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 that 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, and 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.
Highlights
We focus on temporal modulations that satisfy certain integral relations that are the temporal equivalent of the well-established KramersKronig relations, and, thereby, possess a ‘causal spectral response’, i.e. the output frequencies generated by the temporal scattering process do not spectrally precede the input frequencies
To emphasize the importance of the role played by spectral causality in this invisibility/cloaking effect, we have provided in Visualization 2 (†) an alternative case with balanced gain and loss where, the profile does not respect spectral causality
We believe that the present work provides relevant tools – the concept of spectral causality and the temporal anti-Kramers-Kronig relations – to extend and generalize temporally modulatedmaterials to the complex domain
Summary
Modulated systems might naturally lead to time-varying loss or gain, even when the designed modulation only involves the “Hermitian properties” of the system, e.g., the refractive index This could be due to the opening of a radiation/absorption channel by the modulation, or direct energy pumping into or from the optical system as in the process of parametric amplification [16]. Despite the unexplored potential of this research direction, only few studies [16],[17],[18],[19],[20] have focused on the effect of temporal nonHermiticity, in which, for example, a refractive index modulation is deliberately accompanied by a specific modulation of the loss/gain coefficient. The ideas put forward in this article lead to a broader class of dynamically modulated structures with predetermined scattering properties, and they represent a new step toward the goal of rigorously extending the field of metamaterials into the temporal domain
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
