Abstract

Classical optic entanglement between the radial and angular degrees of freedom in Laguerre–Gaussian mode superpositions is explored within the framework of symmetric first-order optical systems. The Gouy phase picked by a Laguerre–Gaussian mode on free propagation is seen to be of consequence to the radial–angular entanglement in the mode superpositions. We illustrate examples of mode superpositions for which radial–angular entanglement is preserved on passage through symmetric first-order optical systems. An indicator of radial–angular entanglement in two-mode Laguerre–Gaussian superpositions is demonstrated to be a robust free space signaler in the presence of atmospheric turbulence, through examples.

© 2018 Optical Society of America

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2018 (1)

P. A. A. Yasir and J. S. Ivan, “Estimation of phases with dislocations in paraxial wave fields from intensity measurements,” Phys. Rev. A 97, 023817 (2018).
[Crossref]

2017 (3)

V. Madhu and J. S. Ivan, “Robustness of the twist parameter of Laguerre-Gaussian mode superpositions against atmospheric turbulence,” Phys. Rev. A 95, 043836 (2017).
[Crossref]

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397–402 (2017).
[Crossref]

P. A. A. Yasir and J. S. Ivan, “Realization of first-order optical systems using thin lenses of positive focal length,” J. Opt. Soc. Am. A 34, 2007–2012 (2017).
[Crossref]

2016 (2)

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, “Quantum and classical optics-emerging links,” Phys. Scr. 91, 063003 (2016).
[Crossref]

X.-F. Qian, T. Malhotra, A. N. Vamivakas, and J. H. Eberly, “Coherence constraints and the last hidden optical coherence,” Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

2015 (5)

2014 (6)

P. A. A. Yasir and J. S. Ivan, “Realization of first-order optical systems using thin convex lenses of fixed focal length,” J. Opt. Soc. Am. A 31, 2011–2020 (2014).
[Crossref]

R. Sharma, J. S. Ivan, and C. S. Narayanamurthy, “Wave propagation analysis using the variance matrix,” J. Opt. Soc. Am. A 31, 2185–2191 (2014).
[Crossref]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

P. Ghose and A. Mukherjee, “Entanglement in classical optics,” Rev. Theor. Sci. 2, 274–288 (2014).
[Crossref]

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement: oxymoron or resource?” New J. Phys. 17, 043024 (2014).
[Crossref]

T. Baumgratz, M. Cramer, and M. B. Plenio, “Quantifying coherence,” Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

2013 (1)

P. Chowdhury, A. S. Majumdar, and G. S. Agarwal, “Nonlocal continuous variable correlations and violation of Bell’s inequality for light beams with topological singularities,” Phys. Rev. A 88, 013830 (2013).
[Crossref]

2011 (1)

2010 (3)

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, “A complete characterization of pre-Mueller and Mueller matrices in polarization optics,” J. Opt. Soc. Am. A 27, 188–199 (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, 023901 (2010).
[Crossref]

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

2009 (1)

2008 (1)

2006 (1)

B. Schäfer, M. Lübbecke, and K. Mann, “Hartmann-Shack wavefront measurements for real time determination of laser beam propagation parameters,” Rev. Sci. Instrum. 77, 053103 (2006).
[Crossref]

2005 (1)

L. Lamata and J. León, “Dealing with entanglement of continuous variables: Schmidt decomposition with discrete sets of orthogonal functions,” J. Opt. B 7, 224–229 (2005).
[Crossref]

2004 (1)

2002 (3)

2001 (1)

R. J. C. Spreeuw, “Classical wave-optics analogy of quantum-information processing,” Phys. Rev. A 63, 062302 (2001).
[Crossref]

2000 (3)

1998 (2)

J. Courtial, “Self-imaging beams and the Gouy effect,” Opt. Commun. 151, 1–4 (1998).
[Crossref]

R. J. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
[Crossref]

1997 (1)

1994 (1)

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

1990 (1)

1988 (1)

1987 (1)

1985 (1)

E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realization of first order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).
[Crossref]

1966 (1)

Aadhi, A.

