Space-Time Fresnel Prism

TL;DR

This paper introduces a practical space-time Fresnel prism design that enables nonreciprocal frequency conversion in metamaterials without requiring impractically large structures, advancing applications in microwave and optical systems.

Contribution

It proposes a space-time transposition of the Fresnel prism that simplifies implementation of space-time metamaterials by re-injecting modulation periodically, overcoming size limitations of previous designs.

Findings

Enables nonreciprocal frequency conversion with finite structures

Provides a scalable approach extendable to various modulations

Facilitates practical development of space-time metamaterials

Abstract

Space-time modulation-based metamaterials have recently spurred considerable interest, owing to the fundamental addition of the time dimension to the medium parameters, and resulting novel properties and potential applications. However, the implementation of most related structures -- e.g., involving step, slab or gradient discontinuities -- has been hindered by the impossible requirement of infinitely or prohibitively large device sizes. We provide here a solution to this issue, consisting in a space-time transposition of the conventional Fresnel prism, whereby a copy of the target modulation is periodically re-injected at the input of a Fresnel-reduced finite structure, so as to provide the same anharmonic and nonreciprocal frequency conversion as the target space-time interface in the case of a modulation step. This concept, which may readily extend to slab or gradient modulations, as well as accelerated profiles for space-time chirping operations, may pave the way for the practical development of a wide range of novel microwave and optical space-time systems.