Abstract

It is demonstrated that a uniform fiber Bragg grating (FBG) working in the linear regime inherently behaves as an optical temporal integrator over a limited time window. Specifically, the reflected temporal waveform from a weak-coupling uniform FBG is proportional to the time integral of an (arbitrary) optical pulse launched at the component input. This integration extends over a time window fixed by the duration of the squarelike temporal impulse response of the FBG. Ultrafast all-optical integrators capable of accurate operation over nanosecond time windows can be implemented using readily feasible FBGs. The introduced concepts are demonstrated by numerical simulations.

© 2008 Optical Society of America

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References

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2007 (2)

2006 (2)

2001 (1)

1997 (1)

L. R. Chen, S. D. Benjamin, P. W. E. Smith, and J. E. Sipe, J. Lightwave Technol. 15, 1503 (1997).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Spectral and temporal response of a 1 cm long weak-coupling FBG: (a) reflectivity as a function of optical frequency deviation ( 193 THz ) ; (b) amplitude of the reflection temporal impulse response, shown in normalized units (n.u.).

Fig. 2
Fig. 2

Results from numerical simulations (all the plots show the complex envelopes in normalized units [n.u.]). Integration example 1: (a) Optical waveform launched at the FBG input (second-time derivative of a 1 ps Gaussian pulse); (b) optical waveform reflected from the FBG (solid, black curve) and numerical time integral of the input complex envelope shown in (a), i.e., first-time derivative of a 1 ps Gaussian pulse (dashed, red curve). Integration example 2: (c) optical waveform launched at the FBG input (first-time derivative of a 1 ps Gaussian pulse); (d) optical waveform reflected from the FBG (solid, black curve) and numerical time integral of the input complex envelope shown in (c), i.e., 1 ps Gaussian pulse (dashed, red curve).

Equations (3)

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y ( t ) 0 t x ( τ ) d τ ,
h ( t ) = { h 0 , 0 t T h 0 , otherwise .
y ( t ) = h ( t ) * x ( t ) = + h ( t ) x ( t t ) d t = h 0 0 T h x ( t t ) d t = h 0 t T h t x ( τ ) d τ ,

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