S. Prabhakar, S. G. Reddy, A. Aadhi, C. Perumangatt, G. K. Samanta, and R. P. Singh, “Violation of Bell’s inequality for phase-singular beams,” Phys. Rev. A 92, 023822 (2015).
[Crossref]

Agarwal, G. S.

P. Chowdhury, A. S. Majumdar, and G. S. Agarwal, “Nonlocal continuous variable correlations and violation of Bell’s inequality for light beams with topological singularities,” Phys. Rev. A 88, 013830 (2013).
[Crossref]

Aiello, A.

S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2, 864–868 (2015).
[Crossref]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement: oxymoron or resource?” New J. Phys. 17, 043024 (2014).
[Crossref]

Al Qasimi, A.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, “Quantum and classical optics-emerging links,” Phys. Scr. 91, 063003 (2016).
[Crossref]

Ali, H.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, “Quantum and classical optics-emerging links,” Phys. Scr. 91, 063003 (2016).
[Crossref]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Alonso, M. A.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, “Quantum and classical optics-emerging links,” Phys. Scr. 91, 063003 (2016).
[Crossref]

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

Arvind,

Arvind, S. Chaturvedi, and N. Mukunda, “Entanglement and complete positivity: relevance and manifestations in classical scalar wave optics,” arXiv:1710.01086 (2017).

Banzer, P.

Baumgratz, T.

T. Baumgratz, M. Cramer, and M. B. Plenio, “Quantifying coherence,” Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Belmonte, A.

Berg-Johansen, S.

Borges, C. V. S.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

Borghi, R.

Bracher, C.

Chaturvedi, S.

Arvind, S. Chaturvedi, and N. Mukunda, “Entanglement and complete positivity: relevance and manifestations in classical scalar wave optics,” arXiv:1710.01086 (2017).

Chowdhury, P.

P. Chowdhury, A. S. Majumdar, and G. S. Agarwal, “Nonlocal continuous variable correlations and violation of Bell’s inequality for light beams with topological singularities,” Phys. Rev. A 88, 013830 (2013).
[Crossref]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2004).

Courtial, J.

J. Courtial, “Self-imaging beams and the Gouy effect,” Opt. Commun. 151, 1–4 (1998).
[Crossref]

Cramer, M.

T. Baumgratz, M. Cramer, and M. B. Plenio, “Quantifying coherence,” Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

Dan, Y.

Davidson, F. M.

Eberly, J. H.

X.-F. Qian, T. Malhotra, A. N. Vamivakas, and J. H. Eberly, “Coherence constraints and the last hidden optical coherence,” Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, “Quantum and classical optics-emerging links,” Phys. Scr. 91, 063003 (2016).
[Crossref]

X.-F. Qian, B. Little, J. C. Howell, and J. H. Eberly, “Shifting the quantum-classical boundary: theory and experiment for statistically classical optical fields,” Optica 2, 611–615 (2015).
[Crossref]

X.-F. Qian and J. H. Eberly, “Entanglement and classical polarization states,” Opt. Lett. 36, 4110–4112 (2011).
[Crossref]

Eisert, J.

J. Eisert, C. Simon, and M. B. Plenio, “On the quantification of entanglement in infinite-dimensional quantum systems,” J. Phys. A 35, 3911–3923 (2002).
[Crossref]

Erdélyi, A.

A. Erdélyi, Tables of Integral Transforms (McGraw-Hill, 1954), Vol. 2, p. 43.

Erden, M. F.

Flatté, S. M.

Forbes, A.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397–402 (2017).
[Crossref]

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A 92, 023833 (2015).
[Crossref]

Gbur, G.

Ghose, P.

P. Ghose and A. Mukherjee, “Entanglement in classical optics,” Rev. Theor. Sci. 2, 274–288 (2014).
[Crossref]

Giacobino, E.

