  We investigate the properties of the most optically faint sources in the
GOODS-N area (R > 26.5 AB). Such extremely optically faint populations present
an uncharted territory despite the fact that they represent an appreciable
fraction of the X-ray sources in the GOODS-N field. They are believed to
contain either red AGN at moderate redshifts or possibly QSO at very high
redshift. We compile our sample by first finding the 3.6um IRAC counterparts of
the X-ray sources and searching for the optical counterparts of the IRAC
sources. 35 sources do not have counterparts in the R-band Subaru optical
images. Of these, 18 have HST-ACS counterparts while the remaining have no
optical counterparts. The vast majority of our 35 sources are classified as
Extremely Red Objects (EROs) on the basis of their V-K lower limits. Their
photometric redshifts show that these populate moderate redshifts (median
z~2.8), being markedly different from the already spectroscopically identified
population which peaks at z~0.7. The Spitzer-IRAC mid-IR colours of the sources
which have no HST counterparts tend to lie within the mid-IR colour diagram AGN
"wedge", suggesting either QSO, ULIRG (Mrk231), or early-type galaxy templates
at z>3. A large fraction of our sources (17/35), regardless of whether they
have HST counterparts, can be classified as mid-IR bright/optically faint
sources (Dust Obscured Galaxies) a class which is believed to include many
heavily absorbed AGN. The co-added X-ray spectrum of the optically faint
sources is very flat having a spectral index of Gamma~0.87, significantly
flatter than the spectrum of the X-ray background. The optically faint R>26.5
X-ray sources constitute more than 50% of the total X-ray population at
redshifts z>2 bearing important implications for the luminosity function and
its evolution; considering X-ray sources with 2<z<4 we find good agreement with
a modified PLE model.
