Use of photoelectron energy spectrum transfer equation for the measurement of a narrowband XUV pulse

To study the time evolution of a molecular state in an ultra-fast chemical reaction, the use of shorter pulses with higher photon energy and narrower bandwidth for both pump and probe is necessary. However, quick and precise measurement of their detailed time structures is a challenge. Over the last decade, great efforts have been made to measure an attosecond extreme ultraviolet (XUV) pulse. To date, several methods have been developed to measure the pulse duration and completely reconstruct it. The attosecond spectral phase interferometry for direct electric field reconstruction (SPIDER) and attosecond frequency-resolved optical gating (FROG) techniques are often used. However, these methods use state-of-the-art experimental set-ups and complicated data analysis procedures. To develop attosecond metrology for practical use (e.g. timing, measurement, evaluation, calibration, optimization, pumping, probing), we propose a quick and analytical method to precisely observe an attosecond XUV pulse with laser-assisted photo-ionization. The method is based on determining the laser-related phase of each streaked electron and using a transfer equation for one-step pulse reconstruction without any time-resolved measurements, iterative calculations, or data fitting procedures. Temporal errors of the pulse reconstruction are calculated from the XUV bandwidth. Because the transfer equation establishes a direct connection between the XUV pulse properties, the crucial laser parameters (peak intensity, phase, carrier envelope phase), the atomic ionization potential, and the measured photoelectron energy spectrum, we can use it to study any one of these properties from other known information and probe the dynamic processes of an ultra-fast reaction.