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Transmission of surface acoustic waves through the interface based on discontinuity of electrical boundary conditions on surface of potassium niobate
Ultrasonics 42 (2004) 373–376 www.elsevier.com/locate/ultras
Transmission of surface acoustic waves through the interface based on discontinuity of electrical boundary conditions on surface of potassium niobate Boris D. Zaitsev a, Irina A. Borodina a, Iren E. Kuznetsova a, Shrinivas G. Joshi b
b,*
a Institute of Radio Engineering and Electronics, Saratov 410019, Russia EECE Department, Marquette University, P.O. Box 1881, Milwaukee, WI 53201, USA
Abstract This paper presents theoretical investigation of the propagation of surface acoustic waves (SAWs) across the boundary between metallized (electrically shorted) and unmetallized (electrically open) regions on the surface of potassium niobate crystals. Potassium niobate is a very strong piezoelectric material and has the interesting property that only one type of SAW, namely a Rayleigh wave, can exist on unmetallized surface, where as two types of SAWs, namely Rayleigh and Bleustein–Gulyaev (BG), can exist on a metallized surface. Analysis shows that the Rayleigh wave propagates through the interface with very little change in amplitude or polarization. On the other hand, almost total reflection of the BG wave is expected. Details of the theoretical analysis and calculated results will be presented. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Potassium niobate; Surface acoustic wave; Negative electro-mechanical coupling; Wave reflection
1. Introduction Potassium niobate has been receiving much attention recently due to its excellent optic, electrooptic, and acoustic properties [1]. The propagation of surface acoustic waves in this material has been investigated previously [2–4]. It has been shown that variations in electrical boundary conditions can result in some unexpected behavior, such as: (1) significant transformation of the wave structure, for example, from a ‘‘generalized Bleustein–Gulyaev (BG) wave’’ into a generalized Rayleigh wave, and (2) disappearance of some types of surface acoustic waves [4]. Based on these results, an interesting question to consider is what would happen when surface acoustic wave encounters the boundary between a metallized and an unmetallized region. The answer to this question is not obvious. One of two distinct situations may occur. (1) One possibility is that transmitted wave displays the same structure as incident wave. That is, the transition from one branch of
solution to another branch occurs. In this case the wave will show a negative value of K 2 , the electromechanical coupling coefficient. This is assuming the traditional definition of K 2 which is K 2 ¼ 2ðv vm Þ=v;
ð1Þ
where v and vm are the values of SAW velocity for electrically open and electrically shorted surface, respectively. (2) The other possibility is that transmitted wave follows the same branch of solution as incident wave. That is, the structure of wave significantly changes. In this case strong wave reflection is expected. Either of these results, besides their fundamental and methodological significance, can have important practical applications. This paper is devoted to theoretical investigation of the transmission and reflection of surface acoustic waves (SAWs) at an interface formed by a change in electrical boundary conditions at the surface of a strong piezoelectric material. 2. Theoretical calculations and results
*
Corresponding author. Tel.: +414-288-1584; fax: +414-288-5579. E-mail addresses: [email protected] (B.D. Zaitsev), shri.joshi@ marquette.edu (S.G. Joshi). 0041-624X/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2004.01.035
Before analysis of the transmission and reflection problem, we will briefly analyze the influence of electrical
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B.D. Zaitsev et al. / Ultrasonics 42 (2004) 373–376 4000
2
1000
1
100
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3600
u 2 /u 3
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-8
10
-6
-4
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10
-8
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d/λ
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-2
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(b) 1.0
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2 0.1 10 -1 shorted
3000 -1
10 shorted
10
-3
10
σS, S
-5
10
-7
open
Fig. 1. Velocity in m/s versus normalized height of air gap d=k (a) and sheet conductance rS (b) for branches (1) and (2) of generalized surface acoustic waves propagating in Y –X þ 15° potassium niobate.
boundary conditions on types of SAW solutions. We shall consider two situations: (a) variation of distance d between an ideal conducting plane and surface of piezoelectric crystal, and (b) change in sheet conductance of a thin film deposited on the surface of the crystal. All calculations in this paper are carried out assuming that the piezoelectric material is Y cut potassium niobate with wave propagation at an angle of 15° with respect to the X -axis. This is a very strong piezoelectric material which exhibits the unusual properties mentioned in the previous section [4].
