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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 6 — Mar. 12, 2012
  • pp: 6429–6438
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Finite element modeling of bulk ultrasonic waves generated by ring-shaped laser illumination in a diamond anvil cell

Wen Feng, Dexing Yang, Yuning Guo, and Ying Chang  »View Author Affiliations


Optics Express, Vol. 20, Issue 6, pp. 6429-6438 (2012)
http://dx.doi.org/10.1364/OE.20.006429


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Abstract

Thermoelastic finite element models are established to study the bulk ultrasonic waves of an aluminum film generated by ring-shaped laser illumination in a diamond anvil cell. By analyzing the amplitudes of bulk ultrasonic waves arrived at the rear surface of film in detail, it shows that there exists strong enhancement effects on the central axis of the ring due to the constructive interference among the waves created by different parts of the ring source. The displacement distributions along the central axis indicate that the focal depth of shear wave is mainly determined by its directivity induced by a point-like laser source in a DAC system while it is more complicated to determine the focal depth of longitudinal wave. In particular, through changing the ring radius, we quantitatively demonstrate that the signal amplitudes generated by a ring source are far greater than those generated by a point-like source.

© 2012 OSA

1. Introduction

Laser ultrasonic has shown significant advantages in nondestructive evaluation field (NDE) [1

1. T. Tanaka and Y. Izawa, “Nondestructive detection of small internal defects in carbon steel by laser ultrasonics,” Jpn. J. Appl. Phys. 40(Part 1, No. 3A), 1477–1481 (2001). [CrossRef]

4

4. S. Dixon, S. E. Burrows, B. Dutton, and Y. Fan, “Detection of cracks in metal sheets using pulsed laser generated ultrasound and EMAT detection,” Ultrasonics 51(1), 7–16 (2011). [CrossRef] [PubMed]

] as its characteristics of non-contact, wideband and simultaneously generating longitudinal, shear and surface waves on a range of materials. In recent years, the precision measurement of sound velocity, which can be applied to evaluate the elastic properties of materials, is an important issue in high pressure physics. Measuring sound velocity under high pressure by combining the diamond anvil cell (DAC) device with the technique of picosecond laser ultrasonic was proposed until 2008 by F. Decremps et al. [5

5. F. Decremps, L. Belliard, B. Perrin, and M. Gauthier, “Sound velocity and absorption measurements under high pressure using picosecond ultrasonics in a diamond anvil cell: application to the stability study of AlPdMn,” Phys. Rev. Lett. 100(3), 035502 (2008). [CrossRef] [PubMed]

]. In the same year, N. Chigarev et al. [6

6. N. Chigarev, P. Zinin, L. C. Ming, G. Amulele, A. Bulou, and V. Gusev, “Laser generation and detection of longitudianal and shear acoustic waves in a diamond anvil cell,” Appl. Phys. Lett. 93(18), 181905 (2008). [CrossRef]

] developed laser ultrasonic in a diamond anvil cell (LU-DAC), they demonstrated that using this LU-DAC point-source-point-receiver technique made it possible to measure both longitudinal and shear velocities of a non-transparent iron film at pressures up to 23GPa. Later, the ultrasonic waves under high pressure were further analyzed by using LU-DAC technique in a point-source-point-receiver [7

7. P. Zinin, N. Chigarev, D. Mounier, A. Bulou, L. C. Ming, T. Acosta, and V. Gusev, “Evaluation of elastic properties of iron in diamond anvil cell by laser ultrasonics technique,” J. Phys. Conf. Ser. 215, 012053 (2010). [CrossRef]

] or line-source-point-receiver [8

8. N. Chigarev, P. Zinin, D. Mounier, A. Bulou, L. C. Ming, T. Acosta, and V. Gusev, “Analysis of ultrasonic echoes induced by pulsed laser action on an iron film in a diamond anvil cell,” High Press. Res. 30(1), 78–82 (2010). [CrossRef]

,9

9. N. Chigarev, P. Zinin, D. Mounier, A. Bulou, A. Zerr, L. C. Ming, and V. Gusev, “Laser ultrasonic measurements in a diamond anvil cell on Fe and the KBr pressure medium,” J. Phys. Conf. Ser. 278, 012017 (2011). [CrossRef]

] configurations. The main advantage of the LU-DAC technique over the technique proposed in Ref. 5

