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The engineering of the optical properties of materials in space and time is opening further directions and possibilities to control wave propagation in four dimensions (x,y,z,t). A key example of such modulations are time interfaces where…

Optics · Physics 2026-04-14 Andrew M. Naylor , Victor Pacheco-Peña

Time modulation of the physical parameters offers interesting new possibilities for wave control. Examples include amplification of waves, harmonic generation and non-reciprocity, without resorting to non-linear mechanisms. Most of the…

Mathematical Physics · Physics 2025-07-25 Michaël Darche , Raphaël Assier , Sébastien Guenneau , Bruno Lombard , Marie Touboul

Time-varying media have recently emerged as a new paradigm for wave manipulation, thanks to thesynergy between the discovery of novel, highly nonlinear materials, such as epsilon-near-zero materials, and the questfor novel wave…

A time interface (a rapid change of the constitutive parameters of a material in time), applied within an unbounded medium where a wave travels, can enable frequency conversion, and is considered the temporal analogue of a spatial interface…

Optics · Physics 2025-09-24 Victor Pacheco-Peña , Mathias Fink , Nader Engheta

Photonic time interfaces, as the temporal analogue of spatial interfaces between two media, consist of a rapid change of the electromagnetic properties of a material (such as permittivity {\epsilon}, and permeability {\mu}) while the wave…

Optics · Physics 2024-11-22 Victor Pacheco-Peña , Nader Engheta

Time-varying media, characterized by dynamic or spacetime-modulated constitutive parameters such as permittivity and permeability, have recently emerged as a transformative paradigm for advanced wave control, transcending the constraints…

Optics · Physics 2026-04-20 Youxiu Yu , Hao Hu , Qianru Yang , Linyang Zou , Dongjue Liu , Hao Chi Zhang , Yu Luo

Four-dimensional optics leverages the simultaneous control of materials in space and time to manipulate light. A key challenge in experimentally realizing many intriguing phenomena is the need for rapid modulation, which is hindered by the…

Optics · Physics 2025-06-26 M. H. Mostafa , M. S. Mirmoosa , E. Galiffi , S. Yin , A. Alù , S. A. Tretyakov

Time-varying metamaterials are artificial materials whose electromagnetic properties change over time. Similar to a spatial medium discontinuity, a sudden change in time of the metamaterial refractive index induces the generation of a…

Classical Physics · Physics 2025-02-06 Davide Ramaccia , Alessandro Toscano , Filiberto Bilotti

Temporal metamaterials have been recently exploited as a novel platform for conceiving several electromagnetic and optical devices based on the anomalous scattering response arising at a single or multiple sudden changes of the material…

We develop the theory of acoustic wave propagation in a waveguide containing an array of time modulated digital meta-atoms, showing the equivalence between this array and a homogeneous, time varying, dispersive material. In the limit of an…

Classical Physics · Physics 2021-09-30 S. A. R. Horsley

Temporal metamaterials, created by modulating the refractive index in time, offer powerful means of controlling wave propagation but still lack a systematic design methodology. Here, we develop an analytic inverse-design framework rooted in…

Temporal modulation unlocks possibilities to dynamically control and modify the response of electromagnetic systems. Employing explicit dependencies of circuit or surface parameters on time enables the engineering of systems with…

Systems and Control · Electrical Eng. & Systems 2023-03-01 Grigorii Ptitcyn , Mohammad Sajjad Mirmoosa , Silvi Hrabar , Sergey Tretyakov

Coherent wave control exploits the interference among multiple waves impinging on a system to suppress or enhance outgoing signals based on their relative phase and amplitude. This process inherently requires non-Hermiticity, in order to…

When coherent light interacts with an ordered lattice whose periodicity is comparable to its wavelength, constructive interference produces a diffraction pattern as in crystallography, where x-rays are employed to reveal atomic structures.…

Space-time modulation of refractive index can produce synthetically moving interfaces with arbitrary apparent velocities, including superluminal motion, offering new ways to control light in dynamic media. On the other hand, space-time wave…

Optics · Physics 2025-12-16 Zeki Hayran , John B. Pendry

Time-reflection is a uniform inversion of the temporal evolution of a signal, which arises when an abrupt change in the properties of the host material occurs uniformly in space. At such a time-interface, a portion of the input signal is…

Applied Physics · Physics 2023-06-28 Hady Moussa , Gengyu Xu , Shixiong Yin , Emanuele Galiffi , Younes Radi , Andrea Alù

Spatiotemporally modulated elastic metamaterials have garnered increasing interest for their potential applications in nonreciprocal wave devices. Most existing studies, however, focus on systems where spatiotemporal modulation is…

Applied Physics · Physics 2025-04-29 Yingrui Ye , Chunxia Liu , Alessandro Marzani , Emanuele Riva , Antonio Palermo , Xiaopeng Wang

Recent experiments on temporal reflection in transmission line metamaterials and theoretical treatments of dispersive time-varying media have unearthed the fundamental role of modulation mechanisms on the interface conditions, underpinning…

Optics · Physics 2026-02-27 Suat Barış İplikçioğlu

A new frontier in optics research has been opened by the recent developments in non-perturbative optical modulation in both time and space that creates temporal boundaries generating ``time-reflection'' and ``time-refraction'' of light in…

Optics · Physics 2023-10-25 Evgenii E. Narimanov

Space-time modulation adds another powerful degree of freedom to the manipulation of classical wave systems. It opens the door for complex control of wave behavior beyond the reach of stationary systems, such as nonreciprocal wave transport…

Classical Physics · Physics 2019-11-06 Junfei Li , Xiaohui Zhu , Chen Shen , Xiuyuan Peng , Steven A. Cummer
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