Modified integral method for weak convergence problems of light scattering on relief grating

A rigorous modified integral method applicable for diffraction grating analysis working from x-ray - up to millimeter range is presented. The changes have been made both in theory, and in numerical realization. In theory special attention has been given to power balance criterion generalization for the case of absorbing gratings and to forms of Green's function representations. In comparison with the well known integral method formulated by Maystre, a lot of fundamental improvements have been made in the following numerical sections: the forms of representation of a groove profile, choice of points for calculation of unknown functions, integration method, choice of numbers of collocation points and Green's function expansion terms and their derivatives. For the first time stable convergence for all types of gratings and wavelengths, including those with very deep profiles, high conductivity, small wavelength-to-period ratios, and, especially, for TM polarization has been achieved and demonstrated. Examples of results are given for a wide range of transmission and reflection gratings and parameters of light. Diffraction efficiencies calculated with the help of the developed method of analysis are compared with published data and calculations performed by other researchers. All results have been obtained using ordinary PC and commercially available program PCGrate (TM) 2000X.