Abstract

The interaction of an optical beam with a traveling surface wave and a stationary holographic reference grating is studied theoretically and experimentally. The spatial phase modulation produced by the traveling wave results in an intensity modulation in the diffracted orders of the optical beam. The intensity modulation is at the fundamental frequency of the traveling wave, and its amplitude depends periodically on the separation distance between the plane of the traveling wave and the plane of the stationary holographic reference grating. Experiments were carried out with 87-MHz surface acoustic waves traveling on a LiNbO3 substrate separated from a holographic reference grating in film. The amplitudes of the detected modulation in the m = 0 and m = ±1 diffraction orders of a probing beam are in close agreement with a plane-wave analysis in the Raman–Nath diffraction regime.

© 1990 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. W. Damon, W. T. Maloney, D. H. McMahon, “Interaction of light with ultrasound: phenomena and applications,” in Physical Acoustics: Principles and Methods, W. P. Mason, R. N. Thurston, eds. (Academic, New York, 1970), Vol. VII, pp. 273–366.
  2. G. I. Stegeman, “Optical probing of surface acoustic waves and surface wave devices,” IEEE Trans. Sonics Ultrason. SU-23, 33–63 (1976).
    [CrossRef]
  3. F. Calligaris, P. Ciuti, I. Gabrielli, “Extended theory of light modulation in thin-screen diffraction by ultrasound,” J. Opt. Soc. Am. 63, 287–292 (1973).
    [CrossRef]
  4. L. N. Deryugin, V. A. Komotskii, “Diffraction of an optical wave with spatial phase modulation by a periodic amplitude grating,” Opt. Spectrosc. (USSR) 46, 79–82 (1979).
  5. V. A. Komotskii, T. D. Black, “Analysis and application of stationary reference grating method for optical detection of surface acoustic waves,” J. Appl. Phys. 52, 129–136 (1981).
    [CrossRef]
  6. A. F. Bessonov, L. N. Deryugin, V. A. Komotskii, “Measurement of phase distributions of a surface acoustic wave by the method of optical probing with reference gratings,” Avtometriya 5, 92–95 (1982).
  7. T. D. Black, V. A. Komotskii, “Infrared detection using acousto-optic interaction with thermally induced grating in optical waveguides,” Appl. Phys. Lett. 38, 113–115 (1981).
    [CrossRef]
  8. O. Leroy, “Diffraction of light by two adjacent parallel ultrasonic beams,” Acustica 29, 303–310 (1973).
  9. O. Leroy, E. Blomme, “Amplitude modulation of diffracted light waves caused by adjacent ultrasonic beams of frequency ratio 1:n,” Ultrasonics 19, 173–178 (1981).
    [CrossRef]
  10. T.-C. Poon, P. P. Banerjee, M. R. Chatterjee, “Analysis of acousto-optic diffraction by adjacent ultrasonic beams using multiple plane-wave scattering techniques,” IEEE Trans. Sonics Ultrason. SU-32, 592–595 (1985).
    [CrossRef]
  11. T.-C. Poon, M. R. Chatterjee, P. P. Banerjee, “Multiple plane-wave analysis of acousto-optic diffraction by adjacent ultrasonic beams of frequency ratio 1:m,” J. Opt. Soc. Am. A 3, 1402–1406 (1986).
    [CrossRef]
  12. R. Magnusson, T. K. Gaylord, “Diffraction regimes of transmission gratings,” J. Opt. Soc. Am. 68, 809–814 (1978).
    [CrossRef]
  13. R. Magnusson, T. D. Black, “Enhanced detection of acoustic waves using thick and thin reference gratings,” J. Opt. Soc. Am. A 4, 498–502 (1987).
    [CrossRef]
  14. L. E. Hargrove, E. A. Hiedemann, R. Mertens, “Diffraction of light by two spatially separated parallel ultrasonic waves of different frequency,” Z. Phys. 167, 326–336 (1962).
    [CrossRef]
  15. F. Calligaris, P. Ciuti, I. Gabrielli, “Temporal light modulation in thick-screen diffraction by ultrasound beam plus amplitude grating,” J. Acoust. Soc. Am. 61, 959–964 (1977).
    [CrossRef]
  16. P. Kwiek, “Light diffraction by two spatially separated ultrasonic waves,” J. Acoust. Soc. Am. 86, 2261–2271 (1989).
    [CrossRef]
  17. A. Alippi, A. Palma, L. Palmeri, G. Socino, “Incident angle and polarization dependence of light diffracted by acoustic surface waves,” J. Appl. Phys. 45, 1492–1497 (1974).
    [CrossRef]
  18. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 657–661.
  19. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), pp. 53–54.
  20. H. Engan, “Excitation of elastic surface waves by spatial harmonics of interdigital transducers,” IEEE Trans. Electron. Devices ED-16, 1014–1017 (1969).
    [CrossRef]

