Influence of chirp and carrier-envelope phase on noninteger high-harmonic generation

High harmonic generation (HHG) is a versatile technique for probing ultrafast electron dynamics. While HHG sensitive to the electronic properties of target, also depends on waveform laser pulse. As well known, (peak) positions, $\omega$, in high-harmonic spectrum can shift when carrier envelope phase (CEP), $\varphi$ varied. We derive formulae describing corresponding parametric dependencies CEP shifts; particular, we have transparent result shift, $d\omega/d\varphi = {-} 2 \bar{\mathfrak f}' \omega/\omega_0$, where $\omega_0$ describes fundamental frequency and $\bar{\mathfrak f}'$ characterizes chirp driving compare analytical formula full-fledged numerical simulations finding only 17 % average relative absolute deviation $d\omega/d\varphi$. Our fully consistent with experimental observations.