Transmission of light through deterministic aperiodic non-Fibonaccian multilayers

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Abstract
Optical transmission through binary multilayers arranged according to deterministic aperiodic distribution rules is investigated using an extension of the trace-map technique. It is proven that in order to get a complete description of this ideal experiment, the usual trace map must be combined with a so-called ‘‘antitrace’’ map containing the off-diagonal elements of the transfer matrix too. The study of the dynamics of the two coupled maps gives useful information concerning the behavior of the transmission coefficient in these structures. Analytical and numerical results are obtained for the two classes of sequences generated by A→AB...B and B→A and by A→A...AB and B→A. It is shown that although these sequences are all generalizations of the Fibonacci sequence, the two families have very different properties.