1989 (1)

P. Kwiek, “Light diffraction by two spatially separated ultrasonic waves,” J. Acoust. Soc. Am. 86, 2261–2271 (1989).
[CrossRef]

1987 (1)

1986 (1)

1985 (1)

T.-C. Poon, P. P. Banerjee, M. R. Chatterjee, “Analysis of acousto-optic diffraction by adjacent ultrasonic beams using multiple plane-wave scattering techniques,” IEEE Trans. Sonics Ultrason. SU-32, 592–595 (1985).
[CrossRef]

1982 (1)

A. F. Bessonov, L. N. Deryugin, V. A. Komotskii, “Measurement of phase distributions of a surface acoustic wave by the method of optical probing with reference gratings,” Avtometriya 5, 92–95 (1982).

1981 (3)

T. D. Black, V. A. Komotskii, “Infrared detection using acousto-optic interaction with thermally induced grating in optical waveguides,” Appl. Phys. Lett. 38, 113–115 (1981).
[CrossRef]

O. Leroy, E. Blomme, “Amplitude modulation of diffracted light waves caused by adjacent ultrasonic beams of frequency ratio 1:n,” Ultrasonics 19, 173–178 (1981).
[CrossRef]

V. A. Komotskii, T. D. Black, “Analysis and application of stationary reference grating method for optical detection of surface acoustic waves,” J. Appl. Phys. 52, 129–136 (1981).
[CrossRef]

1979 (1)

L. N. Deryugin, V. A. Komotskii, “Diffraction of an optical wave with spatial phase modulation by a periodic amplitude grating,” Opt. Spectrosc. (USSR) 46, 79–82 (1979).

1978 (1)

1977 (1)

F. Calligaris, P. Ciuti, I. Gabrielli, “Temporal light modulation in thick-screen diffraction by ultrasound beam plus amplitude grating,” J. Acoust. Soc. Am. 61, 959–964 (1977).
[CrossRef]

1976 (1)

G. I. Stegeman, “Optical probing of surface acoustic waves and surface wave devices,” IEEE Trans. Sonics Ultrason. SU-23, 33–63 (1976).
[CrossRef]

1974 (1)

A. Alippi, A. Palma, L. Palmeri, G. Socino, “Incident angle and polarization dependence of light diffracted by acoustic surface waves,” J. Appl. Phys. 45, 1492–1497 (1974).
[CrossRef]

1973 (2)

1969 (1)

H. Engan, “Excitation of elastic surface waves by spatial harmonics of interdigital transducers,” IEEE Trans. Electron. Devices ED-16, 1014–1017 (1969).
[CrossRef]

1962 (1)

L. E. Hargrove, E. A. Hiedemann, R. Mertens, “Diffraction of light by two spatially separated parallel ultrasonic waves of different frequency,” Z. Phys. 167, 326–336 (1962).
[CrossRef]

Alippi, A.

A. Alippi, A. Palma, L. Palmeri, G. Socino, “Incident angle and polarization dependence of light diffracted by acoustic surface waves,” J. Appl. Phys. 45, 1492–1497 (1974).
[CrossRef]

Banerjee, P. P.

