  We theoretically derive the polarization-resolved intensity distribution of a
$TM$-polarized fundamental Gaussian beam reflected by an air-glass plane
interface at Brewster incidence. The reflected beam has both a dominant ($TM$)
and a cross-polarized ($TE$) component, carried by a $\text{TEM}_{10}$ and a
$\text{TEM}_{01}$ Hermite-Gaussian spatial mode, respectively. Remarkably, we
find that the $TE$-mode power scales quadratically with the angular spread of
the incident beam and it is comparable to the $TM$-mode power. Experimental
confirmations of the theoretical results are also presented.
