Abstract

Deterministic control of coherent random light is highly important for information transmission through complex media. However, only a few simple speckle transformations can be achieved through diffusers without prior characterization. As recently shown, spiral wavefront modulation of the impinging beam allows permuting intensity maxima and intrinsic ±1-charged optical vortices. Here, we study this cyclic-group algebra when combining spiral phase transforms of charge n, with D3- and D4-point-group symmetry starlike amplitude modulations. This combination allows for statistical strengthening of permutations and controlling of the period to be 3 and 4, respectively. Phase saddle points are shown to complete the cycle. These results offer new tools to manipulate critical points in speckles.

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

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References

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2019 (1)

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light Sci. Appl. 8, 27 (2019).
[Crossref]

2017 (4)

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, “Generalized optical memory effect,” Optica 4, 886–892 (2017).
[Crossref]

J. Gateau, H. Rigneault, and M. Guillon, “Complementary speckle patterns: deterministic interchange of intrinsic vortices and maxima through scattering media,” Phys. Rev. Lett. 118, 043903 (2017).
[Crossref]

Z. Yang, O. S. Magaña-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. H. Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light Sci. Appl. 6, e17013 (2017).
[Crossref]

G. Xie, H. Song, Z. Zhao, G. Milione, Y. Ren, C. Liu, R. Zhang, C. Bao, L. Li, Z. Wang, K. Pang, D. Starodubov, B. Lynn, M. Tur, and A. E. Willner, “Using a complex optical orbital-angular-momentum spectrum to measure object parameters,” Opt. Lett. 42, 4482–4485 (2017).
[Crossref]

2016 (2)

W. Zhang and L. Chen, “Encoding and decoding of digital spiral imaging based on bidirectional transformation of light’s spatial eigenmodes,” Opt. Lett. 41, 2843–2846 (2016).
[Crossref]

M. Pascucci, G. Tessier, V. Emiliani, and M. Guillon, “Superresolution imaging of optical vortices in a speckle pattern,” Phys. Rev. Lett. 116, 093904 (2016).
[Crossref]

2015 (2)

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
[Crossref]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).
[Crossref]

2014 (1)

2012 (2)

2011 (1)

F. Tournus, “Random nanoparticle deposition: inter-particle distances in 2D, 3D, and multilayer samples,” J. Nanopart. Res. 13, 5211–5223 (2011).
[Crossref]

2010 (1)

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[Crossref]

2009 (1)

R. W. Schoonover and T. D. Visser, “Creating polarization singularities with an N-pinhole interferometer,” Phys. Rev. A 79, 043809 (2009).
[Crossref]

2008 (1)

G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[Crossref]

2005 (2)

L. Torner, J. P. Torres, and S. Carrasco, “Digital spiral imaging,” Opt. Express 13, 873–881 (2005).
[Crossref]

A. Ferrando, M. Zacarés, M.-A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95, 123901 (2005).
[Crossref]

2003 (1)

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[Crossref]

2001 (1)

1998 (1)

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

1995 (1)

I. Freund, “Amplitude topological singularities in random electromagnetic wavefields,” Phys. Lett. A 198, 139–144 (1995).
[Crossref]

1994 (1)

1993 (1)

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
[Crossref]

1988 (3)

J. Nye, J. Hajnal, and J. Hannay, “Phase saddles and dislocations in two-dimensional waves such as the tides,” Proc. R. Soc. A 417, 7–20 (1988).
[Crossref]

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]

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[Crossref]

1983 (1)

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. A 336, 165–190 (1974).
[Crossref]

1960 (1)

Akkermans, E.

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

Bao, C.

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[Crossref]

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, “Method for probing the orbital angular momentum of optical vortices in electromagnetic waves from astronomical objects,” Phys. Rev. Lett. 101, 100801 (2008).
[Crossref]

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. A 336, 165–190 (1974).
[Crossref]

Bone, D. J.

Boyd, R. W.

Z. Yang, O. S. Magaña-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. H. Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light Sci. Appl. 6, e17013 (2017).
[Crossref]

B. Rodenburg, M. P. J. Lavery, M. Malik, M. N. O’Sullivan, M. Mirhosseini, D. J. Robertson, M. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett. 37, 3735–3737 (2012).
[Crossref]

Carrasco, S.

Chandler, D.

D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University, 1987).

Chávez-Cerda, S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[Crossref]

Chen, L.

Cheng, C.

Creath, K.

