Abstract

We investigate the x-ray diffraction effects from surface acoustic waves (SAW) traveling along a multilayer. The diffraction intensity distribution depends on the incidence angle and the multilayer SAW (MLSAW) amplitude. Particularly, a small departure deviating from the Bragg incidence angle at a certain amplitude will produce a larger variation of the intensity distribution. This shows that the diffraction intensity from MLSAW has an extremely high sensitivity to the Bragg incidence angle, which is different from a SAW traveling along a solid surface without deposited layers. By carefully analyzing the relationship between the intensity distribution I and the incidence angle θ, the corresponding analytic expression of the intensity distribution is theoretically derived. Our theoretical prediction is in great agreement with the experimental results previously obtained. A theoretical model that can be applied to study the x-ray diffraction effect from MLSAW is developed. The extremely high sensitivity to the Bragg angle will help us in acousto-optic instrument research with MLSAW.

© 2010 Optical Society of America

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    [CrossRef]
  4. M. E. Siemens, Q. Li, M. M. Murnane, H. C. Kapteyn, R. Yang, E. H. Anderson, and K. A. Nelson, “High-frequency surface acoustic wave propagation in nanostructures characterized by coherent extreme ultraviolet beams,” Appl. Phys. Lett. 94, 093103 (2009).
    [CrossRef]
  5. K. A. Ingebrigtsen and A. Tonning, “Elastic surface waves in crystals,” Phys. Rev. 184, 942-951 (1969).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. T. Nakao, M. Kadota, K. Nishiyama, Y. Nakai, D. Yamamoto, Y. Ishiura, T. Komura, N. Takada, and R. Kita, “Smaller surface acoustic wave duplexer for US personal communication service having good temperature characteristics,” Jpn. J. Appl. Phys. 46, 4760-4763 (2007).
    [CrossRef]
  9. C. Caliendo, “Theoretical and experimental investigation of gigahertz-band, temperature-compensated electromechanical coupling configurations based on AlN films,” Appl. Phys. Lett. 92, 033505 (2008).
    [CrossRef]
  10. S. Wu, R. Ro, Z. X. Lin, and M. S. Lee, “Rayleigh surface acoustic wave modes of interdigital transducer/(100) AlN/(111) diamond,” J. Appl. Phys. 104, 064919 (2008).
    [CrossRef]
  11. C. C. Sung, Y. F. Chiang, R. Ro, R. Lee, and S. Wu “Effects of conducting layers on surface acoustic wave in AlN films on diamond,” J. Appl. Phys. 106, 124905 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. A. V. Andreev, Yu. V. Ponomarev, L. R. Prudnikov, and N. N. Salashchenko, “X-ray diffuse scattering by multilayer waveguide structures,” Phys. Rev. B 57, 13113-13117 (1998).
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    [CrossRef]

2009 (3)

M. E. Siemens, Q. Li, M. M. Murnane, H. C. Kapteyn, R. Yang, E. H. Anderson, and K. A. Nelson, “High-frequency surface acoustic wave propagation in nanostructures characterized by coherent extreme ultraviolet beams,” Appl. Phys. Lett. 94, 093103 (2009).
[CrossRef]

C. C. Sung, Y. F. Chiang, R. Ro, R. Lee, and S. Wu “Effects of conducting layers on surface acoustic wave in AlN films on diamond,” J. Appl. Phys. 106, 124905 (2009).
[CrossRef]

E. Descrovi, “Resonant diffraction of symmetric and antisymmetric Bloch surface waves on a corrugated periodic multilayer slab,” Opt. Lett. 34, 1973-1975 (2009).
[CrossRef]

2008 (3)

S. H. Yang, B. C. Sell, and C. S. Fadley, “Probing multilayer spintronic structures with photoelectron and x-ray emission spectroscopies excited by x-ray standing waves,” J. Appl. Phys. 103, 07C519 (2008).
[CrossRef]

C. Caliendo, “Theoretical and experimental investigation of gigahertz-band, temperature-compensated electromechanical coupling configurations based on AlN films,” Appl. Phys. Lett. 92, 033505 (2008).
[CrossRef]

S. Wu, R. Ro, Z. X. Lin, and M. S. Lee, “Rayleigh surface acoustic wave modes of interdigital transducer/(100) AlN/(111) diamond,” J. Appl. Phys. 104, 064919 (2008).
[CrossRef]

