Transmission of polarized infrared radiation through lamellar gratings on a silicon wafer

Abstract

Studies of the zero angle of incidence transmission through lamellar gratings on silicon wafers were performed with polarized radiation in the spectral interval from 1.5 to 14 μm. All measured spectra consist of two parts: an oscillatory part at the wavelengths smaller than the grating period, and a nonoscillatory part at the wavelengths larger than the grating period. In some cases the transmittance in the oscillatory parts can be low, down to 4%, that demonstrates the effect of infrared “color separation.” We found experimentally that for gratings with periods larger than the maximum wavelength, the shape of the spectrum is polarization independent, while for gratings with periods smaller than the maximum wavelength the spectrum is very sensitive to the polarization of the radiation, especially in the nonoscillatory part. These results are consistent with the electromagnetic theory which states that at wavelengths smaller than the typical distance of index variations scalar approximation works, making no difference between the polarization states of radiation, whereas in the opposite case vector treatment is required. We developed a method of smoothing the interference fringes that emerge theoretically due to Fabry–Perot resonances in the substrate, but are not seen in the experiment due to the scattering of radiation by imperfections in the substrate. The method assumes this scattering to cause fluctuations of optical-path phase φo through the substrate. To calculate the apparent transmittance, the fringed one is specially filtered over φo. It is shown that for gratings with large periods the transmission spectra measured in our experimental conditions can be accounted for provided that one adopts a certain contribution of the ± first-order beam. The numerical simulations are in good agreement with experimental results.