Abstract

In this work we demonstrate the ability of the spatiotemporal characterization technique STARFISH to retrieve the wavelength dependent wavefront of focused ultrashort laser pulses. The high resolution achievable with this technique allows measuring the wavefront at the focal spot. In particular, the method is applied to study the effects of focusing with a kinoform diffractive lens. The evolution from converging to diverging wavefronts as the pulse propagates along the focal region is analyzed for each wavelength. The spatiotemporal intensity and spatially resolved spectrum structure of the pulses, as well as their profiles on axis, are also presented. Numerical simulations of the propagation of such pulses confirm the experimental results.

© 2012 Optical Society of America

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References

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    [CrossRef]
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2012 (1)

2011 (3)

2010 (4)

2009 (5)

2007 (1)

2005 (2)

2003 (1)

1999 (1)

1997 (1)

V. Moreno, J. F. Román, and J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

1995 (1)

1989 (1)

1971 (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

Alonso, B.

Andrés, P.

Bates, P. K.

Biegert, J.

Bonaretti, F.

Bor, Z.

Borrego-Varillas, R.

Bowlan, P.

Bragheri, F.

Bueno, J. M.

Camino, A.

Chalus, O.

Cheng, Y.

Cheriaux, G.

Chin, S. L.

Chu, W.

Clerici, M.

Climent, V.

Cohen, M.

Couairon, A.

Degiorgio, V.

Di Trapani, P.

Dinh, K. Ba

L. Van Dao, K. Ba Dinh, and P. Hannaford, “Generation of extreme ultraviolet radiation with a Bessel-Gaussian beam,” Appl. Phys. Lett. 95, 131114 (2009).
[CrossRef]

Dorrer, C.

Faccio, D.

Fu, Y.

Gabolde, P.

Gopalan, V.

Griebner, U.

Grunwald, R.

Gu, M.

M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, 1999).

Guérineau, N.

Hannaford, P.

L. Van Dao, K. Ba Dinh, and P. Hannaford, “Generation of extreme ultraviolet radiation with a Bessel-Gaussian beam,” Appl. Phys. Lett. 95, 131114 (2009).
[CrossRef]

Hauri, C. P.

Hernández-Toro, J.

Jasapara, J.

Joffre, M.

Kebbel, V.

Keller, U.

Lancis, J.

Lepetit, L.

Li, H.

Liu, W.

Liu, Z.

Lotti, A.

Mann, K.

Marowski, G.

Matijosius, A.

Méndez, C.

Mendoza-Yero, O.

Mínguez-Vega, G.

Moreno, V.

V. Moreno, J. F. Román, and J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Neumann, U.

Platt, B. C.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

Primot, J.

Reimann, K.

Román, J. F.

V. Moreno, J. F. Román, and J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Romero, C.

Roso, L.

Rubino, E.

Rudolph, W.

Salgueiro, J. R.

V. Moreno, J. F. Román, and J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

San Román, J.

Schaefer, B.

Shack, R. V.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

Shi, K.

Sola, I. J.

Sola, Í. J.

Steinmeyer, G.

Tartara, L.

Trebino, R.

Van Dao, L.

L. Van Dao, K. Ba Dinh, and P. Hannaford, “Generation of extreme ultraviolet radiation with a Bessel-Gaussian beam,” Appl. Phys. Lett. 95, 131114 (2009).
[CrossRef]

Varela, O.

Varela, Ó.

Vázquez de Aldana, J. R.

Velghe, S.

Walmsley, I. A.

Wattellier, B.

Xiong, H.

Xu, H.

Xu, Q.

Xu, Z.

Yang, C.

Yao, J.

Zaïr, A.

Zeng, B.

Adv. Opt. Photon. (1)

Am. J. Phys. (1)

V. Moreno, J. F. Román, and J. R. Salgueiro, “High efficiency diffractive lenses: deduction of kinoform profile,” Am. J. Phys. 65, 556–562 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

L. Van Dao, K. Ba Dinh, and P. Hannaford, “Generation of extreme ultraviolet radiation with a Bessel-Gaussian beam,” Appl. Phys. Lett. 95, 131114 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

J. Opt. Soc. Am. B (4)

Opt. Express (6)

Opt. Lett. (8)

Y. Fu, H. Xiong, H. Xu, J. Yao, B. Zeng, W. Chu, Y. Cheng, Z. Xu, W. Liu, and S. L. Chin, “Generation of extended filaments of femtosecond pulses in air by use of a single-step phase plate,” Opt. Lett. 34, 3752–3754 (2009).
[CrossRef]

