# Experimental Demonstration of Sixth Order Degenerate Band Edge in Coupled Microstrip Waveguides

## TL;DR

This paper demonstrates experimentally a sixth-order degeneracy in a coupled microstrip waveguide, revealing unique dispersion properties that can be used to design advanced microwave devices like high-Q resonators and filters.

## Contribution

The first physical realization and experimental verification of a sixth-order degenerate band edge in a gainless three-way microwave waveguide.

## Key findings

- Experimental confirmation of 6th order degeneracy via scattering parameters.
- Observation of vanishing group velocity at the degenerate point.
- Potential applications in high-Q resonators and filters.

## Abstract

We show the physical realization and experimental demonstration of an exceptional point of 6th order degeneracy in a triple ladder (or three-way) microwave waveguide realized using three coupled microstrips on a grounded dielectric substrate. This threeway waveguide supports six Bloch eigenmodes and all coalesce onto a degenerate single eigenmode at a given frequency. The three-way waveguide is gainless, and this exceptional point is associated to a vanishing group velocity and its multiple derivatives. Indeed the wavenumber-frequency dispersion diagram, that we call 6th order degenerate band edge (6DBE) has six coalescing branches. We provide the experimental verification of a 6th order exceptional point by evaluating the degenerate wavenumber-frequency dispersion diagram from the measurement of scattering parameters of a six-port unit cell. We also show the resonant behavior of a cavity made of the three-way waveguide with finite length. The unique properties of 6DBE can be exploited in designing innovative high-Q resonators, oscillators, filters, and pulse shaping devices.

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Source: https://tomesphere.com/paper/1906.03331