Abstract

A new class of partially coherent light sources is introduced. At the source plane, they exhibit perfect coherence along any annulus that is concentric to the source center. Between two points at different distances from the center, coherence can be partial or even vanishing. Such sources can be synthesized by using a generalized form of van Cittert–Zernike theorem where axial sources are used. Beams radiated by this type of source are analyzed at the source plane and upon free propagation for some simple cases.

© 2017 Optical Society of America

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References

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2017 (1)

Y. Chen, S. A. Ponomarenko, and Y. Cai, Sci. Rep. 7, 39957 (2017).
[Crossref]

2016 (1)

Y. Chen, S. A. Ponomarenko, and Y. Cai, Appl. Phys. Lett. 109, 061107 (2016).
[Crossref]

2015 (3)

2014 (3)

2013 (2)

2012 (1)

2011 (1)

2010 (1)

G. Gbur and T. Visser, Prog. Opt. 55, 285 (2010).
[Crossref]

2009 (1)

2008 (2)

2006 (1)

2004 (1)

O. Korotkova, L. C. Andrews, and R. L. Phillips, Opt. Eng. 43, 330 (2004).
[Crossref]

2003 (1)

2001 (1)

2000 (1)

1994 (2)

F. Gori, V. Bagini, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, Opt. Rev. 1, 143 (1994).
[Crossref]

A. T. Friberg, E. Tervonen, and J. Turunen, J. Opt. Soc. Am. A 11, 1818 (1994).

1993 (1)

1987 (2)

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

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[Crossref]

1984 (1)

1979 (1)

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[Crossref]

1978 (1)

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[Crossref]

Abramowitz, M.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Cambridge University, 1972)

Andrews, L. C.

O. Korotkova, L. C. Andrews, and R. L. Phillips, Opt. Eng. 43, 330 (2004).
[Crossref]

Bagini, V.

F. Gori, V. Bagini, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, Opt. Rev. 1, 143 (1994).
[Crossref]

Bogatyryova, G. V.

Borghi, R.

Cai, Y.

Chen, Y.

Y. Chen, S. A. Ponomarenko, and Y. Cai, Sci. Rep. 7, 39957 (2017).
[Crossref]

Y. Chen, S. A. Ponomarenko, and Y. Cai, Appl. Phys. Lett. 109, 061107 (2016).
[Crossref]

Y. Cai, Y. Chen, and F. Wang, J. Opt. Soc. Am. A 31, 2083 (2014).
[Crossref]

Collett, E.

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[Crossref]

de Sande, J. C. G.

J. C. G. de Sande, M. Santarsiero, G. Piquero, and F. Gori, J. Opt. 17, 125613 (2015).
[Crossref]

M. Santarsiero, G. Piquero, J. C. G. de Sande, and F. Gori, Opt. Lett. 39, 1713 (2014).
[Crossref]

De Santis, P.

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[Crossref]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[Crossref]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[Crossref]

Fel’de, C. V.

Frezza, F.

F. Gori, V. Bagini, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, Opt. Rev. 1, 143 (1994).
[Crossref]

Friberg, A. T.

Gbur, G.

G. Gbur and T. Visser, Prog. Opt. 55, 285 (2010).
[Crossref]

Gori, F.

J. C. G. de Sande, M. Santarsiero, G. Piquero, and F. Gori, J. Opt. 17, 125613 (2015).
[Crossref]

M. Santarsiero, G. Piquero, J. C. G. de Sande, and F. Gori, Opt. Lett. 39, 1713 (2014).
[Crossref]

R. Martínez-Herrero, P. M. Mejías, and F. Gori, Opt. Lett. 34, 1399 (2009).
[Crossref]

F. Gori, M. Santarsiero, R. Borghi, and C.-F. Li, J. Opt. Soc. Am. A 25, 2826 (2008).
[Crossref]

F. Gori, V. Bagini, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, Opt. Rev. 1, 143 (1994).
[Crossref]

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

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[Crossref]

Guattari, G.

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

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[Crossref]

Korotkova, O.

Lajunen, H.

Li, C.-F.

Liang, C.

Liu, X.

Mandel, L.

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

Martínez-Herrero, R.

Mei, Z.

Mejías, P. M.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[Crossref]

Mukunda, N.

Padovani, C.

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

Palma, C.

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[Crossref]

Partanen, H.

Phillips, R. L.

O. Korotkova, L. C. Andrews, and R. L. Phillips, Opt. Eng. 43, 330 (2004).
[Crossref]

Piquero, G.

J. C. G. de Sande, M. Santarsiero, G. Piquero, and F. Gori, J. Opt. 17, 125613 (2015).
[Crossref]

M. Santarsiero, G. Piquero, J. C. G. de Sande, and F. Gori, Opt. Lett. 39, 1713 (2014).
[Crossref]

Polyanskii, P. V.

Ponomarenko, S. A.

Y. Chen, S. A. Ponomarenko, and Y. Cai, Sci. Rep. 7, 39957 (2017).
[Crossref]

Y. Chen, S. A. Ponomarenko, and Y. Cai, Appl. Phys. Lett. 109, 061107 (2016).
[Crossref]

G. V. Bogatyryova, C. V. Fel’de, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, Opt. Lett. 28, 878 (2003).
[Crossref]

S. A. Ponomarenko, J. Opt. Soc. Am. A 18, 150 (2001).
[Crossref]

Saastamoinen, T.

Sahin, S.

Santarsiero, M.

