Propagation of waves in layered structures viewed as number recognition

Abstract

We propose to consider multilayer spatial structures as numbers. An arbitrary finite sequence of layers with N values of a material parameter which determines the speed of wave propagation is considered as a number written in the numeration system with base N. Within the framework of this approach propagation of classical waves and quantum particles can be treated as number recognition. A problem is formulated of identification of a type among spatial sequences featuring unique spectral portraits versus spatial structure. It is shown possible to perform certain arithmetic operations by means of sequential propagation of waves through several structures. Using fractal Cantor structures as a representative example, spectral properties of waves are shown to reproduce certain properties of the corresponding numbers. A possibility is outlined to use the above approach for data storage. If a set of numbers possessing unique spectral portraits forms a complete set, then compact coding of arbitrary numbers will become possible.