Effective medium concept in temporal metamaterials

Abstract

Metamaterials are mostly designed in the timeharmonic scenario where wave propagation can be spatially manipulated. Tailoring the electromagnetic response of media in time has also gained the attention of the scientific community in order to achieve further control on wave-matter interaction both in space and time. In the present work, a temporally effective medium concept in metamaterial is theoretically investigated as a mechanism to create a medium with a desired effective permittivity. Similar to spatially subwavelength multilayered metamaterials, the proposed "temporal multilayered", or "multistepped" metamaterial, is designed by alternating in time the permittivity of the medium between two values. In so doing, the temporally periodic medium can be modeled as an effective metamaterial in time with an effective permittivity initiated by a step function. The analogy between the temporal multistepped and the spatial multilayered metamaterials is presented demonstrating the duality between both domains. The proposed temporal metamaterial is analytically and numerically evaluated showing an excellent agreement with the designed parameters. Moreover, it is shown how the effective permittivity can be arbitrarily tailored by changing the duty cycle of the periodic temporal metamaterial. This performance is also connected to the spatial multilayer scenario in terms of the filling fraction of the different materials used to create the multilayered structures.

Temporal aiming

“…Remarkably, an analogy between this temporal and the spatial interface between two materials with different electromagnetic parameters was demonstrated, showing that the two waves created at a temporal boundary (FW and BW) are the temporal equivalent/analogy to the transmitted and reflected waves in spatial interfaces. In this realm, temporal and spatiotemporal metamaterials have recently been proposed and applied in several exciting and intriguing applications, such as effective medium theory 45 , inverse prisms 46 , nonreciprocity 47,48 , anti-reflection temporal coatings 49 , frequency conversion 50 and time reversal 51 .…”

Artificial neural networks for inverse design of resonant nanophotonic components with oscillatory loss landscapes

“…We demonstrated our technique with Fabry-Pérot and Bragg resonators and quantified the superior search efficiency compared to other optimization methods. Our technique will be particularly valuable for inverse design of optical components based on many nanophotonic resonators, such as coupled or multi-layered resonators [28][29][30], lasers [31], dispersion-engineered metasurfaces [32] and (nonlinear) resonators in the context of integrated optics [33,34]. Finally, because this method can incorporate several parameters of the incident light, we think it will be interesting to study and optimize complex materials interacting with structured light beams [35][36][37][38][39].…”

Metamaterials with high degrees of freedom: space, time, and more

“…The research on time-varying electromagnetic platforms has a long history dating back to 1950s, when one of the early works, by Morgenthaler [17], explored theoretically what would happen to a monochromatic electromagnetic wave in a medium when the medium's phase velocity is rapidly changed in time. In the past decades, there have been numerous efforts in investigating various phenomena related to the temporal variation of electromagnetic media, providing temporal boundaries [18], temporal holography [19], Doppler cloaking [20], temporal band gaps [21][22][23], temporal effective medium concept [24], temporal impedance matching [25,26], Fresnel drag in spatiotemporal metamaterials [27], spacetime cloaks [28,29], modeling time and causality with metamaterials [30,31], rapidly growing plasma and accelerating reference frame [32], and exceptional points in timevarying media [33], just to name a few.…”