  The relativistic jets produced by some Active Galactic Nuclei (AGNs) are
among the most efficient persistent sources of non-thermal radiation and
represent an ideal laboratory for studying high-energy interactions. In
particular, when the relativistic jet propagates along the observer's line of
sight, the beaming effect produces dominant signatures in the observed spectral
energy distribution (SED), from the radio domain up to the highest energies,
with the further possibility of resulting in radiation-particle multi-messenger
associations. In this work, we investigate the relationships between the
emission of $\gamma$ rays and the optical spectra of a sample of AGN, selected
from BL Lac sources detected by the $Fermi$ Large Area Telescope ($Fermi$-LAT).
We find that there is a close relationship between the optical and $\gamma$-ray
spectral indices. Despite all the limitations due to the non-simultaneity of
the data, this observation strongly supports a substantial role of
Synchrotron-Self Compton (SSC) radiation in a single zone leptonic scenario for
most sources. This result simplifies the application of theoretical models to
explore the physical parameters of the jets in this type of sources.
