Fig. 3: Mechanism of lineshape control.
From: Controlling rotational air lasing lineshape by carrier-envelope offset phase
a Amplitude (blue solid line) and phase (green solid line) distribution of a Lorentz lineshape corresponding to one rotational lasing line. The phase of SPM is approximately flat and represented with the magenta line, whereas the SPM amplitude is a constant number (not shown). The relative phase difference between the SPM and the central position (i.e. resonant energy) of the lasing line is 2ΦCEP. The intersection between the green curve and the magenta line is corresponding to the relative phase difference of zero, giving rise to a constructive interference. b Calculated lineshapes after the interference between SPM and Lorentz lineshape at the CEP of 0 and 0.25π. Time-domain pictures for the interference between SPM and Lorentz dipole polarizations at CEP = 0 (c) and CEP = 0.25π (d). The broad-band phase-flat SPM is corresponding to the ultrafast emission at time zero as a delta function, representing with the magenta arrow, whereas the dipole polarization of the Lorentz lineshape, i.e. d(t) (complex-valued), is an amplitude-damped harmonic oscillation representing with the blue curve. At different CEPs, the azimuthal angle at the time zero is different. Only parallel components between SPM and air lasing result in the observed interference. In (e) we show the projections of d(t) on the direction of SPM at CEP of 0 and 0.25π, respectively, where the relative phase shift between them is the so-called Fano phase ΦFano, which is labeled in (e) and strictly equal to 2ΦCEP in our case.
