Abstract

Two types of partially coherent beams with sinc Schell-model-correlated function are introduced. The evolution behaviors of scalar beams generated by these two types of sources in free space are investigated with the help of the weighted superposition method and numerical examples. It is illustrated that the far field produced by these two novel sources carry tunable flat and dark hollow profiles, respectively. Our results suggest two new kinds of modal structure of the correlation source and of the optical field that such sources produce.

© 2014 Optical Society of America

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References

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2014 (3)

2013 (2)

2012 (1)

2007 (1)

1982 (3)

Cai, Y.

de Sande, J. C. G.

Gori, F.

Korotkova, O.

Li, Y.

Liang, C.

Liu, X.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Mei, Z.

Piquero, G.

Sahin, S.

Santarsiero, M.

Starikov, A.

Wang, F.

Wolf, E.

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Figures (6)

Fig. 1.
Fig. 1.

Spectral degree of coherence μ of SSM1 corresponding to the CSD in Eq. (6), as a function x1x2, for several values of a as follows: (a) a=8; (b) a=10; (c) a=12; and (d) a=15.

Fig. 2.
Fig. 2.

Spectral degree of coherence μ of SSM2 corresponding to the CSD in Eq. (11) with A1=A2=1 as a function x1x2 for several values of a1 and a2 as follows: (a) a1=15, a2=8; (b) a1=15, a2=10; (c) a1=12, a2=8; and (d) a1=12, a2=10.

Fig. 3.
Fig. 3.

Propagation of a SSM1 beam with a=12 and A=1. The upper figure shows the evolution of the spectral density on the xz plane, and the lower figure shows the lateral spectral density distribution at selected propagation distances.

Fig. 4.
Fig. 4.

Transverse spectral density distribution of the SSM1 beams with corresponding values of parameter a as in Fig. 1 at the plane z=1m.

Fig. 5.
Fig. 5.

Propagation of a SSM2 beam with a1=15, a2=10 and A1=A2=1. The upper figure shows the evolution of the spectral density on the xz plane, and the lower figure shows the lateral spectral density distribution at selected propagation distances.

Fig. 6.
Fig. 6.

Transverse spectral density distribution of the SSM2 beams with corresponding values of parameters a1 and a2 as in Fig. 2 at the plane z=1m.

Equations (18)

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W(0)(x1,x2)=p(v)H0*(x1,v)H0(x2,v)dv,
H0(x,v)=τ(x)exp[2πivx],
W(0)(x1,x2)=τ*(x1)τ(x2)p˜(x1x2),
p(v)=Arect(v/a),
τ(x)=exp[x2/(2σ2)],
W(0)(x1,x2)=exp(x12+x222σ2)Aasinc[a(x1x2)],
p(v)=p1(v)p2(v).
W(0)(x1,x2)=W1(0)(x1,x2)W2(0)(x1,x2),
Wj(0)(x1,x2)=pj(v)H0*(x1,v)H0(x2,v)dv,(j=1,2).
p(v)=A1rect(v/a1)A2rect(v/a2),
W(0)(x1,x2)=exp(x12+x222σ2)×{A1a1sinc[a1(x1x2)]A2a2sinc[a2(x1x2)]},
W(x1,x2,z)=k2πzW(0)(x1,x2)×exp[ik(x1x1)2(x2x2)22z]dx1dx2.
W(x1,x2,z)=p(v)H*(x1,z,v)H(x2,z,v)dv,
H*(x1,z,v)H(x2,z,v)=k2πzH0*(x1,v)H0(x2,v)×exp[ik(x1x1)2(x2x2)22z]dx1dx2.
H*(x1,z,v)H(x2,z,v)=σ0w(z)exp[k2σ024z2(x1x2)2ik2z(x12x22)]×exp{[x1+x22+2πzvkikσ022z(x1x2)]2/w2(z)},
w2(z)=σ02+z2/(k2σ02).
S(x,z)=W(x,x,z)=p(v)F(x,z,v)dv,
F(x,z,v)=σ0w(z)exp[(x+2πzv/k)2/w2(z)].

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