Abstract

We propose a method for directly producing radially and azimuthally polarized photon pairs through spontaneous parametric downconversion (SPDC). This method constitutes a novel geometry for SPDC, in which a radially polarized Bessel-Gauss pump beam is directed into a nonlinear crystal, with the central propagation direction parallel to the crystal axis. The phasematching conditions are controlled by changing the opening angle of the pump beam; as the crystal axis cannot be tuned, we refer to this process as super-critical phasematching. We model and plot the spatial and polarization output distributions for Type-I and Type-II super-critical phasematching.

© 2016 Optical Society of America

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  1. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
    [Crossref]
  2. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
    [Crossref] [PubMed]
  3. H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
    [Crossref]
  4. G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
    [Crossref] [PubMed]
  5. V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
    [Crossref]
  6. E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
    [Crossref]
  7. G. Milione, T. A. Nguyen, E. Karimi, D. A. Nolan, S. Slussarenko, L. Marrucci, and R. Alfano, “Superdense coding with vector vortex beams: A classical analogy of entanglement,” in Frontiers in Optics 2013, (Optical Society of America, 2013), paper FM3F.4.
    [Crossref]
  8. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
    [Crossref] [PubMed]
  9. G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 gbit / s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
    [Crossref] [PubMed]
  10. R. H. Jordan and D. G. Hall, “Free-space azimuthal paraxial wave equation: the azimuthal bessel–gauss beam solution,” Opt. Lett. 19, 427–429 (1994).
    [Crossref] [PubMed]
  11. D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
    [Crossref]
  12. P. L. Greene and D. G. Hall, “Diffraction characteristics of the azimuthal bessel-gauss beam,” J. Opt. Soc. Am. A 13, 962–966 (1996).
    [Crossref]
  13. D. N. Schimpf, W. P. Putnam, M. D. Grogan, S. Ramachandran, and F. X. Kärtner, “Radially polarized bessel-gauss beams: decentered gaussian beam analysis and experimental verification,” Opt. Express 21, 18469–18483 (2013).
    [Crossref] [PubMed]
  14. S. P. Walborn, C. Monken, S. Pádua, and P. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
    [Crossref]
  15. N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
    [Crossref]
  16. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J Appl. Phys. 39, 3597–3639 (1968).
    [Crossref]
  17. K. Shinozaki, C.-q. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using bessel and gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
    [Crossref]
  18. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Efficiency of second-harmonic generation with bessel beams,” Phys. Rev. A 60, 2438–2441 (1999).
    [Crossref]

2015 (1)

2014 (1)

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

2013 (2)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

D. N. Schimpf, W. P. Putnam, M. D. Grogan, S. Ramachandran, and F. X. Kärtner, “Radially polarized bessel-gauss beams: decentered gaussian beam analysis and experimental verification,” Opt. Express 21, 18469–18483 (2013).
[Crossref] [PubMed]

2012 (1)

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

2010 (2)

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

S. P. Walborn, C. Monken, S. Pádua, and P. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[Crossref]

2008 (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[Crossref]

2005 (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

2000 (2)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

1999 (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Efficiency of second-harmonic generation with bessel beams,” Phys. Rev. A 60, 2438–2441 (1999).
[Crossref]

1997 (1)

K. Shinozaki, C.-q. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using bessel and gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
[Crossref]

1996 (1)

1994 (1)

1968 (1)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J Appl. Phys. 39, 3597–3639 (1968).
[Crossref]

Alfano, R.

G. Milione, T. A. Nguyen, E. Karimi, D. A. Nolan, S. Slussarenko, L. Marrucci, and R. Alfano, “Superdense coding with vector vortex beams: A classical analogy of entanglement,” in Frontiers in Optics 2013, (Optical Society of America, 2013), paper FM3F.4.
[Crossref]

Alfano, R. R.

Allen, L.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Efficiency of second-harmonic generation with bessel beams,” Phys. Rev. A 60, 2438–2441 (1999).
[Crossref]

Aolita, L.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Efficiency of second-harmonic generation with bessel beams,” Phys. Rev. A 60, 2438–2441 (1999).
[Crossref]

Boeuf, N.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Boyd, G. D.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J Appl. Phys. 39, 3597–3639 (1968).
[Crossref]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Branning, D.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Chaperot, I.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Chen, L.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[Crossref]

D’Ambrosio, V.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Dauler, E.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Dholakia, K.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Efficiency of second-harmonic generation with bessel beams,” Phys. Rev. A 60, 2438–2441 (1999).
[Crossref]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Franke-Arnold, S.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Greene, P. L.

Grogan, M. D.

