Interdimensional optical isospectrality inspired by graph networks

TL;DR

This paper introduces a method to design reduced-dimensional optical structures that preserve spectral properties of complex graph networks, enabling simpler broadband devices through interdimensional isospectrality.

Contribution

It leverages the mathematical similarity between Hamiltonians across dimensions to achieve perfect spectral preservation in lower-dimensional optical structures.

Findings

High-degree graph networks can be projected onto 1D structures without losing spectral properties.

Disorder removes degeneracy, enabling isospectral projection across dimensions.

Simplified 1D structures can replicate the broadband multilevel behavior of complex networks.

Abstract

A network picture has been applied to various physical and biological systems to understand their governing mechanisms intuitively. Utilizing discretization schemes, both electrical and optical materials can also be interpreted as abstract 'graph' networks composed of couplings (edges) between local elements (vertices), which define the correlation between material structures and wave flows. Nonetheless, the fertile structural degrees of freedom in graph theory have not been fully exploited in physics owing to the suppressed long-range interaction between far-off elements. Here, by exploiting the mathematical similarity between Hamiltonians in different dimensions, we propose the design of reduced-dimensional optical structures that perfectly preserve the level statistics of disordered graph networks with significant long-range coupling. We show that the disorder-induced removal of the level degeneracy in high-degree networks allows their isospectral projection to one-dimensional structures without any disconnection. This inter-dimensional isospectrality between high- and low-degree graph-like structures enables the ultimate simplification of broadband multilevel devices, from three- to one-dimensional structures.