One-Dimensional Kronig-Penney Model with Positional Disorder: Theory versus Experiment

TL;DR

This paper investigates how random positional disorder affects wave transmission in a one-dimensional Kronig-Penney model, deriving analytical expressions and validating them with microwave experiments, with implications for photonic and semiconductor structures.

Contribution

It provides an analytical formula for localization length under weak disorder and compares theoretical predictions with experimental microwave data.

Findings

Analytical expression for localization length derived

Good agreement between theory and microwave experiments

Results applicable to photonic crystals and superlattices

Abstract

We study the effects of random positional disorder in the transmission of waves in a 1D Kronig-Penny model. For weak disorder we derive an analytical expression for the localization length and relate it to the transmission coefficient for finite samples. The obtained results describe very well the experimental frequency dependence of the transmission in a microwave realization of the model. Our results can be applied both to photonic crystals and semiconductor super lattices.