Guerin, S.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Hall, D. G.

Huang, H.

Jaeger, G.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Jordan, R. H.

Kamijoh, T.

K. Shinozaki, C.-q. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using bessel and gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
[Crossref]

Karimi, E.

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 gbit / s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
[Crossref] [PubMed]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

G. Milione, T. A. Nguyen, E. Karimi, D. A. Nolan, S. Slussarenko, L. Marrucci, and R. Alfano, “Superdense coding with vector vortex beams: A classical analogy of entanglement,” in Frontiers in Optics 2013, (Optical Society of America, 2013), paper FM3F.4.
[Crossref]

Kärtner, F. X.

Kleinman, D. A.

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J Appl. Phys. 39, 3597–3639 (1968).
[Crossref]

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Lavery, M. P. J.

Leach, J.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[Crossref]

Marrucci, L.

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 gbit / s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
[Crossref] [PubMed]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

G. Milione, T. A. Nguyen, E. Karimi, D. A. Nolan, S. Slussarenko, L. Marrucci, and R. Alfano, “Superdense coding with vector vortex beams: A classical analogy of entanglement,” in Frontiers in Optics 2013, (Optical Society of America, 2013), paper FM3F.4.
[Crossref]

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

Migdall, A.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Milione, G.

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 gbit / s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
[Crossref] [PubMed]

G. Milione, T. A. Nguyen, E. Karimi, D. A. Nolan, S. Slussarenko, L. Marrucci, and R. Alfano, “Superdense coding with vector vortex beams: A classical analogy of entanglement,” in Frontiers in Optics 2013, (Optical Society of America, 2013), paper FM3F.4.
[Crossref]

Monken, C.

S. P. Walborn, C. Monken, S. Pádua, and P. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[Crossref]

Muller, A.

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Nagali, E.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Nguyen, T. A.

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 gbit / s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
[Crossref] [PubMed]

G. Milione, T. A. Nguyen, E. Karimi, D. A. Nolan, S. Slussarenko, L. Marrucci, and R. Alfano, “Superdense coding with vector vortex beams: A classical analogy of entanglement,” in Frontiers in Optics 2013, (Optical Society of America, 2013), paper FM3F.4.
[Crossref]

Nolan, D. A.

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 gbit / s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40, 1980–1983 (2015).
[Crossref] [PubMed]

G. Milione, T. A. Nguyen, E. Karimi, D. A. Nolan, S. Slussarenko, L. Marrucci, and R. Alfano, “Superdense coding with vector vortex beams: A classical analogy of entanglement,” in Frontiers in Optics 2013, (Optical Society of America, 2013), paper FM3F.4.
[Crossref]

Padgett, M. J.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Efficiency of second-harmonic generation with bessel beams,” Phys. Rev. A 60, 2438–2441 (1999).
[Crossref]

Pádua, S.

S. P. Walborn, C. Monken, S. Pádua, and P. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[Crossref]

Piccirillo, B.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Putnam, W. P.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

D. N. Schimpf, W. P. Putnam, M. D. Grogan, S. Ramachandran, and F. X. Kärtner, “Radially polarized bessel-gauss beams: decentered gaussian beam analysis and experimental verification,” Opt. Express 21, 18469–18483 (2013).
[Crossref] [PubMed]

Ren, Y.

Ribeiro, P. S.

S. P. Walborn, C. Monken, S. Pádua, and P. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[Crossref]

Santamato, E.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Sasaki, H.

K. Shinozaki, C.-q. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using bessel and gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
[Crossref]

Schimpf, D. N.

Sciarrino, F.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

She, W.

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[Crossref]

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[Crossref]

Shinozaki, K.

K. Shinozaki, C.-q. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using bessel and gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
[Crossref]

Slussarenko, S.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

G. Milione, T. A. Nguyen, E. Karimi, D. A. Nolan, S. Slussarenko, L. Marrucci, and R. Alfano, “Superdense coding with vector vortex beams: A classical analogy of entanglement,” in Frontiers in Optics 2013, (Optical Society of America, 2013), paper FM3F.4.
[Crossref]

Sponselli, A.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Vallone, G.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

Villoresi, P.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

Walborn, S. P.

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

S. P. Walborn, C. Monken, S. Pádua, and P. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[Crossref]

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[Crossref]

Willner, A. E.

Xie, G.

Xu, C.-q.