5. F. Decremps, L. Belliard, B. Perrin, and M. Gauthier, “Sound velocity and absorption measurements under high pressure using picosecond ultrasonics in a diamond anvil cell: application to the stability study of AlPdMn,” Phys. Rev. Lett. 100(3), 035502 (2008). [CrossRef] [PubMed]

for non-transparent amorphous solids is that there is no need of measuring the thickness of the specimen independently of sound velocity [7

7. P. Zinin, N. Chigarev, D. Mounier, A. Bulou, L. C. Ming, T. Acosta, and V. Gusev, “Evaluation of elastic properties of iron in diamond anvil cell by laser ultrasonics technique,” J. Phys. Conf. Ser. 215, 012053 (2010). [CrossRef]

]. In addition, it provides an opportunity to study specimen with certain thickness which is more than tens of micrometers, while picosecond ultrasonic technique requires the thickness of specimen to be thinner than a few micrometers due to the strong sound attenuation in the 10GHz-plus frequency range [8

8. N. Chigarev, P. Zinin, D. Mounier, A. Bulou, L. C. Ming, T. Acosta, and V. Gusev, “Analysis of ultrasonic echoes induced by pulsed laser action on an iron film in a diamond anvil cell,” High Press. Res. 30(1), 78–82 (2010). [CrossRef]

]. However, low intrinsic ultrasonic amplitude generated by a point-like laser source makes it difficult for the precision measurement of ultrasonic waves. Moreover, in those LU-DAC experiments, the probe point and excited source are arranged at the same side of sample. As a consequence, the wave system at the probe point becomes very complex due to the ultrasonic reflection at the aluminum/diamond interface and the wave amplitudes become lower due to the increase of soundpath. It also brings some difficulties when analyzing the signals. Furthermore, the obvious signals of longitudinal and shear waves cannot be detected simultaneously at the same point owing to their remarkable directivity [10

10. W. Feng, D. X. Yang, X. C. Zhu, Y. N. Guo, and W. Liao, “Simulation of laser-generated longitudinal and shear ultrasonic waves in a diamond anvil cell by the finite element method,” J. Appl. Phys. 111(1), 013107 (2012). [CrossRef]

]. In this article, we propose a LU-DAC ring-source-point-receiver technique to overcome the above drawbacks by taking advantage of constructive interference among waves generated by different parts of ring-shaped laser. The ring-shaped laser source can be treated as numerous point-like sources arranged as a circle, where each point-like source can excite the ultrasonic waves at the same time in one irradiation. In the free surface condition, some reports [11

11. X. Wang, M. G. Littman, J. B. McManus, M. Tadi, Y. S. Kim, A. Askar, and H. Rabitz, “Focused bulk ultrasonic waves generated by ring-shaped laser illumination and application to flaw detection,” J. Appl. Phys. 80(8), 4274–4281 (1996). [CrossRef]

,12

12. J. F. Guan, Z. H. Shen, X. W. Ni, J. Lu, J. J. Wang, and B. Q. Xu, “Numerical simulation of the ultrasonic waves genersted by ring-shaped laser illumination patterns,” Opt. Laser Technol. 39(6), 1281–1287 (2007). [CrossRef]

] have demonstrated that an annular illumination pattern, which can be easily formed by an axicon [13

13. P. Cielo, F. Nadeau, and M. Lamontagne, “Laser generation of convergent acoustic waves for materials inspection,” Ultrasonics 23(2), 55–62 (1985). [CrossRef]

], can generate the strong ultrasonic signals along the central axis of the ring. Thus, not only the wave amplitudes can be highly enhanced even if not in the case of ablation but also strong signals of both the longitudinal and shear waves can be detected simultaneously at the same point by using LU-DAC ring-source-point-receiver technique. The sound velocities can also be measured without considering about the thickness of the specimen by modulating the ring radius of laser. However, both sides of the micron film are covered with the rigid diamond whose thickness is much greater than the film in a LU-DAC system. As a result, the excited source, waveforms and propagation laws of ultrasonic waves are different from that generated in the case of free surface. In this paper, our work is to develop numerical models to describe the generation and propagation of bulk ultrasonic waves generated by ring-shaped laser in a DAC system.

