Abstract

We present experimental studies of the interaction between a narrow Gaussian laser beam and a standing cylindrical ultrasonic wave. As a theoretical approach, a Fourier-optics-based successive diffraction model is used. Depending on the ratio of the Gaussian laser beam diameter to the first nodal diameter of the cylindrical ultrasound, light refraction or diffraction is observed. We experimentally investigate the time-averaged light intensity as well as the modulation of light in the far field of light refraction–diffraction by a cylindrical ultrasound. It is revealed that significant focusing appears if the phase front of the incident light is curved. The focusing effects of the acousto-optic system depend on the width of the laser beam and curvature of the phase front. Finally, possible applications are discussed.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  6. A. S. Zadorin, Dynamics of Acousto-Optic Interaction (Tomsk State University, 2004).
  7. L. E. Hargrove, "Diffraction of a Gaussian light beam by ultrasonic cylindrical standing waves," J. Acoust. Soc. Am. 51, 888-893 (1972).
    [CrossRef]
  8. I. Grulkowski and P. Kwiek, "Interaction of light with cylindrical ultrasonic wave," Arch. Acoust. 30, 107-114 (2005).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. L. E. Hargrove, "Optical effects of ultrasonic waves producing phase and amplitude modulation," J. Acoust. Soc. Am. 34, 1547-1552 (1962).
    [CrossRef]
  17. O. Nomoto and Y. Torikai, "Intensity distribution of the ultrasonic light-diffraction spectrum: calculation by the method of successive diffraction," Acustica 24, 284-296 (1971).
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  19. P. P. Banerjee and C.-W. Tarn, "A Fourier transform approach to acousto-optic interactions in the presence of propagational diffraction," Acustica 74, 181-191 (1991).
  20. Ch. Koch and R. Reibold, "Fourier-optical technique for the investigation of ultrasound light diffraction," Acust. Acta Acust. 82, S74 (1996).
  21. I. Grulkowski and P. Kwiek are preparing a manuscript to be called "Successive diffraction model based on Fourier optics as a tool for the studies of light interaction with arbitrary ultrasonic field."
  22. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  23. R. Reibold and P. Kwiek, "Optical near-field investigation into the Raman-Nath and KML regimes of diffraction by ultrasonic waves," Acustica 70, 223-229 (1990).
  24. I. Grulkowski, D. Jankowski, and P. Kwiek are preparing a manuscript to be called, "Interaction of light with standing cylindrical ultrasonic wave in air," based on the invited lecture at the International Congress on Ultrasonics 2007 in Vienna, Austria.

2007 (1)

2006 (3)

S. Zeng, X. Lv, C. Zhan, W. R. Chen, W. Xiong, S. L. Jacques, and Q. Luo, "Simultaneous compensation for spatial and temporal dispersion of acousto-optical deflectors for two-dimensional scanning with a single prism," Opt. Lett. 31, 1091-1093 (2006).
[CrossRef] [PubMed]

I. Grulkowski and P. Kwiek, "Experimental study of light diffraction by standing ultrasonic wave with cylindrical symmetry," Opt. Commun. 267, 14-19 (2006).
[CrossRef]

K. Ferria, I. Grulkowski, and P. Kwiek, "Acousto-optic lens based on interaction of narrow laser beam with cylindrical ultrasound," J. Phys. IV 137, 67-72 (2006).
[CrossRef]

2005 (1)

I. Grulkowski and P. Kwiek, "Interaction of light with cylindrical ultrasonic wave," Arch. Acoust. 30, 107-114 (2005).

2003 (1)

2001 (1)

F. W. Windels and O. Leroy, "The acousto-optical interaction of narrow laser beams under Raman-Nath conditions," J. Opt. A , Pure Appl. Opt. 3, S1-S6 (2001).
[CrossRef]

1997 (1)

1996 (1)

Ch. Koch and R. Reibold, "Fourier-optical technique for the investigation of ultrasound light diffraction," Acust. Acta Acust. 82, S74 (1996).

