Second-order scattering induced reflection divergence and nonlinear depolarization on randomly sub-wavelength corrugated semiconductor nano-pillar surface is observed, which explains the nonlinear transverse electric (TE)/transverse magnetic (TM) mode transformation of the nano-pillar surface reflection with diminishing Brewster angle. The reflected polarization ratios are degraded from 97.5% to 53% and from 96.8% to 40% under TM- and TE-mode incidences by increasing Si nano-pillar height from 30 to 240 nm. A small-perturbation modeling corroborates the scattering induced second-order polarization transformation to depolarize the reflection from highly corrugated Si nano-pillar surface. The lower polarization ratio at TE-mode reflection caused by a severer inhomogeneous Si nano-pillars oriented in parallel with surface normal is concluded. With field polarization ratio under TM-mode incidence, the angular dependent reflectance spectra with a gradually diminished and shifted Brewster angle from 74o to 45o can be simulated. The nano-roughened surface induced second-order scattering model correlates the diminishing Brewster angle with the surface depolarized reflection.
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