Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

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

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.

Authors:
 [1]
+ Show Author Affiliations
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Chemistry
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Solid-State Solar-Thermal Energy Conversion Center (S3TEC)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1470492
Alternate Identifier(s):
OSTI ID: 1421997
Grant/Contract Number:  
SC0001299; FG02-09ER46577
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Applied Physics
Additional Journal Information:
Journal Volume: 123; Journal Issue: 9; Related Information: S3TEC partners with Massachusetts Institute of Technology (lead); Boston College; Oak Ridge National Laboratory; Rensselaer Polytechnic Institute; Journal ID: ISSN 0021-8979
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; solar (photovoltaic); solar (thermal); solid state lighting; phonons; thermal conductivity; thermoelectric; defects; mechanical behavior; charge transport; spin dynamics; materials and chemistry by design; optics; synthesis (novel materials); synthesis (self-assembly); synthesis (scalable processing)

Citation Formats

Maznev, A. A. Bifurcation of avoided crossing at an exceptional point in the dispersion of sound and light in locally resonant media. United States: N. p., 2018. Web. doi:10.1063/1.5012999.
Copy to clipboard
Maznev, A. A. Bifurcation of avoided crossing at an exceptional point in the dispersion of sound and light in locally resonant media. United States. https://doi.org/10.1063/1.5012999
Copy to clipboard
Maznev, A. A. Wed . "Bifurcation of avoided crossing at an exceptional point in the dispersion of sound and light in locally resonant media". United States. https://doi.org/10.1063/1.5012999. https://www.osti.gov/servlets/purl/1470492.
Copy to clipboard
@article{osti_1470492,
title = {Bifurcation of avoided crossing at an exceptional point in the dispersion of sound and light in locally resonant media},
author = {Maznev, A. A.},
abstractNote = {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.},
doi = {10.1063/1.5012999},
journal = {Journal of Applied Physics},
number = 9,
volume = 123,
place = {United States},
year = {2018},
month = {2}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5012999
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Experimental observation of locally-resonant and Bragg band gaps for surface guided waves in a phononic crystal of pillars
journal, March 2011

Experimental Observation of the Topological Structure of Exceptional Points
journal, January 2001

Emergence, Coalescence, and Topological Properties of Multiple Exceptional Points and Their Experimental Realization
journal, April 2016

Simultaneous Occurrence of Structure-Directed and Particle-Resonance-Induced Phononic Gaps in Colloidal Films
journal, May 2008

Observation of exceptional points in electronic circuits
journal, July 2004

  • Stehmann, T.; Heiss, W. D.; Scholtz, F. G.
  • Journal of Physics A: Mathematical and General, Vol. 37, Issue 31
  • DOI: 10.1088/0305-4470/37/31/012

Acoustic metamaterials: From local resonances to broad horizons
journal, February 2016

Complex Contact-Based Dynamics of Microsphere Monolayers Revealed by Resonant Attenuation of Surface Acoustic Waves
journal, May 2016

Reversing the pump dependence of a laser at an exceptional point
journal, June 2014

  • Brandstetter, M.; Liertzer, M.; Deutsch, C.
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms5034

Wave propagation control at the deep subwavelength scale in metamaterials
journal, November 2012

  • Lemoult, Fabrice; Kaina, Nadège; Fink, Mathias
  • Nature Physics, Vol. 9, Issue 1
  • DOI: 10.1038/nphys2480

Vibrational dynamics of a two-dimensional microgranular crystal
journal, July 2017

Locally Resonant Sonic Materials
journal, September 2000

Unified Theoretical Framework for Realizing Diverse Regimes of Strong Coupling between Plasmons and Electronic Transitions
journal, January 2014

  • Faucheaux, Jacob A.; Fu, Jiayi; Jain, Prashant K.
  • The Journal of Physical Chemistry C, Vol. 118, Issue 5
  • DOI: 10.1021/jp412157c

Avoided level crossing and exceptional points
journal, April 1990

Ultrasonic metamaterials with negative modulus
journal, April 2006

  • Fang, Nicholas; Xi, Dongjuan; Xu, Jianyi
  • Nature Materials, Vol. 5, Issue 6
  • DOI: 10.1038/nmat1644

Spawning rings of exceptional points out of Dirac cones
journal, September 2015

  • Zhen, Bo; Hsu, Chia Wei; Igarashi, Yuichi
  • Nature, Vol. 525, Issue 7569
  • DOI: 10.1038/nature14889

Strong coupling, energy splitting, and level crossings: A classical perspective
journal, November 2010

  • Novotny, Lukas
  • American Journal of Physics, Vol. 78, Issue 11
  • DOI: 10.1119/1.3471177

Dispersion characteristics of sound waves in a tunnel with an array of Helmholtz resonators
journal, March 1995

  • Sugimoto, N.; Horioka, T.
  • The Journal of the Acoustical Society of America, Vol. 97, Issue 3
  • DOI: 10.1121/1.412085

Engineered metabarrier as shield from seismic surface waves
journal, December 2016

  • Palermo, Antonio; Krödel, Sebastian; Marzani, Alessandro
  • Scientific Reports, Vol. 6, Issue 1
  • DOI: 10.1038/srep39356

Heterodyned impulsive stimulated Raman scattering of phonon–polaritons in LiTaO3 and LiNbO3
journal, August 2002

  • Crimmins, Timothy F.; Stoyanov, Nikolay S.; Nelson, Keith A.
  • The Journal of Chemical Physics, Vol. 117, Issue 6
  • DOI: 10.1063/1.1491948

Interaction of a Contact Resonance of Microspheres with Surface Acoustic Waves
journal, July 2013

Dynamically encircling an exceptional point for asymmetric mode switching
journal, July 2016

  • Doppler, Jörg; Mailybaev, Alexei A.; Böhm, Julian
  • Nature, Vol. 537, Issue 7618
  • DOI: 10.1038/nature18605

Long wavelength surface oscillations of a crystal with an adsorbed monolayer
journal, February 1989

Fano resonances in photonics
journal, September 2017

  • Limonov, Mikhail F.; Rybin, Mikhail V.; Poddubny, Alexander N.
  • Nature Photonics, Vol. 11, Issue 9
  • DOI: 10.1038/nphoton.2017.142

Interaction of Rayleigh waves with randomly distributed oscillators on the surface
journal, May 1999

Waveguiding by a locally resonant metasurface
journal, September 2015

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Surface acoustic wave modes in two-dimensional shallow void inclusion phononic crystals on GaAs
    journal, July 2019

    • Muzar, Edward; Stotz, James A. H.
    • Journal of Applied Physics, Vol. 126, Issue 2
    • DOI: 10.1063/1.5056311

    Reduced order derivation of the two-dimensional band structure of a mixed-mode resonator array
    journal, December 2018

    • Amirkhizi, Alireza V.; Wang, Weidi
    • Journal of Applied Physics, Vol. 124, Issue 24
    • DOI: 10.1063/1.5057707
      Sort by:
      [ × clear filter / sort ]

      Similar Records in DOE PAGES and OSTI.GOV collections: