As carrier-envelope phase contributes to high-order harmonic phase: effects on the electric field of attosecond pulses

In this work we report on a self-referencing technique for the measurement of the effect of the carrier-envelope phase (CEP) of the driving pulses on the phase difference between consecutive harmonics. By using a numerical model based on the nonadiabatic saddle-point method [1] we demonstrate that, in particular experimental conditions, it is possible to directly control the electric field of the attosecond pulses by controlling the electric field of the driving pulses. Harmonic emission has been produced focusing femtosecond light pulses (800-nm central wavelength), into an argon jet, located around the focus of the laser beam to enhance the contribution of the long quantum paths. The CEP of the infrared (IR) pulses has been stabilized as described in [2] and has been varied by introducing in the beam path a glass plate with variable thickness. Upon increasing the intensity of the IR pulses the harmonic peaks broaden and eventually overlap in the spectral region between consecutive odd harmonics, where distinct spectral peaks, whose position is CEP dependent, are formed. This is due to the fact that the temporal variation of the IR pulse intensity produces a harmonic chirp, which broadens the spectrum of each individual harmonic. This effect is more significant in the case of the long quantum paths. If the spectral broadening is larger than the frequency separation between consecutive harmonics, the high-frequency side of the qth-harmonic spectrum, generated on the leading edge of the IR pulse, overlaps the low-frequency side of the spectrum of (q+2)th harmonic, generated on the pulse trailing edge, thus giving rise to the observed interference effect. We have then varied the CEP, ?. Figure 1 shows the portion between 13th and 15th harmonics of nine spectra for different amounts ?z of glass in the beam path, corresponding to different CEPs in the range ?0