Abstract

Laser speckles have become a fundamental component of the modern optics-research toolbox. Not only are speckle patterns the basis of numerous imaging techniques, but also, they are employed to generate optical potentials for cold atoms and colloidal particles. The ability to manipulate a speckle pattern’s spatial intensity correlations, particularly long-range (non-local) ones, is essential in numerous applications. A typical fully-developed speckle pattern, however, only possesses short-ranged (local) intensity correlations which are determined by the spatial field correlations. Here we experimentally demonstrate and theoretically develop a general method for creating fully-developed speckles with strong non-local intensity correlations. The functional form of the spatial intensity correlations can be arbitrarily tailored without altering the field correlations. Our approach provides a versatile and utilitarian framework for enhancing and controlling non-local correlations in speckle patterns.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (3)

2017 (2)

2016 (1)

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
[Crossref]

2015 (3)

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref] [PubMed]

D. Di Battista, G. Zacharakis, and M. Leonetti, “Enhanced adaptive focusing through semi-transparent media,” Sci. Rep. 5, 17406 (2015).
[Crossref] [PubMed]

A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
[Crossref]

2014 (1)

Y. Bromberg and H. Cao, “Generating non-Rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112, 213904 (2014).
[Crossref]

2013 (1)

T. Strudley, T. Zehender, C. Blejean, E. P. Bakkers, and O. L. Muskens, “Mesoscopic light transport by very strong collective multiple scattering in nanowire mats,” Nat. Photon. 7, 413–418 (2013).
[Crossref]

2012 (3)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref] [PubMed]

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

C. Sun, L. Waller, D. V. Dylov, and J. W. Fleischer, “Spectral dynamics of spatially incoherent modulation instability,” Phys. Rev. Lett. 108, 263902 (2012).
[Crossref] [PubMed]

2011 (3)

L. Pezzé, M. R. de Saint-Vincent, T. Bourdel, J.-P. Brantut, B. Allard, T. Plisson, A. Aspect, P. Bouyer, and L. Sanchez-Palencia, “Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder,” New J. Phys. 13, 095015 (2011).
[Crossref]

J. Mertz, “Optical sectioning microscopy with planar or structured illumination,” Nat. Methods 8, 811–819 (2011).
[Crossref] [PubMed]

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[Crossref]

2010 (1)

M. Robert-de Saint-Vincent, J.-P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D diffusive expansion of ultracold atoms in a disordered potential,” Phys. Rev. Lett. 104, 220602 (2010).
[Crossref] [PubMed]

2008 (2)

A. Yamilov, “Relation between channel and spatial mesoscopic correlations in volume-disordered waveguides,” Phys. Rev. B 78, 045104 (2008).
[Crossref]

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

2007 (2)

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phys. 9, 161 (2007).
[Crossref]

H. Funamizu and J. Uozumi, “Generation of fractal speckles by means of a spatial light modulator,” Opt. Express 15, 7415–7422 (2007).
[Crossref] [PubMed]

2006 (1)

G. Cwilich, L. S. Froufe-Pérez, and J. J. Sáenz, “Spatial wave intensity correlations in quasi-one-dimensional wires,” Phys. Rev. E 74, 045603 (2006).
[Crossref]

2000 (2)

P. Sebbah, R. Pnini, and A. Z. Genack, “Field and intensity correlation in random media,” Phys. Rev. E 62, 7348–7352 (2000).
[Crossref]

M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: A direct measurement of the density correlation function g(r),” Phys. Rev. Lett. 85, 1416–1419 (2000).
[Crossref] [PubMed]

1998 (1)

I. Freund, “"1001" correlations in random wave fields,” Waves Random Media 8, 119–158 (1998).
[Crossref]

1997 (1)

F. Scheffold, W. Härtl, G. Maret, and E. Matijević, “Observation of long-range correlations in temporal intensity fluctuations of light,” Phys. Rev. B 56, 10942–10952 (1997).
[Crossref]

