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Brewster cross-polarization

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.