Abstract

Self-reconstruction refers to an ability of certain fully coherent optical beams to recover their spatial profiles after scattering by obstacles. In this communication, we extend the self-reconstruction concept to partially coherent beams. We show theoretically and verify experimentally that any partially coherent beam can self-reconstruct its intensity profile and state of polarization upon scattering from an opaque obstacle provided the beam coherence area is reduced well below the obstacle area. We stress that our self-reconstruction technique is independent of the obstacle shape and it is scalable to the case of multiple obstacles or even of inhomogeneous media as long as a characteristic obstacle area or a medium inhomogeneity scale is well in excess of the beam coherence area or length, respectively. We anticipate the technique to be instrumental in applications ranging from beam shaping to image transfer and trapped particle manipulation in turbid media.

© 2016 Optical Society of America

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References

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2016 (1)

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nature Photon. 10(3), 167–170 (2016).
[Crossref]

2015 (5)

2014 (5)

L. Ma and S. A. Ponomarenko, “Optical coherence gratings and lattices,” Opt. Lett. 39(23), 6656–6660 (2014).
[Crossref] [PubMed]

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89(4), 043807 (2014).
[Crossref]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, and L. L. Sanchez-Soto, “Wavefront sensing reveals optical coherence,” Nat. Commun. 5, 3275 (2014).
[Crossref] [PubMed]

2013 (2)

K. H. Kagalwala, G. D. Guiseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nature Photon. 7(1), 72–78 (2013).
[Crossref]

T. Saastamoinen and H. Lajunen, “Increase of spatial coherence by subwavelength metallic gratings,” Opt. Lett. 38(23), 5000–5003 (2013).
[Crossref] [PubMed]

2012 (5)

S. Sahin and O. Korotkova, “Light sources generating far fields with tunable flat profiles,” Opt. Lett. 37(14), 2970–2972 (2012).
[Crossref] [PubMed]

J. D. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia, and M. R. Dennis, “Autofocusing and self-healing of Pearcey beams,” Opt. Express 20(17), 18955–18966 (2012).
[Crossref] [PubMed]

L. Waller, G. Situ, and J. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nature Photon. 6(7), 474–479 (2012).
[Crossref]

C. H. Gan, Y. Gu, T.D. Visser, and G. Gbur, “Coherence converting plasmonic hole arrays,” Plasmonics 7(2), 313–322 (2012).
[Crossref]

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (3)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beam,” Nature Photon. 4(11), 780–786 (2010).
[Crossref]

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104(2), 023901 (2010).
[Crossref] [PubMed]

Z. Hradil, J. Rehacek, and L. L. Sanchez-Soto, “Quantum reconstruction of the mutual coherence function,” Phys. Rev. Lett. 105(1), 010401 (2010).
[Crossref] [PubMed]

2009 (1)

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, and K. A. Nugent, “Diffractive imaging using partially coherent X-rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[Crossref]

2008 (2)

2007 (2)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

M. Anguiano-Morales, A. Martinez, M. D. Iturbe-Castillo, S. Chavez-Cerda, and N. Alcala-Ochoa, “Self-healing properties of a caustic optical beam,” Appl. Opt. 46(34), 8284–8290 (2007).
[Crossref] [PubMed]

2006 (1)

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8(5), 477–482 (2006).
[Crossref]

2005 (3)

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref] [PubMed]

M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express 13(23), 9629–9635 (2005).
[Crossref] [PubMed]

A. Aiello and J. P. Woerdeman, “Physical bounds to the entropy-depolarization relation in random light scattering,” Phys. Rev. Lett. 94(9), 090406 (2005).
[Crossref] [PubMed]

2004 (2)

C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 94(4), 043904 (2004).
[Crossref]

S. H. Tao and X. Yuan, “Self-reconstruction property of fractional Bessel beams,” J. Opt. Soc. Am. A 21(7), 1192–1197 (2004).
[Crossref]

2003 (2)

H. Roychowdhury and E. Wolf, “Effects of spatial coherence on near-field spectra,” Opt. Lett. 28(3), 170–172 (2003).
[Crossref] [PubMed]

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91(9), 093901 (2003).
[Crossref] [PubMed]

2002 (2)

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in several planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

Z. Bouchal, “Resistance of nondiffracting vortex beams to amplitude and phase perturbations,” Opt. Commun. 210(3), 155–164 (2002).
[Crossref]

1999 (1)

R. Carminati and J. J. Greffet, “Near-field effects in spatial coherence of thermal sources,” Phys. Rev. Lett. 82(8), 1660–1663 (1999).
[Crossref]

1998 (1)

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80(12), 2586–2589 (1998).
[Crossref]

1997 (1)

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature 387(6636), 880–882 (1997).
[Crossref]

1996 (1)

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77(3), 490–493 (1996).
[Crossref] [PubMed]

1987 (1)

J. Durnin and J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Abouraddy, A. F.

K. H. Kagalwala, G. D. Guiseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nature Photon. 7(1), 72–78 (2013).
[Crossref]

Abourrady, A. F.

