Edge modes in 1D microwave photonic crystal

TL;DR

This paper investigates topological edge modes in a 1D microwave photonic crystal microstrip, demonstrating their control via defects and their potential for high-selectivity microwave filtering.

Contribution

It provides experimental and numerical evidence of topologically induced edge modes in a 1D microwave photonic crystal microstrip, highlighting defect engineering for mode control.

Findings

Edge modes are absent in defect-free finite microstrips with symmetric terminations.

Adding defected cells induces edge modes at both ends.

Edge modes enable high-transitivity microwave tunneling within the frequency gap.

Abstract

The microstrip of modulated width is a realization of a one-dimensional photonic crystal operating in the microwave regime. Like any photonic crystal, the periodic microstrip is characterised by the presence of frequency bands and band gaps that enable and prohibit wave propagation, respectively. The frequency bands for microstrip of symmetric unit cell can be distinguished by $0$ or $\pi$ Zak phase. The sum of these topological parameters for all bands below a given frequency gap determines the value of the surface impedance and whether or not edge modes are present at the end of the microstrip. We demonstrate that edge modes are absent in a finite microstrip terminated at both ends in the centres of unit cells, but they can be induced by adding the defected cells. Edge modes present at both ends of the microstrip enable microwave tunneling with high transitivity in the frequency gap with or without a change in phase. This has been demonstrated experimentally and developed in detail using numerical simulations and model calculations. The investigated system, with a doublet of edge modes in the frequency gap, can be considered as a narrow passband filter of high selectivity.