As a result of the complexity of the generation and propagation of ultrasonic waves in a film in a DAC, the finite element method (FEM), owing to its flexibility in modeling complicated geometry and its capability in obtaining full field numerical solutions [14

14. B. Q. Xu, Z. H. Shen, X. W. Ni, and J. Lu, “Numerical simulation of laser-generated ultrasound by the finite element method,” J. Appl. Phys. 95(4), 2116–2122 (2004). [CrossRef]

], is adopted to deal with such complicated process in our model. In this article, the characteristics of ultrasonic displacement field generated by ring-shaped laser illumination have been simulated by the FEM based on the thermoelastic theory. The superposition effects of both the longitudinal and shear waves on the rear surface of aluminum film are analyzed in detail. By studying the displacement distributions along the central axis of the ring, the focal laws of waves are discussed. In addition, the full field numerical solutions at different times are presented, which makes it more intuitive to understand the evolution characteristics of ultrasonic waves within the specimen.

2. Thermoelastic theory model

The geometry model of ring-shaped laser irradiation on a DAC system which consists of two diamonds and an aluminum film is schematically shown in Fig. 1(a)
Fig. 1 (a) Schematic diagram of the system irradiated by ring-shaped laser. (b) Cross-section of the system.
. The contact between the diamond and the aluminum film is supposed to be perfect. A ring-shaped laser whose energy is below the sample damage threshold is directed on the top interface vertically because of the transparent diamond. The ring, which has two parameters: inner radius and thickness denoted by R and d, represents the laser illumination region. A cylindrical coordinate system is introduced in our model because the geometry of the problem has axial symmetry. Thus, the problem can be considered in the two-dimensional axial symmetric plane, which is shown in Fig. 1(b).

The distribution of transient temperature field is determined by thermal conduction equation, which can be described as [12

12. J. F. Guan, Z. H. Shen, X. W. Ni, J. Lu, J. J. Wang, and B. Q. Xu, “Numerical simulation of the ultrasonic waves genersted by ring-shaped laser illumination patterns,” Opt. Laser Technol. 39(6), 1281–1287 (2007). [CrossRef]

, 15

15. J. J. Wang, B. Q. Xu, Z. H. Shen, X. W. Ni, and J. Lu, “Influence of transparent coating thickness on thermoelastic force source and laser-generated ultrasound waves,” Appl. Surf. Sci. 255(16), 7172–7178 (2009). [CrossRef]

]
ρiciTi(r,z,t)t1rr(rkiTi(r,z,t)r)z(kiTi(r,z,t)z)=Q(r,z,t)
(1)
where subscript i = 1 denotes the film while i = 2, 3 denote the diamond below and above the film respectively. Ti(r, z, t) is the temperature distribution; ρi, ci and ki are the density, thermal capacity and thermal conductive coefficient respectively; Q(r, z, t) is the heat source provided by ring-shaped laser, which can be expressed as
Q(r,z,t)=AI0βexp(βz)f(r)g(t)
(2)
where A is the optical absorptivity of the specimen surface, I0 is the peak intensity of the incident laser, β is the optical absorption coefficient, f(r) and g(t) are the spatial and temporal distributions of the pulsed laser, these two functions are
f(r)=exp[(r(R+d/2))2(d/2)2]
(3)
g(t)=exp[(tt0)2τ2]
(4)
where t0 and τ are the arrival time of peak value and half pulse width of the pulsed laser.

Through introducing the scalar potential function φi and vector potential function ψieθ, we can express Ui (r, z, t) as the functions of these two parameters [16

16. F. A. McDonald, “Practical quantitative theory of photoacoustic pulse generation,” Appl. Phys. Lett. 54(16), 1504–1506 (1989). [CrossRef]

]

Ui(r,z,t)=ϕi+×(ψieθ)
(6)

Then the following longitudinal and shear wave equations are obtained from Eq. (5).

2ϕir2+1rϕir+2ϕiz21CLi22ϕit2=γiTi2ψir2+1rψir+2ψiz2ψir21CSi22ψit2=0
(7)

Here, CLi and CSi are the longitudinal and shear wave velocities respectively, γi = αi(3λi + 2μi)/ (λi + 2μi).The decomposition of the displacement component normal to the interface can be written as

Uzi=ϕiz+ψir+ψir
(8)

In order to solve the displacement field, it is necessary to determine the boundary and initial conditions in the model. As the contact between two materials is perfect, the temperature, heat flux, stress and displacement component are continual at interfaces. The boundary conditions at interfaces between materials are

T1=Ti,k1T1z=kiTizσzz1=σzzi,σzr1=σzri    (i=2,3)Uz1=Uzi,Ur1=Uri
(9)

As the thickness of the diamond is much greater than that of the aluminum film, we can suppose that the front and back surfaces of the DAC system are thermally insulated and mechanically unconstrained.

