# Broadband Nonreciprocal Amplification in Luminal Metamaterials

## TL;DR

This paper introduces a novel approach using luminal gratings in metamaterials to achieve nonreciprocal amplification and wave control, overcoming traditional modulation speed limitations with a traveling-wave refractive index modulation.

## Contribution

It proposes the concept of luminal gratings for nonreciprocal wave amplification, demonstrating a practical implementation in double-layer graphene.

## Key findings

- Achieves giant nonreciprocity in wave propagation
- Enables efficient one-way amplification and pulse compression
- Proposes a realistic graphene-based implementation

## Abstract

Time has emerged as a new degree of freedom for metamaterials, promising new pathways in wave control. However, electromagnetism suffers from limitations in the modulation speed of material parameters. Here we argue that these limitations can be circumvented by introducing a traveling-wave refractive index modulation, with the same phase velocity of the waves. We show how the concept of "luminal grating" can yield giant nonreciprocity, achieve efficient one-way amplification, pulse compression and frequency up-conversion, proposing a realistic implementation in double-layer graphene.