Abstract

We demonstrate the first reprogrammable Fresnel transform pulse shaper based on a modified direct space-to-time pulse shaping apparatus. In our approach, the pulse shaping lens and mask are implemented by a dual-layer liquid crystal spatial light modulator. The input mask subsequently undergoes a free-space Fresnel transform which causes quadratic dispersion of the output temporal waveform. When used as a spectrometer, we demonstrate that the passband function of the apparatus (determined by the Fourier transform of the input spatial mask) may be chosen to exhibit a user-defined scale. Here we present the theory of operation, as well as experimental verification in both the time- and frequency-domains.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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Appl. Phys. B (1)

Y. T. Mazurenko, �??Holography of wave packets,�?? Appl. Phys. B 50, 101�??114 (1990).
[CrossRef]

IEEE J. Quantum Electron. (4)

A. M.Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, �??Femtosecond spectral holography,�?? IEEE J. Quantum Electron. 28, 2251�??2261 (1992).
[CrossRef]

D. E. Leaird and A. M. Weiner, �??Femtosecond direct space-to-time pulse shaping,�?? IEEE J. Quantum Electron. 37, 494�??504 (2001).
[CrossRef]

J. D. McKinney, D. S. Seo, and A. M.Weiner, �??Direct Space-to-Time Pulse Shaping at 1.5 μm,�?? IEEE J. Quantum Electron. 39, 1635�??1644 (2003).
[CrossRef]

A. M.Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, �??Programmable shaping of femtosecond optical pulses by use of a 128-element liquid crystal phase modulator,�?? IEEE J. Quantum Electron. 28, 908�??920 (1992).
[CrossRef]

J. Opt. Soc. Am. A (3)

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

Opt. Express (1)

Opt. Lett. (10)

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, �??Programmable femtosecond pulse shaping by use of a multielement liquid-crystal phase modulator,�?? Opt. Lett. 15, 326�??328 (1990).
[CrossRef] [PubMed]

M. C. Nuss, M. Li, T. H. Chiu, A. M. Weiner, and A. Partovi, �??Time-to-space mapping of femtosecond pulses,�?? Opt. Lett. 19, 664�??666 (1994).
[CrossRef] [PubMed]

M. C. Nuss and R. L. Morrison, �??Time-domain images,�?? Opt. Lett. 20, 740�??742 (1995).
[CrossRef] [PubMed]

M. M. Wefers and K. A. Nelson, �??Generation of high-fidelity programmable ultrafast optical waveforms,�?? Opt. Lett. 20, 1047�??1049 (1995).
[CrossRef] [PubMed]

P. C. Sun, Y. T. Mazurenko, W. C. S. Chang, P. K. L. Yu, and Y. Fainman, �??All optical parallel-to-serial conversion by holographic spatial-to-temporal frequency encoding,�?? Opt. Lett. 20, 1728�??1730 (1995).
[CrossRef] [PubMed]

M. B. Sinclair, M. A. Butler, S. H. Kravitz, W. J. Zubrzycki, and A. J. Ricco, �??Synthetic Infrared Spectra,�?? Opt. Lett. 22, 1036�??1038 (1997).
[CrossRef] [PubMed]

D. E. Leaird and A. M. Weiner, �??Femtosecond optical packet generation by a direct space-to-time pulse shaper,�?? Opt. Lett. 24, 853�??855 (1999).
[CrossRef]

T. Feurer, J. C. Vaughan, R. M. Koehl, and K. A. Nelson, �??Multidimensional control of femtosecond pulses by use of a programmable liquid-crystal matrix,�?? Opt. Lett. 27, 652�??654 (2002).
[CrossRef]

D. E. Leaird and A. M. Weiner, �??Femtosecond direct space-to-time shaping in an integrated optical configuration,�?? Opt. Lett. 29, 1551�??1553 (2004).
[CrossRef] [PubMed]

D. E. Leaird and A. M. Weiner, �??Chirp control in the direct space-to-time pulse shaper,�?? Opt. Lett. 25, 850�??852 (2000).
[CrossRef]

Rev. Sci. Instrum. (1)

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

Other (2)

C. Froehly, B. Colombeau, and M. Vampouille, �??Shaping and analysis of picosecond light pulses,�?? in Prog. Opt. XX, E. Wolf, ed., pp. 65�??153 (Elsevier, Amsterdam, 1983).

A. E. Siegman, Lasers (University Science Books, Sausalito, 1986).

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Figures (6)

Fig. 1.
Fig. 1.

Sketch of the conventional f - f configuration DST pulse shaper. Here, the spatial amplitude distribution immediately prior to the grating may be a projection of a spatial mask applied to the input beam prior to the DST pulse shaper (for example, via an imaging or telescopic operation).

Fig. 2.
Fig. 2.