Assuming the system has no initial heat source, stress and mechanical displacement, the initial conditions can be written as

Ti|t=0=300KUi|t=0=0,Uit|t=0=0       (i=1,2,3)
(10)

3. Numerical results and discussion

3.1 Lasers and materials parameters

The peak power intensity of laser is 3 × 109 W/cm2, and it reaches the top interface at 1ns. The pulse width and thickness of the ring-shaped laser are taken to be 0.5ns and 2μm. The inner radius of the laser ranges from 5μm to 60μm. The radius and thickness of the aluminum are 100μm and 30μm, respectively. In a LU-DAC experiment, the thickness of diamond window is usually within a millimeter magnitude. In order to not affect the accuracy of numerical results and calculate conveniently, the radius and the thickness of diamond windows are taken to be 100μm. The element size of grid is 0.1μm in the vicinity of the laser affected area, while the element size is 0.4μm outside the heat-affected zone. The properties of materials used in the calculation are listed in Table 1

Table 1. Properties of aluminum and diamond used in calculation

table-icon
View This Table
, some parameters of aluminum film are from Refs. 14

14. B. Q. Xu, Z. H. Shen, X. W. Ni, and J. Lu, “Numerical simulation of laser-generated ultrasound by the finite element method,” J. Appl. Phys. 95(4), 2116–2122 (2004). [CrossRef]

and 17

17. C. W. Sun, Effects of Laser Irradiation (National Defense Industry Press, Beijing, 2002), Chap. 1. (in Chinese)

.

3.2 Numerical results and discussion

Figures 2(a)
Fig. 2 Vertical displacement of the bulk wave at different positions on the rear surface of specimen: (a) the epicenter; (b) 4μm; (c) 8μm and (d) 12μm from epicenter.
-2(d) show the vertical displacement waveforms detected at the epicenter and the other positions of 4-μm-off, 8-μm-off, and 12-μm-off the epicenter on the rear surface of aluminum film respectively for a 30μm radius ring. In Fig. 2(a), a sharp rise at 7.91 ns represents the arrival of the longitudinal (L) wave, and an obvious peak at 14.3ns which represents the advent of the shear (S) wave comes next. The corresponding velocities of longitudinal and shear waves are 6243m/s and 3244m/s, respectively, which are very close to the theoretical value. Because the waves created by different portions of the ring source have no longer arrived at the receiver deviated from epicenter at the same time, the sharp longitudinal and shear peaks each splits into two separated peaks with much smaller amplitudes in Figs. 2(b)-2(d). Therefore, we can see that both the longitudinal and shear wave amplitudes fall off sharply and the waveforms are broadened as the probe point away from the epicenter. The longitudinal and shear wave amplitudes, as a function of radial distance from the epicenter, are shown in Figs. 3(a)
Fig. 3 Amplitudes of (a) longitudinal wave and (b) shear wave at different positions along the radial direction on the rear surface of specimen.
and 3(b) for three varied ring radii. The amplitude is the first peak value of each waveform. It can be seen that the sharp focusing at the epicenter is evident, and wave amplitudes drop rapidly as the radial distance from the epicenter increases in these three cases. These phenomena discussed above indicate that the ring-shaped laser can simultaneously generate the amplified displacement signals of the bulk ultrasonic waves on the central axis of the ring-shaped laser.

To further confirm the superposition effects of waves on the rear surface of sample, we have studied the frequency spectrums and superposition patterns by fast Fourier transform (FFT). Figures 4(a)
Fig. 4 The spectrums of (a) longitudinal wave and (b) shear wave received at different points on the rear surface of specimen.
and 4(b) show the spectrums of the longitudinal and shear waves detected at three different points on the rear surface of aluminum film, respectively. It can be seen that the frequency components are consistent in all cases, and the amplitudes of each frequency is larger at the epicenter than those at the other point. However, the spectral distributions are various for different probe points. The superposition patterns of the longitudinal and shear waves at 1.56GHz along the radial direction on the rear surface of aluminum film are presented in Figs. 5(a)
Fig. 5 The interference patterns of (a) longitudinal wave (b) shear wave along the radial direction on the rear surface of specimen.
and 5(b). It is obvious that the maxima and minima amplitudes of each wave appear alternately along the radial direction. The largest amplitudes appear at the epicenter as the result of constructive interference of multi-source with same intensity and phase. Meanwhile, the amplitudes at points deviated from epicenter are different as the superposition is created by multi-source with different intensity and phase.

