Abstract

A class of random sources producing far fields with rectangular intensity profiles is introduced by modeling the source degree of coherence with the help of two one-dimensional multi-Gaussian distributions. By changing the rms correlation widths along the x and y directions and the number of terms in the summation of the multi-Gaussian functions, the shapes and the edge sharpness of the beams can be adjusted. The results based on the derived analytical expression for the far-zone spectral density are supplemented by the computer simulations.

© 2013 Optical Society of America

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References

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    [CrossRef]

2013

2012

2011

2007

2006

G. Wu, H. Guo, and D. Deng, Opt. Commun. 260, 687 (2006).
[CrossRef]

2005

T. Shirai, O. Korotkova, and E. Wolf, J. Opt. A 7, 232 (2005).
[CrossRef]

2003

Y. Li, J. Mod. Opt. 50, 1957 (2003).
[CrossRef]

2001

1987

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Avramov-Zamurovic, S.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, and R. Malek-Madani, Proc. SPIE 8238, 82380J (2012).
[CrossRef]

Cai, Y.

Deng, D.

G. Wu, H. Guo, and D. Deng, Opt. Commun. 260, 687 (2006).
[CrossRef]

Gori, F.

F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
[CrossRef]

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Guo, H.

G. Wu, H. Guo, and D. Deng, Opt. Commun. 260, 687 (2006).
[CrossRef]

Korotkova, O.

Lajunen, H.

Li, Y.

Y. Li, J. Mod. Opt. 50, 1957 (2003).
[CrossRef]

Liu, X.

Malek-Madani, R.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, and R. Malek-Madani, Proc. SPIE 8238, 82380J (2012).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1997).

Mei, Z.

Nelson, C.

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, and R. Malek-Madani, Proc. SPIE 8238, 82380J (2012).
[CrossRef]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Ponomarenko, S. A.

Saastamoinen, T.

Sahin, S.

Santarsiero, M.

Shchepakina, E.

Shirai, T.

T. Shirai, O. Korotkova, and E. Wolf, J. Opt. A 7, 232 (2005).
[CrossRef]

Wang, F.

Wolf, E.

T. Shirai, O. Korotkova, and E. Wolf, J. Opt. A 7, 232 (2005).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1997).

Wu, G.

G. Wu, H. Guo, and D. Deng, Opt. Commun. 260, 687 (2006).
[CrossRef]

Yuan, Y.

J. Mod. Opt.

Y. Li, J. Mod. Opt. 50, 1957 (2003).
[CrossRef]

J. Opt. A

T. Shirai, O. Korotkova, and E. Wolf, J. Opt. A 7, 232 (2005).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

G. Wu, H. Guo, and D. Deng, Opt. Commun. 260, 687 (2006).
[CrossRef]

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).
[CrossRef]

Opt. Lett.

Proc. SPIE

O. Korotkova, S. Avramov-Zamurovic, C. Nelson, and R. Malek-Madani, Proc. SPIE 8238, 82380J (2012).
[CrossRef]

Other

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1997).

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Figures (5)

Fig. 1.
Fig. 1.

Absolute value of the degree of coherence versus x1x2 (horizontal) and y1y2(vertical). The horizontal and vertical scales extend from 5mm to 5 mm.

Fig. 2.
Fig. 2.

Illustration of the notation related to the far field.

Fig. 3.
Fig. 3.

Spectral density of the RGSM beams in the far zone of sources with parameters as in Fig. 1. The horizontal and vertical axes extend from 1mm to 1 mm.

Fig. 4.
Fig. 4.

Computer simulations of the random amplitude distribution for generation of sources with the degree of coherence (1), corresponding to Figs. 1 and 3.

Fig. 5.
Fig. 5.

Computer simulations of the far fields produced by sources with the degree of coherence (1). The source parameters are the same as in Fig. 4.

Equations (17)

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W(0)(ρ1,ρ2;λ)=[S(0)(ρ1;λ)S(0)(ρ2;λ)]1/2μ(0)(ρ1ρ2;λ),
μ(0)(ρ1,ρ2;λ)=1C2m=1M(Mm)(1)m1mexp[(x1x2)22mδx2(λ)]×m=1M(Mm)(1)m1mexp[(y1y2)22mδy2(λ)],
C=m=1M(Mm)(1)m1m,
W(0)(x1,y1,x2,y2)=p(vx,vy)H*(x1,y1,vx,vy)×H(x1,y1,vx,vy)dvxdvy.
H(x,y,vx,vy)=τ(x,y)exp[2πi(vxx+vyy)],
W(0)(x1,y1,x2,y2)=τ*(x1,y1)τ(x2,y2)×p˜x(x1x2)p˜y(y1y2).
p(vx,vy)=δxδyC2m=1M(Mm)(1)m1exp[mδx2vx22]×m=1M(Mm)(1)m1exp[mδy2vy22],
p(vx,vy)=δxδy{1(1exp[δx2vx2/2])M}×{1(1exp[δy2vy2/2])M}/C2.
τ(x,y)=exp(x2+y24σ2),
W(0)(ρ1,ρ2;λ)=1C2exp(x12+x22+y12+y224σ2)×m=1M(Mm)(1)m1mexp[(x1x2)22mδx2(λ)]×m=1M(Mm)(1)m1mexp[(y1y2)22mδy2(λ)].
W()(r1,r2)=k2cosθ1cosθ2exp[ik(r2r1)](2π)2r1r2×W(0)(ρ1,ρ2)exp[i(f1·ρ1+f2·ρ2)]d2ρ1d2ρ2,
W()(r1,r2)=2k2cosθ1cosθ2exp[ikr(s2s1)]C2r1r2×m=1M(Mm)(1)m1amxmbmxexp[cmx(s1x2+s2x2)dmx(s1xs2x)2]×m=1M(Mm)(1)m1amymbmyexp[cmy(s1y2+s2y2)dmy(s1ys2y)2],
amx=σ2mδx2+4σ2mδx2+4σ2,bmx=2mδx2+1σ2,cmx=k2σ2mδx2mδx2+4σ2,dmx=2k2σ4mδx2+4σ2,amy=σ2mδy2+4σ2mδy2+4σ2,bmy=2mδy2+1σ2,cmy=k2σ2mδy2mδy2+4σ2,dmy=2k2σ4mδy2+4σ2.
S()(rs)=2k2cos2θC2r2m=1M(Mm)(1)m1mamxbmxexp[2cmxsx2]×m=1M(Mm)(1)m1mamybmyexp[2cmysy2].
exp[2cxmsx2]0,andexp[2cymsy2]0,
14σ2+1mδx2π2λ2and14σ2+1mδy2π2λ2.
14σ2+1δx2π2λ2and14σ2+1δy2π2λ2.

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