Carrier-envelope-phase characterization of ultrafast mid-infrared laser pulses through harmonic generation and interference in argon

The propagation of an intense, femtosecond, mid-infrared laser pulse in a gaseous medium results in the efficient generation of spectrally overlapping low-order harmonics, whose optical carrier phases are linked to the carrier-envelope phase (CEP) of the mid-infrared driver pulse. Random peak-power fluctuations of the driver pulses, converted to the fluctuations of the nonlinear phases, acquired by the pulses on propagation, cause this phase correlation to smear out. We show that this seemingly irreversible loss of phase can be recovered, and that the complete information needed for the phase correction is contained in the harmonic spectra itself. The optical phases of the intense driver pulse and its harmonics, as fragile as they appear to be against even weak disturbances, evolve deterministically during highly nonlinear propagation through the extended ionization region.