Antitrace maps and light transmission coefficients for a generalized Fibonacci multilayers

By using antitrace map method, we investigate the light transmission for a generalized Fibonacci multilayers. Analytical results are obtained for transmission coefficients in some special cases. We find that the transmission coefficients possess two-cycle property or six-cycle property. The cycle properties of the trace and antitrace are also obtained. PACS numbers: 61.44.Br, 05.45.-a, 42.25.Dd, 71.23.Ft Typeset using REVTEX 1 The transmission of light through the multilayers arranged by the Fibonacci [1–3], nonFibonacci sequence [4,5], Thue-Morse sequence [6], and the generalized Thue-Morse sequence [7] was studied in the literature. Schwartz [8] suggested a possibility of quasiperiodic multilayers as optical switches and memories. Huang et al [9] and Yang et al [10] have found an interesting switch-like property in the light transmission through Fibonacci-class sequences. On the other hand, the trace-map technique, first introduced in 1983 [11], has proven to be a powerful tool to investigate the properties of various aperiodic systems. However, as pointed by Dulea et al [4], we must know the so-called “antitrace map” when we evaluate the light transmission coefficients through aperoidic sequences. Here, the so-called “antitrace” of a 2×2 matrix