1994 (1)

R. Berkovits and S. Feng, “Correlations in coherent multiple scattering,” Phys. Rep. 238, 135–172 (1994).
[Crossref]

1992 (2)

T. Yoshimura and K. Fujiwara, “Statistical properties of doubly scattered image speckle,” J. Opt. Soc. Am. A 9, 91–95 (1992).
[Crossref]

J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B 45, 658–666 (1992).
[Crossref]

1990 (2)

1988 (2)

P. A. Mello, E. Akkermans, and B. Shapiro, “Macroscopic approach to correlations in the electronic transmission and reflection from disordered conductors,” Phys. Rev. Lett. 61, 459–462 (1988).
[Crossref] [PubMed]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref] [PubMed]

1987 (1)

M. J. Stephen and G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
[Crossref] [PubMed]

1986 (1)

1983 (1)

1980 (1)

J. Nocedal, “Updating quasi-Newton matrices with limited storage,” Math. Comp. 35, 773–782 (1980).
[Crossref]

1970 (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

1956 (1)

R. H. Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).
[Crossref]

Akhlaghi, M. I.

Akkermans, E.

P. A. Mello, E. Akkermans, and B. Shapiro, “Macroscopic approach to correlations in the electronic transmission and reflection from disordered conductors,” Phys. Rev. Lett. 61, 459–462 (1988).
[Crossref] [PubMed]

E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2007).
[Crossref]

Allard, B.

L. Pezzé, M. R. de Saint-Vincent, T. Bourdel, J.-P. Brantut, B. Allard, T. Plisson, A. Aspect, P. Bouyer, and L. Sanchez-Palencia, “Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder,” New J. Phys. 13, 095015 (2011).
[Crossref]

M. Robert-de Saint-Vincent, J.-P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D diffusive expansion of ultracold atoms in a disordered potential,” Phys. Rev. Lett. 104, 220602 (2010).
[Crossref] [PubMed]

Ancora, D.

Asakura, T.

Aspect, A.

L. Pezzé, M. R. de Saint-Vincent, T. Bourdel, J.-P. Brantut, B. Allard, T. Plisson, A. Aspect, P. Bouyer, and L. Sanchez-Palencia, “Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder,” New J. Phys. 13, 095015 (2011).
[Crossref]

M. Robert-de Saint-Vincent, J.-P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D diffusive expansion of ultracold atoms in a disordered potential,” Phys. Rev. Lett. 104, 220602 (2010).
[Crossref] [PubMed]

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Bakkers, E. P.

T. Strudley, T. Zehender, C. Blejean, E. P. Bakkers, and O. L. Muskens, “Mesoscopic light transport by very strong collective multiple scattering in nanowire mats,” Nat. Photon. 7, 413–418 (2013).
[Crossref]

Barach, G.

Barakat, R.

Battista, D. Di

D. Di Battista, D. Ancora, G. Zacharakis, G. Ruocco, and M. Leonetti, “Hyperuniformity in amorphous speckle patterns,” Opt. Express 26, 15594–15608 (2018).
[Crossref] [PubMed]

D. Di Battista, G. Zacharakis, and M. Leonetti, “Enhanced adaptive focusing through semi-transparent media,” Sci. Rep. 5, 17406 (2015).
[Crossref] [PubMed]

Bechinger, C.

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
[Crossref]

Bender, N.

Berkovits, R.

R. Berkovits and S. Feng, “Correlations in coherent multiple scattering,” Phys. Rep. 238, 135–172 (1994).
[Crossref]

Bernard, A.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref] [PubMed]

Billy, J.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Blejean, C.

T. Strudley, T. Zehender, C. Blejean, E. P. Bakkers, and O. L. Muskens, “Mesoscopic light transport by very strong collective multiple scattering in nanowire mats,” Nat. Photon. 7, 413–418 (2013).
[Crossref]

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref] [PubMed]

Bourdel, T.