1992 (1)

J. Huang, J. A. Nissen, and E. Bodegom, "Diffraction of light by a focused ultrasonic wave," J. Appl. Phys. 71, 70-75 (1992).
[CrossRef]

1991 (1)

P. P. Banerjee and C.-W. Tarn, "A Fourier transform approach to acousto-optic interactions in the presence of propagational diffraction," Acustica 74, 181-191 (1991).

1990 (2)

R. Reibold and P. Kwiek, "Optical near-field investigation into the Raman-Nath and KML regimes of diffraction by ultrasonic waves," Acustica 70, 223-229 (1990).

M. R. Chatterjee, T.-C. Poon, and D. N. Sitter, Jr., "Transfer function formalism for strong acousto-optic Bragg diffraction of light beams with arbitrary profiles," Acustica 71, 81-92 (1990).

1985 (1)

1972 (1)

L. E. Hargrove, "Diffraction of a Gaussian light beam by ultrasonic cylindrical standing waves," J. Acoust. Soc. Am. 51, 888-893 (1972).
[CrossRef]

1971 (1)

O. Nomoto and Y. Torikai, "Intensity distribution of the ultrasonic light-diffraction spectrum: calculation by the method of successive diffraction," Acustica 24, 284-296 (1971).

1966 (1)

1962 (1)

L. E. Hargrove, "Optical effects of ultrasonic waves producing phase and amplitude modulation," J. Acoust. Soc. Am. 34, 1547-1552 (1962).
[CrossRef]

1937 (1)

P. H. Van Cittert, "Zur Theorie der Lichtbeugung an Ultraschallwellen," Physica (Amsterdam) 4, 590-594 (1937).
[CrossRef]

Acust. Acta Acust. (1)

Ch. Koch and R. Reibold, "Fourier-optical technique for the investigation of ultrasound light diffraction," Acust. Acta Acust. 82, S74 (1996).

Acustica (4)

O. Nomoto and Y. Torikai, "Intensity distribution of the ultrasonic light-diffraction spectrum: calculation by the method of successive diffraction," Acustica 24, 284-296 (1971).

M. R. Chatterjee, T.-C. Poon, and D. N. Sitter, Jr., "Transfer function formalism for strong acousto-optic Bragg diffraction of light beams with arbitrary profiles," Acustica 71, 81-92 (1990).

P. P. Banerjee and C.-W. Tarn, "A Fourier transform approach to acousto-optic interactions in the presence of propagational diffraction," Acustica 74, 181-191 (1991).

R. Reibold and P. Kwiek, "Optical near-field investigation into the Raman-Nath and KML regimes of diffraction by ultrasonic waves," Acustica 70, 223-229 (1990).

Appl. Opt. (3)

Arch. Acoust. (1)

I. Grulkowski and P. Kwiek, "Interaction of light with cylindrical ultrasonic wave," Arch. Acoust. 30, 107-114 (2005).

J. Acoust. Soc. Am. (2)

L. E. Hargrove, "Optical effects of ultrasonic waves producing phase and amplitude modulation," J. Acoust. Soc. Am. 34, 1547-1552 (1962).
[CrossRef]

L. E. Hargrove, "Diffraction of a Gaussian light beam by ultrasonic cylindrical standing waves," J. Acoust. Soc. Am. 51, 888-893 (1972).
[CrossRef]

J. Appl. Phys. (1)

J. Huang, J. A. Nissen, and E. Bodegom, "Diffraction of light by a focused ultrasonic wave," J. Appl. Phys. 71, 70-75 (1992).
[CrossRef]

J. Opt. A (1)

F. W. Windels and O. Leroy, "The acousto-optical interaction of narrow laser beams under Raman-Nath conditions," J. Opt. A , Pure Appl. Opt. 3, S1-S6 (2001).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. IV (1)

K. Ferria, I. Grulkowski, and P. Kwiek, "Acousto-optic lens based on interaction of narrow laser beam with cylindrical ultrasound," J. Phys. IV 137, 67-72 (2006).
[CrossRef]