2.1. SAW characteristics in the structure ‘‘piezoelectric crystal––vacuum gap––ideal conducting plane’’ We consider the influence of an ideal conducting plane separated from the electrically open surface of a piezoelectric crystal on characteristics of generalized Rayleigh and BG waves. The height of the air gap between the crystal and conducting plane is denoted by d. Increase of d from 0 to k (k ¼ acoustic wavelength)
10 -5
10 -3
10 -7
σS,S
Fig. 2. Ratio of mechanical displacement components u2 =u3 versus normalized height of air gap d=k (a) and sheet conductance rS (b) for branches (1) and (2) of generalized surface acoustic waves propagating in Y –X þ 15° potassium niobate.
allows one to realize smooth transition from an electrically short to an electrically open surface. The method of analyzing this problem has been described in [5]. The material constants of potassium niobate are taken from [1]. Dependencies of phase velocity and ratio of mechanical displacement components u2 =u3 are presented in Figs. 1(a) and 2(a), respectively. Here axis x1 coincides with the SAW propagation direction, x3 is normal to the surface of the crystal, and x2 lies on the surface of the crystal normal to the wave propagation direction. Analysis shows that there are two branches of solution. The first branch (1) shows that with increase in distance d from 0 to k, a smooth transition of ‘‘generalized Bleustein–Gulyaev (BG) wave’’ into generalized Rayleigh wave occurs. In this case the ratio u2 =u3 changes from 10 to 0.7 (Fig. 2(a)). As for the second branch (2), it corresponds to the generalized leaky Rayleigh wave, the attenuation of which increases with increase of distance d. It is found that for d P 0:002k the wave ceases to propagate and the second solution disappears.
B.D. Zaitsev et al. / Ultrasonics 42 (2004) 373–376
2.2. SAW characteristics in piezoelectric crystal––thin conducting layer structure Here we analyze the influence of a thin conducting layer located on the surface of the potassium niobate crystal. The method of analysis has been described in [5]. Dependencies of the phase velocity and ratio of the mechanical displacement components u2 =u3 are presented in Figs. 1(b) and 2(b), respectively. One can see that in this case also there exist two branches of solution. In accordance with the first branch (1), the velocity of generalized BG wave increases with decreasing value of sheet conductance rS . This wave is leaky and its attenuation increases with decreasing rS . When rS decreases below 106 S, this wave ceases to be propagating and the first solution disappears. Fig. 1(a) shows that the maximum value of generalized BG wave velocity for the case discussed in Section 2.1 is 3851 m/s, whereas in the present case it is 4500 m/s. This difference can be explained by the anomalous resisto-acoustic effect [6]. The second branch of solution (2) corresponds to a generalized Rayleigh wave. Analysis shows that the velocity of this wave increases slightly with increasing sheet conductance. For large values of rS (corresponding to electrically shorted surface), velocity vm is found to be 3914 m/s, whereas for electrically open surface velocity v ¼ 3885 m/s. So we see that vm is actually greater than v. This means that electromechanical coupling coefficient K 2 defined from Eq. (1) becomes negative! As far as the structures of BG and Rayleigh waves are concerned, it is found that variation in sheet conductance does not result in significant change in the structure of the waves. This result is radically different from that observed in Section 2.1.