E. Rubino, D. Faccio, L. Tartara, P. K. Bates, O. Chalus, M. Clerici, F. Bonaretti, J. Biegert, and P. Di Trapani, “Spatiotemporal amplitude and phase retrieval of space-time coupled ultrashort pulses using the Shackled-FROG technique,” Opt. Lett. 34, 3854–3856 (2009).
[CrossRef]

G. Mínguez-Vega, C. Romero, O. Mendoza-Yero, J. R. Vázquez de Aldana, R. Borrego-Varillas, C. Méndez, P. Andrés, J. Lancis, V. Climent, and L. Roso, “Wavelength tuning of femtosecond pulses generated in nonlinear crystals by using diffractive lenses,” Opt. Lett. 35, 3694–3696 (2010).
[CrossRef]

J. Jasapara and W. Rudolph, “Characterization of sub-10 fs pulse focusing with high-numerical-aperture microscope objectives,” Opt. Lett. 24, 777–779 (1999).
[CrossRef]

R. Grunwald, U. Neumann, U. Griebner, K. Reimann, G. Steinmeyer, and V. Kebbel, “Ultrashort-pulse wave-front autocorrelation,” Opt. Lett. 28, 2399–2401 (2003).
[CrossRef]

S. Velghe, J. Primot, N. Guérineau, M. Cohen, and B. Wattellier, “Wave-front reconstruction from multi-directional phase derivatives generated by multilateral shearing interferometers,” Opt. Lett. 30, 245–247 (2005).
[CrossRef]

C. P. Hauri, J. Biegert, U. Keller, B. Schaefer, K. Mann, and G. Marowski, “Validity of wave-front reconstruction and propagation of ultrabroadband pulses measured with a Hartmann-Shack sensor,” Opt. Lett. 30, 1563–1565 (2005).
[CrossRef]

Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14, 119–121 (1989).
[CrossRef]

Other (1)

M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, 1999).

Supplementary Material (1)

» Media 1: MOV (738 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Scheme of the experimental setup: one replica of the laser pulse is used as reference and another replica is focused by a DL. The pulses are collected by the fibers of the coupler. The fiber in the reference arm controls the relative delay, whereas the fiber in the test arm spatially scans the unknown beam. The spatially resolved spectral interferometry is measured after the fiber coupler in the spectrometer. The position of the lens allows exploring different propagation distances.

Fig. 2.
Fig. 2.

(a) Wavefront as a function of the wavelength for a convergent wave (focused by a refractive lens). The wavefront for each wavelength is plotted in the color given by the colorbar; (b) Curvature of wavefronts (solid blue line) and theoretical value (dashed red line).

Fig. 3.
Fig. 3.

Results of the characterization at the focus of the achromatic doublet lens: (a) Spatially resolved spectrum; (b) Spatiotemporal intensity; (c) Spectrum on axis; (d) Intensity on axis colored by the instantaneous wavelength. The plots (a) and (b) are in a logarithmic scale (see colorbar) that comprises 2 orders of magnitude.

Fig. 4.
Fig. 4.

Simulated (left) and experimental (right): wavefront as a function of the wavelength before and after the focus of the DL. The wavefront for each wavelength is plotted in the color given by the colorbar inset (the same colorbar applies to all subplots in the figure).

Fig. 5.
Fig. 5.

Simulated (left) and experimental (right): spatially resolved spectrum before and after the focus of the DL. The logarithmic scale comprises 2 orders of magnitude (see colorbar inset).

Fig. 6.
Fig. 6.

Simulated (left) and experimental (right): spatiotemporal intensity before and after the focus of the DL. The logarithmic scale comprises 3 orders of magnitude (see colorbar inset).

Fig. 7.
Fig. 7.

On-axis normalized simulated spectrum (first column) and experimental spectrum (second column), simulated intensity (third column) and experimental intensity (forth column), as a function of the propagation distance (see labels on the left). The spectra are colored by their wavelengths. The same color scale applies to represent the instantaneous wavelength in the temporal intensity plots.

Fig. 8.
Fig. 8.

Iso-intensity surfaces I(x,y,t)=α·Imax—colored by the corresponding instantaneous wavelength—before and after the focus of the DL. The simulated (left) and experimental (right) results for α=0.1 are shown. Cylindrical symmetry is assumed to obtain the plot. Media 1 shows the same results for different levels of α ranging from 0.01 to 0.9.

Tables (1)

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Table 1. Spectral and Temporal Parameters of the Pulse Measured on Axis

Equations (2)

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S(ω)=Stest(ω)+Sref(ω)+2Stest(ω)Sref(ω)cos[ϕtest(ω)ϕref(ω)ωτ].
U2(r2,λ)=i2πλzexp(ikr222z)0U1(r1,λ)exp(ikr122z)J0(kr1r2z)r1dr1,

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