Schematic representation of the DST pulse-shaper with controlled output dispersion. In contrast to the conventional DST pulse shaper, the spatial amplitude distribution s(x) is not necessarily related to the mask m(x) by a simple projection operation due to the free space propagation through the distance R. Thus, the spatial amplitude distribution at the grating is now the (tunable, based on the distance R) Fresnel transform of the mask.

Fig. 3.
Fig. 3.

The compact DST pulse shaper. Here, the LC-SLM allows dynamic reprogramming of both the spatial mask m(x) and the focal length of the pulse shaping lens f.

Fig. 4.
Fig. 4.

The solid lines are the measured intensity cross-correlations (bottom axis) of the DST pulse shaper output for a spatial mask m(x) consisting of a slit of width 2a=0.8 mm (in green), 2.4 mm (in red) and 4.8 mm (in blue) and a lens of focal distance f =1.3 m. The SLM is positioned at a distance R=310 mm from the diffraction grating. The dashed lines show the computer simulations of the Fresnel diffraction pattern over the grating (top axis).

Fig. 5.
Fig. 5.

Intensity cross-correlation measurements of the output pulse sequence of the system of Fig. 3. In the setup the distance R (from the SLM to the diffraction grating in Fig. 3) is fixed to R=310 mm and the focal distance takes the values f=0.8 (blue), 1.0 (red) and 1.3 m (green). The mask is a multiple aperture constituted with seven slits of width 2a=0.6mm and spatial period of 1.0 mm.

Fig. 6.
Fig. 6.

Spectral scaling properties of the spectrometer with a periodic binary amplitude sequence as an input mask. In the setup the distance R (from the SLM to the diffraction grating in Fig. 3) is fixed to R=310 mm and the focal distance is varied from f =0.8 (blue), 1.0 (red), to 1.3 m (green). The dashed lines indicate the simulated position of the peaks for a flat spectrum. The top trace illustrates the spectrum that should be obtained in the conventional case of f - f alignment.

Equations (30)

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E g ( x , ω ) E in ( ω ) s ( x ) .
E g + ( x , ω ) E in ( ω ) s ( αx ) exp [ j γ ( ω ω o ) x ] ,
γ = λ o cp cos θ d , ps mm
α = cos θ i cos θ d .
E s ( x , ω ) E in ( ω ) dx s ( αx′ ) exp { j [ ω o cf x γ ( ω ω o ) ] x′ }
E in ( ω ) s { 1 α [ ω o cf x γ ( ω ω o ) ] } ,
E s + ( x , ω ) E in ( ω ) s { γ α [ ω ω ( x s ) ] } ,
e out ( t ) e in ( t ) * s ( α γ t )
γ α = λ o cp cos θ i
s ( x ) = m ( x ) * exp ( i π λ o R x 2 ) .
e out ( t ) e in ( t ) * m ( α γ t ) * exp ( i π λ o R α 2 γ 2 t 2 ) .
s ( x ) = M ( 2 π λ o R x ) exp ( i π λ o R x 2 ) .
e out ( t ) e in ( t ) * [ M ( 2 π λ 0 α t ) exp ( i π λ 0 R α 2 γ 2 t 2 ) ] ,
[ A B C D ] = [ 1 R 0 1 ] [ 1 0 1 / f 1 ]
= [ 1 0 1 / f eq 1 ] [ M eq 0 0 1 / M eq ] [ 1 L eq 0 1 ] .
L eq = Rf f R ,
M eq = f R f ,
f eq = f R .
E g ( x , ω ) = E in ( ω ) s ( x ) = { m ( x M eq ) * exp ( i π λ o L eq x 2 M eq 2 ) } exp ( i π λ o f eq x 2 ) ,
E g + ( x , ω ) = E in ( ω ) { m ( αx M eq ) * exp ( i π λ o L eq α 2 x 2 M eq 2 ) }
× exp ( i π α 2 λ o f eq x 2 ) exp [ j γ ( ω ω o ) x ] .
E s ( x , ω ) = E in ( ω ) { m ( α M eq x ) * exp ( i π λ o L eq α 2 M eq 2 x 2 ) } ,
k = 2 π α 2 f eq λ o x γ ( ω ω 0 ) .
e out ( t ) e in ( t ) * m ( α γ t ) * exp ( i Φ 2 2 α 2 γ′ 2 t 2 ) .
γ′ α = M eq γ α ,
Φ 2 = 2 π λ o 1 L eq .
m ( x ) = rect ( x 2 a ) * n = 1 7 δ ( x nb )
e out ( t ) e in ( t ) * [ rect ( α 2 a γ t ) * exp ( i Φ 2 2 α 2 γ 2 t 2 ) ] * n = 1 7 δ [ α γ ( t + n γ α b ) ] .
E out ( ω ) 2 = E in ( ω ) M { γ α [ ω ω ( x s ) ] } 2
E out ( λ ) 2 E in ( λ ) M [ 2 π λ o f R f ( x s ) λ p cos θ 1 ] 2 .

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