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Interferometric frequency-resolved optical gating

Gero Stibenz and Günter Steinmeyer

Open Access Open Access

Abstract

We demonstrate a novel variant of frequency-resolved optical gating (FROG) that is based on spectrally resolving a collinear interferometric autocorrelation rather than a noncollinear one. From the interferometric FROG trace, one can extract two terms, the standard SHG-FROG trace and a new phase-sensitive modulational component, which both allow for independent retrieval of the pulse shape. We compare the results of both methods and a separate SPIDER measurement using 6.5-fs pulses from a white-light continuum. We find that the novel modulational component allows for robust retrieval of pulse shapes in the few-cycle regime. Together with the added cross-checks, our method significantly enhances choices for pulse characterization in this regime.

©2005 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. Experimental arrangement of a dispersion balanced interferometric autocorrelator. Spectrally resolving the autocorrelation signal results in an interferometric FROG trace (See Fig. 2). The fringe substructure of the IFROG trace is preserved by triggering a fast camera with the encoder signal of a constant moving delay stage. ENC, encoder; OMA, optical multichannel analyzer.

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Fig. 2.
Fig. 2. Interferometric FROG. (a) Spectrally resolved interferometric autocorrelation (IFROG) trace. (b) Fourier transform of (a) along the delay axis. The dc baseband, two modulation side bands at the fundamental frequency ω 0, and two second harmonic side bands (at 2ω 0) are clearly separable. The dashed lines mark the borders of a super-Gaussian filter that was used for isolating the individual components.

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Fig. 3.
Fig. 3. Pulse retrieval from the dc part of the IFROG trace. (a) SH-FROG trace, as extracted from the IFROG trace. (b) Reconstructed SH-FROG trace. The FROG error of this reconstruction is 0.005. The retrieved temporal and spectral phase and intensity profiles of the pulse are plotted in Fig. 6(c) and (d).

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Fig. 4.
Fig. 4. Red curve: Frequency marginal after compensating the bandwidth limitation of the conversion process. Black dashed line: Convolution of the fundamental pulse spectrum.

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Fig. 5.
Fig. 5. Pulse retrieval from the ac part of the IFROG trace. (a) FM-FROG trace, i.e. modulated part at the interference period of the fundamental, phase-sensitively extracted from the IFROG data in Fig. 2(a). (b) Reconstructed FM-FROG trace derived by the implementation of a modified generalized projection method for the pulse-retrieval. The FROG error of this reconstruction is 0.0085. The retrieved temporal and spectral phase and intensity profiles of the pulse are plotted in Fig. 6(e) and (f).

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Fig. 6.
Fig. 6. Comparison of pulse shapes retrieved by SPIDER (a,b), SH-FROG (c,d), and FM-FROG (e,f). Temporal shapes are shown in (a, c, and e), reconstructed spectra are shown in (d) and (f). An independent measurement of the pulse spectrum, which also served for the marginal test, is shown in (b) together with the spectral phase measured in SPIDER. Intensities are shown in black, phases in red. The FWHM pulse durations are: 6.5 fs for SPIDER, 7.4 fs for SH-FROG, and 6.8 fs for FM-FROG.

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Equations (12)

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𝓔 ( t ) = E ( t ) exp ( i ω 0 t )
I IFROG ( ω , τ ) = ∣ ∫ − ∞ ∞ ( 𝓔 ( t ) + 𝓔 ( t − τ ) ) 2 exp ( − i ω t ) d t ∣ 2 .
E FROG ( Δ ω , τ ) = ∫ − ∞ ∞ E ( t ) E ( t − τ ) exp ( − i Δ ω t ) d t
E SH ( Δ ω ) = E FROG ( Δ ω , τ = 0 ) = ∫ − ∞ ∞ E 2 ( t ) exp ( − i Δ ω t ) d t ,
I IFROG ( ω , τ ) = ∣ ( 1 + exp ( − i ( 2 ω 0 + Δ ω ) τ ) ) E SH ( Δ ω ) + 2 exp ( − i ω 0 τ ) E FROG ( Δ ω , τ ) ∣ 2 .
I IFROG ( ω , τ ) = 2 ∣ E SH ( Δ ω ) ∣ 2 + 4 ∣ E FROG ( Δ ω , τ ) ∣ 2
+ 8 cos [ ( ω 0 + Δ ω 2 ) τ ] Re [ E FROG ( Δ ω , τ ) E SH * ( Δ ω ) exp ( i Δ ω 2 τ ) ]
+ 2 cos [ ( 2 ω 0 + Δ ω ) τ ] ∣ E SH ( Δ ω ) ∣ 2 .
I FMFROG ( Δ ω , τ ) = ∣ E FROG ( Δ ω , τ ) ∣ ∣ E FROG ( Δ ω , τ = 0 ) ∣ ×
cos ( φ FROG ( Δ ω , τ ) − φ FROG ( Δ ω , τ = 0 ) + Δ ω 2 τ )
Z = ∑ i , j = 1 N ∣ I FMFROG meas ( Δ ω i , τ j ) − I FMFROG ( k ) ( Δ ω i , τ j ) ∣ 2 .
E ( k + 1 ) ( t i ) = E ( k ) ( t i ) + μ ( ∂ Z ∂ Re [ E ( t i ) ] ) + i μ ( ∂ Z ∂ Im [ E ( t i ) ] )
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