# Flat Lensing by Graded Line Meta-arrays

## TL;DR

This paper demonstrates flat lensing effects using graded line meta-arrays on elastic plates, enabling negative refraction and wave control with potential applications across wave physics domains.

## Contribution

It introduces a novel graded line-array design for flat lensing in elastic plates, with detailed analysis of dispersion and mode coupling leading to wave manipulation.

## Key findings

- Achieved negative refraction via graded line arrays.
- Demonstrated array guided wave reversal and hybridisation.
- Enabled flat lensing effects in elastic wave systems.

## Abstract

Motivated by flat lensing effects, now commonplace utilising negative refraction with finite slabs, we create negative refraction upon a graded line-array. We do so in the setting of flexural waves on a structured Kirchhoff--Love elastic plate, as a paradigm in wave physics, that has direct extensions to electromagnetic and acoustic wave systems. These graded line arrays are geometrically simple and provide strong coupling from the array into the bulk. Thorough analysis of the dispersion curves, and associated mode structure, of these meta--arrays, supported by mode coupling theory, creates array guided wave (AGW) reversal and hybridisation into the bulk that leads to striking wave control via generalised flat lensing.