Aiello, A.

A. Aiello and J. P. Woerdeman, “Physical bounds to the entropy-depolarization relation in random light scattering,” Phys. Rev. Lett. 94(9), 090406 (2005).
[Crossref] [PubMed]

Alcala-Ochoa, N.

Anguiano-Morales, M.

Apostol, A.

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91(9), 093901 (2003).
[Crossref] [PubMed]

Barbier, M.

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nature Photon. 10(3), 167–170 (2016).
[Crossref]

Borghi, R.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104(2), 023901 (2010).
[Crossref] [PubMed]

Bouchal, Z.

Z. Bouchal, “Resistance of nondiffracting vortex beams to amplitude and phase perturbations,” Opt. Commun. 210(3), 155–164 (2002).
[Crossref]

Broky, J.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12885 (2008).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

Brown, C. T. A.

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8(5), 477–482 (2006).
[Crossref]

Cai, Y.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev A 91(1), 013823 (2015).
[Crossref]

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89(4), 043807 (2014).
[Crossref]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

Carminati, R.

R. Carminati and J. J. Greffet, “Near-field effects in spatial coherence of thermal sources,” Phys. Rev. Lett. 82(8), 1660–1663 (1999).
[Crossref]

Chavez-Cerda, S.

Chen, Y.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev A 91(1), 013823 (2015).
[Crossref]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

Chen, Z.

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77(3), 490–493 (1996).
[Crossref] [PubMed]

Christodoulides, D. N.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12885 (2008).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

Clark, J. N.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

D’Angelo, M.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref] [PubMed]

Dennis, M. R.

Dholakia, K.

J. D. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia, and M. R. Dennis, “Autofocusing and self-healing of Pearcey beams,” Opt. Express 20(17), 18955–18966 (2012).
[Crossref] [PubMed]

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8(5), 477–482 (2006).
[Crossref]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in several planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

Dilanian, R. A.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, and K. A. Nugent, “Diffractive imaging using partially coherent X-rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[Crossref]

Divitt, S.

Dogariu, A.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12885 (2008).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91(9), 093901 (2003).
[Crossref] [PubMed]

Duan, Z.

Dudley, J. M.

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nature Photon. 10(3), 167–170 (2016).
[Crossref]

Durnin, J.

J. Durnin and J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Eberly, J. H.

Fahrbach, F. O.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beam,” Nature Photon. 4(11), 780–786 (2010).
[Crossref]

Fischer, P.

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8(5), 477–482 (2006).
[Crossref]

Fleischer, J.

L. Waller, G. Situ, and J. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nature Photon. 6(7), 474–479 (2012).
[Crossref]

Flewett, S.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, and K. A. Nugent, “Diffractive imaging using partially coherent X-rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[Crossref]

Forbes, A.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

Friberg, A. T.

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nature Photon. 10(3), 167–170 (2016).
[Crossref]

Gan, C. H.

C. H. Gan, Y. Gu, T.D. Visser, and G. Gbur, “Coherence converting plasmonic hole arrays,” Plasmonics 7(2), 313–322 (2012).
[Crossref]

Garces-Chavez, V.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in several planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

Gbur, G.

C. H. Gan, Y. Gu, T.D. Visser, and G. Gbur, “Coherence converting plasmonic hole arrays,” Plasmonics 7(2), 313–322 (2012).
[Crossref]

Genty, G.

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nature Photon. 10(3), 167–170 (2016).
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J. W. Goodman, Statistical Optics, 2nd Ed., (Wiley, New York, 2015).

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B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104(2), 023901 (2010).
[Crossref] [PubMed]

Greffet, J. J.

R. Carminati and J. J. Greffet, “Near-field effects in spatial coherence of thermal sources,” Phys. Rev. Lett. 82(8), 1660–1663 (1999).
[Crossref]

Gu, J.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev A 91(1), 013823 (2015).
[Crossref]

Gu, Y.

