Broadband Nonreciprocal Amplification in Luminal Metamaterials

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.