2007 (1)

T. Nakao, M. Kadota, K. Nishiyama, Y. Nakai, D. Yamamoto, Y. Ishiura, T. Komura, N. Takada, and R. Kita, “Smaller surface acoustic wave duplexer for US personal communication service having good temperature characteristics,” Jpn. J. Appl. Phys. 46, 4760-4763 (2007).
[CrossRef]

2006 (1)

R. I. Tobey, M. E. Siemens, M. M. Murnane, H. C. Kapteyn, D. H. Torchinsky, and K. A. Nelson, “Transient grating measurement of surface acoustic waves in thin metal films with extreme ultraviolet radiation,” Appl. Phys. Lett. 89, 091108(2006).
[CrossRef]

2004 (1)

2003 (2)

2002 (1)

R. Miao, Z. Yang, J. Zhu, and C. Shen, “Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction,” Appl. Phys. Lett. 80, 3033-3035 (2002).
[CrossRef]

2000 (1)

1999 (2)

D. V. Roshchupkin, R. Tucoulou, and M. Brunel, Appl. Phys. Lett. 75, 639 (1999).
[CrossRef]

W. Sauer, M. Streibl, T. H. Metzger, and A. G. C. Haubrich, “X-ray imaging and diffraction from surface phonons on GaAs,” Appl. Phys. Lett. 75, 1709-1711 (1999).
[CrossRef]

1998 (2)

D. V. Roshchupkin, R. Tucoulou, A. Masclet, M. Brunel, I. A. Schelokov, and A. S. Kondakov, “X-ray diffraction by standing surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 142, 432-436 (1998).
[CrossRef]

A. V. Andreev, Yu. V. Ponomarev, L. R. Prudnikov, and N. N. Salashchenko, “X-ray diffuse scattering by multilayer waveguide structures,” Phys. Rev. B 57, 13113-13117 (1998).
[CrossRef]

1997 (1)

D. V. Roshchupkin, I. A. Schelokov, R. Tucoulou, and M. Brunel, “X-ray diffraction on a multilayer mirror modulated by surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 129, 414-418 (1997).
[CrossRef]

1996 (1)

P. F. Fewster, “X-ray analysis of thin films and multilayers,” Rep. Prog. Phys. 59, 1339-1407 (1996).
[CrossRef]

1994 (1)

J. A. Rogers, L. Dhar, and K. A. Nelson, “Noncontact determination of transverse isotropic elastic moduli in polyimide thin films using a laser based ultrasonic method,” Appl. Phys. Lett. 65, 312-314 (1994).
[CrossRef]

1986 (1)

J. P. Monchalin, “Optical detection of ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 33, 485-499(1986).
[CrossRef]

1969 (1)

K. A. Ingebrigtsen and A. Tonning, “Elastic surface waves in crystals,” Phys. Rev. 184, 942-951 (1969).
[CrossRef]

Anderson, E. H.

M. E. Siemens, Q. Li, M. M. Murnane, H. C. Kapteyn, R. Yang, E. H. Anderson, and K. A. Nelson, “High-frequency surface acoustic wave propagation in nanostructures characterized by coherent extreme ultraviolet beams,” Appl. Phys. Lett. 94, 093103 (2009).
[CrossRef]

Andreev, A. V.

A. V. Andreev, Yu. V. Ponomarev, L. R. Prudnikov, and N. N. Salashchenko, “X-ray diffuse scattering by multilayer waveguide structures,” Phys. Rev. B 57, 13113-13117 (1998).
[CrossRef]

Bal, M. F.

Birkholz, M.

M. Birkholz, Thin Film Analysis by X-Ray Scattering (Wiley-VCH, 2006), pp. 150-159.

Braat, J. J. M.

Brunel, M.

D. V. Roshchupkin, R. Tucoulou, and M. Brunel, Appl. Phys. Lett. 75, 639 (1999).
[CrossRef]

D. V. Roshchupkin, R. Tucoulou, A. Masclet, M. Brunel, I. A. Schelokov, and A. S. Kondakov, “X-ray diffraction by standing surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 142, 432-436 (1998).
[CrossRef]

D. V. Roshchupkin, I. A. Schelokov, R. Tucoulou, and M. Brunel, “X-ray diffraction on a multilayer mirror modulated by surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 129, 414-418 (1997).
[CrossRef]

Caliendo, C.