L. Pezzé, M. R. de Saint-Vincent, T. Bourdel, J.-P. Brantut, B. Allard, T. Plisson, A. Aspect, P. Bouyer, and L. Sanchez-Palencia, “Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder,” New J. Phys. 13, 095015 (2011).
[Crossref]

M. Robert-de Saint-Vincent, J.-P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D diffusive expansion of ultracold atoms in a disordered potential,” Phys. Rev. Lett. 104, 220602 (2010).
[Crossref] [PubMed]

Bouyer, P.

L. Pezzé, M. R. de Saint-Vincent, T. Bourdel, J.-P. Brantut, B. Allard, T. Plisson, A. Aspect, P. Bouyer, and L. Sanchez-Palencia, “Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder,” New J. Phys. 13, 095015 (2011).
[Crossref]

M. Robert-de Saint-Vincent, J.-P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D diffusive expansion of ultracold atoms in a disordered potential,” Phys. Rev. Lett. 104, 220602 (2010).
[Crossref] [PubMed]

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Brantut, J.-P.

L. Pezzé, M. R. de Saint-Vincent, T. Bourdel, J.-P. Brantut, B. Allard, T. Plisson, A. Aspect, P. Bouyer, and L. Sanchez-Palencia, “Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder,” New J. Phys. 13, 095015 (2011).
[Crossref]

M. Robert-de Saint-Vincent, J.-P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D diffusive expansion of ultracold atoms in a disordered potential,” Phys. Rev. Lett. 104, 220602 (2010).
[Crossref] [PubMed]

Bromberg, Y.

N. Bender, H. Yılmaz, Y. Bromberg, and H. Cao, “Customizing speckle intensity statistics,” Optica 5, 595–600 (2018).
[Crossref]

Y. Bromberg and H. Cao, “Generating non-Rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112, 213904 (2014).
[Crossref]

Brown, R. H.

R. H. Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).
[Crossref]

Cao, H.

N. Bender, H. Yılmaz, Y. Bromberg, and H. Cao, “Customizing speckle intensity statistics,” Optica 5, 595–600 (2018).
[Crossref]

Y. Bromberg and H. Cao, “Generating non-Rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112, 213904 (2014).
[Crossref]

Carminati, R.

A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
[Crossref]

Carpineti, M.

M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: A direct measurement of the density correlation function g(r),” Phys. Rev. Lett. 85, 1416–1419 (2000).
[Crossref] [PubMed]

Chriki, R.

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[Crossref]

Clément, D.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Correia, R. R. B.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref] [PubMed]

Cwilich, G.

G. Cwilich, L. S. Froufe-Pérez, and J. J. Sáenz, “Spatial wave intensity correlations in quasi-one-dimensional wires,” Phys. Rev. E 74, 045603 (2006).
[Crossref]

M. J. Stephen and G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
[Crossref] [PubMed]

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena, Topics in Applied Physics (Springer Berlin Heidelberg, 2013).

Davidson, N.

de Boer, J. F.

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L. Pezzé, M. R. de Saint-Vincent, T. Bourdel, J.-P. Brantut, B. Allard, T. Plisson, A. Aspect, P. Bouyer, and L. Sanchez-Palencia, “Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder,” New J. Phys. 13, 095015 (2011).
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Delande, D.

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phys. 9, 161 (2007).
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Dholakia, K.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
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M. I. Akhlaghi and A. Dogariu, “Tracking hidden objects using stochastic probing,” Optica 4, 447–453 (2017).
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A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
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C. Sun, L. Waller, D. V. Dylov, and J. W. Fleischer, “Spectral dynamics of spatially incoherent modulation instability,” Phys. Rev. Lett. 108, 263902 (2012).
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R. Berkovits and S. Feng, “Correlations in coherent multiple scattering,” Phys. Rep. 238, 135–172 (1994).
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S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
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Fischer, R.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
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Fleischer, J. W.

