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Complex Spatiotemporal Modulations and Non-Hermitian Degeneracies in PT-Symmetric Phononic Materials

M. Moghaddaszadeh1,2, M.A. Attarzadeh2, A. Aref1, and M. Nouh2,*

  • 1Department of Civil, Structural and Environmental Engineering, University at Buffalo (SUNY), Buffalo, New York 14260-4300, USA
  • 2Department of Mechanical and Aerospace Engineering, University at Buffalo (SUNY), Buffalo, New York 14260-4400, USA

  • *Corresponding author. mnouh@buffalo.edu
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Phys. Rev. Applied 18, 044013 – Published 6 October, 2022

DOI: https://doi.org/10.1103/PhysRevApplied.18.044013

Abstract

Unraveling real eigenfrequencies in non-Hermitian PT-symmetric Hamiltonians has opened avenues in quantum physics, photonics, and most recently, phononics. However, the existing literature squarely focuses on exploiting such systems in the context of scattering profiles (i.e., transmission and reflection) at the boundaries of a modulated waveguide, rather than the rich dynamics of the non-Hermitian medium itself. In this work, we investigate the wave propagation behavior of a one-dimensional non-Hermitian elastic medium with a universal complex stiffness modulation that encompasses a static term in addition to real and imaginary harmonic variations in both space and time. Using a plane-wave expansion, we conduct a comprehensive dispersion analysis for a wide set of subscenarios to quantify the onset of complex conjugate eigenfrequencies, and set forth the existence conditions for gaps that emerge along the wave-number space. Upon defining the hierarchy and examining the asymmetry of these wave-number gaps, we show that both the position with respect to the wave-number axis and the imaginary component of the oscillatory frequency largely depend on the modulation type and gap order. Finally, we demonstrate the coalescence of multiple Bloch-wave modes at the emergent exceptional points where significant direction-dependent amplification can be realized by triggering specific harmonics through a process that is detailed herein.

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Phys. Rev. Applied 18, 044013– Published 6 October, 2022
  • Received 29 June 2022
  • Revised 22 August 2022
  • Accepted 9 September 2022
Article part of CHORUS
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