A boundary integral equation method in short-wavelength-to-period diffraction on multilayer 1D gratings and rough mirrors

Diffraction problems by 1D multilayer structures having arbitrary border profiles including edges are considered at smallest wavelength-to-period ratios. The integral equation theory is so flexible that one can point out a few areas of its modifiability. In this work special attention is paid to physical models and low-level details, as well as to the generalization of the power balance criterion for the case of absorbing gratings. In the case of shallow gratings and mirrors, introducing speed-up terms produces an adverse numerical effect because of the ensuing uncontrolled growth of coefficients in analytically improved asymptotic estimations.