Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T05:19:20.826Z Has data issue: false hasContentIssue false
  • English
  • Français

Bound states in the continuum in open acoustic resonators

Published online by Cambridge University Press:  03 September 2015

A. A. Lyapina ,
D. N. Maksimov ,
A. S. Pilipchuk  and
A. F. Sadreev
A. A. Lyapina
Affiliation:
L. V. Kirensky Institute of Physics, Krasnoyarsk 660036, Russia Siberian Federal University, Krasnoyarsk 660041, Russia
D. N. Maksimov*
Affiliation:
L. V. Kirensky Institute of Physics, Krasnoyarsk 660036, Russia
A. S. Pilipchuk
Affiliation:
L. V. Kirensky Institute of Physics, Krasnoyarsk 660036, Russia Siberian Federal University, Krasnoyarsk 660041, Russia
A. F. Sadreev
Affiliation:
L. V. Kirensky Institute of Physics, Krasnoyarsk 660036, Russia
*
†Email address for correspondence: mdn@tnp.krasn.ru
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider bound states in the continuum (BSCs) or embedded trapped modes in two- and three-dimensional acoustic axisymmetric duct–cavity structures. We demonstrate numerically that, under variation of the length of the cavity, multiple BSCs occur due to the Friedrich–Wintgen two-mode full destructive interference mechanism. The BSCs are detected by tracing the resonant widths to the points of the collapse of Fano resonances where one of the two resonant modes acquires infinite life-time. It is shown that the approach of the acoustic coupled mode theory cast in the truncated form of a two-mode approximation allows us to analytically predict the BSC frequencies and shape functions to a good accuracy in both two and three dimensions.