C. Caliendo, “Theoretical and experimental investigation of gigahertz-band, temperature-compensated electromechanical coupling configurations based on AlN films,” Appl. Phys. Lett. 92, 033505 (2008).
[CrossRef]

Chiang, Y. F.

C. C. Sung, Y. F. Chiang, R. Ro, R. Lee, and S. Wu “Effects of conducting layers on surface acoustic wave in AlN films on diamond,” J. Appl. Phys. 106, 124905 (2009).
[CrossRef]

Cui, J. C.

X. Zai and J. C. Cui, Applied Crystals Physics (China Science Press, 1984), p. 200 (in Chinese).

Descrovi, E.

Dhar, L.

J. A. Rogers, L. Dhar, and K. A. Nelson, “Noncontact determination of transverse isotropic elastic moduli in polyimide thin films using a laser based ultrasonic method,” Appl. Phys. Lett. 65, 312-314 (1994).
[CrossRef]

Dieulesaint, E.

E. Dieulesaint and D. Royer, Ondes Clastiques darts les solides (Masson, 1974).

Dinger, U.

Duncan, B. D.

Fadley, C. S.

S. H. Yang, B. C. Sell, and C. S. Fadley, “Probing multilayer spintronic structures with photoelectron and x-ray emission spectroscopies excited by x-ray standing waves,” J. Appl. Phys. 103, 07C519 (2008).
[CrossRef]

Fewster, P. F.

P. F. Fewster, “X-ray analysis of thin films and multilayers,” Rep. Prog. Phys. 59, 1339-1407 (1996).
[CrossRef]

Freeman, D. M.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968), pp. 60-62.

Haubrich, A. G. C.

W. Sauer, M. Streibl, T. H. Metzger, and A. G. C. Haubrich, “X-ray imaging and diffraction from surface phonons on GaAs,” Appl. Phys. Lett. 75, 1709-1711 (1999).
[CrossRef]

Hong, S. S.

Ingebrigtsen, K. A.

K. A. Ingebrigtsen and A. Tonning, “Elastic surface waves in crystals,” Phys. Rev. 184, 942-951 (1969).
[CrossRef]

Ishiura, Y.

T. Nakao, M. Kadota, K. Nishiyama, Y. Nakai, D. Yamamoto, Y. Ishiura, T. Komura, N. Takada, and R. Kita, “Smaller surface acoustic wave duplexer for US personal communication service having good temperature characteristics,” Jpn. J. Appl. Phys. 46, 4760-4763 (2007).
[CrossRef]

Joyeux, D.

Kadota, M.

T. Nakao, M. Kadota, K. Nishiyama, Y. Nakai, D. Yamamoto, Y. Ishiura, T. Komura, N. Takada, and R. Kita, “Smaller surface acoustic wave duplexer for US personal communication service having good temperature characteristics,” Jpn. J. Appl. Phys. 46, 4760-4763 (2007).
[CrossRef]

Kapteyn, H. C.

M. E. Siemens, Q. Li, M. M. Murnane, H. C. Kapteyn, R. Yang, E. H. Anderson, and K. A. Nelson, “High-frequency surface acoustic wave propagation in nanostructures characterized by coherent extreme ultraviolet beams,” Appl. Phys. Lett. 94, 093103 (2009).
[CrossRef]

R. I. Tobey, M. E. Siemens, M. M. Murnane, H. C. Kapteyn, D. H. Torchinsky, and K. A. Nelson, “Transient grating measurement of surface acoustic waves in thin metal films with extreme ultraviolet radiation,” Appl. Phys. Lett. 89, 091108(2006).
[CrossRef]

Kita, R.

T. Nakao, M. Kadota, K. Nishiyama, Y. Nakai, D. Yamamoto, Y. Ishiura, T. Komura, N. Takada, and R. Kita, “Smaller surface acoustic wave duplexer for US personal communication service having good temperature characteristics,” Jpn. J. Appl. Phys. 46, 4760-4763 (2007).
[CrossRef]

Komura, T.

