Optical Properties of One-Dimensional Quasi-Periodic Crystals. II. Modified Fibonacci Lattice with Arbitrary Initial Conditions

Optical properties are reported for a class of quasi-periodic superlattices generated by the rule S(n+1)=S(n)^pS(n-1). p is a positive integer and the first two generations S(1) and S(2) are chosen arbitrarily. The reflectivity spectrum shows the same fractal structure as that of the Fibonacci lattice reported in the preceding paper. The self-simi-larity factor of the spectrum is found to be [formula omitted] independent of the initial generations. Analytic expressions are given of the structure factor and the reflectivity within the bilinear approximation.