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Single-shot, high-repetition rate carrier-envelope-phase detection of ultrashort laser pulses

Chen Guo, Miguel Miranda, Ann-Kathrin Raab, Anne-Lise Viotti, Paulo Tiago Guerreiro, Rosa Romero, Helder Crespo, Anne L’Huillier, and Cord L. Arnold

Open Access Open Access

Abstract

We propose a single-shot, high-repetition rate measurement scheme of the carrier-envelope phase offset of ultrashort laser pulses. The spectral fringes resulting from f-2f nonlinear interferometry, encoding the carrier-envelope-phase, are evaluated completely optically via an optical Fourier transform. For demonstration, the carrier-envelope-phase of a 200 kHz, few-cycle optical parametric chirped-pulse amplification (OPCPA) laser system was measured employing an interferometer as a periodic optical filter. The proposed method shows excellent agreement with simultaneous measurement of the spectral fringes by a fast line-scan camera.

Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Supplementary Material (1)

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Supplement 1       Supplemental Document

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (5)
Fig. 1.
Fig. 1. Basic concept of an optical Fourier transform. (a) Fringes from the f-2f interferometer and (b) absolute value of the Fourier transform of the signal; panels (c) and (d) illustrate sine- and cosine-like filters that are used to perform the partial Fourier transform from which the phase $\varphi$ can be obtained as the arctan between $x_0$ and $y_0$ as illustrated in panel (e), with background $c$ removed.

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Fig. 2.
Fig. 2. Schematic of the experimental setup: PBS, polarizing beam splitter; PD, photodiode; ADC, analog-to-digital converter. The PBS and PD assemblies in the analog detector are rotated by 45$^{\circ }$ relative to the plane of the figure.

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Fig. 3.
Fig. 3. CEP measurements from the analog detector, in a mode where it is compared with the digital detector (blue) or as a stand-alone device (red and yellow). The red and blue results are obtained with unstabilized CEP, whereas the yellow makers correspond to a stabilized CEP. Fitted ellipses, according to Eq. (6), are plotted as cyan dashed lines. The insert illustrates how the phase uncertainty is determined from the intensity fluctuations.

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Fig. 4.
Fig. 4. Measurement results from the digital CEP detector. (a) A single-shot measurement of the spectral fringes from the f-2f interferometer. (b) Absolute value of the Fourier transform of the spectral fringes in logarithmic scale.

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Fig. 5.
Fig. 5. Comparison between the measurement results of the digital and analog detector. (a) Phase differences at maximum overlap and (b) Fourier transform of the phase difference (blue), Fourier transform of the laser intensity (red), and fitted $1/f$ line (dashed black).

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Equations (7)

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x + i y = ∫ − ∞ ∞ I ( ω ) exp ⁡ ( − i ω τ ) d ω ,
x 0 = ∫ − ∞ ∞ I ( ω ) cos ⁡ ( ω τ 0 ) d ω , y 0 = − ∫ − ∞ ∞ I ( ω ) sin ⁡ ( ω τ 0 ) d ω .
A p ( 1 ) ( ω ) = A s ( 1 ) ( ω ) = 1 2 A 0 ( ω ) e i ω τ 1 ,
A p ( 2 ) ( ω ) = 1 2 A 0 ( ω ) e i ( ω τ 2 − π 2 + Δ ϕ ) , A s ( 2 ) ( ω ) = 1 2 A 0 ( ω ) e i ω τ 2 .
x = 1 2 ∫ − ∞ ∞ a ( ω ) I ( ω ) cos ⁡ ( ω τ 0 ) d ω , y = 1 2 ∫ − ∞ ∞ b ( ω ) I ( ω ) sin ⁡ ( ω τ 0 + Δ ϕ ) d ω ,
x = a I 0 cos ⁡ φ , y = b I 0 sin ⁡ ( φ − Δ ϕ ) ,
x ′ = I 0 cos ⁡ φ = x a , y ′ = I 0 sin ⁡ φ = y b cos ⁡ Δ ϕ + x ′ tan ⁡ Δ ϕ .
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