We present the first fabrication and investigation of visible-light subwavelength transmission gratings in high refractive index materials (e.g., amorphous silicon) on silica substrates. The gratings have periods ranging from 100 to 800 nm in 50 nm increments, a thickness of 180 nm (very thin), and they were fabricated using electron-beam lithography and reactive ion etching. Because of the high index, we have observed, for the first time, strong polarization dependence in light transmittance. The polarization effect was found to greatly depend on the ratio of grating period to wavelength, having the largest variation when the period is near half of the wavelength. The largest transmission difference for the polarization parallel and perpendicular to the grating fingers was found to be 12 dB. This observation contradicts the behavior manifested in subwavelength transmission gratings in low index materials, where the transmittance is essentially independent of the light polarization and the grating period. Rigorous electromagnetic theory has been used to model the gratings and agrees with experiments.