Tachyonic Dispersion in Coherent Networks

TL;DR

This paper demonstrates how to engineer a tachyonic band structure in a coherent network using PT-symmetric gain and loss, revealing unique dispersion relations and measurable transmission peaks.

Contribution

It introduces a novel method to realize tachyonic dispersion in a coherent network via PT symmetry, expanding the understanding of non-Hermitian band structures.

Findings

Tachyonic dispersion relations are achieved in a square-lattice network.

The dispersion exhibits a hyperboloid centered at Brillouin zone points.

Transmission peaks vary with gain/loss parameters, enabling experimental probing.

Abstract

We propose a technique to realize a tachyonic band structure in a coherent network, such as an array of coupled ring resonators. This is achieved by adding "PT symmetric" spatially-balanced gain and loss to each node of the network. In a square-lattice network, the quasi-energy bandstructure exhibits a tachyonic dispersion relation, centered at either the center or corner of the Brillouin zone. There is one tachyonic hyperboloid in each gap, unlike in PT-symmetric tight-binding honeycomb lattices where the hyperboloids occur in pairs. The dispersion relation can be probed by measuring the peaks in transmission across a finite network as the gain/loss parameter is varied.