Abstract

Quantitative control of partial coherence by ultrasonic waves is considered theoretically and experimentally. The double coherence modulation factor obtained is space-invariant or not according to whether a light beam passes twice the same path or a different path in a progressive ultrasonic field by reflection at a plane mirror or at a right-angle prism. A double-modulation scheme using a plane mirror reflection system is found to be more effective than a single-modulation scheme for coherence control of low levels of ultrasonic power. The coherence of light is quantitatively varied with the input voltage applied to the ultrasonic transducer.

© 1980 Optical Society of America

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References

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  1. See, for example, L. Mandel, E. Wolf, Eds., Coherence and Fluctuations of Light (Dover, New York, 1970), Vols. 1 and 2.
  2. H. Arsenault, S. Lowenthal, Opt. Commun. 1, 451 (1970).
    [Crossref]
  3. E. Schröder, Opt. Commun. 3, 68 (1971).
    [Crossref]
  4. F. Scudieri, M. Bertolotti, R. Bartolino, Appl. Opt. 13, 181 (1974).
    [Crossref] [PubMed]
  5. J. Braat, S. Lowenthal, J. Opt. Soc. Am. 63, 388 (1973).
    [Crossref]
  6. Y. Ohtsuka, Opt. Commun. 17, 243 (1976).
  7. See, for example, M. Berry, The Diffraction of Light by Ultrasound (Academic, New York, 1966).
  8. C. V. Raman, N. S. N. Nath, Proc. Indian Acad. Sci. Sect. A 2, 406, 413 (1935); C. V. Raman, N. S. N. Nath, Proc. Indian Acad. Sci. Sect. A 3, 75, 119 (1936).
  9. Y. Ohtsuka, Y. Imai, J. Opt. Soc. Am. 69, 684 (1979).
    [Crossref]
  10. W. R. Klein, B. D. Cook, IEEE Trans. Sonics Ultrason. SU-14, 123 (1967).
    [Crossref]
  11. Y. Imai, Y. Ohtsuka, Jpn. J. Opt. 8, 171 (1979).
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 505–508.

1979 (2)

Y. Ohtsuka, Y. Imai, J. Opt. Soc. Am. 69, 684 (1979).
[Crossref]

Y. Imai, Y. Ohtsuka, Jpn. J. Opt. 8, 171 (1979).

1976 (1)

Y. Ohtsuka, Opt. Commun. 17, 243 (1976).

1974 (1)

1973 (1)

1971 (1)

E. Schröder, Opt. Commun. 3, 68 (1971).
[Crossref]

1970 (1)

H. Arsenault, S. Lowenthal, Opt. Commun. 1, 451 (1970).
[Crossref]

1967 (1)

W. R. Klein, B. D. Cook, IEEE Trans. Sonics Ultrason. SU-14, 123 (1967).
[Crossref]

1935 (1)

C. V. Raman, N. S. N. Nath, Proc. Indian Acad. Sci. Sect. A 2, 406, 413 (1935); C. V. Raman, N. S. N. Nath, Proc. Indian Acad. Sci. Sect. A 3, 75, 119 (1936).

Arsenault, H.

H. Arsenault, S. Lowenthal, Opt. Commun. 1, 451 (1970).
[Crossref]

Bartolino, R.

Berry, M.

See, for example, M. Berry, The Diffraction of Light by Ultrasound (Academic, New York, 1966).

Bertolotti, M.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 505–508.

Braat, J.

Cook, B. D.

W. R. Klein, B. D. Cook, IEEE Trans. Sonics Ultrason. SU-14, 123 (1967).
[Crossref]

Imai, Y.

Y. Imai, Y. Ohtsuka, Jpn. J. Opt. 8, 171 (1979).

Y. Ohtsuka, Y. Imai, J. Opt. Soc. Am. 69, 684 (1979).
[Crossref]

Klein, W. R.

W. R. Klein, B. D. Cook, IEEE Trans. Sonics Ultrason. SU-14, 123 (1967).
[Crossref]

Lowenthal, S.

J. Braat, S. Lowenthal, J. Opt. Soc. Am. 63, 388 (1973).
[Crossref]

H. Arsenault, S. Lowenthal, Opt. Commun. 1, 451 (1970).
[Crossref]

Nath, N. S. N.

C. V. Raman, N. S. N. Nath, Proc. Indian Acad. Sci. Sect. A 2, 406, 413 (1935); C. V. Raman, N. S. N. Nath, Proc. Indian Acad. Sci. Sect. A 3, 75, 119 (1936).

Ohtsuka, Y.