K. Creath and J. Schmit, “Interferometry: phase-measurement interferometry,” in Encyclopedia of Modern Optics, R. D. Guenther, ed. (Elsevier, 2005), pp. 364–374.

Curtis, J. E.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[Crossref]

de Córdoba, P. F.

A. Ferrando, M. Zacarés, M.-A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95, 123901 (2005).
[Crossref]

Dennis, M.

M. Dennis, “Topical singularities in wave fields,” Ph.D. thesis (University of Bristol, 2001).

Dennis, M. R.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Singular Optics: Optical Vortices and Polarization Singularities (Elsevier, 2009), pp. 293–363, Chap. 5.

Emiliani, V.

M. Pascucci, G. Tessier, V. Emiliani, and M. Guillon, “Superresolution imaging of optical vortices in a speckle pattern,” Phys. Rev. Lett. 116, 093904 (2016).
[Crossref]

M. Pascucci, S. Ganesan, A. Tripathi, O. Katz, V. Emiliani, and M. Guillon, “Compressive three-dimensional super-resolution microscopy with speckle-saturated fluorescence excitation,” arXiv:abs/1710.05056v2 (2017).

Feng, S.

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]

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[Crossref]

Ferrando, A.

A. Ferrando, M. Zacarés, M.-A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95, 123901 (2005).
[Crossref]

Fonseca, E. J. S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[Crossref]

Freilikher, V.

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
[Crossref]

Freund, I.

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

I. Freund, “Amplitude topological singularities in random electromagnetic wavefields,” Phys. Lett. A 198, 139–144 (1995).
[Crossref]

I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am. A 11, 1644–1652 (1994).
[Crossref]

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
[Crossref]

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[Crossref]

Ganesan, S.

M. Pascucci, S. Ganesan, A. Tripathi, O. Katz, V. Emiliani, and M. Guillon, “Compressive three-dimensional super-resolution microscopy with speckle-saturated fluorescence excitation,” arXiv:abs/1710.05056v2 (2017).

Gao, B.

Z. Yang, O. S. Magaña-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. H. Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light Sci. Appl. 6, e17013 (2017).
[Crossref]

Gao, L.

Z. Yang, O. S. Magaña-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. H. Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light Sci. Appl. 6, e17013 (2017).
[Crossref]

Gao, N.

García-March, M.-A.

A. Ferrando, M. Zacarés, M.-A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95, 123901 (2005).
[Crossref]

Gateau, J.

J. Gateau, H. Rigneault, and M. Guillon, “Complementary speckle patterns: deterministic interchange of intrinsic vortices and maxima through scattering media,” Phys. Rev. Lett. 118, 043903 (2017).
[Crossref]

Gong, L.

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light Sci. Appl. 8, 27 (2019).
[Crossref]

Goodman, J. W.

Grier, D. G.

J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
[Crossref]

Guillon, M.

J. Gateau, H. Rigneault, and M. Guillon, “Complementary speckle patterns: deterministic interchange of intrinsic vortices and maxima through scattering media,” Phys. Rev. Lett. 118, 043903 (2017).
[Crossref]

M. Pascucci, G. Tessier, V. Emiliani, and M. Guillon, “Superresolution imaging of optical vortices in a speckle pattern,” Phys. Rev. Lett. 116, 093904 (2016).
[Crossref]

M. Pascucci, S. Ganesan, A. Tripathi, O. Katz, V. Emiliani, and M. Guillon, “Compressive three-dimensional super-resolution microscopy with speckle-saturated fluorescence excitation,” arXiv:abs/1710.05056v2 (2017).

Hajnal, J.

J. Nye, J. Hajnal, and J. Hannay, “Phase saddles and dislocations in two-dimensional waves such as the tides,” Proc. R. Soc. A 417, 7–20 (1988).
[Crossref]

Hannay, J.

J. Nye, J. Hajnal, and J. Hannay, “Phase saddles and dislocations in two-dimensional waves such as the tides,” Proc. R. Soc. A 417, 7–20 (1988).
[Crossref]

Hickmann, J. M.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[Crossref]

Horstmeyer, R.

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, “Generalized optical memory effect,” Optica 4, 886–892 (2017).
[Crossref]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).
[Crossref]

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
[Crossref]

Hu, X.-Y.

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light Sci. Appl. 8, 27 (2019).
[Crossref]

Huang, K.

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light Sci. Appl. 8, 27 (2019).
[Crossref]

Judkewitz, B.