C. Sun, L. Waller, D. V. Dylov, and J. W. Fleischer, “Spectral dynamics of spatially incoherent modulation instability,” Phys. Rev. Lett. 108, 263902 (2012).
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L. Waller, G. Situ, and J. W. Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photon. 6, 474–479 (2012).
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A. Z. Genack, N. Garcia, and W. Polkosnik, “Long-range intensity correlation in random media,” Phys. Rev. Lett. 65, 2129–2132 (1990).
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P. Sebbah, R. Pnini, and A. Z. Genack, “Field and intensity correlation in random media,” Phys. Rev. E 62, 7348–7352 (2000).
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A. Z. Genack, N. Garcia, and W. Polkosnik, “Long-range intensity correlation in random media,” Phys. Rev. Lett. 65, 2129–2132 (1990).
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M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: A direct measurement of the density correlation function g(r),” Phys. Rev. Lett. 85, 1416–1419 (2000).
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Gilboa, D.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
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Härtl, W.

F. Scheffold, W. Härtl, G. Maret, and E. Matijević, “Observation of long-range correlations in temporal intensity fluctuations of light,” Phys. Rev. B 56, 10942–10952 (1997).
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Hickman, J.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
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S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
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Kato, K.

Kuhn, R. C.

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phys. 9, 161 (2007).
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A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

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J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
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J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B 45, 658–666 (1992).
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S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
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Leonardo, R. Di

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
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Leonetti, M.

D. Di Battista, D. Ancora, G. Zacharakis, G. Ruocco, and M. Leonetti, “Hyperuniformity in amorphous speckle patterns,” Opt. Express 26, 15594–15608 (2018).
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D. Di Battista, G. Zacharakis, and M. Leonetti, “Enhanced adaptive focusing through semi-transparent media,” Sci. Rep. 5, 17406 (2015).
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C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
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J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
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L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University, 1995).
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F. Scheffold, W. Härtl, G. Maret, and E. Matijević, “Observation of long-range correlations in temporal intensity fluctuations of light,” Phys. Rev. B 56, 10942–10952 (1997).
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Matijevic, E.

F. Scheffold, W. Härtl, G. Maret, and E. Matijević, “Observation of long-range correlations in temporal intensity fluctuations of light,” Phys. Rev. B 56, 10942–10952 (1997).
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P. A. Mello, E. Akkermans, and B. Shapiro, “Macroscopic approach to correlations in the electronic transmission and reflection from disordered conductors,” Phys. Rev. Lett. 61, 459–462 (1988).
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Mertz, J.

J. Mertz, “Optical sectioning microscopy with planar or structured illumination,” Nat. Methods 8, 811–819 (2011).
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Miniatura, C.

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phys. 9, 161 (2007).
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E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Photons (Cambridge University, 2007).
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J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
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Müller, C. A.

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phys. 9, 161 (2007).
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Muskens, O. L.

T. Strudley, T. Zehender, C. Blejean, E. P. Bakkers, and O. L. Muskens, “Mesoscopic light transport by very strong collective multiple scattering in nanowire mats,” Nat. Photon. 7, 413–418 (2013).
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Nocedal, J.

J. Nocedal, “Updating quasi-Newton matrices with limited storage,” Math. Comp. 35, 773–782 (1980).
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Pecora, R.

R. Pecora, Dynamic light scattering: applications of photon correlation spectroscopy (Springer Science & Business Media, 2013).

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L. Pezzé, M. R. de Saint-Vincent, T. Bourdel, J.-P. Brantut, B. Allard, T. Plisson, A. Aspect, P. Bouyer, and L. Sanchez-Palencia, “Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder,” New J. Phys. 13, 095015 (2011).
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M. Robert-de Saint-Vincent, J.-P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D diffusive expansion of ultracold atoms in a disordered potential,” Phys. Rev. Lett. 104, 220602 (2010).
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Plisson, T.