T.-C. Poon, M. R. Chatterjee, P. P. Banerjee, “Multiple plane-wave analysis of acousto-optic diffraction by adjacent ultrasonic beams of frequency ratio 1:m,” J. Opt. Soc. Am. A 3, 1402–1406 (1986).
[CrossRef]

T.-C. Poon, P. P. Banerjee, M. R. Chatterjee, “Analysis of acousto-optic diffraction by adjacent ultrasonic beams using multiple plane-wave scattering techniques,” IEEE Trans. Sonics Ultrason. SU-32, 592–595 (1985).
[CrossRef]

Bessonov, A. F.

A. F. Bessonov, L. N. Deryugin, V. A. Komotskii, “Measurement of phase distributions of a surface acoustic wave by the method of optical probing with reference gratings,” Avtometriya 5, 92–95 (1982).

Black, T. D.

R. Magnusson, T. D. Black, “Enhanced detection of acoustic waves using thick and thin reference gratings,” J. Opt. Soc. Am. A 4, 498–502 (1987).
[CrossRef]

V. A. Komotskii, T. D. Black, “Analysis and application of stationary reference grating method for optical detection of surface acoustic waves,” J. Appl. Phys. 52, 129–136 (1981).
[CrossRef]

T. D. Black, V. A. Komotskii, “Infrared detection using acousto-optic interaction with thermally induced grating in optical waveguides,” Appl. Phys. Lett. 38, 113–115 (1981).
[CrossRef]

Blomme, E.

O. Leroy, E. Blomme, “Amplitude modulation of diffracted light waves caused by adjacent ultrasonic beams of frequency ratio 1:n,” Ultrasonics 19, 173–178 (1981).
[CrossRef]

Calligaris, F.

F. Calligaris, P. Ciuti, I. Gabrielli, “Temporal light modulation in thick-screen diffraction by ultrasound beam plus amplitude grating,” J. Acoust. Soc. Am. 61, 959–964 (1977).
[CrossRef]

F. Calligaris, P. Ciuti, I. Gabrielli, “Extended theory of light modulation in thin-screen diffraction by ultrasound,” J. Opt. Soc. Am. 63, 287–292 (1973).
[CrossRef]

Chatterjee, M. R.

T.-C. Poon, M. R. Chatterjee, P. P. Banerjee, “Multiple plane-wave analysis of acousto-optic diffraction by adjacent ultrasonic beams of frequency ratio 1:m,” J. Opt. Soc. Am. A 3, 1402–1406 (1986).
[CrossRef]

T.-C. Poon, P. P. Banerjee, M. R. Chatterjee, “Analysis of acousto-optic diffraction by adjacent ultrasonic beams using multiple plane-wave scattering techniques,” IEEE Trans. Sonics Ultrason. SU-32, 592–595 (1985).
[CrossRef]

Ciuti, P.

F. Calligaris, P. Ciuti, I. Gabrielli, “Temporal light modulation in thick-screen diffraction by ultrasound beam plus amplitude grating,” J. Acoust. Soc. Am. 61, 959–964 (1977).
[CrossRef]

F. Calligaris, P. Ciuti, I. Gabrielli, “Extended theory of light modulation in thin-screen diffraction by ultrasound,” J. Opt. Soc. Am. 63, 287–292 (1973).
[CrossRef]

Damon, R. W.

R. W. Damon, W. T. Maloney, D. H. McMahon, “Interaction of light with ultrasound: phenomena and applications,” in Physical Acoustics: Principles and Methods, W. P. Mason, R. N. Thurston, eds. (Academic, New York, 1970), Vol. VII, pp. 273–366.

Deryugin, L. N.

A. F. Bessonov, L. N. Deryugin, V. A. Komotskii, “Measurement of phase distributions of a surface acoustic wave by the method of optical probing with reference gratings,” Avtometriya 5, 92–95 (1982).

L. N. Deryugin, V. A. Komotskii, “Diffraction of an optical wave with spatial phase modulation by a periodic amplitude grating,” Opt. Spectrosc. (USSR) 46, 79–82 (1979).

Engan, H.