In order to study the focal characteristics of bulk ultrasonic waves, we have calculated the displacement distributions of the longitudinal and shear waves along the central axis of the ring source, which are shown in Figs. 6(a)
Fig. 6 Amplitudes of (a) longitudinal wave and (b) shear wave at different points along the central axis of ring source.
and 6(b). As the depth increases, we can see that the amplitudes of two waves increase and reach the maximum value at a focal depth, then decreased gradually. Meanwhile, the focal depths of each wave are various for different ring radii. The results in the figures suggest that the focal depths of two waves have the positive relationship with the radius of the ring, which means the bigger ring radius are able to produce the greater focal depth. Particularly in Fig. 6(b), the focal depths of the shear wave are 10μm, 15μm and 19μm, which correspond to the ring source with the radii of 10μm, 15μm and 20μm respectively. Thus the angle α ≈45° that denoted in the Fig. 1(b) can be calculated, which is very close to the directional angle of the shear wave induced by a point-like laser source in an aluminum film in a DAC [10

10. W. Feng, D. X. Yang, X. C. Zhu, Y. N. Guo, and W. Liao, “Simulation of laser-generated longitudinal and shear ultrasonic waves in a diamond anvil cell by the finite element method,” J. Appl. Phys. 111(1), 013107 (2012). [CrossRef]

]. For the longitudinal wave in Fig. 6(a), it is very hard to find a similar law because the majority of energy is concentrated near the point-like laser incident direction. However, we can find that the focal depth is larger than the corresponding ring radius. Therefore, the phenomena above suggest that the desired focal depths of two waves can be achieved by modulating the radius of the ring-shaped laser.

As described in the introduction, the FEM has significant advantage in obtaining full field numerical solutions, which are more helpful for us to understand the evolution characteristics of ultrasonic waves within the sample. The displacement magnitude distributions generated by ring-shaped laser irradiation at different times are denoted by grayscale in Figs. 8(a)
Fig. 8 Ultrasonic displacement fields at different times: (a) 3ns; (b) 6ns; (c) 8ns; (d) 11ns.
-8(d) for a 20μm radius ring. We can clearly observe the excited source in the aluminum film and the wavefronts of both the longitudinal and shear waves propagate away from the heated area. In Fig. 8(a), the displacement field is similar to that generated by a point-like source [10

10. W. Feng, D. X. Yang, X. C. Zhu, Y. N. Guo, and W. Liao, “Simulation of laser-generated longitudinal and shear ultrasonic waves in a diamond anvil cell by the finite element method,” J. Appl. Phys. 111(1), 013107 (2012). [CrossRef]

] and the superposition effects of waves are not obvious. However, it can be seen that the wavefronts are asymmetrical from Figs. 8(b)-8(d), the wave amplitudes in the area inside the ring radius are larger than that in the area outside the ring radius, which suggests that the enhancement effects of ultrasonic waves appear in the area inside the ring radius. From these figures, we can also see that the enhanced superposition effect is more apparent in the position closer to the axis, and particularly in Fig. 8(d), the shear wave displacement in the position Ι is far larger than that in the position ΙΙ. Consequently, these pictures further intuitively show the evolution characteristics of waves and the enhanced superposition effects of waves in the area near the central axis.

Finally, in order to further demonstrate the enhancement effects of ultrasonic waves induced by the ring source, the wave amplitudes generated by a point-like source are analyzed for comparison. The peak power intensity and radius of the Gaussian laser pulse are taken to be 3 × 109 W/cm2 and 2μm, which are the same with the peak power and thickness of the ring-shaped laser. As a function of radial distance from the epicenter, the bulk ultrasonic wave amplitudes are displayed in Fig. 9
Fig. 9 Amplitudes of (a) longitudinal wave and (b) shear wave as a function of radial distance from the epicenter for a Gaussian laser point-like source.
. By comparing Figs. 9(a) and 9(b) with Figs. 3(a) and 3(b), it shows that the amplitude distributions on the rear surface by the point-like source are different from those by the ring source. With the increasing of radial distance, the longitudinal wave amplitude gradually reduce, while the shear wave amplitude reach the maximum and then gradually decrease. That comparing Figs. 9(a) and 9(b) with Figs. 7(a) and 7(b) makes it clear that the maximums of wave amplitudes induced by the ring source are far greater than those induced by the point-like source. The amplitudes of longitudinal and shear waves generated by the ring source are almost 30 times and 40 times greater than those induced by the point-like source. This comparison further powerfully demonstrates that the ring-shaped laser has significant advantage in generating the strong signals of ultrasonic waves in a LU-DAC system.

