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Temporal chirp, temporal lensing, and temporal routing via space-time interfaces

Victor Pacheco-Peña1,*, Mathias Fink2,†, and Nader Engheta3,‡

  • 1School of Mathematics, Statistics and Physics, Newcastle University, Newcastle Upon Tyne NE1 7RU, United Kingdom
  • 2Institut Langevin, ESPCI Paris, CNRS, PSL Université, 1 rue Jussieu, 75005 Paris, France
  • 3Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

  • *Contact author: victor.pacheco-pena@newcastle.ac.uk
  • †Contact author: mathias.fink@espci.fr
  • ‡Contact author: engheta@seas.upenn.edu
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Phys. Rev. B 111, L100306 – Published 31 March, 2025

DOI: https://doi.org/10.1103/PhysRevB.111.L100306

Abstract

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 analog of a spatial interface between two materials. Here, we study light-matter interactions in four dimensions, 4D (space, x,y,z, and time, t), by exploring the implications of applying time interfaces, not to the entire space where a wave travels, but to certain regions of space in order to create spatial interfaces in time. Different configurations such as induced perpendicular, parallel, and oblique spatial interfaces via a temporal interface are discussed. It is shown how such four-dimensional combination of temporal and spatial interfaces can enable interesting features such as the 4D generalized Snell's law and temporal chirp, temporal lensing, and temporal routing of electromagnetic waves. Such exotic possibilities may provide new ways to manipulate light-matter interactions via a combination of temporal and spatial interfaces.

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Phys. Rev. B 111, L100306– Published 31 March, 2025
  • Received 22 November 2023
  • Revised 2 June 2024
  • Accepted 11 February 2025
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