K. Shinozaki, C.-q. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using bessel and gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
[Crossref]

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

J Appl. Phys. (1)

G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J Appl. Phys. 39, 3597–3639 (1968).
[Crossref]

J. Opt. Soc. Am. A (1)

Nat. Commun. (1)

V. D’Ambrosio, E. Nagali, S. P. Walborn, L. Aolita, S. Slussarenko, L. Marrucci, and F. Sciarrino, “Complete experimental toolbox for alignment-free quantum communication,” Nat. Commun. 3, 961 (2012).
[Crossref]

Nat. Photonics (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics 2, 501–505 (2008).
[Crossref]

Opt. Commun. (2)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, “Focusing light to a tighter spot,” Opt. Commun. 179, 1–7 (2000).
[Crossref]

K. Shinozaki, C.-q. Xu, H. Sasaki, and T. Kamijoh, “A comparison of optical second-harmonic generation efficiency using bessel and gaussian beams in bulk crystals,” Opt. Commun. 133, 300–304 (1997).
[Crossref]

Opt. Eng. (1)

N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guerin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rep. (1)

S. P. Walborn, C. Monken, S. Pádua, and P. S. Ribeiro, “Spatial correlations in parametric down-conversion,” Phys. Rep. 495, 87–139 (2010).
[Crossref]

Phys. Rev. A (2)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “Efficiency of second-harmonic generation with bessel beams,” Phys. Rev. A 60, 2438–2441 (1999).
[Crossref]

E. Karimi, J. Leach, S. Slussarenko, B. Piccirillo, L. Marrucci, L. Chen, W. She, S. Franke-Arnold, M. J. Padgett, and E. Santamato, “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Phys. Rev. A 82, 022115 (2010).
[Crossref]

Phys. Rev. Lett. (2)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[Crossref] [PubMed]

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2014).
[Crossref] [PubMed]

Science (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[Crossref] [PubMed]

Other (1)

G. Milione, T. A. Nguyen, E. Karimi, D. A. Nolan, S. Slussarenko, L. Marrucci, and R. Alfano, “Superdense coding with vector vortex beams: A classical analogy of entanglement,” in Frontiers in Optics 2013, (Optical Society of America, 2013), paper FM3F.4.
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

The geometry of super-critical phasematching. The x, y, and z axes are the crystallographic axes, where z is the optic axis. The pump (blue) is comprised of a conical distribution of Gaussian beams, each with central k-vector k p 0 ( ϕ p ), where φp is the azimuthal angle. The pump beam cone axis is along the crystal axis z, and the opening half-angle of the cone is θp. The signal (idler), shown in green (red), is emitted with k-vector ks(i). The signal (idler) k-vector is characterized by two angles: θs(i), the half-cone opening angle, measured between the signal (idler) k-vector and the z axis; and φs(i), the azimuthal angle. We also introduce a local frame, denoted by x′, y′, and z′, where z′ is defined along the central k-vector, k p 0, of each Gaussian beam. The other axes are aligned azimuthally (x′) and radially (y′) with respect to z.

Fig. 2
Fig. 2

Marginal probability density (P(ks), P(ki)) for Type-II degenerate down-conversion. The pump cone half-angle is 41.8° in a 500 μm-thick BBO crystal. The pump beam wavelength is 405 nm and the signal and idler wavelengths are 810 nm. Since for degenerate phasematching |ks(i)| is fixed, θs(i) and ϕs(i) completely determine the signal and idler wavevectors. In turn, the position of the photons after the crystal determines these angles, so these plots are given in the crystal frame (x,y) at z=20cm after the crystal exit face. Plots (A), (B), and (C) give (A) the probability density of generating a signal photon at ks, (B) the probability density of generating an idler photon at ki, and (C) P(ks) + P(ki), which is proportional to the photon flux. Plots (a), (b), and (c) are produced from plots (A), (B), and (C), respectively, by plotting along y = 0.

Fig. 3
Fig. 3

Spatial (a) and polarization (c) distributions for degenerate Type-II super-critical phasematching. The polarization distribution in (b) is the typical distibution for a single Gaussian pump beam. When this output is summed over all the Gaussian beams in the Bessel-Gauss pump distribution in Eq. (3), the resulting intensity and polarization distributions become those of (a) and (c). The signal photons (green) are generated with radial polarizations and the idler photons (red) are generated with azimuthal polarizations.

Fig. 4
Fig. 4

Signal photon probability density for Type-II degenerate collinear downconversion with a fixed idler emission direction. Idler angles are fixed at θi = 41.8° and φi = 45°.

Fig. 5
Fig. 5

Proposed setup to reduce the pump opening angle in air. Angles are calculated for Type-II degenerate SPDC from 405 nm to 810 nm. The pump beam angle is reduced by two means: (a) a crystal cut as a double-sided 90° axicon, and (b) two 90° axicons placed tip-to-tip with the crystal at the entry and exit faces. The pump beam is focused into the crystal as it passes through the first axicon. The second axicon reduces the angle of the output beams as they exit the crystal.

