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

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.

arXiv comment16 pages, 7 figures

References in corpus (2)

• Experimental observation of the mobility edge in a waveguide with correlated disorder
• Topological defects in 1D elastic waves

Cited by in corpus (7)

• Anomalous Localization in Low-Dimensional Systems with Correlated Disorder
• Superradiance Transition in Transport Through Nanosystems
• One-Dimensional Kronig-Penney Model with Positional Disorder: Theory versus Experiment
• Using dynamical barriers to control the transmission of light through slowly-varying photonic crystals
• Experimental validation of the theoretical prediction for the optical $S$ matrix
• Coherent control of nonreciprocal optical properties of the defect modes in 1D defective photonic crystals with atomic doping
• A simple model system to study coupled photonic crystal microcavities