L. Pezzé, M. R. de Saint-Vincent, T. Bourdel, J.-P. Brantut, B. Allard, T. Plisson, A. Aspect, P. Bouyer, and L. Sanchez-Palencia, “Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder,” New J. Phys. 13, 095015 (2011).
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M. Robert-de Saint-Vincent, J.-P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D diffusive expansion of ultracold atoms in a disordered potential,” Phys. Rev. Lett. 104, 220602 (2010).
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Pnini, R.

P. Sebbah, R. Pnini, and A. Z. Genack, “Field and intensity correlation in random media,” Phys. Rev. E 62, 7348–7352 (2000).
[Crossref]

Polkosnik, W.

A. Z. Genack, N. Garcia, and W. Polkosnik, “Long-range intensity correlation in random media,” Phys. Rev. Lett. 65, 2129–2132 (1990).
[Crossref] [PubMed]

Prado, S. D.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref] [PubMed]

Reichhardt, C.

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
[Crossref]

Ribeiro-Teixeira, A. C.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
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Ritsch-Marte, M.

Robert-de Saint-Vincent, M.

M. Robert-de Saint-Vincent, J.-P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D diffusive expansion of ultracold atoms in a disordered potential,” Phys. Rev. Lett. 104, 220602 (2010).
[Crossref] [PubMed]

Ruocco, G.

Sáenz, J. J.

G. Cwilich, L. S. Froufe-Pérez, and J. J. Sáenz, “Spatial wave intensity correlations in quasi-one-dimensional wires,” Phys. Rev. E 74, 045603 (2006).
[Crossref]

Sanchez-Palencia, L.

L. Pezzé, M. R. de Saint-Vincent, T. Bourdel, J.-P. Brantut, B. Allard, T. Plisson, A. Aspect, P. Bouyer, and L. Sanchez-Palencia, “Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder,” New J. Phys. 13, 095015 (2011).
[Crossref]

M. Robert-de Saint-Vincent, J.-P. Brantut, B. Allard, T. Plisson, L. Pezzé, L. Sanchez-Palencia, A. Aspect, T. Bourdel, and P. Bouyer, “Anisotropic 2D diffusive expansion of ultracold atoms in a disordered potential,” Phys. Rev. Lett. 104, 220602 (2010).
[Crossref] [PubMed]

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Sars, V. D.

Scheffold, F.

F. Scheffold, W. Härtl, G. Maret, and E. Matijević, “Observation of long-range correlations in temporal intensity fluctuations of light,” Phys. Rev. B 56, 10942–10952 (1997).
[Crossref]

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P. Sebbah, R. Pnini, and A. Z. Genack, “Field and intensity correlation in random media,” Phys. Rev. E 62, 7348–7352 (2000).
[Crossref]

Shapiro, B.

P. A. Mello, E. Akkermans, and B. Shapiro, “Macroscopic approach to correlations in the electronic transmission and reflection from disordered conductors,” Phys. Rev. Lett. 61, 459–462 (1988).
[Crossref] [PubMed]

Sigwarth, O.

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phys. 9, 161 (2007).
[Crossref]

Silberberg, Y.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref] [PubMed]

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

Smartsev, S.

Stephen, M. J.

M. J. Stephen and G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
[Crossref] [PubMed]

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref] [PubMed]

Strudley, T.

T. Strudley, T. Zehender, C. Blejean, E. P. Bakkers, and O. L. Muskens, “Mesoscopic light transport by very strong collective multiple scattering in nanowire mats,” Nat. Photon. 7, 413–418 (2013).
[Crossref]

Sun, C.

C. Sun, L. Waller, D. V. Dylov, and J. W. Fleischer, “Spectral dynamics of spatially incoherent modulation instability,” Phys. Rev. Lett. 108, 263902 (2012).
[Crossref] [PubMed]

Takai, N.

Tradosnky, C.

Twiss, R. Q.

R. H. Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).
[Crossref]

Uozumi, J.

Vailati, A.

