Carrier-envelope phase (${\varphi }_{\mathrm{CE}}$)

The carrier-envelope phase locates the carrier oscillation relative to the envelope of an optical pulse. In $E_{\mathrm{real}}(t)=F(t)\cos ({\omega }_{0}t+{\varphi }_{\mathrm{CE}})$ with envelope maximum at zero, it is the displayed phase modulo $2\pi$. Few-cycle dynamics can depend on it even when cycle-averaged light intensity is unchanged. A pulse train's phase increment is related to its carrier-envelope offset frequency; signs depend on the complex-field convention.