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  • Open Access

Engineering complex dispersion relations

R. G. Edge, S. A. R. Horsley, T. A. Starkey, and G. J. Chaplain

  • Centre for Metamaterial Research and Innovation, Department of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, United Kingdom

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Phys. Rev. B 112, 014304 – Published 7 July, 2025

DOI: https://doi.org/10.1103/3nt5-j5mp

Abstract

Motivated by recent theoretical and experimental interest in metamaterials comprising nonlocal coupling terms, we present an analytic framework to realize materials with arbitrary complex dispersion relations. Building on the inverse design method proposed by Kazemi et al. [Phys. Rev. Lett. 131, 176101 (2023)], which demonstrated arbitrary real dispersion relations with real nonlocal coupling terms, we show that using nonconservative, nonlocal couplings not only can band structures be drawn, but arbitrary attenuation of the supported modes can be achieved by tuning their trajectory in the complex frequency plane. This is demonstrated using a canonical mass-spring lattice with higher-order spatial connections; we consider the energy velocity in such systems and show that competing loss and gain of the complex interactions can produce exotic wave dispersion.

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Phys. Rev. B 112, 014304– Published 7 July, 2025
  • Received 4 April 2025
  • Revised 4 June 2025
  • Accepted 11 June 2025
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