Fig. 6
Fig. 6

Proposed setup to reduce the pump opening angle in air for Type-II degenerate SPDC from 775 nm to 1550 nm: (a) a BBO crystal, placed between (b) two 90° axicons, which are affixed back-to-back on either side of the crystal. The required opening angle of the pump in air is 25.7°; without the axicons at the crystal face this angle would be 51.8°.

Fig. 7
Fig. 7

Probability densities for Type-I degenerate downconversion in a 500 μm -thick BBO crystal for a pump beam wavelength of 405 nm, and signal and idler wavelength of 810 nm. Since for degenerate phasematching |ks(i)| is fixed, θs(i) and ϕs(i) completely determine the signal and idler wavevectors. In turn, the position of the photons after the crystal determines these angles, so these plots are given in the crystal frame (x,y) at z=20cm after the crystal exit face. Plots (A), (B), and (C) give (A) the probability density for the signal photon, P(ks); (B) the probability density for the idler photon, P(ki); and (C) P(ks) + P(ki), which is proportional to the photon flux. Plots (a), (b), and (c) are produced from plots (A), (B), (C), respectively, by plotting along y = 0.

Fig. 8
Fig. 8

Expected output for Type-I collinear downconversion with a conical pump beam centered on the optic axis (z). The signal and idler photons are produced in a single supercone centered on the optic axis.

Equations (22)

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

ω p = ω s + ω i .
k s + k i k p = Δ k .
BG ( k ) 0 2 π e w p 2 ( k k p 0 ( φ p ) ) 2 / 4 d φ p ,
k p , x 0 ( φ p ) = | k p 0 | sin ( θ p ) cos ( φ p ) , k p , y 0 ( φ p ) = | k p 0 | sin ( θ p ) sin ( φ p ) , k p , z 0 = | k p 0 | cos ( θ p )
Φ BG ( k s , k i ) = 1 N 0 2 π Φ G ( k p 0 ( φ p ) , k s , k i ) d φ p ,
Φ G ( k p 0 ( φ p ) , k s , k i ) exp ( w p 2 ( Δ k x 2 + Δ k y 2 ) 4 ) sinc ( L optic Δ k z 2 ) exp ( i L optic Δ k z 2 ) ,
θ s = tan 1 ( x 2 + y 2 z ) , θ i = θ s ,
φ s = tan 1 ( x y ) , φ i = φ s + π ,
s α , x = sin ( θ α ) cos ( φ α ) , s α , y = sin ( θ α ) sin ( φ α ) , s α , z = cos ( θ α ) ,
N α , e = ( 2 B + ( B 2 4 C ) 1 / 2 ) 1 / 2
N α , o = ( 2 B ( B 2 4 C ) 1 / 2 ) 1 / 2 ,
B = s α , x 2 n α , y 2 + n α , z 2 + s α , y 2 n α , x 2 + n α , y 2 + s α , z 2 n α , x 2 + n α , y 2 ,
C = s α , x 2 n α , y 2 n α , z 2 + s α , y 2 n α , x 2 n α , z 2 + s α , z 2 n α , x 2 n α , y 2 .
k α , j = 2 π N α s α , j λ α ,
Δ k j = k s , j + k i , j k p , j ,
[ x y z ] = [ cos ( θ p ) cos ( φ p ) cos ( θ p ) sin ( φ p ) sin ( φ p ) sin ( φ p ) cos ( φ p ) 0 sin ( θ p ) cos ( φ p ) sin ( θ p ) sin ( φ p ) cos ( θ p ) ] [ x y z ] .
Δ k x = Δ k x cos ( θ p ) cos ( φ p ) + Δ k y cos ( θ p ) sin ( φ p ) Δ k z sin ( φ p ) ,
Δ k y = Δ k x sin ( φ p ) + Δ k y cos ( φ p ) ,
Δ k z = Δ k x sin ( θ p ) cos ( φ p ) + Δ k y sin ( θ p ) sin ( φ p ) + Δ k z cos ( θ p ) .
Φ G ( k p 0 , k s , k i ) = exp ( w p 2 ( Δ k x 2 + Δ k y 2 ) 4 ) sinc ( L optic Δ k z 2 ) exp ( i L optic Δ k z 2 ) ,
Φ BG ( k s , k i ) φ p Φ G ( k p 0 ( φ p ) , k s , k i ) ,
P ( k s ) = 1 N k i , x k i , y | Φ BG ( k s , k i ) | 2 Δ k i , x Δ k i , y ,

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