375
Shorted Open 5 3
(a) 1
2
Shorted Open 6
3
(b) 1
2
Shorted Open 6
4 2
(c)
3
2.3. Transmission of SAWs through the interface based on change in electrical boundary conditions Results obtained in previous parts of the paper allow us to resolve the question of what will occur when acoustic wave passes through an interface formed by a change in electrical boundary conditions on the surface of Y –X þ 15° potassium niobate crystal. Previous analysis has shown that for electrically open surface there is only one type of surface wave, namely generalized Rayleigh wave; whereas for electrically shorted surface, a generalized Rayleigh wave as well as a generalized Bleustein–Gulyaev wave can exist. So we will analyze reflection and transmission of waves for the three possible situations shown in Fig. 3. These are: (a) generalized Rayleigh wave encounters the interface ‘‘electrically open surface–electrically shorted surface’’; (b) generalized Rayleigh wave encounters the interface ‘‘electrically shorted surface–electrically open surface’’; (c) generalized Bleustein–Gulyaev wave encounters the interface ‘‘electrically shorted surface–electrically open surface’’.
Fig. 3. Transmission of generalized Rayleigh and Bleustein–Gulyaev surface acoustic waves through the interface based on discontinuity of electrical boundary conditions in Y –X þ 15° potassium niobate. As discussed in the text, three different cases are shown. Numbers 1 through 6 denote the different waves as follows. 1––incident generalized Rayleigh wave, 2––transmitted generalized Rayleigh wave, 3––reflected generalized Rayleigh wave, 4––incident generalized Bleustein–Gulyaev wave, 5––transmitted generalized Bleustein–Gulyaev wave, 6––reflected generalized Bleustein–Gulyaev wave.
It should be noted here that incident, reflected, and transmitted waves can have different polarizations. Therefore the correct determination of transmission and reflection coefficients was based on comparison of total energy flows associated with these waves. From our calculations we have found the following. Generalized Rayleigh wave transmits through both types of interfaces with practically no change in amplitude and polarization. Thus the transmission coefficient for the cases shown in Fig. 3(a) and (b) is very close to
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B.D. Zaitsev et al. / Ultrasonics 42 (2004) 373–376
unity. It should be noted that for this material, Rayleigh wave velocity on electrically shorted surface is slightly higher than on electrically open surface. This means that the wave in this case provides negative value of K 2 , the electromechanical coupling coefficient. It should be noted that in recent years there have appeared several papers which report that for some specific situations electrical shorting of the surface may actually increase SAW velocity [7,8]. The existence of this phenomenon has also been experimentally demonstrated in [9]. It has been suggested that velocity increase may be occurring due to transformation of wave types or due to wave hybridization. As regards the case of incident BG wave considered in Fig. 3(c), total reflection of the wave corresponding to nearly unity reflection coefficient is predicted. This is a very unexpected result and more work is needed to determine if this conclusion is indeed true.
the interface ‘‘electrically shorted surface–electrically open surface’’ and vice versa with practically no change in wave amplitude or polarization. Thus the transmission coefficient is close to unity. The wave in this case has a slightly negative value of coupling coefficient K 2 . As for the generalized BG wave, preliminary calculations predict nearly unity reflection coefficient when the wave is incident from an electrically shorted surface on to an electrically open surface. More work is needed to determine the validity of this conclusion.
Acknowledgements This work was supported by a grant No. 01-0216266a from the Russian Foundation of Basic Research.