T. Nakao, M. Kadota, K. Nishiyama, Y. Nakai, D. Yamamoto, Y. Ishiura, T. Komura, N. Takada, and R. Kita, “Smaller surface acoustic wave duplexer for US personal communication service having good temperature characteristics,” Jpn. J. Appl. Phys. 46, 4760-4763 (2007).
[CrossRef]

Kondakov, A. S.

D. V. Roshchupkin, R. Tucoulou, A. Masclet, M. Brunel, I. A. Schelokov, and A. S. Kondakov, “X-ray diffraction by standing surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 142, 432-436 (1998).
[CrossRef]

Lee, M. S.

S. Wu, R. Ro, Z. X. Lin, and M. S. Lee, “Rayleigh surface acoustic wave modes of interdigital transducer/(100) AlN/(111) diamond,” J. Appl. Phys. 104, 064919 (2008).
[CrossRef]

Lee, R.

C. C. Sung, Y. F. Chiang, R. Ro, R. Lee, and S. Wu “Effects of conducting layers on surface acoustic wave in AlN films on diamond,” J. Appl. Phys. 106, 124905 (2009).
[CrossRef]

Li, Q.

M. E. Siemens, Q. Li, M. M. Murnane, H. C. Kapteyn, R. Yang, E. H. Anderson, and K. A. Nelson, “High-frequency surface acoustic wave propagation in nanostructures characterized by coherent extreme ultraviolet beams,” Appl. Phys. Lett. 94, 093103 (2009).
[CrossRef]

Lin, Z. X.

S. Wu, R. Ro, Z. X. Lin, and M. S. Lee, “Rayleigh surface acoustic wave modes of interdigital transducer/(100) AlN/(111) diamond,” J. Appl. Phys. 104, 064919 (2008).
[CrossRef]

Masclet, A.

D. V. Roshchupkin, R. Tucoulou, A. Masclet, M. Brunel, I. A. Schelokov, and A. S. Kondakov, “X-ray diffraction by standing surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 142, 432-436 (1998).
[CrossRef]

Mermelstein, M. S.

Metzger, T. H.

W. Sauer, M. Streibl, T. H. Metzger, and A. G. C. Haubrich, “X-ray imaging and diffraction from surface phonons on GaAs,” Appl. Phys. Lett. 75, 1709-1711 (1999).
[CrossRef]

Miao, R.

R. Miao, Z. Yang, J. Zhu, and C. Shen, “Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction,” Appl. Phys. Lett. 80, 3033-3035 (2002).
[CrossRef]

Monchalin, J. P.

J. P. Monchalin, “Optical detection of ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 33, 485-499(1986).
[CrossRef]

Murnane, M. M.

M. E. Siemens, Q. Li, M. M. Murnane, H. C. Kapteyn, R. Yang, E. H. Anderson, and K. A. Nelson, “High-frequency surface acoustic wave propagation in nanostructures characterized by coherent extreme ultraviolet beams,” Appl. Phys. Lett. 94, 093103 (2009).
[CrossRef]

R. I. Tobey, M. E. Siemens, M. M. Murnane, H. C. Kapteyn, D. H. Torchinsky, and K. A. Nelson, “Transient grating measurement of surface acoustic waves in thin metal films with extreme ultraviolet radiation,” Appl. Phys. Lett. 89, 091108(2006).
[CrossRef]

Nakai, Y.

T. Nakao, M. Kadota, K. Nishiyama, Y. Nakai, D. Yamamoto, Y. Ishiura, T. Komura, N. Takada, and R. Kita, “Smaller surface acoustic wave duplexer for US personal communication service having good temperature characteristics,” Jpn. J. Appl. Phys. 46, 4760-4763 (2007).
[CrossRef]

Nakao, T.

T. Nakao, M. Kadota, K. Nishiyama, Y. Nakai, D. Yamamoto, Y. Ishiura, T. Komura, N. Takada, and R. Kita, “Smaller surface acoustic wave duplexer for US personal communication service having good temperature characteristics,” Jpn. J. Appl. Phys. 46, 4760-4763 (2007).
[CrossRef]

Nelson, K. A.