M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: A direct measurement of the density correlation function g(r),” Phys. Rev. Lett. 85, 1416–1419 (2000).
[Crossref] [PubMed]

van Albada, M. P.

J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B 45, 658–666 (1992).
[Crossref]

van Putten, E. G.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref] [PubMed]

Vidal, I.

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref] [PubMed]

Volpe, G.

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
[Crossref]

C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016).
[Crossref]

Vos, W. L.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref] [PubMed]

Waller, L.

C. Sun, L. Waller, D. V. Dylov, and J. W. Fleischer, “Spectral dynamics of spatially incoherent modulation instability,” Phys. Rev. Lett. 108, 263902 (2012).
[Crossref] [PubMed]

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

Wolf, E.

L. Mandel and E. Wolf, Optical coherence and quantum optics (Cambridge University, 1995).
[Crossref]

Yamilov, A.

A. Yamilov, “Relation between channel and spatial mesoscopic correlations in volume-disordered waveguides,” Phys. Rev. B 78, 045104 (2008).
[Crossref]

Yilmaz, H.

Yoshimura, T.

Zacharakis, G.

D. Di Battista, D. Ancora, G. Zacharakis, G. Ruocco, and M. Leonetti, “Hyperuniformity in amorphous speckle patterns,” Opt. Express 26, 15594–15608 (2018).
[Crossref] [PubMed]

D. Di Battista, G. Zacharakis, and M. Leonetti, “Enhanced adaptive focusing through semi-transparent media,” Sci. Rep. 5, 17406 (2015).
[Crossref] [PubMed]

Zehender, T.

T. Strudley, T. Zehender, C. Blejean, E. P. Bakkers, and O. L. Muskens, “Mesoscopic light transport by very strong collective multiple scattering in nanowire mats,” Nat. Photon. 7, 413–418 (2013).
[Crossref]

Zuo, Z.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Appl. Opt. (2)

Astron. Astrophys. (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

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

Math. Comp. (1)

J. Nocedal, “Updating quasi-Newton matrices with limited storage,” Math. Comp. 35, 773–782 (1980).
[Crossref]

Nat. Methods (1)

J. Mertz, “Optical sectioning microscopy with planar or structured illumination,” Nat. Methods 8, 811–819 (2011).
[Crossref] [PubMed]

Nat. Photon. (3)

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[Crossref]

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

T. Strudley, T. Zehender, C. Blejean, E. P. Bakkers, and O. L. Muskens, “Mesoscopic light transport by very strong collective multiple scattering in nanowire mats,” Nat. Photon. 7, 413–418 (2013).
[Crossref]

Nature (3)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref] [PubMed]

R. H. Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177, 27–29 (1956).
[Crossref]

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

New J. Phys. (2)

R. C. Kuhn, O. Sigwarth, C. Miniatura, D. Delande, and C. A. Müller, “Coherent matter wave transport in speckle potentials,” New J. Phys. 9, 161 (2007).
[Crossref]

L. Pezzé, M. R. de Saint-Vincent, T. Bourdel, J.-P. Brantut, B. Allard, T. Plisson, A. Aspect, P. Bouyer, and L. Sanchez-Palencia, “Regimes of classical transport of cold gases in a two-dimensional anisotropic disorder,” New J. Phys. 13, 095015 (2011).
[Crossref]

Opt. Express (4)

Optica (2)

Phys. Rep. (2)

R. Berkovits and S. Feng, “Correlations in coherent multiple scattering,” Phys. Rep. 238, 135–172 (1994).
[Crossref]

A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
[Crossref]

Phys. Rev. B (3)

A. Yamilov, “Relation between channel and spatial mesoscopic correlations in volume-disordered waveguides,” Phys. Rev. B 78, 045104 (2008).
[Crossref]

J. F. de Boer, M. P. van Albada, and A. Lagendijk, “Transmission and intensity correlations in wave propagation through random media,” Phys. Rev. B 45, 658–666 (1992).
[Crossref]

