Spectral Causality and the Scattering of Waves

TL;DR

This paper introduces the concept of spectral causality in time-modulated non-Hermitian photonic systems, demonstrating how they obey causality-like relations in the spectral domain with potential applications in wave control.

Contribution

It uncovers a new class of complex, time-modulated metamaterials that exhibit spectral causality, extending the principles of causality into the spectral domain for wave manipulation.

Findings

Spectrally causal response prohibits output frequencies from preceding input frequencies.

Applications include broadband perfect absorption and temporal cloaking.

Enables unidirectional wave propagation along a synthetic dimension.

Abstract

Causality - the principle stating that the output of a system cannot temporally precede the input - is a universal property of nature. Here, we show that analogous input-output relations can also be realized in the spectral domain by leveraging the peculiar properties of time-modulated non-Hermitian photonic systems. Specifically, we uncover the existence of a broad class of complex time-modulated metamaterials which obey the time-domain equivalent of the well-established frequency-domain Kramers-Kronig relations (a direct consequence of causality). We find that, in the scattering response of such time-modulated systems, the output frequencies are inherently prohibited from spectrally preceding the input frequencies, hence we refer to these systems as 'spectrally causal'. We explore the consequences of this newly introduced concept for several relevant applications, including broadband perfect absorption, temporal cloaking of an 'event', and truly unidirectional propagation along a synthetic dimension. By emulating the concept of causality in the spectral domain and providing new tools to extend the field of temporally modulated metamaterials ("chrono-metamaterials") into the complex realm, our findings may open unexplored opportunities and enable relevant technological advances in various areas of photonics and, more broadly, of wave physics and engineering.