S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2, 864–868 (2015).
[Crossref]

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement: oxymoron or resource?” New J. Phys. 17, 043024 (2014).
[Crossref]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).

Gori, F.

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, “A complete characterization of pre-Mueller and Mueller matrices in polarization optics,” J. Opt. Soc. Am. A 27, 188–199 (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, 023901 (2010).
[Crossref]

Goswami, K.

Gutiérrez-Cuevas, R.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, “Quantum and classical optics-emerging links,” Phys. Scr. 91, 063003 (2016).
[Crossref]

Hernandez-Aranda, R. I.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397–402 (2017).
[Crossref]

Hor-Meyll, M.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

Howell, J. C.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, “Quantum and classical optics-emerging links,” Phys. Scr. 91, 063003 (2016).
[Crossref]

X.-F. Qian, B. Little, J. C. Howell, and J. H. Eberly, “Shifting the quantum-classical boundary: theory and experiment for statistically classical optical fields,” Optica 2, 611–615 (2015).
[Crossref]

Huguenin, J. A. O.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

Ivan, J. S.

Khoury, A. Z.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

Kogelnik, H.

Konrad, T.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397–402 (2017).
[Crossref]

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A 92, 023833 (2015).
[Crossref]

Lamata, L.

L. Lamata and J. León, “Dealing with entanglement of continuous variables: Schmidt decomposition with discrete sets of orthogonal functions,” J. Opt. B 7, 224–229 (2005).
[Crossref]

León, J.

L. Lamata and J. León, “Dealing with entanglement of continuous variables: Schmidt decomposition with discrete sets of orthogonal functions,” J. Opt. B 7, 224–229 (2005).
[Crossref]

Leuchs, G.

S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2, 864–868 (2015).
[Crossref]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement: oxymoron or resource?” New J. Phys. 17, 043024 (2014).
[Crossref]

Li, T.

Little, B.

Little, B. J.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, “Quantum and classical optics-emerging links,” Phys. Scr. 91, 063003 (2016).
[Crossref]

Lübbecke, M.

B. Schäfer, M. Lübbecke, and K. Mann, “Hartmann-Shack wavefront measurements for real time determination of laser beam propagation parameters,” Rev. Sci. Instrum. 77, 053103 (2006).
[Crossref]

Madhu, V.

V. Madhu and J. S. Ivan, “Robustness of the twist parameter of Laguerre-Gaussian mode superpositions against atmospheric turbulence,” Phys. Rev. A 95, 043836 (2017).
[Crossref]

Majumdar, A. S.

P. Chowdhury, A. S. Majumdar, and G. S. Agarwal, “Nonlocal continuous variable correlations and violation of Bell’s inequality for light beams with topological singularities,” Phys. Rev. A 88, 013830 (2013).
[Crossref]

Malhotra, T.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, “Quantum and classical optics-emerging links,” Phys. Scr. 91, 063003 (2016).
[Crossref]

X.-F. Qian, T. Malhotra, A. N. Vamivakas, and J. H. Eberly, “Coherence constraints and the last hidden optical coherence,” Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

Mann, K.

B. Schäfer, M. Lübbecke, and K. Mann, “Hartmann-Shack wavefront measurements for real time determination of laser beam propagation parameters,” Rev. Sci. Instrum. 77, 053103 (2006).
[Crossref]

B. Schäfer and K. Mann, “Determination of beam parameters and coherence properties of laser radiation by use of an extended Hartmann-Shack wave-front sensor,” Appl. Opt. 41, 2809–2817 (2002).
[Crossref]

B. Schäfer and K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71, 2663–2668 (2000).
[Crossref]

Marquardt, C.

S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2, 864–868 (2015).
[Crossref]

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement: oxymoron or resource?” New J. Phys. 17, 043024 (2014).
[Crossref]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

Martin, J. M.

