Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses

Abstract

We present a novel, self-referencing interferometric technique for measuring the amplitude and the phase of ultrashort optical pulses. The apparatus uses a collinear geometry that requires no moving components. The phase-retrieval procedure is noniterative and rapid and uses only two one-dimensional Fourier transforms. We apply the technique to characterize ultrashort pulses from a mode-locked Ti:sapphire oscillator.

Retrieval of the amplitude and phase of the dipole matrix element by attosecond electron-wave-packet interferometry

“…The interference of two delayed EWPs leads to an interferogram in the electron momentum distribution, where the relevant phase difference φ 21 is given by Eq. (7) or (12).…”

“…This interferogram carries information on the amplitude and phase of the EWPs. The QSPIDER technique for amplitude and phase retrieval is useful only for a limited range of delays and relative shears between the copies, similar to SPIDER [12,13]. These restrictions come from the conditions under which the retrieval algorithm can be applied.…”

“…We build upon the previous demonstration of the measurement of the EWP phase difference [7] to propose a general interferometric method for full characterization of the complex EWP and the dipole matrix element. We introduce the quantum spectral phase interferometry for direct electron wave-packet reconstruction (QSPIDER) technique which is a variant of the SPIDER [12,13] scheme, now applied to quantum mechanical wave functions.…”

“…A frequency shift, ω, or relative shear is introduced into one delayed copy of the pulse. For a laser pulse, E(ω), the signal measured in SPIDER can be written as S(ω) = |E(ω) + E(ω + ω)e −iωτ | 2 , where E(ω) is the electric field of the pulse to be characterized in the frequency domain and τ is the delay between the two copies [12].…”

Streaking at high energies with electrons and positrons

“…To achieve attosecond time resolution at lower energy scales, a variety of methods are employed. Autocorrelation schemes use the test pulse and its time-shifted replica (Frequency-Resolved Optical Gating (FROG) [20,21]) or the time-and frequency-shifted replica (Spectral Phase Interferometry for Direct Electric field Reconstruction (SPIDER) [22,23]), while cross-correlation schemes are based on the correlation between the test XUV pulse and a femtosecond infrared laser pulse. The latter can be weak, inducing few photon effects (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions (RABBITT) [2]) or strong, yielding attosecond streak imaging [24,25,26].…”