H. Engan, “Excitation of elastic surface waves by spatial harmonics of interdigital transducers,” IEEE Trans. Electron. Devices ED-16, 1014–1017 (1969).
[CrossRef]

Gabrielli, I.

F. Calligaris, P. Ciuti, I. Gabrielli, “Temporal light modulation in thick-screen diffraction by ultrasound beam plus amplitude grating,” J. Acoust. Soc. Am. 61, 959–964 (1977).
[CrossRef]

F. Calligaris, P. Ciuti, I. Gabrielli, “Extended theory of light modulation in thin-screen diffraction by ultrasound,” J. Opt. Soc. Am. 63, 287–292 (1973).
[CrossRef]

Gaylord, T. K.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), pp. 53–54.

Hargrove, L. E.

L. E. Hargrove, E. A. Hiedemann, R. Mertens, “Diffraction of light by two spatially separated parallel ultrasonic waves of different frequency,” Z. Phys. 167, 326–336 (1962).
[CrossRef]

Hiedemann, E. A.

L. E. Hargrove, E. A. Hiedemann, R. Mertens, “Diffraction of light by two spatially separated parallel ultrasonic waves of different frequency,” Z. Phys. 167, 326–336 (1962).
[CrossRef]

Komotskii, V. A.

A. F. Bessonov, L. N. Deryugin, V. A. Komotskii, “Measurement of phase distributions of a surface acoustic wave by the method of optical probing with reference gratings,” Avtometriya 5, 92–95 (1982).

V. A. Komotskii, T. D. Black, “Analysis and application of stationary reference grating method for optical detection of surface acoustic waves,” J. Appl. Phys. 52, 129–136 (1981).
[CrossRef]

T. D. Black, V. A. Komotskii, “Infrared detection using acousto-optic interaction with thermally induced grating in optical waveguides,” Appl. Phys. Lett. 38, 113–115 (1981).
[CrossRef]

L. N. Deryugin, V. A. Komotskii, “Diffraction of an optical wave with spatial phase modulation by a periodic amplitude grating,” Opt. Spectrosc. (USSR) 46, 79–82 (1979).

Kwiek, P.

P. Kwiek, “Light diffraction by two spatially separated ultrasonic waves,” J. Acoust. Soc. Am. 86, 2261–2271 (1989).
[CrossRef]

Leroy, O.

O. Leroy, E. Blomme, “Amplitude modulation of diffracted light waves caused by adjacent ultrasonic beams of frequency ratio 1:n,” Ultrasonics 19, 173–178 (1981).
[CrossRef]

O. Leroy, “Diffraction of light by two adjacent parallel ultrasonic beams,” Acustica 29, 303–310 (1973).

Magnusson, R.

Maloney, W. T.

R. W. Damon, W. T. Maloney, D. H. McMahon, “Interaction of light with ultrasound: phenomena and applications,” in Physical Acoustics: Principles and Methods, W. P. Mason, R. N. Thurston, eds. (Academic, New York, 1970), Vol. VII, pp. 273–366.

McMahon, D. H.

R. W. Damon, W. T. Maloney, D. H. McMahon, “Interaction of light with ultrasound: phenomena and applications,” in Physical Acoustics: Principles and Methods, W. P. Mason, R. N. Thurston, eds. (Academic, New York, 1970), Vol. VII, pp. 273–366.

Mertens, R.

L. E. Hargrove, E. A. Hiedemann, R. Mertens, “Diffraction of light by two spatially separated parallel ultrasonic waves of different frequency,” Z. Phys. 167, 326–336 (1962).
[CrossRef]

Palma, A.

A. Alippi, A. Palma, L. Palmeri, G. Socino, “Incident angle and polarization dependence of light diffracted by acoustic surface waves,” J. Appl. Phys. 45, 1492–1497 (1974).
[CrossRef]

Palmeri, L.

A. Alippi, A. Palma, L. Palmeri, G. Socino, “Incident angle and polarization dependence of light diffracted by acoustic surface waves,” J. Appl. Phys. 45, 1492–1497 (1974).
[CrossRef]

Poon, T.-C.

