Analysis of temporal broadening of isolated attosecond pulses induced by periodic Mo/Si multilayer mirrors reflection

When using a multilayer mirror to reflect an attosecond pulse, the temporal broadening effect always happens, and enlarges the duration of incident attosecond pulse. In this paper, the temporal broadening of an isolated attosecond pulse induced by a periodic Mo/Si multilayer mirror reflection is analyzed. In order to evaluate the effect of pulse broadening quantitatively, two temporal parameters, the pulse broadening coefficient and the pulse reflection coefficient, are used. By studying two temporal parameters of periodic Mo/Si multilayer mirrors with different bi-layers for incident isolated attosecond pulses with various durations, we find that the incident isolated attosecond pulse with smaller duration suffers from more serious pulse broadening and energy loss, when reflected by a periodic Mo/Si multilayer mirror. In addition, a periodic Mo/Si multilayer mirror with more bi-layers causes more serious pulse broadening for an incident isolated attosecond pulse, even though it can provide larger pulse reflection efficiency. Furthermore, by analyzing of the reflectivity and the dispersion of periodic multilayer mirrors in the spectral region of incident pulses, we demonstrate that the spectrum filtering and dispersion inducing by periodic Mo/Si multilayer mirrors are responsible for the pulse broadening of incident isolated attosecond pulses. The study of pulse broadening induced by periodic Mo/Si multilayer mirrors reflection could improve the understanding of the performances of periodic multilayer mirrors for pulse reflection, and provide a guide for high-performance attosecond multilayer mirrors design.