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Emulating time refraction at photonic time interfaces via smooth temporal transitions

Mariya Antyufeyeva1,2 and Victor Pacheco-Peña1,*

  • *victor.pacheco-pena@newcastle.ac.uk
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Phys. Rev. Applied 24, 034004 – Published 2 September, 2025

DOI: https://doi.org/10.1103/s296-5yrq

Abstract

The introduction of time as a new degree of freedom to control wave-matter interactions has opened alternative avenues to fully control wave propagation in four dimensions (x,y,z,t). Time interfaces (rapid changes of the constitutive relationships of the medium where a wave propagates) have recently become popular, as they are the temporal analogue of spatial interfaces. While recent groundbreaking experimental work has demonstrated time interfaces from water waves, microwaves, and the optical regime, rapidly changing, for instance, the permittivity of the medium requires carefully engineered structures. Here, we study the possibility of implementing smooth temporal transitions of the permittivity and permeability of the medium (while considering time-independent impedance) to mimic the response of the time-refracted waves produced by photonic time interfaces. It is shown that indeed, as long as the signal is inside the structure during the modulation time, there are some values of rising or falling time of the smooth modulation that enable a full approximate emulation of time refraction. These results may open further avenues to explore by relaxing the speed at which the time modulation should be introduced when designing four-dimensional media.

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Phys. Rev. Applied 24, 034004– Published 2 September, 2025
  • Received 7 April 2025
  • Revised 12 June 2025
  • Accepted 8 July 2025
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