  In this paper, we compute a full atlas of radio, X-ray and $\gamma$-ray pulse
profiles relying on the force-free magnetosphere model. Our goal is to use such
data bank of multi-wavelength profiles to fit a substantial number of
radio-loud $\gamma$-ray pulsars also detected in non-thermal X-rays to decipher
the X-ray radiation mechanism and sites. Using results from the third
$\gamma$-ray pulsar catalogue (3PC), we investigate the statistical properties
of this population. We assume that radio emission emanates from field lines
rooted to the polar caps, at varying height above the surface, close to the
surface, at an altitude about 5-10% of the light-cylinder radius $r_{\rm L}$.
The X-ray photons are produced in the separatrix region within the
magnetosphere, i.e. the current sheet formed by the jump from closed to open
magnetic field lines. We allow for substantial variations in emission height.
The $\gamma$-ray are produced within the current sheet of the striped wind,
outside the light-cylinder. A comprehensive set of light-curves in radio, X-ray
and $\gamma$-ray has been computed. Based on only geometric considerations
about magnetic obliquity, line of sight inclination and radio beam cone opening
angle, pulsars can be classified as radio-loud or quiet and $\gamma$-ray loud
or quiet. We found that the 3PC sample is compatible with an isotropic
distribution of obliquity and line of sight. The atlases constructed in this
work are the fundamental tools to explore individual pulsars and fit their
multi-wavelength pulse profiles in order to constrain their magnetic topology,
the emission sites as well as the observer line of sight.