McLaren, M.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397–402 (2017).
[Crossref]

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A 92, 023833 (2015).
[Crossref]

Mouane, O.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397–402 (2017).
[Crossref]

Mukherjee, A.

P. Ghose and A. Mukherjee, “Entanglement in classical optics,” Rev. Theor. Sci. 2, 274–288 (2014).
[Crossref]

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, 023901 (2010).
[Crossref]

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, “A complete characterization of pre-Mueller and Mueller matrices in polarization optics,” J. Opt. Soc. Am. A 27, 188–199 (2010).
[Crossref]

R. Simon and N. Mukunda, “Optical phase space, Wigner representation, and invariant quality parameters,” J. Opt. Soc. Am. A 17, 2440–2463 (2000).
[Crossref]

E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realization of first order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).
[Crossref]

Arvind, S. Chaturvedi, and N. Mukunda, “Entanglement and complete positivity: relevance and manifestations in classical scalar wave optics,” arXiv:1710.01086 (2017).

Narayanamurthy, C. S.

Ndagano, B.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397–402 (2017).
[Crossref]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2004).

Ornigotti, M.

Ozaktas, H. M.

Perez-Garcia, B.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397–402 (2017).
[Crossref]

Perumangatt, C.

S. Prabhakar, S. G. Reddy, A. Aadhi, C. Perumangatt, G. K. Samanta, and R. P. Singh, “Violation of Bell’s inequality for phase-singular beams,” Phys. Rev. A 92, 023822 (2015).
[Crossref]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

Plenio, M. B.

T. Baumgratz, M. Cramer, and M. B. Plenio, “Quantifying coherence,” Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

J. Eisert, C. Simon, and M. B. Plenio, “On the quantification of entanglement in infinite-dimensional quantum systems,” J. Phys. A 35, 3911–3923 (2002).
[Crossref]

Prabhakar, S.

S. Prabhakar, S. G. Reddy, A. Aadhi, C. Perumangatt, G. K. Samanta, and R. P. Singh, “Violation of Bell’s inequality for phase-singular beams,” Phys. Rev. A 92, 023822 (2015).
[Crossref]

Qian, X.-F.

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, “Quantum and classical optics-emerging links,” Phys. Scr. 91, 063003 (2016).
[Crossref]

X.-F. Qian, T. Malhotra, A. N. Vamivakas, and J. H. Eberly, “Coherence constraints and the last hidden optical coherence,” Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

X.-F. Qian, B. Little, J. C. Howell, and J. H. Eberly, “Shifting the quantum-classical boundary: theory and experiment for statistically classical optical fields,” Optica 2, 611–615 (2015).
[Crossref]

X.-F. Qian and J. H. Eberly, “Entanglement and classical polarization states,” Opt. Lett. 36, 4110–4112 (2011).
[Crossref]

Reddy, S. G.

S. Prabhakar, S. G. Reddy, A. Aadhi, C. Perumangatt, G. K. Samanta, and R. P. Singh, “Violation of Bell’s inequality for phase-singular beams,” Phys. Rev. A 92, 023822 (2015).
[Crossref]

Ricklin, J. C.

Rosales-Guzman, C.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397–402 (2017).
[Crossref]

Roux, F. S.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397–402 (2017).
[Crossref]

Samanta, G. K.

S. Prabhakar, S. G. Reddy, A. Aadhi, C. Perumangatt, G. K. Samanta, and R. P. Singh, “Violation of Bell’s inequality for phase-singular beams,” Phys. Rev. A 92, 023822 (2015).
[Crossref]

Santarsiero, M.

Schäfer, B.

B. Schäfer, M. Lübbecke, and K. Mann, “Hartmann-Shack wavefront measurements for real time determination of laser beam propagation parameters,” Rev. Sci. Instrum. 77, 053103 (2006).
[Crossref]

B. Schäfer and K. Mann, “Determination of beam parameters and coherence properties of laser radiation by use of an extended Hartmann-Shack wave-front sensor,” Appl. Opt. 41, 2809–2817 (2002).
[Crossref]

B. Schäfer and K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71, 2663–2668 (2000).
[Crossref]

Sharma, R.

