Method of matrix Riccati equation for nanoshape control of diffraction gratings

Reflection spectra of one dimensional diffraction gratings are calculated on the basis of an exact, fast approach, uniting several modern methods, to the theory of electromagnetic wave multiple scattering in two dimensional inhomogeneous dielectric media which uses the technique of matrix Riccati equation. The sensitivity of computed reflection spectra to distortions of a grating shape (strip like, triangular, trapezoidal) for metal and dielectric structures is demonstrated. Distortions of the lamellar grating shape are simulated by the roundness of sharp edges of the grating. In particular, the computations shows that the roundness of grating ruling (150 nm wide and 300 nm hegh) edges with a curvature radius as small as 10 nm can be detected by changing the intensity of specular reflected light (500 nm wavelength) provided that the grating has a subwavelength period (300 nm) even in the case of low dielectric contrast.