Carrier Envelope Phase Description for an Isolated Attosecond Pulse by Momentum Vortices

As a crucial parameter for a few-cycle laser pulse, the carrier envelope phase (CEP) substantially determines the laser waveform. We propose a method to directly describe the CEP of an isolated attosecond pulse (IAP) by the vortex-shaped momentum pattern, which is generated from the tunneling ionization of a hydrogen atom by a pair of time-delayed, oppositely and circularly polarized IAP-IR pulses. Superior to the angular streaking method that characterizes the CEP in terms of only one streak, our method describes the CEP of an IAP by the features of multiple streaks in the vortex pattern. The proposed method may open the possibility of capturing sub-cycle extreme ultraviolet dynamics.