In the present study a two-dimensional axisymmetric numerical model is developed for supercritical parametric phase conjugation of ultrasound in a solid active element of cylindrical shape and finite length. The pseudospectral time domain algorithm (PSTD) is used owing to its efficiency to model large-scale problems. PSTD solves elastic wave equation in time-dependent heterogeneous isotropic and axisymmetric anisotropic solids using FFTs for high order approximation of the spatial differential operator on staggered grid, and a fourth-order Adams–Bashforth time integrator. In order to truncate the computational domain absorbing boundary conditions are introduced with complex frequency shifted perfectly matched layers. This procedure is highly effective at absorbing signals of long time-signature. The free surface of the active ceramic rod is introduced through the method of images. A systematic study of the influence of lateral limitations of the active medium on parametric wave phase conjugation of sound is made. It is shown that retro-focusing of the incident pulse takes place even in the case of mode conversions inside the active zone. Nevertheless, amplitude and form of the obtained conjugate pulse depend on the simulated configuration. Numerical simulation correctly describes the parametric amplification and retro-focusing of ultrasound observed in experiments.
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November 2005
November 01 2005
Two-dimensional axisymmetric numerical simulation of supercritical phase conjugation of ultrasound in active solid media
Olivier Bou Matar;
Olivier Bou Matar
a)
Institut d’Electronique
, de Micro-électronique et de Nanotechnologie (IEMN-DOAE UMR CNRS 8520), Ecole Centrale de Lille, BP 48, 59651 Villeneuve d’ascq Cedex, France
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Vladimir Preobrazhensky;
Vladimir Preobrazhensky
b)
Institut d’Electronique
, de Micro-électronique et de Nanotechnologie (IEMN-DOAE UMR CNRS 8520), Ecole Centrale de Lille, BP 48, 59651 Villeneuve d’ascq Cedex, France
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Philippe Pernod
Philippe Pernod
Institut d’Electronique
, de Micro-électronique et de Nanotechnologie (IEMN-DOAE UMR CNRS 8520), Ecole Centrale de Lille, BP 48, 59651 Villeneuve d’ascq Cedex, France
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Olivier Bou Matar
a)
Vladimir Preobrazhensky
b)
Philippe Pernod
Institut d’Electronique
, de Micro-électronique et de Nanotechnologie (IEMN-DOAE UMR CNRS 8520), Ecole Centrale de Lille, BP 48, 59651 Villeneuve d’ascq Cedex, Francea)
On leave from GIP Ultrasons/LUSSI, Université de Tours, 2 bis Bd. Tonnellé, 37032 Tours, France; electronic mail: [email protected]
b)
Also with Wave Research Center of General Physics Institute (RAS), 38 Vavilova Str., 119991 Moscow, Russia.
J. Acoust. Soc. Am. 118, 2880–2890 (2005)
Article history
Received:
September 24 2004
Accepted:
August 17 2005
Citation
Olivier Bou Matar, Vladimir Preobrazhensky, Philippe Pernod; Two-dimensional axisymmetric numerical simulation of supercritical phase conjugation of ultrasound in active solid media. J. Acoust. Soc. Am. 1 November 2005; 118 (5): 2880–2890. https://doi.org/10.1121/1.2062467
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