F. Scheffold, W. Härtl, G. Maret, and E. Matijević, “Observation of long-range correlations in temporal intensity fluctuations of light,” Phys. Rev. B 56, 10942–10952 (1997).
[Crossref]

Phys. Rev. E (2)

P. Sebbah, R. Pnini, and A. Z. Genack, “Field and intensity correlation in random media,” Phys. Rev. E 62, 7348–7352 (2000).
[Crossref]

G. Cwilich, L. S. Froufe-Pérez, and J. J. Sáenz, “Spatial wave intensity correlations in quasi-one-dimensional wires,” Phys. Rev. E 74, 045603 (2006).
[Crossref]

Phys. Rev. Lett. (9)

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[Crossref] [PubMed]

M. J. Stephen and G. Cwilich, “Intensity correlation functions and fluctuations in light scattered from a random medium,” Phys. Rev. Lett. 59, 285–287 (1987).
[Crossref] [PubMed]

P. A. Mello, E. Akkermans, and B. Shapiro, “Macroscopic approach to correlations in the electronic transmission and reflection from disordered conductors,” Phys. Rev. Lett. 61, 459–462 (1988).
[Crossref] [PubMed]

A. Z. Genack, N. Garcia, and W. Polkosnik, “Long-range intensity correlation in random media,” Phys. Rev. Lett. 65, 2129–2132 (1990).
[Crossref] [PubMed]

R. Fischer, I. Vidal, D. Gilboa, R. R. B. Correia, A. C. Ribeiro-Teixeira, S. D. Prado, J. Hickman, and Y. Silberberg, “Light with tunable non-Markovian phase imprint,” Phys. Rev. Lett. 115, 073901 (2015).
[Crossref] [PubMed]

C. Sun, L. Waller, D. V. Dylov, and J. W. Fleischer, “Spectral dynamics of spatially incoherent modulation instability,” Phys. Rev. Lett. 108, 263902 (2012).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 Enhancing non-local correlations in speckles. A Rayleigh speckle pattern (a,c) with C I ( Δ r ) = | C E ( Δ r ) | 2 (e), is compared to an "enlarged Rayleigh" speckle pattern (b,d) with C I ( Δ r ) much broader than | C E ( Δ r ) | 2 (f). The non-local intensity correlations, C N L ( Δ r ) , have comparable strength to the local correlations, C L ( Δ r ) = | C E ( Δ r ) | 2 , in (f). The correlation functions in (e,f) are obtained by averaging over 100 independent speckle patterns. Similar to the Rayleigh speckle pattern, the customized speckle field is fully developed with a uniform phase distribution between 0 and 2 π .
Fig. 2
Fig. 2 Creating speckle patterns with spatially oscillating, anisotropic long-range intensity correlations. The intensity correlation function C I ( Δ r ) (a), determines the Fourier amplitude profile of I ( r ) (b). An experimentally generated speckle intensity-pattern I ( r ) (c) possessing the correlations given in (a), and the corresponding phase profile θ ( r ) (d). θ is uniformly distributed between 0 and 2 π , confirming that the speckle pattern is fully developed. The local intensity correlation function C L ( Δ r ) (e) has a maximum value of 1, while the non-local intensity correlation function C L ( Δ r ) (f) has a maximum/minimum value of ± 0.1 . The correlation functions in (a,e,f) are obtained by averaging over 100 speckle patterns. The origins in (a,b,e,f) are located at the plots' centers.
Fig. 3
Fig. 3 Tuning the speckle contrast independently from the spatial intensity correlation function. Two experimentally generated speckle patterns (a,c) with congruent intensity correlation functions (b,d). The intensity contrast is 0.68 in (a) and 1.35 in (c). The origin for (b) and (d) is located at the center of the plots.
Fig. 4
Fig. 4 Introducing spatially simple anisotropic non-local correlations into speckles. The spatial intensity correlation function (a) is sparse. The local correlation function (b) has a maximum amplitude of 1, while the non-local correlation function (c) has a maximum/minimum amplitude of ± 0.2 . An ordered intensity pattern g ( r ) (d), produced by the Gerchberg Saxton algorithm, is convolved with super-Rayleigh speckle pattern J ( r ) (e) to generate a speckle intensity pattern I ( r ) (f) with the desired non-local correlations given in (c). The correlation functions in (a,b,c) are obtained by averaging over 100 speckle patterns and the origins are located at the plots' centers.
Fig. 5
Fig. 5 Axial evolution of a customized speckle pattern. An example customized speckle pattern (a), on the plane of customization z = 0, is juxtaposed with it’s corresponding spatial intensity correlation function (d). The speckle pattern (b) and its intensity correlation function (e), after axially propagating to z = R l / 3 , are presented. At this distance, the magnitude of the non-local correlations has reduced by half. The speckle pattern (c) and its intensity correlation function (f) are shown after further propagation to z = 2 R l / 3 . At this point, the non-local correlations are completely erased and only the local correlations remain. The correlation functions in (d,e,f) are obtained by averaging over 100 different speckle patterns, and the origins are located at the center of the plots.