JFM classification

Acoustics: Aeroacoustics Acoustics: Noise control Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 780 , 10 October 2015 , pp. 370 - 387
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aslanyan, A., Parnovski, L. & Vassiliev, D. 2000 Complex resonances in acoustic waveguides. Q. J. Mech. Appl. Maths 53 (3), 429–447.Google Scholar
Berenger, J.-P. 1994 A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 144, 185–200.Google Scholar
Bulgakov, E. & Sadreev, A. 2008 Bound states in the continuum in photonic waveguides inspired by defects. Phys. Rev. B 78 (7), 075105.Google Scholar
Bulgakov, E. N. & Sadreev, A. F. 2014 Robust bound state in the continuum in a nonlinear microcavity embedded in a photonic crystal waveguide. Opt. Lett. 39 (17), 5212–5215.Google Scholar
Cattapan, G. & Lotti, P. 2007 Fano resonances in stubbed quantum waveguides with impurities. Eur. Phys. J. B 60 (1), 51–60.Google Scholar
Corrielli, G., Della Valle, G., Crespi, A., Osellame, R. & Longhi, S. 2013 Observation of surface states with algebraic localization. Phys. Rev. Lett. 111 (22), 220403.Google Scholar
Dittes, F. 2000 The decay of quantum systems with a small number of open channels. Phys. Rep. 339 (4), 215–316.Google Scholar
Duan, Y., Koch, W., Linton, C. M. & McIver, M. 2007 Complex resonances and trapped modes in ducted domains. J. Fluid Mech. 571, 119–147.Google Scholar
Evans, D. V., Levitin, M. & Vassiliev, D. 1994 Existence theorems for trapped modes. J. Fluid Mech. 261 (1), 21–31.Google Scholar
Evans, D. V. & Linton, C. M. 1991 Trapped modes in open channels. J. Fluid Mech. 225 (1), 153–175.Google Scholar
Fonda, L. 1961 Resonance reactions and continuous channels. Ann. Phys. 12 (3), 476–484.Google Scholar
Friedrich, H. & Wintgen, D. 1985 Interfering resonances and bound states in the continuum. Phys. Rev. A 32 (6), 3231–3242.Google Scholar
Hein, S. & Koch, W. 2008 Acoustic resonances and trapped modes in pipes and tunnels. J. Fluid Mech. 605, 401–428.Google Scholar
Hein, S., Koch, W. & Nannen, L. 2010 Fano resonances in acoustics. J. Fluid Mech. 664, 238–264.Google Scholar
Hein, S., Koch, W. & Nannen, L. 2012 Trapped modes and fano resonances in two-dimensional acoustical duct-cavity systems. J. Fluid Mech. 692, 257–287.CrossRefGoogle Scholar
Hsu, C. W., Zhen, B., Chua, S.-L., Johnson, S. G., Joannopoulos, J. D. & Soljačić, M. 2013 Bloch surface eigenstates within the radiation continuum. Light Sci. Appl. 2 (7), e84.Google Scholar
Jungowski, W. M., Botros, K. K. & Studzinski, W. 1989 Cylindrical side-branch as tone generator. J. Sound Vib. 131 (2), 265–285.Google Scholar
Kim, C., Satanin, A., Joe, Y. & Cosby, R. 1999 Resonant tunneling in a quantum waveguide: effect of a finite-size attractive impurity. Phys. Rev. B 60 (15), 10962–10970.Google Scholar
Kriesels, P. C., Peters, M. C. A. M., Hirschberg, A., Wijnands, A. P. J., Iafrati, A., Riccardi, G., Piva, R. & Bruggeman, J. C. 1995 High amplitude vortex-induced pulsations in a gas transport system. J. Sound Vib. 184 (2), 343–368.Google Scholar
Ladrón de Guevara, M., Claro, F. & Orellana, P. 2003 Ghost fano resonance in a double quantum dot molecule attached to leads. Phys. Rev. B 67 (19), 195335.Google Scholar
Lepetit, T., Akmansoy, E., Ganne, J.-P. & Lourtioz, J.-M. 2010 Resonance continuum coupling in high-permittivity dielectric metamaterials. Phys. Rev. B 82 (19), 195307.Google Scholar
Lepetit, T. & Kanté, B. 2014 Controlling multipolar radiation with symmetries for electromagnetic bound states in the continuum. Phys. Rev. B 90 (24), 241103(R).Google Scholar
Linton, C. M. & McIver, P. 2007 Embedded trapped modes in water waves and acoustics. Wave Motion 45 (1–2), 16–29.Google Scholar
Maksimov, D. N. & Sadreev, A. F. 2006 Bound states in elastic waveguides. Phys. Rev. E 74 (1), 016201.Google Scholar
Maksimov, D. N., Sadreev, A. F., Lyapina, A. A. & Pilipchuk, A. S. 2015 Coupled mode theory for acoustic resonators. Wave Motion 56, 52–66.Google Scholar
Marinica, D., Borisov, A. & Shabanov, S. 2008 Bound states in the continuum in photonics. Phys. Rev. Lett. 100 (18), 183902.CrossRefGoogle ScholarPubMed
Moiseyev, N. 1998 Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling. Phys. Rep. 302, 212–293.Google Scholar
von Neumann, J. & Wigner, E. P. 1929 Über merkwürdige diskrete eigenwerte. Z. Physik 50, 291–293.Google Scholar
Nöckel, J. U. 1992 Resonances in quantum-dot transport. Phys. Rev. B 46 (23), 15348–15356.Google Scholar
Olendski, O. & Mikhailovska, L. 2002 Bound-state evolution in curved waveguides and quantum wires. Phys. Rev. B 66 (3), 035331.Google Scholar
Parker, R. 1966 Resonance effects in wake shedding from parallel plates: some experimental observations. J. Sound Vib. 4 (1), 62–72.Google Scholar
Parker, R. 1967 Resonance effects in wake shedding from parallel plates: calculation of resonant frequencies. J. Sound Vib. 5 (2), 330–343.Google Scholar
Pichugin, K., Schanz, H. & Seba, P. 2001 Effective coupling for open billiards. Phys. Rev. E 64 (5), 056227.Google Scholar
Plotnik, Y., Peleg, O., Dreisow, F., Heinrich, M., Nolte, S., Szameit, A. & Segev, M. 2011 Experimental observation of optical bound states in the continuum. Phys. Rev. Lett. 107 (18), 183901.Google Scholar
Racec, P. N., Racec, E. R. & Neidhardt, H. 2009 Evanescent channels and scattering in cylindrical nanowire heterostructures. Phys. Rev. B 79 (15), 155305.Google Scholar
Sadreev, A., Bulgakov, E. & Rotter, I. 2006 Bound states in the continuum in open quantum billiards with a variable shape. Phys. Rev. B 73 (23), 235342.Google Scholar
Schult, R., Ravenhall, D. & Wyld, H. 1989 Quantum bound states in a classically unbound system of crossed wires. Phys. Rev. B 39 (8), 5476–5479.Google Scholar
Shahbazyan, T. & Raikh, M. 1994 Two-channel resonant tunneling. Phys. Rev. B 49 (24), 17123–17129.Google Scholar
Shipman, S. & Venakides, S. 2005 Resonant transmission near nonrobust periodic slab modes. Phys. Rev. E 71 (2), 026611.Google Scholar
Stillinger, F. & Herrick, D. 1975 Bound states in the continuum. Phys. Rev. A 11 (2), 446–454.Google Scholar
Sugimoto, N. & Imahori, H. 2005 Localized mode of sound in a waveguide with helmholtz resonators. J. Fluid Mech. 546 (1), 89–111.Google Scholar
Tonon, D., Hirschberg, A., Golliard, J. & Ziada, S. 2011 Aeroacoustics of pipe systems with closed branches. Noise Notes 10 (3), 27–88.Google Scholar
Weimann, S., Xu, Y., Keil, R., Miroshnichenko, A., Tünnermann, A., Nolte, S., Sukhorukov, A., Szameit, A. & Kivshar, Y. 2013 Compact surface fano states embedded in the continuum of waveguide arrays. Phys. Rev. Lett. 111 (24), 240403.Google Scholar
Wiersig, J. & Main, J. 2008 Fractal weyl law for chaotic microcavities: Fresnel’s laws imply multifractal scattering. Phys. Rev. E 77 (3), 036205.Google Scholar
Yang, Y., Peng, C., Liang, Y., Li, Z. & Noda, S. 2014 Analytical perspective for bound states in the continuum in photonic crystal slabs. Phys. Rev. Lett. 113 (3), 037401.Google Scholar
Zhang, M. & Zhang, X. 2015 Ultrasensitive optical absorption in graphene based on bound states in the continuum. Sci. Rep. 5, 8266.Google Scholar
Ziada, S. & Bühlmann, E. T. 1992 Self-excited resonances of two side-branches in close proximity. J. Fluids Struct. 6 (5), 583–601.Google Scholar
Ziada, S. & Shine, S. 1999 Strouhal numbers of flow-excited acoustic resonance of closed side branches. J. Fluids Struct. 13 (1), 127–142.Google Scholar