C. H. Gan, Y. Gu, T.D. Visser, and G. Gbur, “Coherence converting plasmonic hole arrays,” Plasmonics 7(2), 313–322 (2012).
[Crossref]

Guiseppe, G. D.

K. H. Kagalwala, G. D. Guiseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nature Photon. 7(1), 72–78 (2013).
[Crossref]

Harder, R.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

Howell, J. C.

Hradil, Z.

B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, and L. L. Sanchez-Soto, “Wavefront sensing reveals optical coherence,” Nat. Commun. 5, 3275 (2014).
[Crossref] [PubMed]

Z. Hradil, J. Rehacek, and L. L. Sanchez-Soto, “Quantum reconstruction of the mutual coherence function,” Phys. Rev. Lett. 105(1), 010401 (2010).
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Huang, X.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
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Iturbe-Castillo, M. D.

Jeng, C. C.

C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 94(4), 043904 (2004).
[Crossref]

Kagalwala, K. H.

K. H. Kagalwala, G. D. Guiseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nature Photon. 7(1), 72–78 (2013).
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Kivshar, Y.

C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 94(4), 043904 (2004).
[Crossref]

Korotkova, O.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
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Lindberg, J.

Little, B.

Little, H.

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8(5), 477–482 (2006).
[Crossref]

Liu, L.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

Lopez-Mariscal, C.

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8(5), 477–482 (2006).
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Mandel, L.

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

McGloin, D.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in several planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
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M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

Melville, H.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in several planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
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M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
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J. Durnin and J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
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M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature 387(6636), 880–882 (1997).
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M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77(3), 490–493 (1996).
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Miyamoto, Y.

Motka, L.

B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, and L. L. Sanchez-Soto, “Wavefront sensing reveals optical coherence,” Nat. Commun. 5, 3275 (2014).
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Motzek, K.

C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 94(4), 043904 (2004).
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Mourka, A.

Mukunda, N.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104(2), 023901 (2010).
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Novotny, L.

Nugent, K. A.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, and K. A. Nugent, “Diffractive imaging using partially coherent X-rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
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D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80(12), 2586–2589 (1998).
[Crossref]

Padgett, M. J.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

Paganin, D.

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80(12), 2586–2589 (1998).
[Crossref]

Ponomarenko, S. A.

Qian, X. F.

Quiney, H. M.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, and K. A. Nugent, “Diffractive imaging using partially coherent X-rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[Crossref]

Rehacek, J.

B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, and L. L. Sanchez-Soto, “Wavefront sensing reveals optical coherence,” Nat. Commun. 5, 3275 (2014).
[Crossref] [PubMed]

Z. Hradil, J. Rehacek, and L. L. Sanchez-Soto, “Quantum reconstruction of the mutual coherence function,” Phys. Rev. Lett. 105(1), 010401 (2010).
[Crossref] [PubMed]

Ring, J. D.

Robinson, I. K.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

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F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beam,” Nature Photon. 4(11), 780–786 (2010).
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Roux, F. S.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

Roychowdhury, H.

Ryczkowski, P.

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nature Photon. 10(3), 167–170 (2016).
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Saastamoinen, T.

Sahin, S.

Saleh, B. E. A.

K. H. Kagalwala, G. D. Guiseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nature Photon. 7(1), 72–78 (2013).
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T. Yarnall, A. F. Abourrady, B. E. A. Saleh, and M. C. Teich, “Spatial coherence effects in second-and fourth-order temporal interference,” Opt. Express 16(11), 7634–7640 (2008).
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B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, and L. L. Sanchez-Soto, “Wavefront sensing reveals optical coherence,” Nat. Commun. 5, 3275 (2014).
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Z. Hradil, J. Rehacek, and L. L. Sanchez-Soto, “Quantum reconstruction of the mutual coherence function,” Phys. Rev. Lett. 105(1), 010401 (2010).
[Crossref] [PubMed]

Santarsiero, M.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104(2), 023901 (2010).
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Scarcelli, G.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref] [PubMed]

Segev, M.

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature 387(6636), 880–882 (1997).
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M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77(3), 490–493 (1996).
[Crossref] [PubMed]

Shih, M.

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77(3), 490–493 (1996).
[Crossref] [PubMed]

Shih, M. F.