References 3. Summary Theoretical analysis of generalized SAWs propagating in Y –X þ 15° potassium niobate crystal shows that the method used to change boundary condition from electrically shorted surface to electrically open surface can influence the observed results. If the transition from shorted to open surface is performed by moving an ideal conducting plane away from the crystal surface, the transformation of generalized BG wave into generalized Rayleigh wave is possible. In this case the transition is accompanied by an increase in wave velocity. On the other hand if the transition is performed by decreasing sheet conductance of a conducting layer deposited on the crystal surface, there is no transformation of SAW types. But in this case the velocity of generalized Rayleigh wave for electrically shorted surface is found to be slightly higher than for electrically open surface. This means that electromechanical coupling coefficient defined in accordance with Eq. (1) is negative! In this case definition of electromechanical coupling coefficient should be based on energy considerations. Analysis of wave reflection and transmission problem shows that generalized Rayleigh wave transmits through
[1] M. Zgonik, R. Schlesser, I. Biaggio, J. Tscherry, P. Gunter, E. Voit, Material constants of KNbO3 relevant for electro and acoustooptics, J. Appl. Phys. 74 (1993) 1287–1297. [2] K. Yamanouchi, H. Odagawa, T. Kojima, T. Matsumura, Theoretical and experimental study of super high electromechanical coupling surface acoustic wave propagation in KNbO3 single crystal, Electron. Lett. 33 (1997) 193–194. [3] K. Nakamura, M. Oshiki, Theoretical analysis of horizontal shear mode piezoelectric surface acoustic waves in potassium niobate, Appl. Phys. Lett. 71 (1997) 3203–3205. [4] B.D. Zaitsev, I. Kuznetsova, S.G. Joshi, Influence of electrical boundary conditions on structure of surface acoustic waves in potassium niobate, Electron. Lett. 35 (1999) 1205–1206. [5] B.D. Zaitsev, S.G. Joshi, I.E. Kuznetsova, Propagation of QSH (quasi shear horizontal) acoustic waves in piezoelectric plates, IEEE Trans. UFFC 46 (1999) 1298–1302. [6] B.D. Zaitsev, I.E. Kuznetsova, S.G. Joshi, Anomalous resistoacoustic effect, J. Appl. Phys. 86 (1999) 6868–6874. [7] V.G. Mozhaev, M. Weihnacht, Incredible negative values of effective electromechanical coupling coefficient for surface acoustic waves in piezoelectrics, Ultrasonics 37 (2000) 687–691. [8] V.G. Mozhaev, M. Weihnacht, Extraordinary case of acoustic wave acceleration due to electrical shorting of piezoelecrics, 1999 IEEE Ultrason. Symp. (1999) 73–76. [9] Sh. Kakio, H. Nakamura, Y. Kanmori, Y. Nakagava, Reversal phenomenon in phase velocity of surface acoustic waves on free and metallized surfaces by proton-exchange, Jpn. J. Appl. Phys. 38 (1999) 3261–3264.
Transmission of surface acoustic waves through the interface based on discontinuity of electrical boundary conditions on surface of potassium niobate Boris D. Zaitsev a, Irina A. Borodina a, Iren E. Kuznetsova a, Shrinivas G. Joshi b
b,*
a Institute of Radio Engineering and Electronics, Saratov 410019, Russia EECE Department, Marquette University, P.O. Box 1881, Milwaukee, WI 53201, USA
Abstract This paper presents theoretical investigation of the propagation of surface acoustic waves (SAWs) across the boundary between metallized (electrically shorted) and unmetallized (electrically open) regions on the surface of potassium niobate crystals. Potassium niobate is a very strong piezoelectric material and has the interesting property that only one type of SAW, namely a Rayleigh wave, can exist on unmetallized surface, where as two types of SAWs, namely Rayleigh and Bleustein–Gulyaev (BG), can exist on a metallized surface. Analysis shows that the Rayleigh wave propagates through the interface with very little change in amplitude or polarization. On the other hand, almost total reflection of the BG wave is expected. Details of the theoretical analysis and calculated results will be presented. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Potassium niobate; Surface acoustic wave; Negative electro-mechanical coupling; Wave reflection
1. Introduction Potassium niobate has been receiving much attention recently due to its excellent optic, electrooptic, and acoustic properties [1]. The propagation of surface acoustic waves in this material has been investigated previously [2–4]. It has been shown that variations in electrical boundary conditions can result in some unexpected behavior, such as: (1) significant transformation of the wave structure, for example, from a ‘‘generalized Bleustein–Gulyaev (BG) wave’’ into a generalized Rayleigh wave, and (2) disappearance of some types of surface acoustic waves [4]. Based on these results, an interesting question to consider is what would happen when surface acoustic wave encounters the boundary between a metallized and an unmetallized region. The answer to this question is not obvious. One of two distinct situations may occur. (1) One possibility is that transmitted wave displays the same structure as incident wave. That is, the transition from one branch of
