ cos ( κ L ) + j σ κ sin ( κ L ) ] exp ( j β co , 0 L ) ,
H cl ( ω opt ) j { sin ( κ L ) + σ 2 2 κ 2 [ κ L cos ( κ L ) sin ( κ L ) ] } exp ( j β cl , 0 L ) ,

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