Abstract

The concept of a partially coherent nonparaxial beam is proposed. A closed-form expression for the propagation of nonparaxial Gaussian Schell model (GSM) beams in free space is derived and applied to study the propagation properties of nonparaxial GSM beams. It is shown that for partially coherent nonparaxial beams a new parameter fσ has to be introduced, which together with the parameter f, determines the beam nonparaxiality.

© 2004 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. S. Nemoto, Appl. Opt. 29, 1940 (1990).
    [Crossref] [PubMed]
  4. X. Zeng, C. Liang, and Y. An, Appl. Opt. 36, 2042 (1997).
    [Crossref] [PubMed]
  5. H. Laabs, Opt. Commun. 147, 1 (1998).
    [Crossref]
  6. A. Ciattoni, B. Crosignami, and P. D. Porto, Opt. Commun. 202, 17 (2002).
    [Crossref]
  7. C. G. Chen, P. T. Konkola, J. Ferrera, R. K. Heilmann, and M. L. Schattenburg, J. Opt. Soc. Am. A 19, 404 (2002).
    [Crossref]
  8. B. Lu and K. Duan, Opt. Lett. 28, 2440 (2003).
    [Crossref]
  9. R. Gase, J. Mod. Opt. 38, 1107 (1991).
    [Crossref]
  10. L. Mandel and E. Wolf, Optics Coherence and Quantum Optics (Cambridge U. Press, Cambridge, England, 1995).
    [Crossref]
  11. A. T. Friberg and R. J. Sudol, Opt. Commun. 41, 383 (1982).
    [Crossref]
  12. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1978).

2003 (1)

2002 (2)

1998 (1)

H. Laabs, Opt. Commun. 147, 1 (1998).
[Crossref]

1997 (1)

1991 (1)

R. Gase, J. Mod. Opt. 38, 1107 (1991).
[Crossref]

1990 (1)

1982 (1)

A. T. Friberg and R. J. Sudol, Opt. Commun. 41, 383 (1982).
[Crossref]

1975 (1)

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

An, Y.

Chen, C. G.

Ciattoni, A.

A. Ciattoni, B. Crosignami, and P. D. Porto, Opt. Commun. 202, 17 (2002).
[Crossref]

Crosignami, B.

A. Ciattoni, B. Crosignami, and P. D. Porto, Opt. Commun. 202, 17 (2002).
[Crossref]

Duan, K.

Ferrera, J.

Friberg, A. T.

A. T. Friberg and R. J. Sudol, Opt. Commun. 41, 383 (1982).
[Crossref]

Gase, R.

R. Gase, J. Mod. Opt. 38, 1107 (1991).
[Crossref]

Heilmann, R. K.

Konkola, P. T.

Laabs, H.

H. Laabs, Opt. Commun. 147, 1 (1998).
[Crossref]

Lax, M.

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

Liang, C.

Louisell, W. H.

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

Lu, B.

Mandel, L.

L. Mandel and E. Wolf, Optics Coherence and Quantum Optics (Cambridge U. Press, Cambridge, England, 1995).
[Crossref]

Marcuse, D.

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1978).

McKnight, W. B.

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

Nemoto, S.

Porto, P. D.

A. Ciattoni, B. Crosignami, and P. D. Porto, Opt. Commun. 202, 17 (2002).
[Crossref]

Schattenburg, M. L.

Siegman, A. E.

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

Sudol, R. J.

A. T. Friberg and R. J. Sudol, Opt. Commun. 41, 383 (1982).
[Crossref]

Wolf, E.

L. Mandel and E. Wolf, Optics Coherence and Quantum Optics (Cambridge U. Press, Cambridge, England, 1995).
[Crossref]

Zeng, X.

Appl. Opt. (2)

J. Mod. Opt. (1)

R. Gase, J. Mod. Opt. 38, 1107 (1991).
[Crossref]

J. Opt. Soc. Am. A (1)

Opt. Commun. (3)

H. Laabs, Opt. Commun. 147, 1 (1998).
[Crossref]

A. Ciattoni, B. Crosignami, and P. D. Porto, Opt. Commun. 202, 17 (2002).
[Crossref]

A. T. Friberg and R. J. Sudol, Opt. Commun. 41, 383 (1982).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (1)

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

Other (3)

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

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1978).

L. Mandel and E. Wolf, Optics Coherence and Quantum Optics (Cambridge U. Press, Cambridge, England, 1995).
[Crossref]

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Figures (2)

Fig. 1
Fig. 1

Normalized transversal irradiance distributions Ix,0,20zR and Ipx,0,20zR in the x direction at the plane z=20zR with Ix,0,20zR (solid curves) by use of Eq. (7) and Ipx,0,20zR (circles) by use of Eq. (9). (a) f=0.01, fσ=0.17; (b) f=0.6, fσ=0.01; (c) f=0.24, fρ=0.01; (d) f=0.01, fσ=0.4.

Fig. 2
Fig. 2

(a) Far-field divergence angles θ (solid curves) and θp (dashed curves) versus parameter fσ-1 for different values of f. (b) Far-field divergence angles θ (solid curves) and θp (dashed curves) versus parameter f-1 for different values of fσ.

Equations (9)

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Wρ01,ρ02,z=0=exp-ρ01-ρ0222σ02×exp-ρ012+ρ0222w02,
Wρ1,ρ2,z= 1λ2z=0Wρ01,ρ02,0cos θ1 cos θ2R1R2×expikR2-R1d2ρ01d2ρ02,
Rjrj+x0j2+y0j2-2xjx0j-2yjy0j2rj,
Wx1,x2,y1,y2,z=-k2z24s1s2+k4fσ4expikr2-r1r12r22×exp-k24s1x12+y12r12expk2s14s1s2+k4fσ4×x2r2-k2fσ22s1x1r12+y2r2-k2fσ22s1y1r12, 
Ix,y,z= z2r211+k2f2f2+2fσ2r2×exp-k2f21+k2f2f2+2fσ2r2x2+y2.
Ix,y,z= z2r211+k2f4r2×exp-k2f21+k2f4r2x2+y2,
Ifx,y,z=z2k2f4r4exp-1f2x2+y2r2,
Wρρ1,ρ2,z= w02w2zexp-ρ12+ρ222w2z×exp-ρ1-ρ222σ2z×exp-ikρ12-ρ222Rz,
Ipx,y,z=w02w2zexp-x2+y2w2z.

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