Optical Properties of One-Dimensional Quasi-Periodic Crystals. I. Optical Reflectivity Spectrum of a Fibonacci Lattice

Optical reflectivity of the semiconductor Fibonacci superlattice is calculated. The frequencies at which spiky singularities appear in the spectrum exhibit the self-similar and nested structure. An analytic expression of the reflectivity spectrum is derived by assuming that the difference of the dielectric constants of the constituent layers is small. Based on the analytic expression, the reflectivity spectrum is analyzed. The effect of fluctuation of layer thickness is also investigated analytically.