Abstract

We show that the spatio-temporal distortion, spatial chirp, is naturally and easily measured by single-shot versions of second-harmonic generation frequency-resolved optical gating (SHG FROG) (including the extremely simple version, GRENOUILLE). While SHG FROG traces are ordinarily symmetrical, a pulse with spatial chirp yields a trace with a shear that is approximately twice the pulse spatial chirp. As a result, the trace shear unambiguously reveals both the magnitude and sign of the pulse spatial chirp. The effects of spatial chirp can then be removed from the trace and the intensity and phase vs. time also retrieved, yielding a full description of the spatially chirped pulse in space and time.

© 2002 Optical Society of America

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References

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    [CrossRef]
  6. C. Dorrer, E.M. Kosik, I.A. Walmsley, �??Spatio-temporal characterization of the electric field of ultrashort optical pulses using two-dimensional shearing interferometry,�?? Appl. Phys. B 74 [Suppl.], S209-S217 (2002).
    [CrossRef]

Appl. Phys. B (1)

C. Dorrer, E.M. Kosik, I.A. Walmsley, �??Spatio-temporal characterization of the electric field of ultrashort optical pulses using two-dimensional shearing interferometry,�?? Appl. Phys. B 74 [Suppl.], S209-S217 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. G. Kostenbauder, �??Ray-Pulse Matrices: A Rational Treatment for Dispersive Optical Systems,�?? IEEE J. Quantum Electron. 26, 1148-1157 (1990).
[CrossRef]

J. Quantum Electron. (1)

C. Iaconis, C., I.A. Walmsley, �??Self-referencing spectral interferometry for measuring ultrashort optical pulses," J. Quantum Electron. 35, 501-509 (1999).
[CrossRef]

Opt. Commun. (1)

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco and A. Mysyrowicz, �??A simple method for the determination of the intensity and phase of ultrashort optical pulses,�?? Opt. Commun. 113, 79-84 (1994).
[CrossRef]

Opt. Lett. (1)

Other (1)

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic Publishers, 2002).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

A prism compressor, which utilizes four identical Brewster prisms (or two and a mirror), which, if misaligned, yields spatial chirp in a pulse. If the prism separations, apex angles, or incidence angles are not precisely the same, spatial chirp results. Even slight amounts of beam divergence or expansion inside this device can yield significant spatial chirp in the output pulse.

Fig. 2.
Fig. 2.

An ultrashort pulse propagating through a simple plane-parallel window. Even a slight tilt of the window yields spatial chirp in the transmitted pulse, despite the absence of angular dispersion.

Fig. 3.
Fig. 3.

Spatial chirp in single-shot SHG FROG. Two spatially chirped pulses are crossed at an angle in the SHG crystal. This yields variable delay mapped onto transverse axis. The crystal yields the autocorrelation signal of the pulse for the purpose of measuring its intensity and phase vs. time. However, spatial chirp causes a variation of the autocorrelation signal wavelength vs. distance (i.e., vs. delay). This yields a shear in the SHG FROG trace proportional to the magnitude of the spatial chirp.

Fig. 4.
Fig. 4.

Spatial chirp and GRENOUILLE. A spatially chirped pulse enters the Fresnel biprism from the left. The Fresnel biprism splits the pulse into two, which then cross in the SHG crystal. While the crystal yields the autocorrelation signal of the pulse for the purpose of measuring its intensity and phase vs. time, spatial chirp causes a variation of the autocorrelation signal wavelength vs. distance. This yields a shear in the GRENOUILLE trace proportional to the magnitude of the spatial chirp. Note that the slopes in both single-shot SHG FROG and GRENOUILLE are exactly the same.

Fig. 5.
Fig. 5.

Spatial chirp causes shear in both GRENOUILLE traces and spatio-spectral plots. The spatial-chirp-induced slope of the FROG trace is approximately twice the spatial chirp and hence twice that of the spatio-spectral trace.

Fig. 6.
Fig. 6.

Modified prism pulse compressor: translation stage used between last two prism provides variable prism separation and can be used to align and misalign the compressor.

Fig. 7.
Fig. 7.

Experimental GRENOUILLE traces and spatio-spectral plots. The shear in GRENOUILLE traces clearly reveals the existence and sign of spatial chirp.

Fig. 8.
Fig. 8.

Slopes of GRENOUILLE traces and corresponding spectrum vs. position slopes for various amounts of spatial chirp.

Fig. 9.
Fig. 9.

Retrieval of intensity and phase of a pulse which does not have significant amount of spatial chirp. The FWHM pulse width is 123.7 fs. FROG error is 0.42% for this measurement.

Fig. 10.
Fig. 10.

Retrieval of intensity and phase of a pulse with spatial chirp after the shear is taken out from the trace. The FWHM pulse width is 129.3 fs. Note that the pulse broadens due to its narrower spectrum. The FROG error is 0.41% for this measurement.

Equations (9)

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I FROG SHG ω τ = { E ( t ) exp [ i ω 0 t ] } { E ( t τ ) exp [ i ω 0 ( t τ ) ] } exp [ i ω t ] dt 2
I FROG SHG ω τ = E ( t ) E ( t τ ) exp [ i ( ω 2 ω 0 ) t ] dt 2
I FROG SHG sp ch ω τ =
E ( t ) exp [ i ( ω 0 + ξ x ) t ] E ( t τ ) exp [ i ( ω 0 + ξ x ) ( t τ ) ] exp [ iωt ] dt 2
I FROG SHG sp ch ω τ = E ( t ) E ( t τ ) exp [ i ( ω 2 ω 0 2 ξ x ) t ] dt 2
I FROG SHG sp ch ω τ = I FROG SHG ω 2 ξ x τ
I FROG SHG sp ch ω τ = I FROG SHG ω 2 ξ x αx
I FROG SHG ω αx = I FROG SHG sp ch ω + 2 ξx αx
E x t = I ( t ) exp [ i ( ω 0 + ξ x ) t i ϕ ( t ) ]

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