Bifurcation of avoided crossing at an exceptional point in the dispersion of sound and light in locally resonant media

A. A. Maznev

doi:10.1063/1.5012999

journal article Feb 21, 2018

Bifurcation of avoided crossing at an exceptional point in the dispersion of sound and light in locally resonant media

A. A. Maznev

Journal of Applied Physics Vol. 123 No. 9 · AIP Publishing

View at Publisher Save 10.1063/1.5012999

Abstract

The avoided crossing behavior in the interaction of propagating sound or light waves with resonant inclusions is analyzed using a simple model of an acoustic medium containing damped mass-spring oscillators, which is shown to be equivalent to the Lorentz oscillator model in the elementary dispersion theory in optics. Two classes of experimental situations dictating the choice in the analysis of the dispersion relation are identified. If the wavevector is regarded as the independent variable and frequency as a complex function of the wavevector, then the avoided crossing bifurcates at an exceptional point at a certain value of the parameter γβ−1/2, where γ and β characterize the oscillator damping and interaction strength, respectively. This behavior is not observed if the wavevector is regarded as a complex function of frequency.

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Details

Published: Feb 21, 2018
Vol/Issue: 123(9)

Authors

A

A. A. Maznev

Department of Chemistry, Massachusetts Institute of Technology , Cambridge, Massachusetts 02139, USA

Funding

U.S. Department of Energy Award: DE-SC0001299/DEFG02-09ER46577

Cite This Article

A. A. Maznev (2018). Bifurcation of avoided crossing at an exceptional point in the dispersion of sound and light in locally resonant media. Journal of Applied Physics, 123(9). https://doi.org/10.1063/1.5012999

Bifurcation of avoided crossing at an exceptional point in the dispersion of sound and light in locally resonant media

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