M. E. Siemens, Q. Li, M. M. Murnane, H. C. Kapteyn, R. Yang, E. H. Anderson, and K. A. Nelson, “High-frequency surface acoustic wave propagation in nanostructures characterized by coherent extreme ultraviolet beams,” Appl. Phys. Lett. 94, 093103 (2009).
[CrossRef]

R. I. Tobey, M. E. Siemens, M. M. Murnane, H. C. Kapteyn, D. H. Torchinsky, and K. A. Nelson, “Transient grating measurement of surface acoustic waves in thin metal films with extreme ultraviolet radiation,” Appl. Phys. Lett. 89, 091108(2006).
[CrossRef]

J. A. Rogers, L. Dhar, and K. A. Nelson, “Noncontact determination of transverse isotropic elastic moduli in polyimide thin films using a laser based ultrasonic method,” Appl. Phys. Lett. 65, 312-314 (1994).
[CrossRef]

Nishiyama, K.

T. Nakao, M. Kadota, K. Nishiyama, Y. Nakai, D. Yamamoto, Y. Ishiura, T. Komura, N. Takada, and R. Kita, “Smaller surface acoustic wave duplexer for US personal communication service having good temperature characteristics,” Jpn. J. Appl. Phys. 46, 4760-4763 (2007).
[CrossRef]

Ponomarev, Yu. V.

A. V. Andreev, Yu. V. Ponomarev, L. R. Prudnikov, and N. N. Salashchenko, “X-ray diffuse scattering by multilayer waveguide structures,” Phys. Rev. B 57, 13113-13117 (1998).
[CrossRef]

Prudnikov, L. R.

A. V. Andreev, Yu. V. Ponomarev, L. R. Prudnikov, and N. N. Salashchenko, “X-ray diffuse scattering by multilayer waveguide structures,” Phys. Rev. B 57, 13113-13117 (1998).
[CrossRef]

Ro, R.

C. C. Sung, Y. F. Chiang, R. Ro, R. Lee, and S. Wu “Effects of conducting layers on surface acoustic wave in AlN films on diamond,” J. Appl. Phys. 106, 124905 (2009).
[CrossRef]

S. Wu, R. Ro, Z. X. Lin, and M. S. Lee, “Rayleigh surface acoustic wave modes of interdigital transducer/(100) AlN/(111) diamond,” J. Appl. Phys. 104, 064919 (2008).
[CrossRef]

Rogers, J. A.

J. A. Rogers, L. Dhar, and K. A. Nelson, “Noncontact determination of transverse isotropic elastic moduli in polyimide thin films using a laser based ultrasonic method,” Appl. Phys. Lett. 65, 312-314 (1994).
[CrossRef]

Roshchupkin, D. V.

D. V. Roshchupkin, R. Tucoulou, and M. Brunel, Appl. Phys. Lett. 75, 639 (1999).
[CrossRef]

D. V. Roshchupkin, R. Tucoulou, A. Masclet, M. Brunel, I. A. Schelokov, and A. S. Kondakov, “X-ray diffraction by standing surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 142, 432-436 (1998).
[CrossRef]

D. V. Roshchupkin, I. A. Schelokov, R. Tucoulou, and M. Brunel, “X-ray diffraction on a multilayer mirror modulated by surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 129, 414-418 (1997).
[CrossRef]

Royer, D.

E. Dieulesaint and D. Royer, Ondes Clastiques darts les solides (Masson, 1974).

Salashchenko, N. N.

A. V. Andreev, Yu. V. Ponomarev, L. R. Prudnikov, and N. N. Salashchenko, “X-ray diffuse scattering by multilayer waveguide structures,” Phys. Rev. B 57, 13113-13117 (1998).
[CrossRef]

Sauer, W.

W. Sauer, M. Streibl, T. H. Metzger, and A. G. C. Haubrich, “X-ray imaging and diffraction from surface phonons on GaAs,” Appl. Phys. Lett. 75, 1709-1711 (1999).
[CrossRef]

Schelokov, I. A.

D. V. Roshchupkin, R. Tucoulou, A. Masclet, M. Brunel, I. A. Schelokov, and A. S. Kondakov, “X-ray diffraction by standing surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 142, 432-436 (1998).
[CrossRef]

D. V. Roshchupkin, I. A. Schelokov, R. Tucoulou, and M. Brunel, “X-ray diffraction on a multilayer mirror modulated by surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 129, 414-418 (1997).
[CrossRef]

Sell, B. C.