Simon, B. N.

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, “A complete characterization of pre-Mueller and Mueller matrices in polarization optics,” J. Opt. Soc. Am. A 27, 188–199 (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, 023901 (2010).
[Crossref]

Simon, C.

J. Eisert, C. Simon, and M. B. Plenio, “On the quantification of entanglement in infinite-dimensional quantum systems,” J. Phys. A 35, 3911–3923 (2002).
[Crossref]

Simon, R.

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, 023901 (2010).
[Crossref]

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, “A complete characterization of pre-Mueller and Mueller matrices in polarization optics,” J. Opt. Soc. Am. A 27, 188–199 (2010).
[Crossref]

Singh, R. P.

S. Prabhakar, S. G. Reddy, A. Aadhi, C. Perumangatt, G. K. Samanta, and R. P. Singh, “Violation of Bell’s inequality for phase-singular beams,” Phys. Rev. A 92, 023822 (2015).
[Crossref]

Spreeuw, R. J.

R. J. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
[Crossref]

Spreeuw, R. J. C.

R. J. C. Spreeuw, “Classical wave-optics analogy of quantum-information processing,” Phys. Rev. A 63, 062302 (2001).
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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Stiller, B.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), p. 372.

Sudarshan, E. C. G.

E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realization of first order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).
[Crossref]

Taché, J. P.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

Töppel, F.

S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2, 864–868 (2015).
[Crossref]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement: oxymoron or resource?” New J. Phys. 17, 043024 (2014).
[Crossref]

Tyson, R. K.

Vamivakas, A. N.

X.-F. Qian, T. Malhotra, A. N. Vamivakas, and J. H. Eberly, “Coherence constraints and the last hidden optical coherence,” Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, “Quantum and classical optics-emerging links,” Phys. Scr. 91, 063003 (2016).
[Crossref]

Wang, G.-Y.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

Yasir, P. A. A.

Zhang, B.

Zhang, Y.

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397–402 (2017).
[Crossref]

Appl. Opt. (5)

Found. Phys. (1)

R. J. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
[Crossref]

J. Opt. B (1)

L. Lamata and J. León, “Dealing with entanglement of continuous variables: Schmidt decomposition with discrete sets of orthogonal functions,” J. Opt. B 7, 224–229 (2005).
[Crossref]

J. Opt. Soc. Am. A (12)

J. M. Martin and S. M. Flatté, “Simulation of point-source scintillation through three-dimensional random media,” J. Opt. Soc. Am. A 7, 838–847 (1990).
[Crossref]

S. M. Flatté, C. Bracher, and G.-Y. Wang, “Probability-density functions of irradiance for waves in atmospheric turbulence calculated by numerical simulation,” J. Opt. Soc. Am. A 11, 2080–2092 (1994).
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R. Sharma, J. S. Ivan, and C. S. Narayanamurthy, “Wave propagation analysis using the variance matrix,” J. Opt. Soc. Am. A 31, 2185–2191 (2014).
[Crossref]

R. Borghi, M. Santarsiero, and R. Simon, “Shape invariance and a universal form for the Gouy phase,” J. Opt. Soc. Am. A 21, 572–579 (2004).
[Crossref]

P. A. A. Yasir and J. S. Ivan, “Realization of first-order optical systems using thin convex lenses of fixed focal length,” J. Opt. Soc. Am. A 31, 2011–2020 (2014).
[Crossref]

P. A. A. Yasir and J. S. Ivan, “Realization of first-order optical systems using thin lenses of positive focal length,” J. Opt. Soc. Am. A 34, 2007–2012 (2017).
[Crossref]

R. Simon and N. Mukunda, “Optical phase space, Wigner representation, and invariant quality parameters,” J. Opt. Soc. Am. A 17, 2440–2463 (2000).
[Crossref]

