Impurity effects on the band structure of one-dimensional photonic crystals: Experiment and theory

TL;DR

This study investigates how single impurities affect the transmission and band structure in one-dimensional photonic crystals using microwave experiments and theoretical analysis, providing insights applicable to quantum models.

Contribution

The paper presents analytical formulas for impurity effects in 1D photonic crystals and validates them with experiments, bridging photonic and quantum Kronig-Penney models.

Findings

Analytical expressions accurately predict defect mode frequencies.

Experimental data confirms the theoretical band structure modifications.

Impurity characteristics can be inferred from transmission features.

Abstract

We study the effects of single impurities on the transmission in microwave realizations of the photonic Kronig-Penney model, consisting of arrays of Teflon pieces alternating with air spacings in a microwave guide. As only the first propagating mode is considered, the system is essentially one dimensional obeying the Helmholtz equation. We derive analytical closed form expressions from which the band structure, frequency of defect modes, and band profiles can be determined. These agree very well with experimental data for all types of single defects considered (e.g. interstitial, substitutional) and shows that our experimental set-up serves to explore some of the phenomena occurring in more sophisticated experiments. Conversely, based on the understanding provided by our formulas, information about the unknown impurity can be determined by simply observing certain features in the experimental data for the transmission. Further, our results are directly applicable to the closely related quantum 1D Kronig-Penney model.