Abstract

It is shown that the full four-dimensional Wigner transform of a coherent, rotationally symmetric light beam can be completely recovered by measurement, in one step, of the Wigner transform of an equivalent one-dimensional light beam. The method of generating this equivalent light beam from a two-dimensional circular light beam is presented.

© 2000 Optical Society of America

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References

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1998

1997

D. Dragoman, Prog. Opt. 37, 1 (1997).
[CrossRef]

1986

M. J. Bastiaans, J. Opt. Soc. Am. A 3, 1227 (1986).
[CrossRef]

T. Iwai, A. K. Gupta, and T. Asakura, Opt. Commun. 58, 15 (1986).
[CrossRef]

1985

1983

R. Bamler and H. Glünder, Opt. Acta 30, 1789 (1983).
[CrossRef]

1982

K. H. Brenner and A. W. Lohmann, Opt. Commun. 42, 310 (1982).
[CrossRef]

1980

H. O. Bartelt, K. H. Brenner, and A. W. Lohmann, Opt. Commun. 32, 32 (1980).
[CrossRef]

1979

Asakura, T.

T. Iwai, A. K. Gupta, and T. Asakura, Opt. Commun. 58, 15 (1986).
[CrossRef]

Bamler, R.

R. Bamler and H. Glünder, Opt. Acta 30, 1789 (1983).
[CrossRef]

Bartelt, H. O.

H. O. Bartelt, K. H. Brenner, and A. W. Lohmann, Opt. Commun. 32, 32 (1980).
[CrossRef]

Bastiaans, M. J.

Brenner, K. H.

K. H. Brenner and A. W. Lohmann, Opt. Commun. 42, 310 (1982).
[CrossRef]

H. O. Bartelt, K. H. Brenner, and A. W. Lohmann, Opt. Commun. 32, 32 (1980).
[CrossRef]

Conner, M.

Dragoman, D.

D. Dragoman, Prog. Opt. 37, 1 (1997).
[CrossRef]

Glünder, H.

R. Bamler and H. Glünder, Opt. Acta 30, 1789 (1983).
[CrossRef]

Gupta, A. K.

T. Iwai, A. K. Gupta, and T. Asakura, Opt. Commun. 58, 15 (1986).
[CrossRef]

Iwai, T.

T. Iwai, A. K. Gupta, and T. Asakura, Opt. Commun. 58, 15 (1986).
[CrossRef]

Li, Y.

Lohmann, A. W.

K. H. Brenner and A. W. Lohmann, Opt. Commun. 42, 310 (1982).
[CrossRef]

H. O. Bartelt, K. H. Brenner, and A. W. Lohmann, Opt. Commun. 32, 32 (1980).
[CrossRef]

Mendlovic, D.

Shabtay, G.

Zalevsky, Z.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Acta

R. Bamler and H. Glünder, Opt. Acta 30, 1789 (1983).
[CrossRef]

Opt. Commun.

T. Iwai, A. K. Gupta, and T. Asakura, Opt. Commun. 58, 15 (1986).
[CrossRef]

H. O. Bartelt, K. H. Brenner, and A. W. Lohmann, Opt. Commun. 32, 32 (1980).
[CrossRef]

K. H. Brenner and A. W. Lohmann, Opt. Commun. 42, 310 (1982).
[CrossRef]

Prog. Opt.

D. Dragoman, Prog. Opt. 37, 1 (1997).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Schematic representation of the method of generation of a 1D light from a circular 2D light source.

Equations (10)

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Wx,p=-φx+xφ*x-xexpi2pxdx.
Wr,p=-ψr+r2ψ*r-r2expi2prdr.
Wx,y,px,py=--φx+x,y+y×φ*x-x,y-y×expi2pxx+i2pyydxdy.
x=r cos θ,  x=r cos θ,  px=q cos ϕ,  y=r sin θ,  y=r sin θ,  py=q sin ϕ,
Wr,θ,q,ϕ=0dr02πdθ×ψr2+r2+2rr cosθ-θ×ψ*r2+r2+2rr cosθ-θ×r expi2rq cosϕ-θ.
r2+r2=y2+R2y,s,  rr cosθ-θ=Ry,sy,  rq cosϕ-θ=ys.
Wr,θ,q,ϕ=φR2y,s+y2+2Ry,sy×φ*R2y,s+y2-2Ry,sy×exp2iysfr,θ,q,ϕ,y,sdyds,
Wr,θ,q,ϕ=14π2-dtWRy,s,t×exp2iys-tfr,θ,q,ϕ,y,sdyds.
r=yrsin ϑrsq2+R2-2Rrsq cos ϑ1/2,  θ=θ-arccosR sin ϑrsq2+R2-2Rrsq cos ϑ1/2R=-y2s cos ϑqr sin2 ϑ±r2-y21/21-y2r2 sin2 ϑ+y2s2r2q2sin2 ϑ1/21-y2r2 sin2 ϑ,
Dr,θDy,s=gR cos ϑ-rs/q×R cos ϑ-rs/qyqg2Ry+2Rqg+Rs1r-2RrgR-rs cos ϑq,

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