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Threshold of stimulated acoustic scattering and relation to noise amplification
Research notes Conclusions The signal to noise ratio for the WC process by SBS has a connection with the critical temperature of phase transition II. There is a constant temperature for optically active media (depending on the properties of the media) where the level of the noise in the system becomes equal to the level of the WC signal and under these conditions we cannot separate the WC signal from the noise. This means that the WC signal disappears. When SBS is used for monitoring the signal of wave front conjugation the dependence of the signal intensity on temperature should
References I 2 3 4
Andreev, N.P.. Korobkin, V.V, Molikov, M.R., Sabiev, ShSh, Poljakh, D.N. aad Saidov, X.Sh. Lphedec lnsr Rep ( 1984) 2 50-54 Seldovitch, iLJ.. Pilipetskii, N.F. and Shkuaov, V.V. Ware Front Conjugation Science Press. Moscow ( 1985) 240 Anisimov. M.A. Investiaation of critical ohenomena in liquids Usp ’ Fiz Nauk.( 1974) 114 2 >49-294 Landau, L.D. and Liphshits, E.M. Elecrrocl.wumics 01 Continua, I Course of Throreticul Physics, 8 j Science Press, Moscow ( 1982)
The main goal of the work reported here is the determination of the threshold value of the complete gain &, = (Yl,L),h, where g is the gain coefficient. amplitude of the spontaneously scattered acoustic wave I, must exceed the amplitude of the pump wave I,. This The growth of the spontaneously scattered sound wave intensity relative to the pump wave intensity is the fundamental requirement for the experimental determination of STAS
Threshdld of stimulated acoustic scattering and relation to noise amplification I.N.
be kept in mind in order to avoid wasteful work near the optical temperature of phase transition II.
Kozhevnikova
L exp( Gth) 2 1,
Wave Phenomena Department, General Physics Institute, Academy of Sciences of the USSR, Vavilov St. 38, Moscow, USSR Received 16 July 1989; revised 28 July 1989
Keywords: stimulated acoustic scattering; amplification; non-linear acoustics
hulse
where I, = *dR . (1, - I,)/AQ . V), AR is the angle of effective amplification of the noise signal, I, = (gl,)- ’ is the length of exitation’,V is the active volume and (da/do) is the cross section of sound scattering based on thermal fluctuation. From the theory of spontaneous acoustic scattering4, the value of (da/dR) can be determined and, correspondingly, the threshold value of G,,, may be found from G,h = In
The investigation of stimulated acoustic scattering (SAS) is an important area of non-linear acoustics. In this paper we report a study of the SAS of Rayleigh waves where the frequency shift of the scattered wave is equal to the width of the spectra. The influence of temperature on stimulated scattering (STAS) is also considered; the pump wave and scattered wave heat the medium, creating a temperature gradient which is responsible for scattering. The liquids in which STAS can be observed must satisfy the requirement that the length of stimulated scattering L should not exceed either I, or the characteristic scale of convection I,, where I, is the length required for the formation of a shock wave (i.e. the discontinuity distance). There are two different ways of determining the stimulated scattering threshold intensity I,,. The first is the determination of I,, by comparing amplification and absorption’. However, this method causes experimental problems’ because for all types of SAS the amplification of scattering waves starts close to the level of spontaneous noise in the system. This noise can produce spontaneous scattering of pump waves in media showing thermal fluctuations. The correlation between stimulated and spontaneous acoustic scattering may be monitored using general principles known from optics3. Therefore to determine the STAS threshold experimentally, the amplitude of the spontaneously scattered acoustic wave I, must exceed the amplitude of the pump wave IP. This forms the basis of the second method of determinmg I,,,. 0041-624X/ 90/010057-01 $03.00 @ 1990 Butterworth & Co (Publishers)
Ltd
(1)
4n2c,pc;G,, KT2y2AClto4L> ’
where c,, is the heat capacity at constant pressure, c,, is the undistributed sound speed, p is the medium density, w is the angular frequency of the acoustic pump wave, JJ= d(ln c8)/d7’, K is Boltzman’s constant and T is the temperature. For typical parameters of liquids and for L = 1 cm, AR = 10s2 (steradian), we obtain G,,, 5 ln( 1020f-4G,,), wheref= w/211(in MHz). Forf= 10MHz the condition for the observation of STAS is G z G,,, = 40
(3)
Two main conclusions follow from these theoretical considerations. ( 1) The stimulated analogue of the phenomena exists for all typs of spontaneous scattering. This is correct not only for optics but also for acoustics. (2) The threshold of STAS calculated from absorption is lower than the real threshold found based on the spontaneous noise of the system.
References 1
Rankin.
F.V.,
Volyak.