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, “Generalized optical memory effect,” Optica 4, 886–892 (2017).
[Crossref]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).
[Crossref]

Kane, C.

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]

Katz, O.

M. Pascucci, S. Ganesan, A. Tripathi, O. Katz, V. Emiliani, and M. Guillon, “Compressive three-dimensional super-resolution microscopy with speckle-saturated fluorescence excitation,” arXiv:abs/1710.05056v2 (2017).

Larkin, K. G.

Lavery, M. P. J.

Lee, P. A.

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]

Li, L.

Li, Y.-M.

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light Sci. Appl. 8, 27 (2019).
[Crossref]

Li, Z.

Liu, C.

Long, G.-L.

Z. Yang, O. S. Magaña-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. H. Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light Sci. Appl. 6, e17013 (2017).
[Crossref]

Longuet-Higgins, M. S.

Lynn, B.

Magaña-Loaiza, O. S.

Z. Yang, O. S. Magaña-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. H. Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light Sci. Appl. 6, e17013 (2017).
[Crossref]

Malik, M.

Milione, G.

Mirhosseini, M.

Z. Yang, O. S. Magaña-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. H. Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light Sci. Appl. 6, e17013 (2017).
[Crossref]

B. Rodenburg, M. P. J. Lavery, M. Malik, M. N. O’Sullivan, M. Mirhosseini, D. J. Robertson, M. Padgett, and R. W. Boyd, “Influence of atmospheric turbulence on states of light carrying orbital angular momentum,” Opt. Lett. 37, 3735–3737 (2012).
[Crossref]

Monsoriu, J. A.

A. Ferrando, M. Zacarés, M.-A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95, 123901 (2005).
[Crossref]

Montambaux, G.

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

Nye, J.

J. Nye, J. Hajnal, and J. Hannay, “Phase saddles and dislocations in two-dimensional waves such as the tides,” Proc. R. Soc. A 417, 7–20 (1988).
[Crossref]

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. A 336, 165–190 (1974).
[Crossref]

O’Holleran, K.

M. R. Dennis, K. O’Holleran, and M. J. Padgett, Singular Optics: Optical Vortices and Polarization Singularities (Elsevier, 2009), pp. 293–363, Chap. 5.

O’Sullivan, M. N.

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Pang, K.

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M. Pascucci, G. Tessier, V. Emiliani, and M. Guillon, “Superresolution imaging of optical vortices in a speckle pattern,” Phys. Rev. Lett. 116, 093904 (2016).
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M. Pascucci, S. Ganesan, A. Tripathi, O. Katz, V. Emiliani, and M. Guillon, “Compressive three-dimensional super-resolution microscopy with speckle-saturated fluorescence excitation,” arXiv:abs/1710.05056v2 (2017).

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J. Gateau, H. Rigneault, and M. Guillon, “Complementary speckle patterns: deterministic interchange of intrinsic vortices and maxima through scattering media,” Phys. Rev. Lett. 118, 043903 (2017).
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R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
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K. Creath and J. Schmit, “Interferometry: phase-measurement interferometry,” in Encyclopedia of Modern Optics, R. D. Guenther, ed. (Elsevier, 2005), pp. 364–374.

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J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
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Tur, M.

Vellekoop, I. M.

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, “Generalized optical memory effect,” Optica 4, 886–892 (2017).
[Crossref]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).
[Crossref]

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R. W. Schoonover and T. D. Visser, “Creating polarization singularities with an N-pinhole interferometer,” Phys. Rev. A 79, 043809 (2009).
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Willner, A. E.

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[Crossref]

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
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L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light Sci. Appl. 8, 27 (2019).
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Zhou, Y.

Z. Yang, O. S. Magaña-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. H. Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light Sci. Appl. 6, e17013 (2017).
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Appl. Opt. (1)

J. Nanopart. Res. (1)

F. Tournus, “Random nanoparticle deposition: inter-particle distances in 2D, 3D, and multilayer samples,” J. Nanopart. Res. 13, 5211–5223 (2011).
[Crossref]

J. Opt. Soc. Am. (2)

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

Light Sci. Appl. (2)

Z. Yang, O. S. Magaña-Loaiza, M. Mirhosseini, Y. Zhou, B. Gao, L. Gao, S. M. H. Rafsanjani, G.-L. Long, and R. W. Boyd, “Digital spiral object identification using random light,” Light Sci. Appl. 6, e17013 (2017).
[Crossref]