C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 94(4), 043904 (2004).
[Crossref]

Shih, Y.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref] [PubMed]

Sibbett, W.

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8(5), 477–482 (2006).
[Crossref]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in several planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

Simon, B. N.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104(2), 023901 (2010).
[Crossref] [PubMed]

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beam,” Nature Photon. 4(11), 780–786 (2010).
[Crossref]

Simon, R.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104(2), 023901 (2010).
[Crossref] [PubMed]

Simon, S.

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104(2), 023901 (2010).
[Crossref] [PubMed]

Singh, P. R.

Situ, G.

L. Waller, G. Situ, and J. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nature Photon. 6(7), 474–479 (2012).
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J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express 16(17), 12880–12885 (2008).
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G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
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Smith, R. L.

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8(5), 477–482 (2006).
[Crossref]

Stoklasa, B.

B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, and L. L. Sanchez-Soto, “Wavefront sensing reveals optical coherence,” Nat. Commun. 5, 3275 (2014).
[Crossref] [PubMed]

Takeda, M.

Tao, S. H.

Teich, M. C.

Vainty, P.

Valencia, A.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref] [PubMed]

Vine, D. J.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, and K. A. Nugent, “Diffractive imaging using partially coherent X-rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[Crossref]

Visser, T.D.

C. H. Gan, Y. Gu, T.D. Visser, and G. Gbur, “Coherence converting plasmonic hole arrays,” Plasmonics 7(2), 313–322 (2012).
[Crossref]

Vyas, S.

Waller, L.

L. Waller, G. Situ, and J. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nature Photon. 6(7), 474–479 (2012).
[Crossref]

Wang, F.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev A 91(1), 013823 (2015).
[Crossref]

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89(4), 043807 (2014).
[Crossref]

Wang, W.

Whitehead, L. W.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, and K. A. Nugent, “Diffractive imaging using partially coherent X-rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[Crossref]

Williams, G. J.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, and K. A. Nugent, “Diffractive imaging using partially coherent X-rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[Crossref]

Woerdeman, J. P.

A. Aiello and J. P. Woerdeman, “Physical bounds to the entropy-depolarization relation in random light scattering,” Phys. Rev. Lett. 94(9), 090406 (2005).
[Crossref] [PubMed]

Wolf, E.

H. Roychowdhury and E. Wolf, “Effects of spatial coherence on near-field spectra,” Opt. Lett. 28(3), 170–172 (2003).
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E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

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

Wu, G.

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89(4), 043807 (2014).
[Crossref]

Yarnall, T.

Yuan, X.

Zhao, C.

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

Appl. Opt. (1)

J. Opt. A (1)

P. Fischer, H. Little, R. L. Smith, C. Lopez-Mariscal, C. T. A. Brown, W. Sibbett, and K. Dholakia, “Wavelength dependent propagation and reconstruction of white light Bessel beams,” J. Opt. A 8(5), 477–482 (2006).
[Crossref]

J. Opt. Soc. Am. A (2)

Nat. Commun. (3)

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref] [PubMed]

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

B. Stoklasa, L. Motka, J. Rehacek, Z. Hradil, and L. L. Sanchez-Soto, “Wavefront sensing reveals optical coherence,” Nat. Commun. 5, 3275 (2014).
[Crossref] [PubMed]

Nature (2)

M. Mitchell and M. Segev, “Self-trapping of incoherent white light,” Nature 387(6636), 880–882 (1997).
[Crossref]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in several planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref] [PubMed]

Nature Photon. (4)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beam,” Nature Photon. 4(11), 780–786 (2010).
[Crossref]

L. Waller, G. Situ, and J. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nature Photon. 6(7), 474–479 (2012).
[Crossref]

P. Ryczkowski, M. Barbier, A. T. Friberg, J. M. Dudley, and G. Genty, “Ghost imaging in the time domain,” Nature Photon. 10(3), 167–170 (2016).
[Crossref]

K. H. Kagalwala, G. D. Guiseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nature Photon. 7(1), 72–78 (2013).
[Crossref]

Opt. Commun. (1)

Z. Bouchal, “Resistance of nondiffracting vortex beams to amplitude and phase perturbations,” Opt. Commun. 210(3), 155–164 (2002).
[Crossref]

Opt. Express (5)

Opt. Lett. (6)

Optica (2)

Phys. Rev A (1)

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev A 91(1), 013823 (2015).
[Crossref]

Phys. Rev. A (2)