J. C. G. de Sande, M. Santarsiero, G. Piquero, and F. Gori, J. Opt. 17, 125613 (2015).
[Crossref]

M. Santarsiero, G. Piquero, J. C. G. de Sande, and F. Gori, Opt. Lett. 39, 1713 (2014).
[Crossref]

F. Gori, M. Santarsiero, R. Borghi, and C.-F. Li, J. Opt. Soc. Am. A 25, 2826 (2008).
[Crossref]

F. Gori, V. Bagini, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, Opt. Rev. 1, 143 (1994).
[Crossref]

Schettini, G.

F. Gori, V. Bagini, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, Opt. Rev. 1, 143 (1994).
[Crossref]

Sharmin, N.

Shchegrov, A. V.

Shchepakina, E.

Simon, R.

Singh, M.

Soskin, M. S.

Spagnolo, G. S.

F. Gori, V. Bagini, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, Opt. Rev. 1, 143 (1994).
[Crossref]

Stegun, I.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Cambridge University, 1972)

Tervo, J.

Tervonen, E.

Turunen, J.

Vahimaa, P.

Visser, T.

G. Gbur and T. Visser, Prog. Opt. 55, 285 (2010).
[Crossref]

Wang, F.

Wolf, E.

G. V. Bogatyryova, C. V. Fel’de, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, Opt. Lett. 28, 878 (2003).
[Crossref]

A. V. Shchegrov and E. Wolf, Opt. Lett. 25, 141 (2000).
[Crossref]

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[Crossref]

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

Appl. Phys. Lett. (1)

Y. Chen, S. A. Ponomarenko, and Y. Cai, Appl. Phys. Lett. 109, 061107 (2016).
[Crossref]

J. Opt. (1)

J. C. G. de Sande, M. Santarsiero, G. Piquero, and F. Gori, J. Opt. 17, 125613 (2015).
[Crossref]

J. Opt. Soc. Am. A (8)

Opt. Commun. (3)

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

E. Wolf and E. Collett, Opt. Commun. 25, 293 (1978).
[Crossref]

P. De Santis, F. Gori, G. Guattari, and C. Palma, Opt. Commun. 29, 256 (1979).
[Crossref]

Opt. Eng. (1)

O. Korotkova, L. C. Andrews, and R. L. Phillips, Opt. Eng. 43, 330 (2004).
[Crossref]

Opt. Express (2)

Opt. Lett. (9)

Opt. Rev. (1)

F. Gori, V. Bagini, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, Opt. Rev. 1, 143 (1994).
[Crossref]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[Crossref]

Prog. Opt. (1)

G. Gbur and T. Visser, Prog. Opt. 55, 285 (2010).
[Crossref]

Sci. Rep. (1)

Y. Chen, S. A. Ponomarenko, and Y. Cai, Sci. Rep. 7, 39957 (2017).
[Crossref]

Other (2)

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

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Cambridge University, 1972)

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Figures (3)

Fig. 1.
Fig. 1.

Absolute value of the spectral degree of coherence, with g(·)=sinc(·): across the source plane for r1=1 (upper plot); as a function of r2 for several values of r1 (central plot); across the plane r1,r2 (lower plot). All lengths are normalized to the value of δμ.

Fig. 2.
Fig. 2.

Absolute value of the spectral degree of coherence across a transverse plane in the far zone, with g(·)=sinc(·), τ(r)=exp(ar2), and a=1 (in units of δμ): across the plane (R1/z,R2/z) (upper plot) and as a function of R2/z for several values of R1/z (lower plot).

Fig. 3.
Fig. 3.

Basic experimental scheme.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

W0(r1,r2)=τ*(r1)τ(r2)g(r22r12δμ2),
μ0(r1,r2)=W0(r1,r2)W0(r1,r1)W0(r2,r2),
μ0(r1,r2)=τ*(r1)τ(r2)|τ(r1)τ(r2)|g(r22r12δμ2),
r22r12δμ2=(r2+r1)(r2r1)δμ2=2r¯δμ2(r2r1),
W(R1,R2,z)=1λ2z2W0(r1,r2)×exp[ik2z(|R1r1|2|R2r2|2)]dr1dr2,
W(R1,R2,z)=k2z2exp[ik2z(R22R12)]×00τ*(r1)τ(r2)g(r22r12δμ2)exp[ik2z(r22r12)]×J0(kR1zr1)J0(kR2zr2)r1r2dr1dr2,
dV0(r)=iλfA(ξ)eik(ξ+f)eik2f(1ξf)r2dξ,
V0(r)=τ(r)iλfA(ξ)eik(ξ+f)eik2f(1ξf)r2dξ.
W0(r1,r2)=V0*(r1)V0(r2),
W0(r1,r2)=1(λf)2τ*(r1)τ(r2)eik2f(r22r12)×WS(ξ1,ξ2)eik(ξ2ξ1)eik2f2(r22ξ2r12ξ1)dξ1dξ2,
WS(ξ1,ξ2)=A*(ξ1)A(ξ2),
WS(ξ1,ξ2)=IS(ξ1)δ(ξ1ξ2),
W0(r1,r2)=1(λf)2τ*(r1)τ(r2)eik2f(r22r12)×IS(ξ)e2πi(r22r122λf2)ξdξ.
W0(r1,r2)=1(λf)2τ*(r1)τ(r2)eik2f(1ξ¯f)(r22r12)×L/2L/2G(ζ)e2πi(r22r122λf2)ζdζ.
W0(r1,r2)=1(λf)2τ*(r1)τ(r2)G˜(r22r122λf2),
g(r22r12δμ2)=1(λf)2G˜(r22r122λf2).
G(ζ)=G0rect(ζ/L),
W0(r1,r2)=LG0(λf)2τ*(r1)τ(r2)sinc[L(r22r12)2λf2],

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