Abstract
Brief historical background is given of appearing of unified exact approach, the so called transfer relations, to the theory of multiple scattering of wave fields in inhomogeneous discrete dielectric media. One dimensional (1D) diffraction gratings and two dimensional (2D) photonic crystals (PCs) are considered as particular types of inhomogeneous media with spatial periodicity. A few application oriented items are presented as a result of computations on the basis of transfer relations, regarding 2D PCs as a stack of 1D diffraction gratings and applying technique of matrix Riccati equation. Two first items are 2D PCs and hollow pin structure. The last two items are two methods of optical monitoring. The first is a quantitative approach to optical grating nanoshape control. The last item that is spatial spectroscopy of electromagnetic wave near fields definitely answered the question is it possible to retrieve subwavelength information in the near field microscopy.
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