Abstract

We present a study of the interference of light produced by a pair of mutually correlated Gaussian Schell-model sources. The spatial distributions of the fields produced by these sources are symmetric with respect to a plane through their common center and differ by a phase factor exp(iϕ). When ϕ=0, the resulting radiation is a beam with an intensity distribution that displays a narrow bright line at its center. When the sources can be regarded as Collett–Wolf sources, the resulting bright line diverges much more slowly than the beam itself. When ϕ=π the radiated beam has an intensity distribution with a narrow dark line at its center. The theoretical results are supported by experimental results obtained by use of a modified Michelson interferometer and suggest that the interference of a pair of correlated Collett–Wolf beams can be used to produce a pseudo-nondiffracting beam.

© 2005 Optical Society of America

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References

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  1. A. C. Schell, “The multiple plate antenna,” Ph.D. dissertation (Massachusetts Institute of Technology, 1961), Sec. 7.5.
  2. E. Collett and E. Wolf, Opt. Lett. 2, 27 (1978).
    [CrossRef]
  3. E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
    [CrossRef]
  4. P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
    [CrossRef]
  5. J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1978).
    [CrossRef]
  6. F. Gori, M. Santarsiero, and A. Sona, Opt. Commun. 82, 197 (1991).
    [CrossRef]
  7. F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 68, 239 (1988).
    [CrossRef]

1991

F. Gori, M. Santarsiero, and A. Sona, Opt. Commun. 82, 197 (1991).
[CrossRef]

1988

F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 68, 239 (1988).
[CrossRef]

1979

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

1978

J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1978).
[CrossRef]

E. Collett and E. Wolf, Opt. Lett. 2, 27 (1978).
[CrossRef]

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[CrossRef]

Collett, E.

E. Collett and E. Wolf, Opt. Lett. 2, 27 (1978).
[CrossRef]

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[CrossRef]

De Santis, P.

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Foley, J. T.

J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1978).
[CrossRef]

Gori, F.

F. Gori, M. Santarsiero, and A. Sona, Opt. Commun. 82, 197 (1991).
[CrossRef]

F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 68, 239 (1988).
[CrossRef]

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 68, 239 (1988).
[CrossRef]

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 68, 239 (1988).
[CrossRef]

Palma, C.

F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 68, 239 (1988).
[CrossRef]

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

Santarsiero, M.

F. Gori, M. Santarsiero, and A. Sona, Opt. Commun. 82, 197 (1991).
[CrossRef]

Schell, A. C.

A. C. Schell, “The multiple plate antenna,” Ph.D. dissertation (Massachusetts Institute of Technology, 1961), Sec. 7.5.

Sona, A.

F. Gori, M. Santarsiero, and A. Sona, Opt. Commun. 82, 197 (1991).
[CrossRef]

Wolf, E.

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[CrossRef]

E. Collett and E. Wolf, Opt. Lett. 2, 27 (1978).
[CrossRef]

Zubairy, M. S.

J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1978).
[CrossRef]

Opt. Commun.

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[CrossRef]

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[CrossRef]

J. T. Foley and M. S. Zubairy, Opt. Commun. 26, 297 (1978).
[CrossRef]

F. Gori, M. Santarsiero, and A. Sona, Opt. Commun. 82, 197 (1991).
[CrossRef]

F. Gori, G. Guattari, C. Palma, and C. Padovani, Opt. Commun. 68, 239 (1988).
[CrossRef]

Opt. Lett.

Other

A. C. Schell, “The multiple plate antenna,” Ph.D. dissertation (Massachusetts Institute of Technology, 1961), Sec. 7.5.

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Figures (2)

Fig. 1
Fig. 1

Theoretical gray-level plot of the cross section of the normalized intensity of the symmetric beams with (a) ϕ = 0 and (b) ϕ = π . The distance from the source plane is x 3 = 1 m , σ s = 2.432 mm , σ g = 179.6 μ m , and λ = 632.8 nm .

Fig. 2
Fig. 2

Experimental gray-level images of the normalized intensity of the symmetric beams for (a) constructive interference and (b) destructive interference. The horizontal lines in the images show the positions where the intensity scans in the lower graphs were taken.

Equations (13)

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W ( 0 ) ( ρ 1 , ρ 2 ω ) = U ( ρ 1 , 0 ω ) U * ( ρ 2 , 0 ω ) = [ S ( 0 ) ( ρ 1 ω ) ] 1 2 g ( 0 ) ( ρ 1 ρ 2 ω ) [ S ( 0 ) ( ρ 2 ω ) ] 1 2 .
S ( 0 ) ( ρ ω ) = A 2 ( ω ) exp [ ρ 2 2 σ s 2 ( ω ) ] ,
g ( 0 ) ( ρ ω ) = exp [ ρ 2 2 σ g 2 ( ω ) ] ,
U ( ρ , x 3 ω ) = ω 2 π i c x 3 exp ( i ω c x 3 ) d 2 ρ 1 U ( ρ 1 , 0 ω ) exp [ i ω 2 c x 3 ( ρ ρ 1 ) 2 ] .
J ( ρ , x 3 ω ) = 2 σ s 2 σ eff 2 ( x 3 ) exp [ ρ 2 σ eff 2 ( x 3 ) ] ,
σ eff 2 ( x 3 ) = 2 σ s 2 + x 3 2 c 2 ω 2 ( 1 2 σ s 2 + 2 σ g 2 ) ,
U ( ρ , x 3 ω ) = U 1 ( ρ , x 3 ω ) + U 2 ( ρ , x 3 ω ) exp ( i ϕ ) ,
U 2 ( x 1 , x 2 , x 3 ω ) = U 1 ( x 1 , x 2 , x 3 ω ) .
J ( ρ , x 3 ω ) = ( ω 2 π c x 3 ) 2 d 2 ρ d 2 ρ exp [ i ω 2 c x 3 ( ρ ρ ) 2 ] exp [ i ω 2 c x 3 ( ρ ρ ) 2 ] × [ 2 W ( 0 ) ( ρ , ρ ω ) + U 1 ( ρ , 0 ω ) U 2 * ( ρ , 0 ω ) exp ( i ϕ ) + U 1 * ( ρ , 0 ω ) U 2 ( ρ , 0 ω ) exp ( i ϕ ) ] .
U 1 ( ρ , 0 ω ) U 2 * ( ρ , 0 ω ) = U 1 ( x 1 ; x 2 ; 0 ω ) U 1 * ( x 1 ; x 2 ; 0 ω ) = W ( 0 ) ( x 1 , x 2 ; x 1 , x 2 ω ) ,
J ( ρ , x 3 ω ) = 2 ( ω 2 π c x 3 ) 2 d 2 ρ d 2 ρ exp [ i ω 2 c x 3 ( ρ ρ ) 2 ] exp [ i ω 2 c x 3 ( ρ ρ ) 2 ] × [ W ( 0 ) ( x 1 , x 2 ; x 1 , x 2 ω ) + ( cos ϕ ) W ( 0 ) ( x 1 , x 2 ; x 1 , x 2 ω ) ] .
J ( ρ , x 3 ω ) = 4 σ s 2 σ eff 2 ( x 3 ) exp [ ρ 2 σ eff 2 ( x 3 ) ] { 1 + ( cos ϕ ) exp [ x 2 2 σ 2 2 ( x 3 ) ] } ,
σ 2 2 ( x 3 ) = 1 2 σ g 2 σ s 2 σ eff 2 ( x 3 ) = 1 2 σ g 2 + x 3 2 c 2 ω 2 ( σ g 2 8 σ s 4 + 1 2 σ s 2 ) .

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