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Quasi-periodicity under certain conditions of the dependence of grating properties on groove depth is explained from the point of view of energy flow distribution (EFD). The formation of curls in flow maps is followed as a function of the groove depth h for two general types of gratings having one or two propagating diffraction orders. An equivalence between shallow and deep gratings is established: the EFD above the grooves is one and the same, while in deep gratings a definite number of curls exists, totally hidden inside each groove. Perfect blazing and antiblazing are connected with the position of these curls with respect to the top of the grooves.
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Popov et al. (1990) studied this question.
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