Y. Ohtsuka, Y. Imai, J. Opt. Soc. Am. 69, 684 (1979).
[Crossref]

Y. Imai, Y. Ohtsuka, Jpn. J. Opt. 8, 171 (1979).

Y. Ohtsuka, Opt. Commun. 17, 243 (1976).

Raman, C. V.

C. V. Raman, N. S. N. Nath, Proc. Indian Acad. Sci. Sect. A 2, 406, 413 (1935); C. V. Raman, N. S. N. Nath, Proc. Indian Acad. Sci. Sect. A 3, 75, 119 (1936).

Schröder, E.

E. Schröder, Opt. Commun. 3, 68 (1971).
[Crossref]

Scudieri, F.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 505–508.

Appl. Opt. (1)

IEEE Trans. Sonics Ultrason. (1)

W. R. Klein, B. D. Cook, IEEE Trans. Sonics Ultrason. SU-14, 123 (1967).
[Crossref]

J. Opt. Soc. Am. (2)

Jpn. J. Opt. (1)

Y. Imai, Y. Ohtsuka, Jpn. J. Opt. 8, 171 (1979).

Opt. Commun. (3)

Y. Ohtsuka, Opt. Commun. 17, 243 (1976).

H. Arsenault, S. Lowenthal, Opt. Commun. 1, 451 (1970).
[Crossref]

E. Schröder, Opt. Commun. 3, 68 (1971).
[Crossref]

Proc. Indian Acad. Sci. Sect. A (1)

C. V. Raman, N. S. N. Nath, Proc. Indian Acad. Sci. Sect. A 2, 406, 413 (1935); C. V. Raman, N. S. N. Nath, Proc. Indian Acad. Sci. Sect. A 3, 75, 119 (1936).

Other (3)

See, for example, L. Mandel, E. Wolf, Eds., Coherence and Fluctuations of Light (Dover, New York, 1970), Vols. 1 and 2.

See, for example, M. Berry, The Diffraction of Light by Ultrasound (Academic, New York, 1966).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 505–508.

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of double modulation. Normally incident light is reflected by a plane mirror and then reenters the ultrasonic column. The doubly modulated light is correlated in wave front.

Fig. 2
Fig. 2

Schematic representation for the oblique incidence of light. Single and double modulations are shown in (a) and (b).

Fig. 3
Fig. 3

Two curves denoted by ● and ○ are of single and double modulations, respectively. These curves are obtained with the conditions h = 0, L = 1 cm, and λ = 0.015 cm.

Fig. 4
Fig. 4

Double modulation by a right-angle prism.

Fig. 5
Fig. 5

Experimental arrangement for measurement of the degree of coherence using doubly modulated laser light. The ultrasonic transducer is driven at a frequency of 10.0 MHz in pure water.

Fig. 6
Fig. 6

Some Young’s interference fringes and their intensity distributions observed across the detection plane. Picture (a) is taken in the absence of the ultrasonic wave, whereas (b) and (c) represent the pictures taken under single and double modulations with the same condition of v = 0.67.

Fig. 7
Fig. 7

Degree of coherence obtained from single- (●) and double-modulated (○) laser light. Solid lines denote the theoretical curves. The upper and lower figures are plotted with v = 0.45 and v = 0.62, respectively.

Equations (25)

