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

Maznev, A. A.

doi:10.1063/1.5012999

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

Journal Article · 20 February 2018 · Journal of Applied Physics

DOI: https://doi.org/10.1063/1.5012999 · OSTI ID:1470492

Maznev, A. A. ^[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.

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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

OSTI ID:: 1470492

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)

Dynamic Mass Density and Acoustic Metamaterials Mei, Jun; Ma, Guancong; Yang, Min Acoustic Metamaterials and Phononic Crystals https://doi.org/10.1007/978-3-642-31232-8_5	book	October 2012
Long wavelength surface oscillations of a crystal with an adsorbed monolayer Kosevich, Yu. A.; Syrkin, E. S. Physics Letters A, Vol. 135, Issue 4-5 https://doi.org/10.1016/0375-9601(89)90118-7	journal	February 1989
Unified Theoretical Framework for Realizing Diverse Regimes of Strong Coupling between Plasmons and Electronic Transitions Faucheaux, Jacob A.; Fu, Jiayi; Jain, Prashant K. The Journal of Physical Chemistry C, Vol. 118, Issue 5 https://doi.org/10.1021/jp412157c	journal	January 2014
Spawning rings of exceptional points out of Dirac cones Zhen, Bo; Hsu, Chia Wei; Igarashi, Yuichi Nature, Vol. 525, Issue 7569 https://doi.org/10.1038/nature14889	journal	September 2015
Dynamically encircling an exceptional point for asymmetric mode switching Doppler, Jörg; Mailybaev, Alexei A.; Böhm, Julian Nature, Vol. 537, Issue 7618 https://doi.org/10.1038/nature18605	journal	July 2016
Reversing the pump dependence of a laser at an exceptional point Brandstetter, M.; Liertzer, M.; Deutsch, C. Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5034	journal	June 2014
Ultrasonic metamaterials with negative modulus Fang, Nicholas; Xi, Dongjuan; Xu, Jianyi Nature Materials, Vol. 5, Issue 6 https://doi.org/10.1038/nmat1644	journal	April 2006
Fano resonances in photonics Limonov, Mikhail F.; Rybin, Mikhail V.; Poddubny, Alexander N. Nature Photonics, Vol. 11, Issue 9 https://doi.org/10.1038/nphoton.2017.142	journal	September 2017
Wave propagation control at the deep subwavelength scale in metamaterials Lemoult, Fabrice; Kaina, Nadège; Fink, Mathias Nature Physics, Vol. 9, Issue 1 https://doi.org/10.1038/nphys2480	journal	November 2012
Engineered metabarrier as shield from seismic surface waves Palermo, Antonio; Krödel, Sebastian; Marzani, Alessandro Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep39356	journal	December 2016
Heterodyned impulsive stimulated Raman scattering of phonon–polaritons in LiTaO3 and LiNbO3 Crimmins, Timothy F.; Stoyanov, Nikolay S.; Nelson, Keith A. The Journal of Chemical Physics, Vol. 117, Issue 6 https://doi.org/10.1063/1.1491948	journal	August 2002
Avoided level crossing and exceptional points Heiss, W. D.; Sannino, A. L. Journal of Physics A: Mathematical and General, Vol. 23, Issue 7 https://doi.org/10.1088/0305-4470/23/7/022	journal	April 1990
Observation of exceptional points in electronic circuits Stehmann, T.; Heiss, W. D.; Scholtz, F. G. Journal of Physics A: Mathematical and General, Vol. 37, Issue 31 https://doi.org/10.1088/0305-4470/37/31/012	journal	July 2004
Interaction of Rayleigh waves with randomly distributed oscillators on the surface Garova, E. A.; Maradudin, A. A.; Mayer, A. P. Physical Review B, Vol. 59, Issue 20 https://doi.org/10.1103/PhysRevB.59.13291	journal	May 1999
Experimental observation of locally-resonant and Bragg band gaps for surface guided waves in a phononic crystal of pillars Achaoui, Younes; Khelif, Abdelkrim; Benchabane, Sarah Physical Review B, Vol. 83, Issue 10 https://doi.org/10.1103/PhysRevB.83.104201	journal	March 2011
Waveguiding by a locally resonant metasurface Maznev, A. A.; Gusev, V. E. Physical Review B, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevB.92.115422	journal	September 2015
Vibrational dynamics of a two-dimensional microgranular crystal Vega-Flick, A.; Duncan, R. A.; Wallen, S. P. Physical Review B, Vol. 96, Issue 2 https://doi.org/10.1103/PhysRevB.96.024303	journal	July 2017
Simultaneous Occurrence of Structure-Directed and Particle-Resonance-Induced Phononic Gaps in Colloidal Films Still, T.; Cheng, W.; Retsch, M. Physical Review Letters, Vol. 100, Issue 19 https://doi.org/10.1103/PhysRevLett.100.194301	journal	May 2008
Interaction of a Contact Resonance of Microspheres with Surface Acoustic Waves Boechler, N.; Eliason, J. K.; Kumar, A. Physical Review Letters, Vol. 111, Issue 3 https://doi.org/10.1103/PhysRevLett.111.036103	journal	July 2013
Complex Contact-Based Dynamics of Microsphere Monolayers Revealed by Resonant Attenuation of Surface Acoustic Waves Hiraiwa, M.; Abi Ghanem, M.; Wallen, S. P. Physical Review Letters, Vol. 116, Issue 19 https://doi.org/10.1103/PhysRevLett.116.198001	journal	May 2016
Experimental Observation of the Topological Structure of Exceptional Points Dembowski, C.; Gräf, H. -D.; Harney, H. L. Physical Review Letters, Vol. 86, Issue 5 https://doi.org/10.1103/PhysRevLett.86.787	journal	January 2001
Emergence, Coalescence, and Topological Properties of Multiple Exceptional Points and Their Experimental Realization Ding, Kun; Ma, Guancong; Xiao, Meng Physical Review X, Vol. 6, Issue 2 https://doi.org/10.1103/PhysRevX.6.021007	journal	April 2016
Strong coupling, energy splitting, and level crossings: A classical perspective Novotny, Lukas American Journal of Physics, Vol. 78, Issue 11 https://doi.org/10.1119/1.3471177	journal	November 2010
Dispersion characteristics of sound waves in a tunnel with an array of Helmholtz resonators Sugimoto, N.; Horioka, T. The Journal of the Acoustical Society of America, Vol. 97, Issue 3 https://doi.org/10.1121/1.412085	journal	March 1995
Acoustic metamaterials: From local resonances to broad horizons Ma, Guancong; Sheng, Ping Science Advances, Vol. 2, Issue 2 https://doi.org/10.1126/sciadv.1501595	journal	February 2016
Locally Resonant Sonic Materials Liu, Z. Science, Vol. 289, Issue 5485 https://doi.org/10.1126/science.289.5485.1734	journal	September 2000

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

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