K.I. and Lyakhov,
G.A.,
Sor Ph~s Acoust
(1982) 28 607-613 2 3
4
Bankin. F.V. and Lyakhov, G.A. Lehder Insr Rep (1984) 156 3-19 Zeldovitch. J.B. and Sobelman. 1.1. Usp Fi: Nauk ( 1970) 101 3-20 Isakovitch, M.A. func/mrnra/s oJ’Acoustics Moscow. Nauka Press
(1973)
Ultrasonics 1990 Vol 28 January
57
References I 2 3 4
Andreev, N.P.. Korobkin, V.V, Molikov, M.R., Sabiev, ShSh, Poljakh, D.N. aad Saidov, X.Sh. Lphedec lnsr Rep ( 1984) 2 50-54 Seldovitch, iLJ.. Pilipetskii, N.F. and Shkuaov, V.V. Ware Front Conjugation Science Press. Moscow ( 1985) 240 Anisimov. M.A. Investiaation of critical ohenomena in liquids Usp ’ Fiz Nauk.( 1974) 114 2 >49-294 Landau, L.D. and Liphshits, E.M. Elecrrocl.wumics 01 Continua, I Course of Throreticul Physics, 8 j Science Press, Moscow ( 1982)
The main goal of the work reported here is the determination of the threshold value of the complete gain &, = (Yl,L),h, where g is the gain coefficient. amplitude of the spontaneously scattered acoustic wave I, must exceed the amplitude of the pump wave I,. This The growth of the spontaneously scattered sound wave intensity relative to the pump wave intensity is the fundamental requirement for the experimental determination of STAS
Threshdld of stimulated acoustic scattering and relation to noise amplification I.N.
be kept in mind in order to avoid wasteful work near the optical temperature of phase transition II.
Kozhevnikova
L exp( Gth) 2 1,
Wave Phenomena Department, General Physics Institute, Academy of Sciences of the USSR, Vavilov St. 38, Moscow, USSR Received 16 July 1989; revised 28 July 1989
Keywords: stimulated acoustic scattering; amplification; non-linear acoustics
hulse
where I, = *dR . (1, - I,)/AQ . V), AR is the angle of effective amplification of the noise signal, I, = (gl,)- ’ is the length of exitation’,V is the active volume and (da/do) is the cross section of sound scattering based on thermal fluctuation. From the theory of spontaneous acoustic scattering4, the value of (da/dR) can be determined and, correspondingly, the threshold value of G,,, may be found from G,h = In
The investigation of stimulated acoustic scattering (SAS) is an important area of non-linear acoustics. In this paper we report a study of the SAS of Rayleigh waves where the frequency shift of the scattered wave is equal to the width of the spectra. The influence of temperature on stimulated scattering (STAS) is also considered; the pump wave and scattered wave heat the medium, creating a temperature gradient which is responsible for scattering. The liquids in which STAS can be observed must satisfy the requirement that the length of stimulated scattering L should not exceed either I, or the characteristic scale of convection I,, where I, is the length required for the formation of a shock wave (i.e. the discontinuity distance). There are two different ways of determining the stimulated scattering threshold intensity I,,. The first is the determination of I,, by comparing amplification and absorption’. However, this method causes experimental problems’ because for all types of SAS the amplification of scattering waves starts close to the level of spontaneous noise in the system. This noise can produce spontaneous scattering of pump waves in media showing thermal fluctuations. The correlation between stimulated and spontaneous acoustic scattering may be monitored using general principles known from optics3. Therefore to determine the STAS threshold experimentally, the amplitude of the spontaneously scattered acoustic wave I, must exceed the amplitude of the pump wave IP. This forms the basis of the second method of determinmg I,,,. 0041-624X/ 90/010057-01 $03.00 @ 1990 Butterworth & Co (Publishers)
Ltd
(1)
4n2c,pc;G,, KT2y2AClto4L> ’
where c,, is the heat capacity at constant pressure, c,, is the undistributed sound speed, p is the medium density, w is the angular frequency of the acoustic pump wave, JJ= d(ln c8)/d7’, K is Boltzman’s constant and T is the temperature. For typical parameters of liquids and for L = 1 cm, AR = 10s2 (steradian), we obtain G,,, 5 ln( 1020f-4G,,), wheref= w/211(in MHz). Forf= 10MHz the condition for the observation of STAS is G z G,,, = 40
(3)
Two main conclusions follow from these theoretical considerations. ( 1) The stimulated analogue of the phenomena exists for all typs of spontaneous scattering. This is correct not only for optics but also for acoustics. (2) The threshold of STAS calculated from absorption is lower than the real threshold found based on the spontaneous noise of the system.
References 1
Rankin.
F.V.,
Volyak.
K.I. and Lyakhov,
G.A.,
Sor Ph~s Acoust
(1982) 28 607-613 2 3
4
Bankin. F.V. and Lyakhov, G.A. Lehder Insr Rep (1984) 156 3-19 Zeldovitch. J.B. and Sobelman. 1.1. Usp Fi: Nauk ( 1970) 101 3-20 Isakovitch, M.A. func/mrnra/s oJ’Acoustics Moscow. Nauka Press
(1973)
Ultrasonics 1990 Vol 28 January
57