Carrier-envelope-phase dependence of harmonics induced by a few-cycle vortex laser

When a few-cycle vortex laser interacted with an inversion-symmetric atomic-like system, beyond the usual odd-order harmonics, some additional components also occur. The detailed numerical investigation on their transverse field distributions discloses that they depend sensitively on the carrier-envelope-phase (CEP) and the rotation period of the transverse distribution is 2π. This could be used to directly determine the CEP value of an incident pulse, unique without falling back on specific polar molecules or static electric fields.