T.-C. Poon, M. R. Chatterjee, P. P. Banerjee, “Multiple plane-wave analysis of acousto-optic diffraction by adjacent ultrasonic beams of frequency ratio 1:m,” J. Opt. Soc. Am. A 3, 1402–1406 (1986).
[CrossRef]

T.-C. Poon, P. P. Banerjee, M. R. Chatterjee, “Analysis of acousto-optic diffraction by adjacent ultrasonic beams using multiple plane-wave scattering techniques,” IEEE Trans. Sonics Ultrason. SU-32, 592–595 (1985).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 657–661.

Socino, G.

A. Alippi, A. Palma, L. Palmeri, G. Socino, “Incident angle and polarization dependence of light diffracted by acoustic surface waves,” J. Appl. Phys. 45, 1492–1497 (1974).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, “Optical probing of surface acoustic waves and surface wave devices,” IEEE Trans. Sonics Ultrason. SU-23, 33–63 (1976).
[CrossRef]

Acustica (1)

O. Leroy, “Diffraction of light by two adjacent parallel ultrasonic beams,” Acustica 29, 303–310 (1973).

Appl. Phys. Lett. (1)

T. D. Black, V. A. Komotskii, “Infrared detection using acousto-optic interaction with thermally induced grating in optical waveguides,” Appl. Phys. Lett. 38, 113–115 (1981).
[CrossRef]

Avtometriya (1)

A. F. Bessonov, L. N. Deryugin, V. A. Komotskii, “Measurement of phase distributions of a surface acoustic wave by the method of optical probing with reference gratings,” Avtometriya 5, 92–95 (1982).

IEEE Trans. Electron. Devices (1)

H. Engan, “Excitation of elastic surface waves by spatial harmonics of interdigital transducers,” IEEE Trans. Electron. Devices ED-16, 1014–1017 (1969).
[CrossRef]

IEEE Trans. Sonics Ultrason. (2)

G. I. Stegeman, “Optical probing of surface acoustic waves and surface wave devices,” IEEE Trans. Sonics Ultrason. SU-23, 33–63 (1976).
[CrossRef]

T.-C. Poon, P. P. Banerjee, M. R. Chatterjee, “Analysis of acousto-optic diffraction by adjacent ultrasonic beams using multiple plane-wave scattering techniques,” IEEE Trans. Sonics Ultrason. SU-32, 592–595 (1985).
[CrossRef]

J. Acoust. Soc. Am. (2)

F. Calligaris, P. Ciuti, I. Gabrielli, “Temporal light modulation in thick-screen diffraction by ultrasound beam plus amplitude grating,” J. Acoust. Soc. Am. 61, 959–964 (1977).
[CrossRef]

P. Kwiek, “Light diffraction by two spatially separated ultrasonic waves,” J. Acoust. Soc. Am. 86, 2261–2271 (1989).
[CrossRef]

J. Appl. Phys. (2)

A. Alippi, A. Palma, L. Palmeri, G. Socino, “Incident angle and polarization dependence of light diffracted by acoustic surface waves,” J. Appl. Phys. 45, 1492–1497 (1974).
[CrossRef]

V. A. Komotskii, T. D. Black, “Analysis and application of stationary reference grating method for optical detection of surface acoustic waves,” J. Appl. Phys. 52, 129–136 (1981).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Spectrosc. (USSR) (1)

L. N. Deryugin, V. A. Komotskii, “Diffraction of an optical wave with spatial phase modulation by a periodic amplitude grating,” Opt. Spectrosc. (USSR) 46, 79–82 (1979).

Ultrasonics (1)

O. Leroy, E. Blomme, “Amplitude modulation of diffracted light waves caused by adjacent ultrasonic beams of frequency ratio 1:n,” Ultrasonics 19, 173–178 (1981).
[CrossRef]

Z. Phys. (1)

L. E. Hargrove, E. A. Hiedemann, R. Mertens, “Diffraction of light by two spatially separated parallel ultrasonic waves of different frequency,” Z. Phys. 167, 326–336 (1962).
[CrossRef]

Other (3)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 657–661.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), pp. 53–54.