Equations (12)

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C I ( Δ r ) I ( r ) I ( r + Δ r ) / I ( r ) I ( r + Δ r ) 1 = C L ( Δ r ) + C N L ( Δ r ) .
E ( r ) = 1 L ρ = 0 L 1 ε ( ρ ) e i 2 π L r ρ
C E ( Δ r ) = 1 L ρ = 0 L 1 | ε ( ρ ) | 2 e i 2 π L Δ r ρ .
C L ( Δ r ) = 1 L 2 ρ 1 , ρ 2 = 0 L 1 | ε ( ρ 1 ) | 2 | ε ( ρ 2 ) | 2 e i 2 π L Δ r ( ρ 2 ρ 1 ) .
I ( r ) I ( r + Δ r ) = 1 L 2 ρ 1 , ρ 2 , ρ 3 , ρ 4 = 0 L 1 ε ( ρ 1 ) ε * ( ρ 2 ) ε ( ρ 3 ) ε * ( ρ 4 ) e i 2 π L [ r ( ρ 1 ρ 2 ) + ( r + Δ r ) ( ρ 3 ρ 4 ) ] .
C I ( Δ r ) = C 1 ( Δ r ) + C 2 ( Δ r ) + C 3 ( Δ r ) + C 4 ( Δ r ) 1
C 1 ( Δ r ) = 1 L 2 ρ 1 = 0 L 1 | ε ( ρ 1 ) | 4
C 2 ( Δ r ) = 1 L 2 ρ 1 , ρ 2 = 0 ρ 1 ρ 2 L 1 | ε ( ρ 1 ) | 2 | ε ( ρ 2 ) | 2 ( 1 + e i 2 π L Δ r ( ρ 2 ρ 1 ) )
C 3 ( Δ r ) = 2 L 2 [ ρ 1 , ρ 2 = 0 ρ 1 ρ 2 L 1 ε ( ρ 1 ) 2 ε * ( ρ 2 ) ε * ( 2 ρ 1 ρ 2 ) e i 2 π L Δ r ( ρ 2 ρ 1 ) ]
C 4 ( Δ r ) = 1 L 2 ρ 1 , ρ 2 , ρ 3 = 0 ρ 1 ρ 2 ρ 3 L 1 ε ( ρ 1 ) ε * ( ρ 2 ) ε ( ρ 3 ) ε * ( ρ 1 ρ 2 + ρ 3 ) e i 2 π L Δ r ( ρ 2 ρ 1 ) .
C I ( Δ r ) C 2 ( Δ r ) + C 4 ( Δ r ) 1.
C I ( Δ r ) = C L ( Δ r ) + C 4 ( Δ r )

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