This paper presents, in one dimension, the general analytical solution of the acoustic phase conjugation in an active medium in contact with passive media of arbitrary impedance. The homogeneous case where no impedance jumps exist at the edge of the active zone is obtained as a particular case. This homogeneous case was the only one treated explicitly in the literature but mostly in the frame of Brillouin scattering. In contrast to this previous work, the present theory is based on a preliminary straightforward analysis using a dual-time-scale method and provides very practical results like the threshold of the supercritical modes, the rate of amplification, and its link with the stress repartition in the conjugator.
REFERENCES
1.
N. M.
Kroll
, “Excitation of hypersonic vibrations by means of photoelastic coupling of high-intensity light waves to elastic waves
,” J. Appl. Phys.
36
(1
), 34
–43
(1965
).2.
D. L.
Bobroff
, “Coupled-modes analysis of the phonon-photon parametric backward-wave oscillator
,” J. Appl. Phys.
36
(5
), 1760
–1769
(1965
).3.
D. L.
Bobroff
and H. A.
Haus
, “Impulse response of active coupled wave systems
,” J. Appl. Phys.
38
, 390
–403
(1967
).4.
B. A.
Auld
and H.
Mathews
, “Parametric traveling-wave acoustic amplification in ferromagnets
,” J. Appl. Phys.
36
(11
), 3599
–3605
(1965
).5.
R. B.
Thompson
and C. F.
Quate
, “Nonlinear interaction of microwave electric fields and sound in
,” J. Appl. Phys.
42
(3
), 907
–919
(1971
).6.
A. A.
Chaban
, “On one nonlinear effect in piezoelectric semiconductors
,” Sov. Phys. Solid State
9
, 3334
–3335
(1967
).7.
H. J.
Simpson
, P. L.
Marston
, “Parametric Layers, Four-wave mixing and wave front reversal
,” Non Linear Acoustics
, edited by M. F.
Hamilton
and D. T.
Blackstock
(Academic
, New York, 1998
), pp. 399
–420
.8.
F. V.
Bunkin
, D. V.
Vlasov
, and Yu. A.
Kravtsov
, “On problem of sound wave phase conjugation with amplification of conjugate wave
,” Sov. J. Quantum Electron.
11
, 687
–688
(1981
).9.
F. V.
Bunkin
, D. V.
Vlasov
, E. A.
Zabolotskaya
, and Yu. A.
Kravtsov
, “Wave-front inversion of sound beams and other nonlinear effects in a medium containing bubbles
,” Sov. Phys. Acoust.
28
, 249
(1982
).10.
L. M.
Kustov
, V. E.
Nazarov
, and A. M.
Sutin
, “Nonlinear sound scattering by a bubble layer
,” Sov. Phys. Acoust.
32
(6
), 500
–503
(1986
).11.
A. P.
Brysev
, L. M.
Krutyianskii
, and V. L.
Preobrazhenskii
, “Wave phase conjugation of ultrasonic beams
,” Sov. Phys. Usp.
41
(8
), 793
–805
(1998
).12.
M.
Fink
, D.
Cassereau
, A.
Derode
, C.
Prada
, P.
Roux
, M.
Tanter
, J. L.
Thomas
, and F.
Wu
, “Time-reversed acoustics
,” Rep. Prog. Phys.
63
, 1933
–1995
(2000
).13.
A.
Brysev
, L.
Krutyansky
, P.
Pernod
, and V.
Preobrazhensky
, “Acoustic microscope based on magneto-elastic wave phase conjugator
,” Appl. Phys. Lett.
76
(21
), 3133
–3135
(2000
).14.
15.
M. W.
Bowers
and R. W.
Boyd
, “Phase locking via Brillouin-enhanced four-wave-mixing phase conjugation
,” IEEE J. Quantum Electron.
34
(4
), 634
–644
(1998
).16.
M.
Tsang
and D.
Psaltis
, “Spectral phase conjugation with cross-phase modulation compensation
,” Opt. Express
12
(10
), 2207
–2219
(2004
).17.
S.
Ben Khelil
, A.
Merlen
, V.
Preobrazhensky
, and P.
Pernod
, “Numerical simulation of acoustic wave phase conjugation in active media
,” J. Acoust. Soc. Am.
109
(1
), 75
–83
(2001
).18.
A.
Merlen
, V. L.
Preobrazhenskii
, and P.
Pernod
, “Supercritical parametric phase conjugation of ultrasound. Numerical simulation of non linear and non stationary modes
,” J. Acoust. Soc. Am.
112
, 2656
–2665
(2002
).19.
K.
Yamamoto
, P.
Pernod
, and V.
Preobrazhensky
, “Visualization of phase conjugate ultrasound waves passed through inhomogeneous layer
,” Ultrasonics
42
, 1049
–1052
(2004
).20.
P.
Voinovich
, A.
Merlen
, E.
Timofeev
, and K.
Takayama
, “A Godunov-type finite-volume scheme for unified solid-liquid elastodynamics on arbitrary two-dimensional grids
,” Shock Waves
13
, 221
–230
(2003
).21.
P.
Voinovich
and A.
Merlen
, “2-D numerical simulation of acoustic wave phase conjugation in active medium
,” J. Acoust. Soc. Am.
118
(6
), 3491
–3498
(2005
).22.
F.
Verhulst
, “Nonlinear Differential Equations and Dynamical Systems
” (Universitext Springer-Verlag
, Berlin, 1996
), pp. 152
–155
.23.
P.
Pernod
and V.
Preobrazhensky
, “Parametric phase conjugation of a wide-band acoustic pulse in supercritical mode
,” Appl. Phys. Lett.
76
(3
), 387
–389
(2000
).© 2006 Acoustical Society of America.
2006
Acoustical Society of America
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