S. H. Yang, B. C. Sell, and C. S. Fadley, “Probing multilayer spintronic structures with photoelectron and x-ray emission spectroscopies excited by x-ray standing waves,” J. Appl. Phys. 103, 07C519 (2008).
[CrossRef]

Shen, C.

R. Miao, Z. Yang, J. Zhu, and C. Shen, “Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction,” Appl. Phys. Lett. 80, 3033-3035 (2002).
[CrossRef]

Shilo, D.

D. Shilo and E. Zolotoyabko, “Interaction of a surface wave with a dislocation,” Phys. Rev. Lett. 91, 115506 (2003).
[CrossRef]

Siemens, M. E.

M. E. Siemens, Q. Li, M. M. Murnane, H. C. Kapteyn, R. Yang, E. H. Anderson, and K. A. Nelson, “High-frequency surface acoustic wave propagation in nanostructures characterized by coherent extreme ultraviolet beams,” Appl. Phys. Lett. 94, 093103 (2009).
[CrossRef]

R. I. Tobey, M. E. Siemens, M. M. Murnane, H. C. Kapteyn, D. H. Torchinsky, and K. A. Nelson, “Transient grating measurement of surface acoustic waves in thin metal films with extreme ultraviolet radiation,” Appl. Phys. Lett. 89, 091108(2006).
[CrossRef]

Singh, M.

Streibl, M.

W. Sauer, M. Streibl, T. H. Metzger, and A. G. C. Haubrich, “X-ray imaging and diffraction from surface phonons on GaAs,” Appl. Phys. Lett. 75, 1709-1711 (1999).
[CrossRef]

Sung, C. C.

C. C. Sung, Y. F. Chiang, R. Ro, R. Lee, and S. Wu “Effects of conducting layers on surface acoustic wave in AlN films on diamond,” J. Appl. Phys. 106, 124905 (2009).
[CrossRef]

Takada, N.

T. Nakao, M. Kadota, K. Nishiyama, Y. Nakai, D. Yamamoto, Y. Ishiura, T. Komura, N. Takada, and R. Kita, “Smaller surface acoustic wave duplexer for US personal communication service having good temperature characteristics,” Jpn. J. Appl. Phys. 46, 4760-4763 (2007).
[CrossRef]

Tobey, R. I.

R. I. Tobey, M. E. Siemens, M. M. Murnane, H. C. Kapteyn, D. H. Torchinsky, and K. A. Nelson, “Transient grating measurement of surface acoustic waves in thin metal films with extreme ultraviolet radiation,” Appl. Phys. Lett. 89, 091108(2006).
[CrossRef]

Tonning, A.

K. A. Ingebrigtsen and A. Tonning, “Elastic surface waves in crystals,” Phys. Rev. 184, 942-951 (1969).
[CrossRef]

Torchinsky, D. H.

R. I. Tobey, M. E. Siemens, M. M. Murnane, H. C. Kapteyn, D. H. Torchinsky, and K. A. Nelson, “Transient grating measurement of surface acoustic waves in thin metal films with extreme ultraviolet radiation,” Appl. Phys. Lett. 89, 091108(2006).
[CrossRef]

Tucoulou, R.

D. V. Roshchupkin, R. Tucoulou, and M. Brunel, Appl. Phys. Lett. 75, 639 (1999).
[CrossRef]

D. V. Roshchupkin, R. Tucoulou, A. Masclet, M. Brunel, I. A. Schelokov, and A. S. Kondakov, “X-ray diffraction by standing surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 142, 432-436 (1998).
[CrossRef]

D. V. Roshchupkin, I. A. Schelokov, R. Tucoulou, and M. Brunel, “X-ray diffraction on a multilayer mirror modulated by surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 129, 414-418 (1997).
[CrossRef]

Wu, S.

C. C. Sung, Y. F. Chiang, R. Ro, R. Lee, and S. Wu “Effects of conducting layers on surface acoustic wave in AlN films on diamond,” J. Appl. Phys. 106, 124905 (2009).
[CrossRef]

S. Wu, R. Ro, Z. X. Lin, and M. S. Lee, “Rayleigh surface acoustic wave modes of interdigital transducer/(100) AlN/(111) diamond,” J. Appl. Phys. 104, 064919 (2008).
[CrossRef]

Yamamoto, D.

