Abstract

We demonstrate that a conventional two-arm interferometer can implement first-order temporal differentiation of ultrafast arbitrary optical waveforms. Straightforward extension of this technique to nth-order optical differentiation is also suggested. This approach is experimentally demonstrated by an efficient and accurate first- and second-order temporal differentiation of (sub-)picosecond Gaussian optical pulses.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]

2006 (3)

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., J. Lightwave Technol. 24, 2484 (2006).
[CrossRef]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, Opt. Express 14, 10699 (2006).
[CrossRef] [PubMed]

Y. Park, F. Li, and J. Azaña, IEEE Photon. Technol. Lett. 18, 1798 (2006).
[CrossRef]

2005 (2)

M. Kulishov and J. Azaña, Opt. Lett. 30, 2700 (2005).
[CrossRef] [PubMed]

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902-1-3 (2005).
[CrossRef]

2004 (1)

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

1995 (1)

1989 (1)

Azaña, J.

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., J. Lightwave Technol. 24, 2484 (2006).
[CrossRef]

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azaña, Opt. Express 14, 10699 (2006).
[CrossRef] [PubMed]

Y. Park, F. Li, and J. Azaña, IEEE Photon. Technol. Lett. 18, 1798 (2006).
[CrossRef]

M. Kulishov and J. Azaña, Opt. Lett. 30, 2700 (2005).
[CrossRef] [PubMed]

Chériaux, G.

Cincontti, G.

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., J. Lightwave Technol. 24, 2484 (2006).
[CrossRef]

Da Silva, H. J. A.

Joffre, M.

Kam, C. H.

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

Kulishov, M.

Lepetit, L.

Li, F.

Y. Park, F. Li, and J. Azaña, IEEE Photon. Technol. Lett. 18, 1798 (2006).
[CrossRef]

Madsen, C. K.

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., J. Lightwave Technol. 24, 2484 (2006).
[CrossRef]

Mitschke, F.

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902-1-3 (2005).
[CrossRef]

Morandotti, R.

Ngo, N. Q.

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

O'Reilly, J. J.

Pagel, T.

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902-1-3 (2005).
[CrossRef]

Park, Y.

Slavík, R.

Stratmann, M.

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902-1-3 (2005).
[CrossRef]

Takiguchi, K.

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., J. Lightwave Technol. 24, 2484 (2006).
[CrossRef]

Tjin, S. C.

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

Yu, S. F.

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

IEEE Photon. Technol. Lett. (1)

Y. Park, F. Li, and J. Azaña, IEEE Photon. Technol. Lett. 18, 1798 (2006).
[CrossRef]

J. Lightwave Technol. (1)

J. Azaña, C. K. Madsen, K. Takiguchi, and G. Cincontti, eds., J. Lightwave Technol. 24, 2484 (2006).
[CrossRef]

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

Opt. Commun. (1)

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

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

M. Stratmann, T. Pagel, and F. Mitschke, Phys. Rev. Lett. 95, 143902-1-3 (2005).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Simulated magnitude and phase of the spectral transfer function of a single (solid curves) and a two-stage (dashed curves) Michelson interferometer over a half of its period. The square and circle ticks show the corresponding experimental curves measured over the differentiation usable bandwidth.

Fig. 2
Fig. 2

Optical differentiator (gray box) and FTSI setup. FFL, femtosecond fiber laser; B, beam splitter; M, mirror; PC, polarization controller; L, lens; P, primary output; S, secondary output.

Fig. 3
Fig. 3

Measured intensity and phase of the first-order differentiated pulses generated from 1.9 ps (dashed curves) and 0.9 ps (solid curves) pulses. The ticks show the characteristics of the theoretical first time derivative of 1.9 ps (squares) and 0.9 ps (circles) ideal Gaussian pulses.

Fig. 4
Fig. 4

Measured second-order differentiated pulse using a 1.2 ps input pulse. Circles show the characteristics of the theoretical second time derivative of an ideal Gaussian pulse.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

H t ( ω ω 0 ) 1 + exp ( i ω τ ) = 1 + exp [ i ( ω ω 0 ) τ ] exp ( i ω 0 τ ) ,
τ = π ( 2 m + 1 ) ω 0 ,
H t ( ω ω 0 ) 1 exp [ i π ( 2 m + 1 ) ( ω ω 0 ) ω 0 ] .
cos ( π ( 2 m + 1 ) ( ω ω 0 ) ω 0 ) 1 ,
sin [ π ( 2 m + 1 ) ( ω ω 0 ) ω 0 ] π ( 2 m + 1 ) ( ω ω 0 ) ω 0 ,
H t ( ω ω 0 ) i ( ω ω 0 ) π ( 2 m + 1 ) ω 0 ,

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