J. S. Ivan and K. Goswami, “Free space optical communication using beam parameters with translational and transverse rotational invariance,” J. Opt. Soc. Am. A 32, 1118–1125 (2015).
[Crossref]

B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, “A complete characterization of pre-Mueller and Mueller matrices in polarization optics,” J. Opt. Soc. Am. A 27, 188–199 (2010).
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M. F. Erden and H. M. Ozaktas, “Accumulated Gouy phase shift in Gaussian beam propagation through first-order optical systems,” J. Opt. Soc. Am. A 14, 2190–2194 (1997).
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G. Gbur and R. K. Tyson, “Vortex beam propagation through atmospheric turbulence and topological charge conservation,” J. Opt. Soc. Am. A 25, 225–230 (2008).
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J. C. Ricklin and F. M. Davidson, “Atmospheric turbulence effects on a partially coherent Gaussian beam: implications for free-space laser communication,” J. Opt. Soc. Am. A 19, 1794–1802 (2002).
[Crossref]

J. Phys. A (1)

J. Eisert, C. Simon, and M. B. Plenio, “On the quantification of entanglement in infinite-dimensional quantum systems,” J. Phys. A 35, 3911–3923 (2002).
[Crossref]

Nat. Phys. (1)

B. Ndagano, B. Perez-Garcia, F. S. Roux, M. McLaren, C. Rosales-Guzman, Y. Zhang, O. Mouane, R. I. Hernandez-Aranda, T. Konrad, and A. Forbes, “Characterizing quantum channels with non-separable states of classical light,” Nat. Phys. 13, 397–402 (2017).
[Crossref]

New J. Phys. (2)

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement: oxymoron or resource?” New J. Phys. 17, 043024 (2014).
[Crossref]

F. Töppel, A. Aiello, C. Marquardt, E. Giacobino, and G. Leuchs, “Classical entanglement in polarization metrology,” New J. Phys. 16, 073019 (2014).
[Crossref]

Opt. Acta (1)

E. C. G. Sudarshan, N. Mukunda, and R. Simon, “Realization of first order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).
[Crossref]

Opt. Commun. (1)

J. Courtial, “Self-imaging beams and the Gouy effect,” Opt. Commun. 151, 1–4 (1998).
[Crossref]

Opt. Lett. (2)

Optica (2)

Phys. Rev. A (8)

R. J. C. Spreeuw, “Classical wave-optics analogy of quantum-information processing,” Phys. Rev. A 63, 062302 (2001).
[Crossref]

P. Chowdhury, A. S. Majumdar, and G. S. Agarwal, “Nonlocal continuous variable correlations and violation of Bell’s inequality for light beams with topological singularities,” Phys. Rev. A 88, 013830 (2013).
[Crossref]

S. Prabhakar, S. G. Reddy, A. Aadhi, C. Perumangatt, G. K. Samanta, and R. P. Singh, “Violation of Bell’s inequality for phase-singular beams,” Phys. Rev. A 92, 023822 (2015).
[Crossref]

M. McLaren, T. Konrad, and A. Forbes, “Measuring the nonseparability of vector vortex beams,” Phys. Rev. A 92, 023833 (2015).
[Crossref]

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[Crossref]

V. Madhu and J. S. Ivan, “Robustness of the twist parameter of Laguerre-Gaussian mode superpositions against atmospheric turbulence,” Phys. Rev. A 95, 043836 (2017).
[Crossref]

P. A. A. Yasir and J. S. Ivan, “Estimation of phases with dislocations in paraxial wave fields from intensity measurements,” Phys. Rev. A 97, 023817 (2018).
[Crossref]

Phys. Rev. Lett. (3)

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, 023901 (2010).
[Crossref]

T. Baumgratz, M. Cramer, and M. B. Plenio, “Quantifying coherence,” Phys. Rev. Lett. 113, 140401 (2014).
[Crossref]

X.-F. Qian, T. Malhotra, A. N. Vamivakas, and J. H. Eberly, “Coherence constraints and the last hidden optical coherence,” Phys. Rev. Lett. 117, 153901 (2016).
[Crossref]