solution to another branch occurs. In this case the wave will show a negative value of K 2 , the electromechanical coupling coefficient. This is assuming the traditional definition of K 2 which is K 2 ¼ 2ðv vm Þ=v;
ð1Þ
where v and vm are the values of SAW velocity for electrically open and electrically shorted surface, respectively. (2) The other possibility is that transmitted wave follows the same branch of solution as incident wave. That is, the structure of wave significantly changes. In this case strong wave reflection is expected. Either of these results, besides their fundamental and methodological significance, can have important practical applications. This paper is devoted to theoretical investigation of the transmission and reflection of surface acoustic waves (SAWs) at an interface formed by a change in electrical boundary conditions at the surface of a strong piezoelectric material. 2. Theoretical calculations and results
*
Corresponding author. Tel.: +414-288-1584; fax: +414-288-5579. E-mail addresses: [email protected] (B.D. Zaitsev), shri.joshi@ marquette.edu (S.G. Joshi). 0041-624X/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2004.01.035
Before analysis of the transmission and reflection problem, we will briefly analyze the influence of electrical
374
B.D. Zaitsev et al. / Ultrasonics 42 (2004) 373–376 4000
2
1000
1
100
(a)
3600
u 2 /u 3
Velocity, m/s
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3400
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(a)
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-8
10
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-4
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10
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1 10
(b) 1.0
3500
2 0.1 10 -1 shorted
3000 -1
10 shorted
10
-3
10
σS, S
-5
10
-7
open
Fig. 1. Velocity in m/s versus normalized height of air gap d=k (a) and sheet conductance rS (b) for branches (1) and (2) of generalized surface acoustic waves propagating in Y –X þ 15° potassium niobate.
boundary conditions on types of SAW solutions. We shall consider two situations: (a) variation of distance d between an ideal conducting plane and surface of piezoelectric crystal, and (b) change in sheet conductance of a thin film deposited on the surface of the crystal. All calculations in this paper are carried out assuming that the piezoelectric material is Y cut potassium niobate with wave propagation at an angle of 15° with respect to the X -axis. This is a very strong piezoelectric material which exhibits the unusual properties mentioned in the previous section [4].
2.1. SAW characteristics in the structure ‘‘piezoelectric crystal––vacuum gap––ideal conducting plane’’ We consider the influence of an ideal conducting plane separated from the electrically open surface of a piezoelectric crystal on characteristics of generalized Rayleigh and BG waves. The height of the air gap between the crystal and conducting plane is denoted by d. Increase of d from 0 to k (k ¼ acoustic wavelength)
10 -5
10 -3
10 -7
σS,S
Fig. 2. Ratio of mechanical displacement components u2 =u3 versus normalized height of air gap d=k (a) and sheet conductance rS (b) for branches (1) and (2) of generalized surface acoustic waves propagating in Y –X þ 15° potassium niobate.
allows one to realize smooth transition from an electrically short to an electrically open surface. The method of analyzing this problem has been described in [5]. The material constants of potassium niobate are taken from [1]. Dependencies of phase velocity and ratio of mechanical displacement components u2 =u3 are presented in Figs. 1(a) and 2(a), respectively. Here axis x1 coincides with the SAW propagation direction, x3 is normal to the surface of the crystal, and x2 lies on the surface of the crystal normal to the wave propagation direction. Analysis shows that there are two branches of solution. The first branch (1) shows that with increase in distance d from 0 to k, a smooth transition of ‘‘generalized Bleustein–Gulyaev (BG) wave’’ into generalized Rayleigh wave occurs. In this case the ratio u2 =u3 changes from 10 to 0.7 (Fig. 2(a)). As for the second branch (2), it corresponds to the generalized leaky Rayleigh wave, the attenuation of which increases with increase of distance d. It is found that for d P 0:002k the wave ceases to propagate and the second solution disappears.
