Abstract

The performance of incoherent pulse shaping based on temporal gating and dispersive propagation of a broadband incoherent optical source is analyzed. The average temporal intensity of the dispersed gated source is essentially proportional to the spectral density of the incoherent source scaled along the temporal axis; therefore temporal waveforms are synthesized by spectral density modulation of the incoherent source. Although the coherence time of the shaped waveform is longer than that of the initial incoherent source, the shaped-intensity probability density function at any given time is identical to the probability density function of a polarized incoherent source. This restricts the signal-to-noise ratio of the shaped waveform to 1. Statistical analysis describes how the signal-to-noise ratio is affected by polarization multiplexing and averaging over multiple realizations of the incoherent process. The signal-to-noise ratio of highspeed electric waveforms generated by photodetection of the shaped optical waveform is described.

© 2009 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2008 (1)

2007 (1)

2006 (1)

V. Torres-Company, J. Lancis, and P. Andrés, "Arbitrary waveform generator based on all-incoherent pulse shaping," IEEE Photon. Technol. Lett. 18, 2626−2628 (2006).
[CrossRef]

2004 (2)

2003 (1)

J. Chou, Y. Han, and B. Jalali, "Adaptive RF-photonic arbitrary waveform generator," IEEE Photon. Technol. Lett. 15, 581-583 (2003).
[CrossRef]

2001 (2)

2000 (2)

1999 (1)

L. Wang and A. M. Weiner, "Programmable spectral phase coding of an amplified spontaneous emission light source," Opt. Comm. 167, 211-224 (1999).
[CrossRef]

1996 (1)

Andrés, P.

Belabas, N.

Binjrajka, V.

Bousquet, B.

Canioni, L.

Chang, C.-C.

Chen, L. R.

Cheng, Z.

Chou, J.

J. Chou, Y. Han, and B. Jalali, "Adaptive RF-photonic arbitrary waveform generator," IEEE Photon. Technol. Lett. 15, 581-583 (2003).
[CrossRef]

Dorrer, C.

Emanuel, A.W. R.

Feurer, T.

Hacker, M.

Han, Y.

J. Chou, Y. Han, and B. Jalali, "Adaptive RF-photonic arbitrary waveform generator," IEEE Photon. Technol. Lett. 15, 581-583 (2003).
[CrossRef]

Jalali, B.

J. Chou, Y. Han, and B. Jalali, "Adaptive RF-photonic arbitrary waveform generator," IEEE Photon. Technol. Lett. 15, 581-583 (2003).
[CrossRef]

Joffre, M.

Lancis, J.

Laude, V.

Leaird, D. E.

Likforman, J.-P.

Lucza, T.

Sauerbrey, R.

Spielmann, Ch.

Szabo, G.

Torres-Company, V.

Tournois, P.

Verluise, F.

Wang, L.

L. Wang and A. M. Weiner, "Programmable spectral phase coding of an amplified spontaneous emission light source," Opt. Comm. 167, 211-224 (1999).
[CrossRef]

Weiner, A. M.

IEEE Photon. Technol. Lett. (2)

V. Torres-Company, J. Lancis, and P. Andrés, "Arbitrary waveform generator based on all-incoherent pulse shaping," IEEE Photon. Technol. Lett. 18, 2626−2628 (2006).
[CrossRef]

J. Chou, Y. Han, and B. Jalali, "Adaptive RF-photonic arbitrary waveform generator," IEEE Photon. Technol. Lett. 15, 581-583 (2003).
[CrossRef]

J. Lightwave Technol. (1)

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

J. Opt. Soc. Am. B (2)

Opt. Comm. (1)

L. Wang and A. M. Weiner, "Programmable spectral phase coding of an amplified spontaneous emission light source," Opt. Comm. 167, 211-224 (1999).
[CrossRef]

Opt. Lett. (4)

Rev. Sci. Instrum. (1)

A. M. Weiner, "Femtosecond pulse shaping using spatial light modulators," Rev. Sci. Instrum. 71, 1929−1960 (2000).
[CrossRef]

Other (4)

V. Torres-Company, J. Lancis, P. Andrés, and L. R. Chen, "20 GHz arbitrary radio-frequency waveform generator based on incoherent pulse shaping," Opt. Express 16, 564-569 (2008).
[CrossRef]

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University Press, Cambridge, England, 1995).

J. W. Goodman, Statistical optics, Wiley series in pure and applied optics (Wiley, New York, 1985).

J. W. Goodman, Speckle phenomena in optics: Theory and applications, 1st ed. (Roberts and Company Publishers, Englewood, CO, 2006).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Principle of incoherent pulse shaping based on temporal gating and spectral dispersion. (b) Example of one realization of the shaped intensity (black line) and scaled spectral density of the incoherent process (red line).

Fig. 2.
Fig. 2.

Probability density function of the intensity of the waveforms of Fig. 1 (black line), with the theoretical prediction of Eq. (13) (red markers).

Fig. 3.
Fig. 3.