Y. Chen, F. Wang, L. Liu, C. Zhao, Y. Cai, and O. Korotkova, “Generation and propagation of a partially coherent vector beam with special correlation functions,” Phys. Rev. A 89(1), 013801 (2014).
[Crossref]

G. Wu, F. Wang, and Y. Cai, “Generation and self-healing of a radially polarized Bessel-Gauss beam,” Phys. Rev. A 89(4), 043807 (2014).
[Crossref]

Phys. Rev. Lett. (12)

J. Durnin and J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77(3), 490–493 (1996).
[Crossref] [PubMed]

D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80(12), 2586–2589 (1998).
[Crossref]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, and K. A. Nugent, “Diffractive imaging using partially coherent X-rays,” Phys. Rev. Lett. 103(24), 243902 (2009).
[Crossref]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref] [PubMed]

A. Aiello and J. P. Woerdeman, “Physical bounds to the entropy-depolarization relation in random light scattering,” Phys. Rev. Lett. 94(9), 090406 (2005).
[Crossref] [PubMed]

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91(9), 093901 (2003).
[Crossref] [PubMed]

R. Carminati and J. J. Greffet, “Near-field effects in spatial coherence of thermal sources,” Phys. Rev. Lett. 82(8), 1660–1663 (1999).
[Crossref]

C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 94(4), 043904 (2004).
[Crossref]

Z. Hradil, J. Rehacek, and L. L. Sanchez-Soto, “Quantum reconstruction of the mutual coherence function,” Phys. Rev. Lett. 105(1), 010401 (2010).
[Crossref] [PubMed]

B. N. Simon, S. Simon, F. Gori, M. Santarsiero, R. Borghi, N. Mukunda, and R. Simon, “Nonquantum entanglement resolves a basic issue in polarization optics,” Phys. Rev. Lett. 104(2), 023901 (2010).
[Crossref] [PubMed]

Plasmonics (1)

C. H. Gan, Y. Gu, T.D. Visser, and G. Gbur, “Coherence converting plasmonic hole arrays,” Plasmonics 7(2), 313–322 (2012).
[Crossref]

Other (4)

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

J. W. Goodman, Statistical Optics, 2nd Ed., (Wiley, New York, 2015).

J. W. Goodman, Introduction to Fourier Optics, 2nd Ed., (McGraw-Hill, 1998).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

Supplementary Material (3)

NameDescription
» Visualization 1: MOV (926 KB)      visualization 1
» Visualization 2: MOV (750 KB)      visualization 2
» Visualization 3: MOV (141 KB)      visualization 3

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Figures (11)