B.D. Zaitsev et al. / Ultrasonics 42 (2004) 373–376
2.2. SAW characteristics in piezoelectric crystal––thin conducting layer structure Here we analyze the influence of a thin conducting layer located on the surface of the potassium niobate crystal. The method of analysis has been described in [5]. Dependencies of the phase velocity and ratio of the mechanical displacement components u2 =u3 are presented in Figs. 1(b) and 2(b), respectively. One can see that in this case also there exist two branches of solution. In accordance with the first branch (1), the velocity of generalized BG wave increases with decreasing value of sheet conductance rS . This wave is leaky and its attenuation increases with decreasing rS . When rS decreases below 106 S, this wave ceases to be propagating and the first solution disappears. Fig. 1(a) shows that the maximum value of generalized BG wave velocity for the case discussed in Section 2.1 is 3851 m/s, whereas in the present case it is 4500 m/s. This difference can be explained by the anomalous resisto-acoustic effect [6]. The second branch of solution (2) corresponds to a generalized Rayleigh wave. Analysis shows that the velocity of this wave increases slightly with increasing sheet conductance. For large values of rS (corresponding to electrically shorted surface), velocity vm is found to be 3914 m/s, whereas for electrically open surface velocity v ¼ 3885 m/s. So we see that vm is actually greater than v. This means that electromechanical coupling coefficient K 2 defined from Eq. (1) becomes negative! As far as the structures of BG and Rayleigh waves are concerned, it is found that variation in sheet conductance does not result in significant change in the structure of the waves. This result is radically different from that observed in Section 2.1.
375
Shorted Open 5 3
(a) 1
2
Shorted Open 6
3
(b) 1
2
Shorted Open 6
4 2
(c)
3
2.3. Transmission of SAWs through the interface based on change in electrical boundary conditions Results obtained in previous parts of the paper allow us to resolve the question of what will occur when acoustic wave passes through an interface formed by a change in electrical boundary conditions on the surface of Y –X þ 15° potassium niobate crystal. Previous analysis has shown that for electrically open surface there is only one type of surface wave, namely generalized Rayleigh wave; whereas for electrically shorted surface, a generalized Rayleigh wave as well as a generalized Bleustein–Gulyaev wave can exist. So we will analyze reflection and transmission of waves for the three possible situations shown in Fig. 3. These are: (a) generalized Rayleigh wave encounters the interface ‘‘electrically open surface–electrically shorted surface’’; (b) generalized Rayleigh wave encounters the interface ‘‘electrically shorted surface–electrically open surface’’; (c) generalized Bleustein–Gulyaev wave encounters the interface ‘‘electrically shorted surface–electrically open surface’’.
Fig. 3. Transmission of generalized Rayleigh and Bleustein–Gulyaev surface acoustic waves through the interface based on discontinuity of electrical boundary conditions in Y –X þ 15° potassium niobate. As discussed in the text, three different cases are shown. Numbers 1 through 6 denote the different waves as follows. 1––incident generalized Rayleigh wave, 2––transmitted generalized Rayleigh wave, 3––reflected generalized Rayleigh wave, 4––incident generalized Bleustein–Gulyaev wave, 5––transmitted generalized Bleustein–Gulyaev wave, 6––reflected generalized Bleustein–Gulyaev wave.
It should be noted here that incident, reflected, and transmitted waves can have different polarizations. Therefore the correct determination of transmission and reflection coefficients was based on comparison of total energy flows associated with these waves. From our calculations we have found the following. Generalized Rayleigh wave transmits through both types of interfaces with practically no change in amplitude and polarization. Thus the transmission coefficient for the cases shown in Fig. 3(a) and (b) is very close to
376
B.D. Zaitsev et al. / Ultrasonics 42 (2004) 373–376
unity. It should be noted that for this material, Rayleigh wave velocity on electrically shorted surface is slightly higher than on electrically open surface. This means that the wave in this case provides negative value of K 2 , the electromechanical coupling coefficient. It should be noted that in recent years there have appeared several papers which report that for some specific situations electrical shorting of the surface may actually increase SAW velocity [7,8]. The existence of this phenomenon has also been experimentally demonstrated in [9]. It has been suggested that velocity increase may be occurring due to transformation of wave types or due to wave hybridization. As regards the case of incident BG wave considered in Fig. 3(c), total reflection of the wave corresponding to nearly unity reflection coefficient is predicted. This is a very unexpected result and more work is needed to determine if this conclusion is indeed true.