R. W. Damon, W. T. Maloney, D. H. McMahon, “Interaction of light with ultrasound: phenomena and applications,” in Physical Acoustics: Principles and Methods, W. P. Mason, R. N. Thurston, eds. (Academic, New York, 1970), Vol. VII, pp. 273–366.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Expanded view of the transmission proximity probing configuration is shown with b ≈ Λ.

Fig. 2
Fig. 2

Plot of the small-signal-conversion sensitivities for the three lowest diffraction orders determined by using the results of the spatial-frequency analysis. For the plots that are shown, L = 0 corresponding to L ˜ = n π, where n = 0, 1, 2, …, and b = Λ = 40.75 μm.

Fig. 3
Fig. 3

Experimental arrangement used for transmission proximity probing investigations.

Fig. 4
Fig. 4

Absolute value of the normalized detected intensity modulation versus proximity for a normally incident probing beam. The modulation frequency was approximately 87 MHz corresponding to a SAW wavelength of approximately 40 μm. The holographic reference grating had a measured period of approximately 41 μm. The solid curves were produced by using Eqs. (17), (18), and (19) assuming ϕM = 1.16 rad and b = Λ = 40.75 μm.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

A ( ξ ) = + a ( z ) exp ( i 2 π ξ z ) d z ,
A i n ( ξ ) = δ ( ξ ξ i n ) ,
A G ( ξ ) = k = k = + a k δ ( ξ k ξ 1 ) ,
a W ( z , t ) = exp [ i ϕ s sin ( 2 π ξ 1 z Ω t ) ] ,
A W ( ξ , t ) = n = n = + J n ( ϕ s ) δ ( ξ n ξ 1 ) exp ( i n Ω t ) ,
T ( ξ ) = exp ( i π ξ 2 λ L ) ,
S T = A W ( ξ , t ) * T ( ξ ) A G ( ξ ) * A i n ( ξ ) ,
S T = m = m = + A m δ ( ξ m ξ 1 ) ,
A m = n = n = + a m n J n ( ϕ s ) exp [ i ( m n ) 2 L ˜ ] × exp [ i ( m n ) r ] exp ( i n Ω t ) ,
L ˜ = π λ ξ 1 2 L = π λ L / Λ 2
r = 2 π λ L ξ 1 ξ i n = ( 2 π / Λ ) L sin ( θ )
G m = A m * A m = G m ( = ) + G m ( Ω ) + G m ( 2 Ω ) + ,
G 0 ( Ω ) = 2 ϕ s J 0 ( ϕ M ) J 1 ( ϕ M ) cos ( L ˜ ) cos ( Ω t r )
G ± 1 ( Ω ) = ϕ s J 1 ( ϕ M ) [ J 0 ( ϕ M ) cos ( Ω t r L ˜ ) J 2 ( ϕ M ) cos ( Ω t r 3 L ˜ ) ] .
G ± 1 ( Ω ) = ϕ s J 1 ( ϕ M ) [ J 0 2 ( ϕ M ) + J 2 2 ( ϕ M ) 2 J 0 ( ϕ M ) J 2 ( ϕ M ) cos ( 2 L ˜ ) ] 1 / 2 cos ( Ω t r L ˜ ϕ L ) ,
ϕ L = J 2 ( ϕ M ) sin ( 2 L ˜ ) / [ J 0 ( ϕ M ) J 2 ( ϕ M ) cos ( 2 L ˜ ) ] .
g 0 ( Ω ) = 2 ϕ s J 0 ( ϕ M ) J 1 ( ϕ M ) cos ( L ˜ ) ,
g ± 1 ( Ω ) = ϕ s J 1 ( ϕ M ) [ J 0 2 ( ϕ M ) + J 2 2 ( ϕ M ) 2 J 0 ( ϕ M ) J 2 ( ϕ M ) cos ( 2 L ˜ ) ] 1 / 2 .
q m ( Ω ) = | g m ( Ω ) | / ϕ s .

Metrics