Wave propagation in one-dimension: Methods and applications to complex and fractal structures

TL;DR

This paper reviews methods for analyzing wave propagation in one-dimensional complex structures, highlighting how different spatial arrangements like fractals and disorder influence wave behavior and mode spectra.

Contribution

It provides a comprehensive comparison of formal methods and applies them to various complex structures, including fractals and disordered systems.

Findings

Wave structure significantly affects mode spectra.

Different formal methods yield consistent results.

Complex structures influence local mode intensities.

Abstract

This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We present examples for transport through finite-sized layered dielectric systems with periodic, quasi-periodic, fractal, disordered, and random structure, illustrating how can spatial structure affect the spectrum of modes as well as the local mode intensity.