Operator approach to electromagnetic coupled-wave calculations of lamellar gratings: Infrared optical properties of intrinsic silicon gratings

The system of coupled-wave equations for electromagnetic calculations of lamellar gratings is transformed to a new operator-vector form. The numerical procedure is based on truncation of the transformed system and proves to be stable, to be free of ill conditioning, and to preserve the power-conservation requirement for a lossless dielectric with high accuracy. To execute the procedure a very compact MATLAB-basperdo gram is developed, and numerical simulations for thick intrinsic silicon gratings are performed. Zero-reflectance phenomena at normal incidence for both TE and TM polarizations are studied. The ratios of the grating dimensions to be wavelengths at which these anomalies occur are found numerically. It is shown that by keeping the period- and slot-width-towavelength ratios constant and by increasing the slot depth one can repeat the anomalies. An antiblazing property at oblique incidence is also considered. The connection with recent directional polarized-emission experiments on intrinsic silicon gratings is discussed.