T. Nakao, M. Kadota, K. Nishiyama, Y. Nakai, D. Yamamoto, Y. Ishiura, T. Komura, N. Takada, and R. Kita, “Smaller surface acoustic wave duplexer for US personal communication service having good temperature characteristics,” Jpn. J. Appl. Phys. 46, 4760-4763 (2007).
[CrossRef]

Yang, R.

M. E. Siemens, Q. Li, M. M. Murnane, H. C. Kapteyn, R. Yang, E. H. Anderson, and K. A. Nelson, “High-frequency surface acoustic wave propagation in nanostructures characterized by coherent extreme ultraviolet beams,” Appl. Phys. Lett. 94, 093103 (2009).
[CrossRef]

Yang, S. H.

S. H. Yang, B. C. Sell, and C. S. Fadley, “Probing multilayer spintronic structures with photoelectron and x-ray emission spectroscopies excited by x-ray standing waves,” J. Appl. Phys. 103, 07C519 (2008).
[CrossRef]

Yang, Z.

R. Miao, Z. Yang, J. Zhu, and C. Shen, “Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction,” Appl. Phys. Lett. 80, 3033-3035 (2002).
[CrossRef]

Zai, X.

X. Zai and J. C. Cui, Applied Crystals Physics (China Science Press, 1984), p. 200 (in Chinese).

Zhu, J.

R. Miao, Z. Yang, J. Zhu, and C. Shen, “Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction,” Appl. Phys. Lett. 80, 3033-3035 (2002).
[CrossRef]

Zolotoyabko, E.

D. Shilo and E. Zolotoyabko, “Interaction of a surface wave with a dislocation,” Phys. Rev. Lett. 91, 115506 (2003).
[CrossRef]

Appl. Opt. (3)

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D. V. Roshchupkin, R. Tucoulou, and M. Brunel, Appl. Phys. Lett. 75, 639 (1999).
[CrossRef]

W. Sauer, M. Streibl, T. H. Metzger, and A. G. C. Haubrich, “X-ray imaging and diffraction from surface phonons on GaAs,” Appl. Phys. Lett. 75, 1709-1711 (1999).
[CrossRef]

R. Miao, Z. Yang, J. Zhu, and C. Shen, “Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction,” Appl. Phys. Lett. 80, 3033-3035 (2002).
[CrossRef]

C. Caliendo, “Theoretical and experimental investigation of gigahertz-band, temperature-compensated electromechanical coupling configurations based on AlN films,” Appl. Phys. Lett. 92, 033505 (2008).
[CrossRef]

R. I. Tobey, M. E. Siemens, M. M. Murnane, H. C. Kapteyn, D. H. Torchinsky, and K. A. Nelson, “Transient grating measurement of surface acoustic waves in thin metal films with extreme ultraviolet radiation,” Appl. Phys. Lett. 89, 091108(2006).
[CrossRef]

M. E. Siemens, Q. Li, M. M. Murnane, H. C. Kapteyn, R. Yang, E. H. Anderson, and K. A. Nelson, “High-frequency surface acoustic wave propagation in nanostructures characterized by coherent extreme ultraviolet beams,” Appl. Phys. Lett. 94, 093103 (2009).
[CrossRef]

J. A. Rogers, L. Dhar, and K. A. Nelson, “Noncontact determination of transverse isotropic elastic moduli in polyimide thin films using a laser based ultrasonic method,” Appl. Phys. Lett. 65, 312-314 (1994).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

J. P. Monchalin, “Optical detection of ultrasound,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 33, 485-499(1986).
[CrossRef]

J. Appl. Phys. (3)

S. Wu, R. Ro, Z. X. Lin, and M. S. Lee, “Rayleigh surface acoustic wave modes of interdigital transducer/(100) AlN/(111) diamond,” J. Appl. Phys. 104, 064919 (2008).
[CrossRef]

C. C. Sung, Y. F. Chiang, R. Ro, R. Lee, and S. Wu “Effects of conducting layers on surface acoustic wave in AlN films on diamond,” J. Appl. Phys. 106, 124905 (2009).
[CrossRef]

