$\Gamma_i$’s define a positive linear chirp; i.e., smaller frequencies (longer wavelengths) arrive first. On the contrary, negative chirps arise for negative $\Gamma_i$ values. In both cases, two parts of the pulse separated by a duration $\Delta t$ have different frequencies, whose separation is, according to Eq. \[frequency\]: $$\label{dw}
\Delta\omega(\Delta t) = 2\Gamma_i\Delta t.$$ For a CHG FEL that operates in the pulse splitting regime, with the radiators tuned at the harmonic $n$ and the two sub-pulses separated by $\Delta t$, we thus expect the frequency separation between the two spectral peaks to be: $$\label{dwn}
\Delta\omega _n = n\Delta\omega$$ For the sake of convenience, in the reminder of this paper, we will speak in terms of wavelength $\lambda$, instead of angular frequency $\omega$ and will therefore consider $\Delta\lambda _n$ as the spectral separation of the two peaks of the FEL emission.

![Evolution of $\Delta\lambda(4\sigma_t)$ as a function of $\sigma_t$ for the following bandwidths of the seed carrying a linear positive chirp: $\sigma_{\lambda}=0.3\,$nm (dashed line) and $\sigma_{\lambda}=0.5\,$nm (full line). These values correspond to limiting cases of accessible Gaussian spectra at FERMI@Elettra. For a negative chirp, one gets the same values of $\Delta\lambda(4\sigma_t)$, but with opposite sign. The $\sigma_t$ corresponding to $\Delta\lambda(4\sigma_t) = 