4. Conclusions

In the study of high-pressure physics based on a LU-DAC technique, low intrinsic ultrasonic amplitudes make it difficult to detect the generated waves for the precision measurement of sound velocities. Therefore, it is very meaningful to generate the strong signals of both the longitudinal and shear waves by some feasible approaches. In this paper, based on the thermoelastic theory, finite element method is used to establish the model of bulk ultrasonic waves generated by ring-shaped laser in a DAC system. By analyzing the amplitude distributions in an aluminum film in detail, we have demonstrated that the strong enhancement effects of ultrasonic waves appear on the central axis of ring source owing to the constructive interference of the waves generated by different parts of the ring. The discussions of the displacement distributions along the central axis reveal that the directivity of shear wave plays a crucial role in determining its focal depth, whereas it is more complicated to determine the focal depth of longitudinal wave. By changing the ring radius, the strongest signals at the epicenter can be obtained for a given sample. The further comparative study indicates that the maximums of wave amplitudes induced by a ring source are far greater than those induced by a point-like source.

Acknowledgments

We acknowledge the project support from the China Academy of Engineering Physics. We also thank the technical support by the Center for High Performance Computing of Northwestern Polytechnical University.

References and links

1.

T. Tanaka and Y. Izawa, “Nondestructive detection of small internal defects in carbon steel by laser ultrasonics,” Jpn. J. Appl. Phys. 40(Part 1, No. 3A), 1477–1481 (2001). [CrossRef]

2.

V. V. Kozhushko and P. Hess, “Laser-induced focused ultrasound for nondestructive testing and evaluation,” J. Appl. Phys. 103(12), 124902 (2008). [CrossRef]

3.

H. C. Wang, S. Fleming, Y. C. Lee, S. Law, M. Swain, and J. Xue, “Laser ultrasonic surface wave dispersion technique for non-destructive evaluation of human dental enamel,” Opt. Express 17(18), 15592–15607 (2009). [CrossRef] [PubMed]

4.

S. Dixon, S. E. Burrows, B. Dutton, and Y. Fan, “Detection of cracks in metal sheets using pulsed laser generated ultrasound and EMAT detection,” Ultrasonics 51(1), 7–16 (2011). [CrossRef] [PubMed]

5.

F. Decremps, L. Belliard, B. Perrin, and M. Gauthier, “Sound velocity and absorption measurements under high pressure using picosecond ultrasonics in a diamond anvil cell: application to the stability study of AlPdMn,” Phys. Rev. Lett. 100(3), 035502 (2008). [CrossRef] [PubMed]

6.

N. Chigarev, P. Zinin, L. C. Ming, G. Amulele, A. Bulou, and V. Gusev, “Laser generation and detection of longitudianal and shear acoustic waves in a diamond anvil cell,” Appl. Phys. Lett. 93(18), 181905 (2008). [CrossRef]

7.

P. Zinin, N. Chigarev, D. Mounier, A. Bulou, L. C. Ming, T. Acosta, and V. Gusev, “Evaluation of elastic properties of iron in diamond anvil cell by laser ultrasonics technique,” J. Phys. Conf. Ser. 215, 012053 (2010). [CrossRef]

8.

N. Chigarev, P. Zinin, D. Mounier, A. Bulou, L. C. Ming, T. Acosta, and V. Gusev, “Analysis of ultrasonic echoes induced by pulsed laser action on an iron film in a diamond anvil cell,” High Press. Res. 30(1), 78–82 (2010). [CrossRef]

9.

N. Chigarev, P. Zinin, D. Mounier, A. Bulou, A. Zerr, L. C. Ming, and V. Gusev, “Laser ultrasonic measurements in a diamond anvil cell on Fe and the KBr pressure medium,” J. Phys. Conf. Ser. 278, 012017 (2011). [CrossRef]

10.

W. Feng, D. X. Yang, X. C. Zhu, Y. N. Guo, and W. Liao, “Simulation of laser-generated longitudinal and shear ultrasonic waves in a diamond anvil cell by the finite element method,” J. Appl. Phys. 111(1), 013107 (2012). [CrossRef]

11.

