Contribution of multiple electron trajectories to high-harmonic generation in the few-cycle regime

We use a few-cycle, carrier-envelope-phase (CEP) stabilized laser system to generate high-harmonic emission in argon, neon, and carbon dioxide. The high-harmonic spectra consist of discrete harmonic orders whose positions shift as a function of the CEP. Near the cutoff harmonic, the peaks are separated by two photon orders, and can correspond to either even or odd harmonics of the driving laser frequency, depending on the value of the CEP. In the plateau region, harmonic orders are separated by only one photon order. We develop a simple model which predicts the observed behavior. We use the observed dependence of the harmonic peaks as a function of CEP as a method to measure the statistical CEP fluctuations of the laser system. The measured rms fluctuation of 0.17 radians agrees with optical measurements. The high-harmonic approach to measuring CEP stability has the advantage that it is less sensitive to laser intensity fluctuations than are optical methods.