Phys. Scr. (1)

J. H. Eberly, X.-F. Qian, A. Al Qasimi, H. Ali, M. A. Alonso, R. Gutiérrez-Cuevas, B. J. Little, J. C. Howell, T. Malhotra, and A. N. Vamivakas, “Quantum and classical optics-emerging links,” Phys. Scr. 91, 063003 (2016).
[Crossref]

Rev. Sci. Instrum. (2)

B. Schäfer and K. Mann, “Investigation of the propagation characteristics of excimer lasers using a Hartmann-Shack sensor,” Rev. Sci. Instrum. 71, 2663–2668 (2000).
[Crossref]

B. Schäfer, M. Lübbecke, and K. Mann, “Hartmann-Shack wavefront measurements for real time determination of laser beam propagation parameters,” Rev. Sci. Instrum. 77, 053103 (2006).
[Crossref]

Rev. Theor. Sci. (1)

P. Ghose and A. Mukherjee, “Entanglement in classical optics,” Rev. Theor. Sci. 2, 274–288 (2014).
[Crossref]

Other (8)

Arvind, S. Chaturvedi, and N. Mukunda, “Entanglement and complete positivity: relevance and manifestations in classical scalar wave optics,” arXiv:1710.01086 (2017).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2004).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), p. 372.

A. Erdélyi, Tables of Integral Transforms (McGraw-Hill, 1954), Vol. 2, p. 43.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).

R. K. Tyson, Principles of Adaptive Optics, 3rd ed. (CRC Press, 2010).

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation through Random Media (SPIE, 2005).

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Figures (3)

Fig. 1.
Fig. 1. Radial–angular entanglement E(Ψ) against distance of propagation d for the three-mode superposition given in Eq. (24) for c00=c11=13 and c21=i3.
Fig. 2.
Fig. 2. (a), (b) [(d), (e)] Indicator of radial–angular entanglement S against distance of propagation d for 100 samples for n=1,3,5, and 7 and Cn21012  m23 and 1013  m23, respectively, for Ψ1n(r,θ) [Ψ2n(r,θ)] given in Eq. (36) [Eq. (38)], for d up to 1 km and 2 km, respectively; (c) [(f)] same, but for n=1,2,3, and 4 and Cn21014  m23, and for d up to 5 km for Ψ1n(r,θ) [Ψ2n(r,θ)]. The dark line (the vertical axis ticks) in each of these frames shows S for the respective Ψ1n(r,θ) [Ψ2n(r,θ)] in the absence of atmospheric turbulence.
Fig. 3.
Fig. 3. (a), (c) E(Ψp) against distance of propagation d for Ψ1n(r,θ) with n=2 [Eq. (36)] and Cn21013  m23 and 1014  m23, respectively, for 100 samples, for d up to 2 km and 4 km; (b), (d) N against distance of propagation d for the samples in (a) and (c), and corresponding strengths of turbulence; (e), (g) [and (f), (h)] same, but for Ψ1n(r,θ) with n=3 for the respective strengths of turbulence; (i), (k) [and (j), (l)] same, but for Ψ2n(r,θ) with n=2 [Eq. (38)] for the respective strengths of turbulence. In all the frames, the dark line shows either E(Ψ) or N(=1) in the absence of atmospheric turbulence.