L. Gong, Q. Zhao, H. Zhang, X.-Y. Hu, K. Huang, J.-M. Yang, and Y.-M. Li, “Optical orbital-angular-momentum-multiplexed data transmission under high scattering,” Light Sci. Appl. 8, 27 (2019).
[Crossref]

Nat. Photonics (1)

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9, 563–571 (2015).
[Crossref]

Nat. Phys. (1)

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).
[Crossref]

Opt. Commun. (1)

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).
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Opt. Express (1)

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Phys. Rev. A (1)

R. W. Schoonover and T. D. Visser, “Creating polarization singularities with an N-pinhole interferometer,” Phys. Rev. A 79, 043809 (2009).
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Phys. Rev. Lett. (8)

A. Ferrando, M. Zacarés, M.-A. García-March, J. A. Monsoriu, and P. F. de Córdoba, “Vortex transmutation,” Phys. Rev. Lett. 95, 123901 (2005).
[Crossref]

J. Gateau, H. Rigneault, and M. Guillon, “Complementary speckle patterns: deterministic interchange of intrinsic vortices and maxima through scattering media,” Phys. Rev. Lett. 118, 043903 (2017).
[Crossref]

M. Pascucci, G. Tessier, V. Emiliani, and M. Guillon, “Superresolution imaging of optical vortices in a speckle pattern,” Phys. Rev. Lett. 116, 093904 (2016).
[Crossref]

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]

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[Crossref]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
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Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1. (a) Experimental setup used to measure the intensity and the phase of speckle patterns corresponding to the different binary amplitude masks. A spatial light modulator (SLM) is illuminated with a collimated laser beam at 635 nm. The phase is measured by phase-stepping interferometry. Both the reference and the signal wavefronts are imprinted on the SLM, in addition to a blazed grating that allows the sending of undiffracted light to a beam block (BB) and the first-order diffracted beam to a camera (Cam.). A stack of eight images was then sequentially recorded while phase shifting the reference beam. (b)–(d) The measured intensity I0 maps (top, green color scale) and phase Φ0 maps (bottom, gray colorscale) are presented for (b) a circular aperture (BA), (c) periodic angular slits with a point group symmetry D3 (BA3), and (d) periodic angular slits with a point group symmetry D4 (BA4). Miniatures of the BA masks are displayed for illustration.
Fig. 2.
Fig. 2. Statistical analysis of the separation distances between one set of critical points (here V0) and the closest point of another set (notated X). The distance between V0 and the closest X is denoted d(V0,X). (a) The radial probability density functions (RPDFs) of the nearest neighbor and (b) the corresponding weighted median distance (WMD) are shown. (c) Radial distribution functions (RDFs) of the nearest neighbor and (d) the corresponding weighted median normalized distance (WMND) provide a statistical toolbox for studying the spatial correlation between pairs of critical points. The results were derived from experimental measurements of In and Φn obtained for the amplitude mask BA.
Fig. 3.
Fig. 3. Weighted median normalized distance (WMND) for all possible pairs of critical points screened here and for the addition of spiral phase masks with charges up to n=±6. The WMND were computed from experimental measurements of In and Φn.
Fig. 4.
Fig. 4. (a) Cross correlation of the speckle patterns I0 and In with n0;6. The cross correlations illustrate the spatial distribution of the intensity in the point spread function associated with the combined amplitude and spiral phase masks. The color scale was set for the autocorrelations xcorr(I0,I0) and was kept for the intercorrelations xcorr(I0,In). A N periodicity is observed for the aperture BAN with N=3 or 4. Green circles mark the radial distance to the strongest peak. (b) Radial distance and (c) normalized amplitude of the strongest peak as a function of the charge of the spiral phase mask. The radial distance keeps increasing for the circular aperture BA, while it remains close or below λ/(2·NA) (the coherence length of the speckle) even for SPn with n3 for the aperture BAN and N=3 or 4. The amplitude decreases for BA, while it remains above 0.3 for BA3 and BA4.

Tables (3)

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Table 1. Notations for the Main Critical Points

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Table 2. Measured Average Number Density of Critical Points [Length Unit: λ/(2.NA)]a

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Table 3. Macroscopic Transformations Observed for the Critical Points Y0 with the Amplitude Mask BAa

Equations (1)

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BAN(θ)={1,if|θ(k12).2.πN|<π32withk1;N0,otherwise

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