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μ ( x , t ) = μ 0 - Δ μ sin ( Ω t - K x ) ,
V ( x , t ) = V 0 ( x , t ) exp [ - i k L μ ( x , t ) ] ,
V ( x , t ) = V 0 ( x , t ) exp [ - 2 i k [ h + L μ ( x , t ) ] }
exp [ i ( m - n ) t ] = { 1 for m = n 0 for m n ,
exp ( i v sin θ ) = m = - J m ( v ) exp ( i m θ ) ,
m = - J m 2 ( v ) exp ( i m θ ) = J 0 [ 2 v sin ( θ / 2 ) ] ,
Γ ( x 1 , x 2 ; t 1 , t 2 ) = V ( x 1 , t 1 ) V * ( x 2 , t 2 ) = V 0 ( x 1 , t 1 ) V 0 * ( x 2 , t 2 ) m = - m = - J m ( 2 v ) J n ( 2 v ) × exp i [ ( m t 1 - n t 2 ) Ω ] exp [ i k ( n x 2 - m x 1 ) ] = Γ 0 ( x 1 , x 2 ; t 1 , t 2 ) J 0 [ 4 v sin ( ½ ) ( Ω τ - K Δ x ) ] ,
γ 12 ( 0 ) = γ 12 ( 0 ) J 0 [ 4 v sin ( K Δ x / 2 ) ] ,
γ 12 ( 0 ) = γ 12 ( 0 ) J 0 [ 2 v sin ( K Δ x / 2 ) ] .
0 L sec ϕ μ ( s , t ) d s = μ 0 L sec ϕ + 2 Δ μ K sin ϕ sin ( K L tan ϕ 2 ) × sin [ ( Ω t - K x ) + K L tan ϕ 2 ] .
V ( x , t ) = V 0 ( x , t ) exp { i k ( 2 Δ μ K sin ϕ ) sin ( K L tan ϕ 2 ) × sin [ ( Ω t - K x ) + K L tan ϕ 2 ] } .
γ 12 ( 0 ) = γ 12 ( 0 ) J 0 [ 2 v sin ( K Δ x / 2 ) ] ,
v = v | 1 cos ϕ sinc ( K L tan ϕ 2 ) | ,
V ( x , t ) = V 0 ( x , t ) exp [ - i k Δ μ 0 L sec ϕ ( - sin [ Ω t - K ( x - s sin ϕ ) ] - sin { Ω t - K [ x - ( L + 2 h ) tan ϕ - s sin ϕ ] } ) d s ] = V 0 ( x , t ) exp { i k ( 4 Δ μ K sin ϕ ) sin ( K L tan ϕ 2 ) × sin [ Ω t - K x + 2 K ( L + h ) tan ϕ ] × cos [ 2 K ( L + 2 h ) tan ϕ ] } .
γ 12 ( 0 ) = γ 12 ( 0 ) J 0 [ 4 v | sin ( K Δ x / 2 ) | ] ,
v = v | 1 cos ϕ sinc ( K L tan ϕ 2 ) cos [ K ( L + 2 h ) tan ϕ 2 ] | .
V ( x 1 , t 1 ) = V 0 ( x 1 + x 0 , t 1 ) exp ( i k L Δ μ { sin [ Ω t 1 - K [ ( x 1 + x 0 ) ] + sin ( Ω t 1 + K x 1 ) } )             at P 1 ,
V ( x 1 - Δ x , t 2 ) = V 0 ( x 1 + x 0 + Δ x , t 2 ) exp ( i k L Δ μ { sin [ Ω t 2 - K ( x 1 + x 0 + Δ x ) ] } + sin ( Ω t 2 + K ( x 1 - Δ x ) ] )             at P 2 .
Γ ( x 1 , x 1 - Δ x ; t 1 , t 2 ) = Γ 0 ( x 1 + x 0 , x 1 + x 0 + Δ x ; t 1 , t 2 ) × J 0 { 4 v | sin ( Ω τ + K Δ x 2 ) cos [ K ( 2 x 0 + x 0 ) 2 ] | } .
γ ( x 1 , x 1 - Δ x ) = γ 0 ( x 1 + x 0 , x 1 + x 0 + Δ x ) × J 0 { 4 v | sin ( K Δ x / 2 ) cos [ K ( 2 x 1 + x 0 ) 2 ] | } .
γ 12 ( 0 ) = ( I max - I min I max + I min ) [ I 1 + I 2 2 ( I 1 I 2 ) 1 / 2 ] ,
Γ ( x 1 , x 1 - Δ x ; t 1 , t 2 ) = Γ 0 ( x 1 + x 0 , x 1 + x 0 + Δ x ; t 1 , t 2 ) m = - n = - p = - q = - × J m ( v ) J n ( v ) J p ( v ) J q ( v ) × exp [ i Ω t ( m + n - p - q ) ] × exp { i [ Ω τ ( p + q ) - K x 0 ( m - p ) + K Δ x ( p + q ) - K x 1 ( m - n - p + q ) ] } ,
Γ ( x 1 , x 1 - Δ x ; t 1 , t 2 ) = Γ 0 ( x 1 + x 0 , x 1 + x 0 + Δ x ; t 1 , t 2 ) × r + p = - r + q = - p = - q = - J r + p ( v ) J r + q ( v ) × J p ( v ) J q ( v ) exp { i [ Ω τ ( p + q ) - K x 0 r + K Δ x ( p + q ) - 2 K x 1 r ] } .
m = - J m + n ( Z ) J n ( z ) exp ( i m θ ) = J n ( W ) [ Z - z exp ( - i θ ) Z - z exp ( i θ ) ] n / 2 ,
Γ ( x 1 , x 1 - Δ x ; t 1 , t 2 ) = Γ 0 ( x 1 + x 0 , x 1 + x 0 + Δ x ; t 1 , t 2 ) × r = - J r 2 ( 2 v | sin Ω t + K Δ x 2 | ) exp { i r [ π - K ( 2 x 1 + x 0 ) ] } .

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