the interface ‘‘electrically shorted surface–electrically open surface’’ and vice versa with practically no change in wave amplitude or polarization. Thus the transmission coefficient is close to unity. The wave in this case has a slightly negative value of coupling coefficient K 2 . As for the generalized BG wave, preliminary calculations predict nearly unity reflection coefficient when the wave is incident from an electrically shorted surface on to an electrically open surface. More work is needed to determine the validity of this conclusion.
Acknowledgements This work was supported by a grant No. 01-0216266a from the Russian Foundation of Basic Research.
References 3. Summary Theoretical analysis of generalized SAWs propagating in Y –X þ 15° potassium niobate crystal shows that the method used to change boundary condition from electrically shorted surface to electrically open surface can influence the observed results. If the transition from shorted to open surface is performed by moving an ideal conducting plane away from the crystal surface, the transformation of generalized BG wave into generalized Rayleigh wave is possible. In this case the transition is accompanied by an increase in wave velocity. On the other hand if the transition is performed by decreasing sheet conductance of a conducting layer deposited on the crystal surface, there is no transformation of SAW types. But in this case the velocity of generalized Rayleigh wave for electrically shorted surface is found to be slightly higher than for electrically open surface. This means that electromechanical coupling coefficient defined in accordance with Eq. (1) is negative! In this case definition of electromechanical coupling coefficient should be based on energy considerations. Analysis of wave reflection and transmission problem shows that generalized Rayleigh wave transmits through
[1] M. Zgonik, R. Schlesser, I. Biaggio, J. Tscherry, P. Gunter, E. Voit, Material constants of KNbO3 relevant for electro and acoustooptics, J. Appl. Phys. 74 (1993) 1287–1297. [2] K. Yamanouchi, H. Odagawa, T. Kojima, T. Matsumura, Theoretical and experimental study of super high electromechanical coupling surface acoustic wave propagation in KNbO3 single crystal, Electron. Lett. 33 (1997) 193–194. [3] K. Nakamura, M. Oshiki, Theoretical analysis of horizontal shear mode piezoelectric surface acoustic waves in potassium niobate, Appl. Phys. Lett. 71 (1997) 3203–3205. [4] B.D. Zaitsev, I. Kuznetsova, S.G. Joshi, Influence of electrical boundary conditions on structure of surface acoustic waves in potassium niobate, Electron. Lett. 35 (1999) 1205–1206. [5] B.D. Zaitsev, S.G. Joshi, I.E. Kuznetsova, Propagation of QSH (quasi shear horizontal) acoustic waves in piezoelectric plates, IEEE Trans. UFFC 46 (1999) 1298–1302. [6] B.D. Zaitsev, I.E. Kuznetsova, S.G. Joshi, Anomalous resistoacoustic effect, J. Appl. Phys. 86 (1999) 6868–6874. [7] V.G. Mozhaev, M. Weihnacht, Incredible negative values of effective electromechanical coupling coefficient for surface acoustic waves in piezoelectrics, Ultrasonics 37 (2000) 687–691. [8] V.G. Mozhaev, M. Weihnacht, Extraordinary case of acoustic wave acceleration due to electrical shorting of piezoelecrics, 1999 IEEE Ultrason. Symp. (1999) 73–76. [9] Sh. Kakio, H. Nakamura, Y. Kanmori, Y. Nakagava, Reversal phenomenon in phase velocity of surface acoustic waves on free and metallized surfaces by proton-exchange, Jpn. J. Appl. Phys. 38 (1999) 3261–3264.