Intensity correlation function γ for a Gaussian temporal gate of duration 10 ps, 20 ps, and 40 ps (upper row, from left to right). The correlation functions calculated with simulations of the shaped waveforms are plotted with a black line, and the predictions of Eq. (21) are plotted with red markers. The lower row represents close-ups of realizations of the shaped waveforms, where the horizontal dashed line indicates the value of the temporal intensity expected after averaging over an infinite number of realizations of the incoherent process.

Fig. 4.
Fig. 4.

(a) One realization of the unpolarized shaped intensity (black line) and spectrum of the incoherent process plotted versus the temporal variable φ 2 ω (red line). (b) Intensity probability density function of the unpolarized shaped waveform.

Fig. 5.
Fig. 5.

Examples of shaped intensity averaged over 10, 100, and 1000 realizations of the incoherent process (upper row, from left to right) and corresponding pdf p 10,p100, and p1000 (lower row, from left to right).

Equations (32)

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E ( t ) = 1 2 π E ˜ ( ω ) exp ( iωt ) d ω
E ˜ ( ω ) = 1 2 π E ( t ) exp ( iωt ) d t ,
E 0 , ω ( t ) = S inc ( ω ) exp [ i φ inc ( ω ) ] exp ( iωt )
E 1 , ω ( t ) = g ( t ) S inc ( ω ) exp [ i φ inc ( ω ) ] exp ( iωt ) ,
E ˜ 1 , ω ( ω′ ) = S inc ( ω ) exp [ i φ inc ( ω ) ] g ˜ ( ω′ ω ) .
E ˜ 2 , ω ( ω′ ) = E ˜ 1 , ω ( ω′ ) exp ( i φ 2 ω′ 2 2 ) .
E ˜ 2 , ω ( ω′ ) = S inc ( ω ) exp [ i φ inc ( ω ) + i φ 2 ω 2 2 ]
× g ˜ ( ω′ ω ) exp [ i φ 2 ( ω′ ω 2 ) 2 ] exp [ i φ 2 ( ω′ ω ) ω ] .
E 2 , ω ( t ) = S inc ( ω ) exp [ i φ inc ( ω ) ] g chirped ( t φ 2 ω ) exp ( iωt ) .
E 2 ( t ) = S inc ( ω ) exp [ i φ inc ( ω ) ] g chirped ( t φ 2 ω ) exp ( iωt ) d ω .
I 2 ( t ) = E 2 ( t ) E 2 * ( t )
= S inc ( ω ) S inc ( ω′ ) g chirped ( t φ 2 ω ) g * chirped ( t φ 2 ω′ )
× exp [ i φ inc ( ω ) i φ inc ( ω′ ) ] exp [ i ( ω ω′ ) t ] d ω .
I 2 ( t ) = S inc ( ω ) G chirped ( t φ 2 ω ) d ω ,
I 2 ( t ) = S inc ( t / φ 2 ) / φ 2 ,
p ( I ) = 1 I exp ( I / I ) ,
E 2 ( t ) = S inc ( t 0 / φ 2 ) exp [ i φ inc ( ω ) ] g chirped ( t φ 2 ω ) exp ( iωt ) .
E 2 ( t ) E 2 * ( t′ ) = S inc ( t 0 / φ ) g chirped ( t φ 2 ω ) g chirped * ( t′ φ 2 ω′ )
× exp [ i ( ωt ω′t′ ) ] exp [ i φ inc ( ω ) i φ inc ( ω′ ) ] d ω .
E 2 ( t ) E 2 * ( t′ ) = S inc ( t 0 / φ 2 ) g chirped ( t φ 2 ω ) g chirped * ( t′ φ 2 ω )
× exp [ ( t′ t ) ] d ω .
E 2 ( t ) E 2 * ( t′ ) = S inc ( t 0 / φ 2 ) exp [ i t′ 2 t 2 2 φ 2 ] g ˜ ( ω ) g ˜ * ( ω + t′ t φ 2 ) d ω .
g ˜ ( ω ) g ˜ * ( ω + t′ t φ 2 ) d ω = G ( τ ) exp ( i t′ t φ 2 ) d τ ,
μ ( t , t′ ) = E 2 ( t ) E 2 * ( t′ ) I 2 ( t ) I 2 ( t′ )
μ ( t , t′ ) = G ( τ ) exp ( i t′ t φ 2 ) d τ .
I 2 ( t ) I 2 * ( t′ ) = [ 1 + μ ( t , t′ ) 2 ] S ( t 0 / φ 2 ) 2 .
γ ( τ ) = I 2 ( t ) I 2 * ( t′ ) I 2 ( t ) I 2 ( t′ ) = 1 + μ ( τ ) 2 ,
μ ( τ ) = D ( τ′ ) exp ( i ττ′ φ 2 ) d τ′ .
p 2 ( I ) = 4 I I 2 exp ( 2 I I ) .
p N ( I ) = N N I N 1 ( N 1 ) ! I N exp ( NI I ) .
I convolved ( t ) = I ( t t′ ) R ( t′ ) d t .
p convolved ( I ) = M M I M 1 ( M 1 ) ! I M exp ( MI I ) .

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