X. Wang, M. G. Littman, J. B. McManus, M. Tadi, Y. S. Kim, A. Askar, and H. Rabitz, “Focused bulk ultrasonic waves generated by ring-shaped laser illumination and application to flaw detection,” J. Appl. Phys. 80(8), 4274–4281 (1996). [CrossRef]

12.

J. F. Guan, Z. H. Shen, X. W. Ni, J. Lu, J. J. Wang, and B. Q. Xu, “Numerical simulation of the ultrasonic waves genersted by ring-shaped laser illumination patterns,” Opt. Laser Technol. 39(6), 1281–1287 (2007). [CrossRef]

13.

P. Cielo, F. Nadeau, and M. Lamontagne, “Laser generation of convergent acoustic waves for materials inspection,” Ultrasonics 23(2), 55–62 (1985). [CrossRef]

14.

B. Q. Xu, Z. H. Shen, X. W. Ni, and J. Lu, “Numerical simulation of laser-generated ultrasound by the finite element method,” J. Appl. Phys. 95(4), 2116–2122 (2004). [CrossRef]

15.

J. J. Wang, B. Q. Xu, Z. H. Shen, X. W. Ni, and J. Lu, “Influence of transparent coating thickness on thermoelastic force source and laser-generated ultrasound waves,” Appl. Surf. Sci. 255(16), 7172–7178 (2009). [CrossRef]

16.

F. A. McDonald, “Practical quantitative theory of photoacoustic pulse generation,” Appl. Phys. Lett. 54(16), 1504–1506 (1989). [CrossRef]

17.

C. W. Sun, Effects of Laser Irradiation (National Defense Industry Press, Beijing, 2002), Chap. 1. (in Chinese)

OCIS Codes
(140.3390) Lasers and laser optics : Laser materials processing
(140.3560) Lasers and laser optics : Lasers, ring
(350.5340) Other areas of optics : Photothermal effects
(280.3375) Remote sensing and sensors : Laser induced ultrasonics

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: January 11, 2012
Manuscript Accepted: February 19, 2012
Published: March 5, 2012

Citation
Wen Feng, Dexing Yang, Yuning Guo, and Ying Chang, "Finite element modeling of bulk ultrasonic waves generated by ring-shaped laser illumination in a diamond anvil cell," Opt. Express 20, 6429-6438 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-6-6429


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References

  1. T. Tanaka and Y. Izawa, “Nondestructive detection of small internal defects in carbon steel by laser ultrasonics,” Jpn. J. Appl. Phys.40(Part 1, No. 3A), 1477–1481 (2001). [CrossRef]
  2. V. V. Kozhushko and P. Hess, “Laser-induced focused ultrasound for nondestructive testing and evaluation,” J. Appl. Phys.103(12), 124902 (2008). [CrossRef]
  3. H. C. Wang, S. Fleming, Y. C. Lee, S. Law, M. Swain, and J. Xue, “Laser ultrasonic surface wave dispersion technique for non-destructive evaluation of human dental enamel,” Opt. Express17(18), 15592–15607 (2009). [CrossRef] [PubMed]
  4. S. Dixon, S. E. Burrows, B. Dutton, and Y. Fan, “Detection of cracks in metal sheets using pulsed laser generated ultrasound and EMAT detection,” Ultrasonics51(1), 7–16 (2011). [CrossRef] [PubMed]
  5. F. Decremps, L. Belliard, B. Perrin, and M. Gauthier, “Sound velocity and absorption measurements under high pressure using picosecond ultrasonics in a diamond anvil cell: application to the stability study of AlPdMn,” Phys. Rev. Lett.100(3), 035502 (2008). [CrossRef] [PubMed]
  6. N. Chigarev, P. Zinin, L. C. Ming, G. Amulele, A. Bulou, and V. Gusev, “Laser generation and detection of longitudianal and shear acoustic waves in a diamond anvil cell,” Appl. Phys. Lett.93(18), 181905 (2008). [CrossRef]
  7. P. Zinin, N. Chigarev, D. Mounier, A. Bulou, L. C. Ming, T. Acosta, and V. Gusev, “Evaluation of elastic properties of iron in diamond anvil cell by laser ultrasonics technique,” J. Phys. Conf. Ser.215, 012053 (2010). [CrossRef]
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