  We present a new method to quantify the value of the escape fraction of
ionizing photons, and the existence of ultra-faint galaxies clustered around
brighter objects during the epoch of cosmic reionization, using the diffuse
Ly$\alpha$, continuum and H$\alpha$ emission observed around galaxies at
$z\sim6$. We model the surface brightness profiles of the diffuse halos
considering the fluorescent emission powered by ionizing photons escaping from
the central galaxies, and the nebular emission from satellite star-forming
sources, by extending the formalisms developed in Mas-Ribas & Dijkstra (2016)
and Mas-Ribas et al. (2017). The comparison between our predicted profiles and
Ly$\alpha$ observations at $z=5.7$ and $z=6.6$ favors a low ionizing escape
fraction, $f_{\rm esc}^{\rm ion}\sim5\%$, for galaxies in the range $-19\gtrsim
M_{\rm UV} \gtrsim -21.5$. However, uncertainties and possible systematics in
the observations do not allow for firm conclusions. We predict H$\alpha$ and
rest-frame visible continuum observations with JWST, and show that JWST will be
able to detect extended (a few tens of kpc) fluorescent H$\alpha$ emission
powered by ionizing photons escaping from a bright, $L\gtrsim 5L^*$, galaxy.
Such observations can differentiate fluorescent emission from nebular emission
by satellite sources. We discuss how observations and stacking of several
objects may provide unique constraints on the escape fraction for faint
galaxies and/or the abundance of ultra-faint radiation sources.
