Abstract

Based on the vectorial Rayleigh diffraction integral, the nonparaxial propagation of vectorial Gaussian beams diffracted at a circular aperture is studied. The far-field and paraxial cases are treated as special cases of our general result. It is shown that for the apertured case the f parameter still plays an important role in determining the nonparaxiality of vectorial diffracted Gaussian beams, but both the f parameter and truncation affect the beam evolution behavior.

© 2003 Optical Society of America

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References

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  1. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  2. M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
    [CrossRef]
  3. T. Takenaka, M. Yokota, and O. Fukumitsu, J. Opt. Soc. Am. A 2, 826 (1985).
    [CrossRef]
  4. A. Wünsche, J. Opt. Soc. Am. A 9, 765 (1992).
    [CrossRef]
  5. G. P. Agrawal and D. N. Pattanayak, J. Opt. Soc. Am. 69, 575 (1979).
  6. S. R. S. Seshadri, Opt. Lett. 28, 595 (2003).
    [CrossRef] [PubMed]
  7. R. K. Luneberg, Mathematical Theory of Optics (U. California Press, Berkely, Calif., 1964).
  8. C. G. Chen, P. T. Konkola, J. Ferrera, R. K. Heilmann, and M. L. Schattenburg, J. Opt. Soc. Am. A 19, 404 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]

2003

2002

1992

1990

1986

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

1985

T. Takenaka, M. Yokota, and O. Fukumitsu, J. Opt. Soc. Am. A 2, 826 (1985).
[CrossRef]

1979

1975

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

1964

R. K. Luneberg, Mathematical Theory of Optics (U. California Press, Berkely, Calif., 1964).

Agrawal, G. P.

Chen, C. G.

Ferrera, J.

Fukumitsu, O.

T. Takenaka, M. Yokota, and O. Fukumitsu, J. Opt. Soc. Am. A 2, 826 (1985).
[CrossRef]

Heilmann, R. K.

Konkola, P. T.

Lax, M.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Louisell, W. H.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Luneberg, R. K.

R. K. Luneberg, Mathematical Theory of Optics (U. California Press, Berkely, Calif., 1964).

McKnight, W. B.

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Nemoto, S.

Pattanayak, D. N.

Schattenburg, M. L.

Seshadri, S. R. S.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Takenaka, T.

T. Takenaka, M. Yokota, and O. Fukumitsu, J. Opt. Soc. Am. A 2, 826 (1985).
[CrossRef]

Wünsche, A.

Yokota, M.

T. Takenaka, M. Yokota, and O. Fukumitsu, J. Opt. Soc. Am. A 2, 826 (1985).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

T. Takenaka, M. Yokota, and O. Fukumitsu, J. Opt. Soc. Am. A 2, 826 (1985).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Phys. Rev. A

M. Lax, W. H. Louisell, and W. B. McKnight, Phys. Rev. A 11, 1365 (1975).
[CrossRef]

Other

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

R. K. Luneberg, Mathematical Theory of Optics (U. California Press, Berkely, Calif., 1964).

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Figures (2)

Fig. 1
Fig. 1

Transversal irradiance distributions of Ix,0,zR,Izx,0,zR, and Ipx,0,zR at the plane z=zR. (a) f=0.1, δ=2; (b) f=0.5,δ=2; (c) f=0.5,δ=0.5.

Fig. 2
Fig. 2

Normalized irradiance Iz,maxx,0,zR/Ix0,0,zR versus f parameter for δ.

Equations (21)

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E0xx0,y0,0=exp-x02+y022w02,
E0yx0,y0,0=0,
Exx0,y0,0=tx0,y0exp-x02+y022w02,
Eyx0,y0,0=0,
tx0,y0=1x02+y02a20otherwise.
Exr=-12π-Exx0,y0,0Gr,r0zdx0dy0,
Eyr=-12π-Eyx0,y0,0Gr,r0zdx0dy0,
Ezr=12π-Exx0,y0,0Gr,r0x+Eyx0,y0,0Gr,r0ydx0dy0,
Gr,r0=expikr-r0r-r0.
r-r0r+x02+y02-2xx0-2yy02r.
Exx,y,z=-ikzrexpikrr×0aρ0 expgρ02J0khρ0dρ0,
Eyx,y,0=0,
Ezx,y,z=ikxrexpikrr×0aρ0 expgρ02J0khρ0dρ0-kxrexpikrr1x2+y2×0aρ02 expgρ02J1khρ0dρ0,
Exx,y,z=-ikzrexpikrrm=0k2m22m+1m!2×h2mgm+1Γ1+m,-a2g-m!,
Eyx,y,0=0,
Ezx,y,z=ikxrexpikrrm=0k2m22m+1m!2×h2mgm+1Γ1+m,-a2g-m!+kxr2expikrrm=0k2m+122m+2m!m+1!×h2mgm+2Γm+2,-a2g-m+1!,
Exfx,y,z=izkrexpikrrm=0-1m22mm!2f2m+2×h2mΓ1+m,12δ2-m!,
Eyfx,y,0=0,
Ezfx,y,z=-ixkrexpikrrm=001m2mm!2f2m+2×h2mΓ1+m,12δ2-m!+xk2r2expikrrm=0-1m2mm!m+1!f2m+4×h2mΓm+2,12δ2-m+1!,
Expx,y,z=-ikexpikrzexpik2zx2+y2×m=0k2m22m+1m!2d2mtm+1Γ1+m,-a2t-m!,
Expfx,y,z=iexpiknzkexpik2zx2+y2×m=0-1m2mm!2d2mf2m+2Γ1+m,12δ2-m!.

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