Opt. Commun. (1)

I. Grulkowski and P. Kwiek, "Experimental study of light diffraction by standing ultrasonic wave with cylindrical symmetry," Opt. Commun. 267, 14-19 (2006).
[CrossRef]

Opt. Lett. (2)

Physica (1)

P. H. Van Cittert, "Zur Theorie der Lichtbeugung an Ultraschallwellen," Physica (Amsterdam) 4, 590-594 (1937).
[CrossRef]

Other (5)

E. Skudrzyk, The Foundations of Acoustics (Springer-Verlag, 1971).

A. S. Zadorin, Dynamics of Acousto-Optic Interaction (Tomsk State University, 2004).

I. Grulkowski, D. Jankowski, and P. Kwiek are preparing a manuscript to be called, "Interaction of light with standing cylindrical ultrasonic wave in air," based on the invited lecture at the International Congress on Ultrasonics 2007 in Vienna, Austria.

I. Grulkowski and P. Kwiek are preparing a manuscript to be called "Successive diffraction model based on Fourier optics as a tool for the studies of light interaction with arbitrary ultrasonic field."

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

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Figures (8)

Fig. 1
Fig. 1

Acousto-optic geometry.

Fig. 2
Fig. 2

FO formalism in the frame of a successive diffraction model.

Fig. 3
Fig. 3

Experimental setup.

Fig. 4
Fig. 4

(Color online) Far-field patterns of light interaction with cylindrical ultrasound: (a) laser spot (no ultrasound), (b) refraction of Gaussian laser beam ( F = 484   kHz ) , (c) diffraction of Gaussian laser beam ( F = 1318   kHz ) , (d) diffraction of wide plane light beam ( F = 1318   kHz ) .

Fig. 5
Fig. 5

Time-averaged normalized light intensity I / I 0 versus Raman–Nath parameter ν for (a) fundamental ultrasonic frequency and (b) the third harmonic ultrasound. Curves, numerical results; dots, experiment.

Fig. 6
Fig. 6

Modulation of light intensity in the center of the far-field refraction pattern ( F = 484   kHz ) . Curves, numerical results; dots, experiment.

Fig. 7
Fig. 7

Modulation of light intensity in the center of the far-field diffraction pattern ( F = 1318   kHz ) . Curves, numerical results; dots, experiment.

Fig. 8
Fig. 8

Numerical simulations of light modulation in the center of the refraction pattern for (a) various radii of curvature of incident light wavefronts ( w = 1.09   mm = const ) and (b) for various widths of the light beam ( s = 6.015   m = const ) .

Equations (8)

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E ( r , z ) = w 0 w  exp [ r 2 w 2 ] exp [ i k ( z + r 2 2 s ) i ϕ ] ,
w ( z ) = w 0 1 + ( λ z π w 0 2 ) 2 , s ( z ) = z [ 1 + ( π w 0 2 λ z ) 2 ] ,
Δ p ( r , t ) = p 1 J 0 ( K r ) cos ( Ω t ) ,
n ( r , t ) = n 0 + n 1 ( r , t ) = n 0 + n 1 J 0 ( K r ) cos ( Ω t ) ,
U ˜ ( f x , f y , j Δ z ) = U ˜ i n ( f x , f y , ( j 1 ) Δ z ) H ( f x , f y ) ,
H ( f x , f y ) = { exp [ i 2 π Δ z ( n 0 / λ ) 2 f x 2 f y 2 ] for   ( n 0 / λ ) 2 f x 2 f y 2 0 exp [ 2 π Δ z f x 2 + f y 2 ( n 0 / λ ) 2 ] for   ( n 0 / λ ) 2 f x 2 f y 2 < 0 .
u o u t ( x , y , j Δ z ) = u ( x , y , j Δ z ) t ( x , y ) ,
t ( x , y ) = exp [ i k n 1 ( x , y ) Δ z ] .

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