DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Journal Article · · Journal of Applied Physics
DOI: https://doi.org/10.1063/1.5012999 · OSTI ID:1470492
 [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Chemistry

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.

Research Organization:
Energy Frontier Research Centers (EFRC) (United States). Solid-State Solar-Thermal Energy Conversion Center (S3TEC)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Grant/Contract Number:
SC0001299; SC0001299
OSTI ID:
1470492
Alternate ID(s):
OSTI ID: 1421997
Journal Information:
Journal of Applied Physics, Journal Name: Journal of Applied Physics Journal Issue: 9 Vol. 123; ISSN 0021-8979
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (26)

Simultaneous Occurrence of Structure-Directed and Particle-Resonance-Induced Phononic Gaps in Colloidal Films journal May 2008
Vibrational dynamics of a two-dimensional microgranular crystal journal July 2017
Engineered metabarrier as shield from seismic surface waves journal December 2016
Ultrasonic metamaterials with negative modulus journal April 2006
Strong coupling, energy splitting, and level crossings: A classical perspective journal November 2010
Fano resonances in photonics journal September 2017
Dynamically encircling an exceptional point for asymmetric mode switching journal July 2016
Acoustic metamaterials: From local resonances to broad horizons journal February 2016
Observation of exceptional points in electronic circuits journal July 2004
Locally Resonant Sonic Materials journal September 2000
Dynamic Mass Density and Acoustic Metamaterials book October 2012
Complex Contact-Based Dynamics of Microsphere Monolayers Revealed by Resonant Attenuation of Surface Acoustic Waves journal May 2016
Dispersion characteristics of sound waves in a tunnel with an array of Helmholtz resonators journal March 1995
Long wavelength surface oscillations of a crystal with an adsorbed monolayer journal February 1989
Interaction of a Contact Resonance of Microspheres with Surface Acoustic Waves journal July 2013
Unified Theoretical Framework for Realizing Diverse Regimes of Strong Coupling between Plasmons and Electronic Transitions journal January 2014
Wave propagation control at the deep subwavelength scale in metamaterials journal November 2012
Avoided level crossing and exceptional points journal April 1990
Experimental Observation of the Topological Structure of Exceptional Points journal January 2001
Interaction of Rayleigh waves with randomly distributed oscillators on the surface journal May 1999
Heterodyned impulsive stimulated Raman scattering of phonon–polaritons in LiTaO3 and LiNbO3 journal August 2002
Waveguiding by a locally resonant metasurface journal September 2015
Emergence, Coalescence, and Topological Properties of Multiple Exceptional Points and Their Experimental Realization journal April 2016
Experimental observation of locally-resonant and Bragg band gaps for surface guided waves in a phononic crystal of pillars journal March 2011
Spawning rings of exceptional points out of Dirac cones journal September 2015
Reversing the pump dependence of a laser at an exceptional point journal June 2014

Cited By (3)

Surface acoustic wave modes in two-dimensional shallow void inclusion phononic crystals on GaAs journal July 2019
Reduced order derivation of the two-dimensional band structure of a mixed-mode resonator array journal December 2018
Dissipation engineering in metamaterials by localized structural dynamics preprint January 2018