Equations (43)

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

Ψjm(r,θ)=ψjm(r;q)×Θm(θ),
ψjm(r;q)=2πw2((j|m|)!(j+|m|)!)12×(2rw)2|m|Lj|m|2|m|(2r2w2)exp[iπr2λq],
with  1q=1R+iλπw2andΘm(θ)=exp[i2mθ].
w2w2(d)=w2(0)[1+(ddr)2],and
RR(d)=d[1+(drd)2],
Ψjm(r,θ)UΨjm(r,θ).
Uf(d)=exp[idλ4π2],
2=2r2+1rr+1r22θ2.
Ul(f)=exp[iπλfr2].
Uf(d)ψjm(r;q)Θm(θ)=eiϕj(q;d)ψjm(r;q)Θm(θ),where  q=q+d,and
ϕj(q;d)=(2j+1)tan1(λπw21d+1R).
Ul(f)ψjm(r;q)Θm(θ)=ψjm(r;q)Θm(θ),where  1q=1q1f.
Ufoψjm(r;q)Θm(θ)=eiϕ(j)ψjm(r;q˜)Θm(θ),
2π0ψjm*(r;q)ψjm(r;q)rdr=δjj.
12π02πΘm*(θ)Θm(θ)dθ=δmm.
ψjm(r;q)=jdjjψj(r;q),
Ψ(r,θ)=j,mcjmΨjm(r,θ)=j,mcjmψjm(r;q)Θm(θ),
Ψ(r,θ)=j,mdjmψj(r;q)Θm(θ),where
djm=jdjjcjm,
Λ=DD,
E(Ψ)=iλilogλi,
UfoΨ(r,θ)=j,mcj,meiϕ(j)ψjm(r;q˜)Θm(θ).
UfoΨ(r,θ)=eiϕ(j)mcjmψjm(r;q˜)Θm(θ).
Ψ(r,θ)=c00Ψ00(r,θ)+c11Ψ11(r,θ)+c21Ψ21(r,θ).
Uf(d)Ψ(r,θ)=c00ψ00(r;q)eiϕ0(q;d)+(c11ψ11(r;q)eiϕ1(q;d)+c21ψ21(r;q)eiϕ2(q;d))ei2θ,
Uf(d)Ψ(r,θ)=c00ψ0(r;q)eiϕ0(q;d)+(c112eiϕ1(q;d)+c216eiϕ2(q;d))ψ0(r;q)ei2θ+(c112eiϕ1(q;d)+c216eiϕ2(q;d))ψ1(r;q)ei2θ2c216ψ2(r;q)eiϕ2(q;d)ei2θ.
λ±=12[1±14η],where
η=|c00|2[|c11|22+5|c21|26R(c11c21*3ei(ϕ1(q;d)ϕ2(q;d)))].
Ψ(r,θ)=cj1m1Ψj1m1(r,θ)+cj2m2Ψj2m2(r,θ).
λ±=12(1±14det(Λ)),
S=r2w2(d)iθiθr2w2(d),
Sj2m2j1m1=2|cj1m1|2|cj2m2|2(j1j2)(m1m2),
ϕθ(K)=2π(2πλ)2δdϕn(K),
ϕn(K)=0.033Cn2K113.
N=002πΨp*(r,θ)Ψp(r,θ)rdrdθ,
Ψ1n(r,θ)=n1nΨ00(r,θ)+1nΨn2n2(r,θ).
Sn2n200=n12.
Ψ2n(r,θ)=n1nΨ00(r,θ)+1nΨ3n2n2(r,θ).
S3n2n200=3(n1)2.
F(Ψjm(r,θ))=1iλf002πΨjm(r,θ)×exp[ikfρrcos(ϕθ)]rdrdθ.
F(Ψjm(r,θ))=i2πw2((j|m|)!(j+|m|)!)12×(2ρw)2|m|Lj|m|2|m|(2ρ2w2)exp[ikρ22q]ei2mϕ×eiπ(j|m|m)(iR+λπw2)2j+1(1R2+λ2π2w4)2j+1,where1q=qf2=1R+iλπw2.
Uf(f)Ψjm(r,θ)=eikf2πw2((j|m|)!(j+|m|)!)12×(2rw)2|m|exp[ikr22q]Lj|m|2|m|(2r2w2)ei2mθ×(exp[itan1(λπw21f+1R)])2j+1,where
q=q+f,with1q=1R+iλw2.

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