Abstract

The effects of thermal turbulence on the phase fluctuations of a laser beam are investigated in laboratory. The turbulent region created by means of a horizontal heated Nichrome grid is made to shift upwards owing to the convective motion. A Mach-Zehnder interference experiment is performed in which two beams from a laser source are superimposed after crossing the turbulent region. The displacements of the fringe pattern allow one to study the temporal decay of the mean square refractive index fluctuation. An interpretation of the results is given on the basis of the theory of an isotropic turbulent scalar field.

© 1969 Optical Society of America

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References

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  1. See, for example, P. Burlamacchi, A. Consortini, L. Ronchi, Appl. Opt. 6, 1273 (1967).
    [CrossRef] [PubMed]
  2. M. Bertolotti, M. Carnevale, L. Muzii, D. Sette, Appl. Opt. 7, 2246 (1968).
    [CrossRef] [PubMed]
  3. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, Inc., New York, 1961).
  4. H. Hodara, Proc. IEEE 54, 368 (1966).
    [CrossRef]
  5. M. Carnevale, B. Crosignani, P. Di Porto, Appl. Opt. 7, 1121 (1968).
    [CrossRef] [PubMed]
  6. A. J. Chapman, Heat Transfer (The Macmillan Company, New York, 1960), p. 266.
  7. P. Burlamacchi, A. Consortini, L. Ronchi, G. Toraldo di Francia, URSI Symposium on Electromagnetic Waves, Stresa, Italy, 1968.

1968

1967

1966

H. Hodara, Proc. IEEE 54, 368 (1966).
[CrossRef]

Bertolotti, M.

Burlamacchi, P.

See, for example, P. Burlamacchi, A. Consortini, L. Ronchi, Appl. Opt. 6, 1273 (1967).
[CrossRef] [PubMed]

P. Burlamacchi, A. Consortini, L. Ronchi, G. Toraldo di Francia, URSI Symposium on Electromagnetic Waves, Stresa, Italy, 1968.

Carnevale, M.

Chapman, A. J.

A. J. Chapman, Heat Transfer (The Macmillan Company, New York, 1960), p. 266.

Consortini, A.

See, for example, P. Burlamacchi, A. Consortini, L. Ronchi, Appl. Opt. 6, 1273 (1967).
[CrossRef] [PubMed]

P. Burlamacchi, A. Consortini, L. Ronchi, G. Toraldo di Francia, URSI Symposium on Electromagnetic Waves, Stresa, Italy, 1968.

Crosignani, B.

Di Porto, P.

Hodara, H.

H. Hodara, Proc. IEEE 54, 368 (1966).
[CrossRef]

Muzii, L.

Ronchi, L.

See, for example, P. Burlamacchi, A. Consortini, L. Ronchi, Appl. Opt. 6, 1273 (1967).
[CrossRef] [PubMed]

P. Burlamacchi, A. Consortini, L. Ronchi, G. Toraldo di Francia, URSI Symposium on Electromagnetic Waves, Stresa, Italy, 1968.

Sette, D.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, Inc., New York, 1961).

Toraldo di Francia, G.

P. Burlamacchi, A. Consortini, L. Ronchi, G. Toraldo di Francia, URSI Symposium on Electromagnetic Waves, Stresa, Italy, 1968.

Appl. Opt.

Proc. IEEE

H. Hodara, Proc. IEEE 54, 368 (1966).
[CrossRef]

Other

A. J. Chapman, Heat Transfer (The Macmillan Company, New York, 1960), p. 266.

P. Burlamacchi, A. Consortini, L. Ronchi, G. Toraldo di Francia, URSI Symposium on Electromagnetic Waves, Stresa, Italy, 1968.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill Book Company, Inc., New York, 1961).

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Figures (9)

Fig. 1
Fig. 1

Schematic geometry of the problem.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

Theoretical behavior and experimental values of 〈(Δϕ)2〉 vs the grid distance xT ∼ 1.7°C, l ∼ 20 cm).

Fig. 4
Fig. 4

Theoretical behavior and experimental values of 〈(Δϕ)2〉 vs the grid distance xT ∼ 3°C, l ∼ 70 cm).

Fig. 5
Fig. 5

Theoretical behavior and experimental values of 〈(Δϕ)2〉 vs the grid distance xT ∼6°C, l ∼100 cm).

Fig. 6
Fig. 6

Theoretical behavior and experimental values of 〈(Δϕ)2〉 vs the grid distance xT ∼9°C, l ∼150 cm).

Fig. 7
Fig. 7

Expermental geometry for testing the behavior of 〈(Δϕ)2〉 with the beam separation.

Fig. 8
Fig. 8

Theoretical behavior and experimental values of 〈(Δϕ)2〉 vs the beam separation dT ∼1.7°C, x ∼100 cm).

Fig. 9
Fig. 9

Theoretical behaviors and experimental values of 〈(Δϕ)2〉 vs the beam separation dT ∼6°C, x ∼160 cm).

Equations (5)

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( Δ ϕ ) 2 = D t ( 8 χ t ) 1 2 [ 1 exp ( d 2 8 χ t ) ] { L ( 8 χ t ) 1 2 erf [ L ( 8 χ t ) 1 2 ] + 1 π 1 2 exp ( L 2 ( 8 χ t ) ) 1 π 1 2 } ,
erf ( z ) = 2 π 1 2 0 z exp ( x 2 ) d x ,
( 1 / 2 ) ( d / dx ) υ 2 ( x ) = g β [ T ( x ) T f ] ,
υ ( x ) υ 2 1 2 = [ 1 x 0 x υ 2 ( x ) d x ] 1 2 = ( 2 g β Δ T ) 1 2 × { 1 l x [ 1 exp ( x l ) ] } 1 2 .
( Δ ϕ ) 2 = ( D L / t ) [ 1 exp ( d 2 / 8 χ t ) ] .

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