# Scale‐Invariant Waveguiding in Flatland

## TL;DR

The paper introduces a new type of flat metasurface waveguide that maintains consistent performance regardless of its width, with potential uses in optics and communications.

## Contribution

The novel concept of scale-invariant surface waveguiding with uniform modal field distribution and core-width-independent effective index is introduced.

## Key findings

- Scale-invariant metasurface waveguides were designed with uniform modal field distribution in the core region.
- The effective index remains invariant with respect to the core width, validated through microwave experiments in the C band.
- The design supports both capacitive/inductive scenarios and complex junctions with coupled line waves.

## Abstract

Electromagnetic metasurfaces with suitably designed spatial modulations of surface impedance can guide surface waves similarly to volumetric dielectric waveguides. As a result, the transverse distribution of the fundamental mode is usually nonuniform (peaked at the center), and its effective index is influenced by the electrical size of the central (core) region. Here, we introduce the concept of scale‐invariant surface waveguiding, extending the recent advancements in dielectric waveguides to flatland settings. By leveraging spatial symmetry and fine‐tuning the in‐plane mode profile at the bound‐leaky boundary, we design metasurface waveguides with uniform modal field distribution in the core region, where the effective index remains invariant with respect to the core width. Our findings encompass not only fully capacitive or inductive scenarios but also complex capacitive‐inductive junctions supporting coupled line waves. Experimental validation through near‐field measurements on a microwave prototype operating in the C band confirms our theoretical predictions. These results hold intriguing potentials for applications in flat optics, sensing, and communications.

The study introduces scale‐invariant metasurface waveguides with uniform modal field distribution and an effective index independent of the core width. By leveraging spatial symmetry and fine‐tuning mode profiles, the design is validated through near‐field measurements in the C band, offering potential applications in flat optics, sensing, and communications.