Abstract

A simple and practical all-fiber design for implementing arbitrary-order temporal integration of ultrafast optical waveforms is proposed and numerically investigated. We demonstrate that an ultrafast photonics integrator of any desired integration order can be implemented using a uniform-period fiber Bragg grating (FBG) with a properly designed amplitude-only grating apodization profile. In particular, the grating coupling strength must vary according to the (N1) power of the fiber distance for implementing an Nth-order photonics integrator (N=1,2,). This approach requires the same level of practical difficulty for realizing any given integration order. The proposed integration devices operate over a limited time window, which is approximately fixed by the round-trip propagation time in the FBG. Ultrafast arbitrary-order all-optical integrators capable of accurate operation over nanosecond time windows can be implemented using readily feasible FBGs.

© 2008 Optical Society of America

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References

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  1. A. V. Oppenheim, A. S. Willsky, S. N. Nawab, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996).
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2008 (1)

2007 (1)

2006 (1)

2002 (1)

1997 (1)

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

Azaña, J.

Binh, L. N.

Chen, L. R.

Erdogan, T.

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

Nawab, S. H.

A. V. Oppenheim, A. S. Willsky, S. N. Nawab, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996).

Nawab, S. N.

A. V. Oppenheim, A. S. Willsky, S. N. Nawab, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996).

Ngo, N. Q.

Oppenheim, A. V.

A. V. Oppenheim, A. S. Willsky, S. N. Nawab, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996).

Willsky, A. S.

A. V. Oppenheim, A. S. Willsky, S. N. Nawab, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996).

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Other (1)

A. V. Oppenheim, A. S. Willsky, S. N. Nawab, and S. H. Nawab, Signals and Systems, 2nd ed. (Prentice Hall, 1996).

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Figures (3)

Fig. 1
Fig. 1

Spectral and temporal responses of a second-order optical integrator based on a 1 cm long uniform-period FBG with the apodization profile plotted in the inset of Fig. 1b: (a) Reflectivity as a function of optical frequency deviation (around 193 THz ); (b) amplitude of the reflection temporal impulse response (solid curve), shown in normalized units (n.u.). The impulse response amplitude of an ideal second-order integrator is also shown (dotted curve).

Fig. 2
Fig. 2

Spectral and temporal responses of a third-order optical integrator based on a 1 cm long weak-coupling FBG with the apodization profile plotted in the inset of Fig. 2b, with the same captions as for Fig. 1.

Fig. 3
Fig. 3

Results from numerical simulations [all the plots show the complex envelopes in normalized units (n.u.)] for second- and third-order integrators: (a) Optical waveform launched at the devices’ input (third-time derivative of a 10 ps Gaussian); (b) optical waveform reflected from the FBG-based second-order integrator (solid curve) and ideal second-order integration of the input pulse, i.e., first-time derivative of a 10-ps Gaussian (circles); (c) optical waveform reflected from the FBG-based third-order integrator (solid curve) and ideal third-order integration of the input pulse, i.e., a 10 ps Gaussian (circles).

Equations (2)

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y ( t ) τ N = t τ 1 = τ 2 x ( τ 1 ) d τ 1 d τ N ,
h N ( t ) τ N = t τ 1 = τ 2 δ ( τ 1 ) d τ 1 d τ N = t N 1 ( N 1 ) ! U ( t ) ,

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