Self‐scaling properties of the reflection coefficient of Cantor prefactal multilayers

Abstract

We highlight the self-familar features of the frequency-dependent (absolute) reflection coefficient of a dielectric Cantor prefractal obtained by applying the well-known Cantor-set construction to the optical (rather than physical) layer lengths. The referred properties are first obtained using an exact characteristic matrix representation of the reflection coefficient and then resorting to an (accurate) small-reflection approximatio

Omnidirectional bandgap in Cantor dielectric multilayers

“…The transmission coefficient of the multilayer can be computed using the method of the characteristic matrixes along with the Snell's law at each interface [11]. Some papers [5][6][7][8][9][10] dealt with the analysis of transmission properties of Cantor multilayers for normal incidence. In this case the transmissivity of the multilayer exhibits several transparency/opacity windows.…”

“…A triadic Cantor multilayer is a one dimensional structure with fractal morphology [9,10]. Generally, a fractal set can be obtained starting from a basic structure (initiator) and repeating ad infinitum a specific operation (generator) on smaller and smaller scales.…”

Numerical Investigation on the Spectral Properties of One-Dimensional Triadic-Cantor Quasi-Periodic Structure

“…1. It is generated by a simple substitution rule: H → HLH, L → LLL with H and L being two different elementary materials [17,18]. If the sequence begins with the generator H, the first generations become what are shown in Table 1.…”

Circular dielectric cantor fibers

“…The thickness of the layers is chosen according to the triadic Cantor fractal construction [6,7], which results in a cylindrical multilayer with a number of layers depending on the stage of growth of the fractal. At the stage 0, the cladding consists of a single layer of refractive index n A and thickness ⌬ coating the core.…”