Optical Waves in One-Dimensional Fractal Inhomogeneous Media

Fractal multilayer structures as a class of deterministic non-periodic discrete inhomogeneous media are investigated on the basis of classical wave propagation. This includes optical properties of dielectric layered media and quantum particle behaviour in a fractal stepwise potential. The primary focus of the present review is drawing a correlation between topological properties and eigenvalue spectra. Namely, it is shown both numerically and analytically that geometrical self-similarity of fractal structures directly results in spectral scalability. Some other spectral properties resulting from minor topological details of fractal multilayers (such as resonance peak splitting and spectral self-similarity) are considered.