Fig. 1
Fig. 1 Qualitative illustration of nearly incoherent beam scattering by an obstacle. Nearly incoherent beam of diameter σI and coherence length σc has a specular structure with each speckle beamlet having the spot size equal to the beam coherence length. The obstacle is modeled by a circular aperture of width σa.
Fig. 2
Fig. 2 Numerical self-reconstruction of a radially polarized Schell-model beam scattered by a sector-shaped opaque object (SSOO). Intensity and Stokes’ parameter distribution of the beam in the source plane and in the image plane with no obstruction (left column) and with the SSOO with the angle φ = 7π/4 (middle column) and φ = 71π/36 (right column). The beam parameters are: σI = 1.5mm and σc = 75µm and the SSOO has the same diameter as the beam, σa = σI.
Fig. 3
Fig. 3 Numerical transient dynamics of the RPSM beam scattered by a sector-shaped opaque object (SSOO) at several distances. a Intensity distribution of the beam at several propagation distance without obstructed. b Intensity distribution of the beam at several propagation distance with the SSOO center angle φ = 7π/4 and c with the SSOO center angle φ = 71π/36. The beam parameters are the same as Fig. 2.
Fig. 4
Fig. 4 Experimental transient dynamics of the RPSM beam scattered by a sector-shaped opaque object (SSOO) at several distances. a Intensity distribution of the beam at several propagation distance without obstructed. b Intensity distribution of the beam at several propagation distance with the SSOO center angle φ = 7π/4 and c with the SSOO center angle φ = 71π/36. The beam parameters are the same as Fig. 2.
Fig. 5
Fig. 5 Numerical self-reconstruction ability of a RPSM beam scattered by a SSOO. a Intensity distribution of the beam in the source plane with SSOO center angle φ = 71π/36. b, c, d and e Intensity distribution of the beam in the focal plane with different coherence length σc.
Fig. 6
Fig. 6 Experimental self-reconstruction ability of a RPSM beam scattered by a SSOO with center angle φ = 71π/36. a, b, c, and d Intensity distribution of the beam in the focal plane with different coherence length σc.
Fig. 7
Fig. 7 Experimental setup for RPSM beam self-reconstruction demonstration. Beam expander (BE), reflecting mirror; (RM), radial polarization converter (RPC), rotating ground-glass disk (RGGD); L1, L2, L3, thin lenses, Gaussian amplitude filter (GAF), sector-shaped opaque obstacle (SSOO), charge-coupled device (CCD).
Fig. 8
Fig. 8 Experimental beam self-reconstruction: Case 1. SSOO. Left column: Intensity and polarization distributions of the RPSM beam in the source and focal planes in the absence of obstruction. Middle column: The same as in the left column, except the SSOO blocking half of the beam cross-section is placed in the source plane. Right column: Same as the middle one with the SSOO having the center angle φ = 7π/4. The linearly polarized-with an inserted linear polarizer not shown in Fig. 3-imaged beam has the polarization direction indicated by the arrow. The beam polarization direction makes the angle θ with the x-axis.
Fig. 9
Fig. 9 Experimental beam self-reconstruction: case 2. Turbid medium. (a) Experimental setup for analyzing fully coherent radially polarized beam transmission through a turbid medium with random refractive index fluctuations. (b) Experimental setup for analyzing the RPSM beam transmission through the same turbid medium. (c) Photograph of the turbid medium (diluted milk). (d) Experimental intensity profile self-reconstruction of the fully coherent radially polarized beam passing through diluted milk at different instances of time t. (see also Visualization 1) (e) Experimental intensity profile self-reconstruction of the RPSM beam passing through diluted milk at different time instances t. (see Visualization 2 as well).
Fig. 10
Fig. 10 Radially polarized beam array generation through the RPSM source self-reconstruction. (a) Schematics of the apparatus for generation of a radially polarized beam array. (b) Numerical simulation results of the generated beam array intensity profile and the state of polarization. Both the diameter of each lens and the distance between the centers of adjacent lenses are 1mm. The focal length of the lens array is 65.6mm. (c), (d), (e) Stokes’ parameter distributions of the radially polarized beam array; (f), (g), (h), (i) experimental results of the generated radially polarized beam array intensity and the state of polarization. The arrow indicates the polarization direction of the beam.
Fig. 11
Fig. 11 Numerical formation of radial polarized beam array as a function of the input beam coherence. a-e Numerical simulation results of the generated beam array intensity profile with difference beam coherence.

Equations (12)

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A c A a < A I .
W i j ( 0 ) ( ρ 1 , ρ 2 ) = E i ( ρ 1 ) E j ( ρ 2 ) ,
W i j ( 0 ) ( ρ 1 , ρ 2 ) = I i ( ρ 1 ) I j ( ρ 2 ) g i j ( ρ 1 ρ 2 ) ,
S 0 ( ρ ) = W x x ( ρ , ρ ) + W y y ( ρ , ρ ) ,
S 1 ( ρ ) = W x x ( ρ , ρ ) W y y ( ρ , ρ ) ,
S 2 ( ρ ) = W x y ( ρ , ρ ) + W y x ( ρ , ρ ) ,
S 3 ( ρ ) = i ( W y x ( ρ , ρ ) W x y ( ρ , ρ ) ) ,
g a a ( ρ 1 , ρ 2 ) = [ 1 ( a 1 a 2 ) 2 σ c 2 ] exp [ ( ρ 1 ρ 2 ) 2 2 σ c 2 ]
g x y ( ρ 1 , ρ 2 ) = g y x ( ρ 1 , ρ 2 ) = ( x 1 x 2 ) ( y 1 y 2 ) σ c 2 exp [ ( ρ 1 ρ 2 ) 2 2 σ c 2 ] ,
T ( ρ ) = { 1 transmission region , 0 opaque region .
W i j ( s c ) ( ρ 1 , ρ 2 ) = T ( ρ 1 ) T ( ρ 2 ) I ( ρ 1 ) I ( ρ 2 ) g i j ( ρ 1 ρ 2 ) .
W i j ( ρ 1 , ρ 2 ) = 1 λ 2 f 2 W ˜ i j ( s c ) ( ρ 1 / λ f , ρ 2 / λ f ) ,

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