S. H. Yang, B. C. Sell, and C. S. Fadley, “Probing multilayer spintronic structures with photoelectron and x-ray emission spectroscopies excited by x-ray standing waves,” J. Appl. Phys. 103, 07C519 (2008).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Nakao, M. Kadota, K. Nishiyama, Y. Nakai, D. Yamamoto, Y. Ishiura, T. Komura, N. Takada, and R. Kita, “Smaller surface acoustic wave duplexer for US personal communication service having good temperature characteristics,” Jpn. J. Appl. Phys. 46, 4760-4763 (2007).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. B (2)

D. V. Roshchupkin, I. A. Schelokov, R. Tucoulou, and M. Brunel, “X-ray diffraction on a multilayer mirror modulated by surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 129, 414-418 (1997).
[CrossRef]

D. V. Roshchupkin, R. Tucoulou, A. Masclet, M. Brunel, I. A. Schelokov, and A. S. Kondakov, “X-ray diffraction by standing surface acoustic waves,” Nucl. Instrum. Methods Phys. Res. B 142, 432-436 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

K. A. Ingebrigtsen and A. Tonning, “Elastic surface waves in crystals,” Phys. Rev. 184, 942-951 (1969).
[CrossRef]

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A. V. Andreev, Yu. V. Ponomarev, L. R. Prudnikov, and N. N. Salashchenko, “X-ray diffuse scattering by multilayer waveguide structures,” Phys. Rev. B 57, 13113-13117 (1998).
[CrossRef]

Phys. Rev. Lett. (1)

D. Shilo and E. Zolotoyabko, “Interaction of a surface wave with a dislocation,” Phys. Rev. Lett. 91, 115506 (2003).
[CrossRef]

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P. F. Fewster, “X-ray analysis of thin films and multilayers,” Rep. Prog. Phys. 59, 1339-1407 (1996).
[CrossRef]

Other (4)

E. Dieulesaint and D. Royer, Ondes Clastiques darts les solides (Masson, 1974).

X. Zai and J. C. Cui, Applied Crystals Physics (China Science Press, 1984), p. 200 (in Chinese).

M. Birkholz, Thin Film Analysis by X-Ray Scattering (Wiley-VCH, 2006), pp. 150-159.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968), pp. 60-62.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup [12].

Fig. 2
Fig. 2

Diffraction intensity I obtained (a) at and (b) around the Bragg incidence angle θ = 0.832 ° , for different MLSAW amplitudes [12].

Fig. 3
Fig. 3

Theoretical intensity distribution of the diffraction pattern obtained at the Bragg incidence angle [predicted by Eq. (4)] for different MLSAW amplitudes.

Fig. 4
Fig. 4

Theoretical intensity distribution of the diffraction pattern obtained around the Bragg incidence angle [predicted by Eq. (6)] for different MLSAW amplitudes.

Equations (8)

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exp [ Φ ( x ) ] = [ 1 / 2 + R N 2 cos ( ω t k x ) ] · exp [ i 2 π λ [ ( 2 h cos θ ) sin ( ω t k x ) ] ,
R N = sin 2 ( N Γ 2 ) sin 2 ( Γ 2 ) exp [ 2 α ( N 1 ) d / sin θ ] ,
R N = sin 2 ( N π ) sin 2 ( π ) exp [ 2 α ( N 1 ) d / sin θ B ]
R N = sin 2 ( N π ) sin 2 ( π ) exp [ 2 α ( N 1 ) d / sin θ B ]
exp [ Φ ( x ) ] = [ ( 1 2 + 1 2 cos ( ω t k x ) ) ] · exp [ i 2 π λ ( 2 h cos θ ) sin ( ω t k x ) ] .
I ( x ) = J 0 2 ( 2 π h cos θ / λ ) δ ( f x ) + 1 4 J 1 2 ( 2 π h cos θ / λ ) δ ( f x + f 0 ) + 1 4 J + 1 2 ( 2 π h cos θ / λ ) δ ( f x f 0 ) ,
exp [ Φ ( x ) ] = exp [ i 1 2 · 2 π λ ( 2 h cos θ ) sin ( ω t k x ) ] .
I ( x ) = q J q 2 ( 2 π h cos θ / λ ) · δ ( f x q Λ cos θ ) .

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