Abstract

Propagating acoustic waves typically produce small effective refractive-index variations and can thus be difficult to detect by simple optical probing. It has been shown that use of stationary reference gratings can greatly facilitate the detection of these waves. In this paper, the application of thick (Bragg diffraction regime) and thin (Raman–Nath diffraction regime) sinusoidal-phase reference gratings is considered for enhanced detection of acoustic waves, and their relative performance is compared. Simple, analytical expressions are obtained that describe the diffraction characteristics in each case. It is shown that thick reference gratings produce a purely sinusoidal temporal-intensity modulation, whereas thin gratings, in general, produce nonsinusoidal modulation.

© 1987 Optical Society of America

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References

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  1. G. I. Stegeman, “Optical probing of surface waves and surface wave devices,”IEEE Trans. Sonics Ultrason. SU-23, 33–63 (1976).
    [CrossRef]
  2. 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]
  3. 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]
  4. L. M. 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. 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]
  7. R. Magnusson, T. K. Gaylord, “Diffraction regimes of transmission gratings,”J. Opt. Soc. Am. 68, 809–814 (1978).
    [CrossRef]
  8. M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
    [CrossRef]
  9. M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Raman–Nath regime diffraction by phase gratings,” Opt. Commun. 32, 19–23 (1980).
    [CrossRef]
  10. R. Magnusson, T. K. Gaylord, “Diffraction efficiencies of thin phase gratings with arbitrary grating shape,”J. Opt. Soc. Am. 68, 806–809 (1978).
    [CrossRef]
  11. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

1981 (2)

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]

1980 (2)

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Raman–Nath regime diffraction by phase gratings,” Opt. Commun. 32, 19–23 (1980).
[CrossRef]

1979 (1)

L. M. 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 (2)

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 waves and surface wave devices,”IEEE Trans. Sonics Ultrason. SU-23, 33–63 (1976).
[CrossRef]

1973 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Black, T. D.

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]

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]

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]

Deryugin, L. M.

L. M. 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).

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.

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Raman–Nath regime diffraction by phase gratings,” Opt. Commun. 32, 19–23 (1980).
[CrossRef]

R. Magnusson, T. K. Gaylord, “Diffraction regimes of transmission gratings,”J. Opt. Soc. Am. 68, 809–814 (1978).
[CrossRef]

R. Magnusson, T. K. Gaylord, “Diffraction efficiencies of thin phase gratings with arbitrary grating shape,”J. Opt. Soc. Am. 68, 806–809 (1978).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Komotskii, V. A.

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. M. 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).

Magnusson, R.

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Raman–Nath regime diffraction by phase gratings,” Opt. Commun. 32, 19–23 (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
[CrossRef]

R. Magnusson, T. K. Gaylord, “Diffraction regimes of transmission gratings,”J. Opt. Soc. Am. 68, 809–814 (1978).
[CrossRef]

R. Magnusson, T. K. Gaylord, “Diffraction efficiencies of thin phase gratings with arbitrary grating shape,”J. Opt. Soc. Am. 68, 806–809 (1978).
[CrossRef]

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Raman–Nath regime diffraction by phase gratings,” Opt. Commun. 32, 19–23 (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
[CrossRef]

Stegeman, G. I.

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

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]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

IEEE Trans. Sonics Ultrason. (1)

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

J. Acoust. Soc. Am. (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]

J. Appl. Phys. (1)

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. (3)

Opt. Commun. (2)

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg regime diffraction by phase gratings,” Opt. Commun. 32, 14–18 (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Raman–Nath regime diffraction by phase gratings,” Opt. Commun. 32, 19–23 (1980).
[CrossRef]

Opt. Spectrosc. (USSR) (1)

L. M. 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).

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Figures (3)

Fig. 1
Fig. 1

Model for plane-wave diffraction by (a) thin acoustic grating and (b) superimposed thin acoustic grating and a stationary reference grating.

Fig. 2
Fig. 2

Model for plane-wave diffraction by a thick grating.

Fig. 3
Fig. 3

Example configurations for enhanced detection of acoustic waves using a thick stationary reference grating: (a) oblique incidence of probing beam and (b) normal incidence of probing beam.

Equations (19)

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Δ n s ( x , t ) = n s sin ( K x - Ω t ) ,
τ s ( x , t ) = exp ( - j 2 π d Δ n s / λ cos θ ) ,
S i = S i ( t ) = L - 1 0 L exp [ - j 2 π d n s sin ( K x - Ω t ) / λ cos θ ] × exp ( - j i K x ) d x ,
S i = ( - 1 ) i exp ( - j i Ω t ) J i ( ϕ s ) ,
I ( x , t ) = R 2 + J i 2 ( ϕ s ) + 2 ( - 1 ) i R J i ( ϕ s ) cos ( K x + i Ω t ) ,
τ s r ( x , t ) = exp [ - j ϕ s sin ( K x - Ω t ) - j ϕ r sin ( K x ) ] ,
C i = L - 1 0 L exp [ - j ϕ s sin ( K x - Ω t ) - j ϕ r sin ( K x ) ] × exp ( - j i K x ) d x ,
C i = ( - 1 ) i exp ( - j i β ) J i { [ ϕ s 2 + 2 ϕ s ϕ r cos ( Ω t ) + ϕ r 2 ] 1 / 2 } ,
η i = J i 2 { [ ϕ s 2 + 2 ϕ s ϕ r cos ( Ω t ) + ϕ r 2 ] 1 / 2 } ,
η i J i 2 [ ϕ r + ϕ s cos ( Ω t ) ] = { l = - J i - l ( ϕ r ) J l [ ϕ s cos ( Ω t ) ] } 2 ,
η 0 J 0 2 ( ϕ r ) - 2 J 0 ( ϕ r ) J 1 ( ϕ r ) ϕ s cos ( Ω t ) ,
cos θ d T d z = - j κ U , cos θ d U d z = - j κ T ,
T ( 0 ) = T 0 exp ( - j ϕ T ) , U ( 0 ) = U 0 exp ( - j ϕ U ) .
T ( D ) = - j U 0 exp ( - j ϕ U ) sin γ + T 0 exp ( - j ϕ T ) cos γ ,
I T = U 0 2 sin 2 γ + T 0 2 cos 2 γ - U 0 T 0 sin ( 2 γ ) sin ( ϕ U - ϕ T ) .
I T ( t ) = J 1 2 ( ϕ s ) sin 2 γ + J 0 2 ( ϕ s ) cos 2 γ + J 1 ( ϕ s ) J 0 ( ϕ s ) sin ( 2 γ ) sin ( Ω t ) .
I T ( t ) = cos 2 γ + ( ϕ s / 2 ) sin ( 2 γ ) sin ( Ω t ) ,
q i ( Ω ) = g i ( Ω ) / ϕ s ,
η i = η r i + η r i ϕ s cos ( Ω t ) + η r i ϕ s 2 cos 2 ( Ω t ) / 2 + ,

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