Polarized spectral emittance from periodic micromachined surfaces. I. Doped silicon: The normal direction.

The normal, polarized spectral (3 \ensuremath{\mu}m\ensuremath{\le}\ensuremath{\lambda}\ensuremath{\le}14 \ensuremath{\mu}m) emittances of highly doped, micromachined, periodic structures on heavily phosphorus-doped (110) silicon ([P]\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$) were measured for pattern repeat scales, \ensuremath{\Lambda}, of 10, 14, 18, and 22 \ensuremath{\mu}m and depths ranging from 0.7 to 45 \ensuremath{\mu}m. These structures have dimensions that are comparable to the wavelengths of the measured radiation. The s-polarization vector in these measurements was perpendicular to the grating vector. The data demonstrated that the emittance from the deep structures is dominated by standing (quantized) electromagnetic waves in a direction normal to the surface similar to those in an organ pipe. Wood's singularities were clearly visible in the p-polarized emission on shallow gratings (depth \ensuremath{\le}1.5 \ensuremath{\mu}m). It is concluded that these measurements, particularly the s-polarized emission from deep gratings, cannot be explained by calculations of electromagnetic singularities on lamellar gratings.