Abstract

Recent measurements have highlighted that even in vacuum spatially shaped photons travel slower than c, the speed of monochromatic plane waves. Here we investigate the intrinsic delay introduced by “twisting” a photon, i.e., by introducing orbital angular momentum (OAM), and measure the photon time of flight with a Hong–Ou–Mandel interferometer. When all other parameters are held constant, the addition of OAM reduces the delay (accelerates) with respect to the same beam with no OAM. We support our results using a theoretical method to calculate the group velocity and gain an intuitive understanding of the measured OAM acceleration by considering a geometrical ray-tracing approach.

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References

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  1. Z. L. Horváth, J. Vinkó, Z. Bor, and D. von der Linde, “Acceleration of femtosecond pulses to superluminal velocities by Gouy phase shift,” Appl. Phys. B 63, 481–484 (1996).
    [Crossref]
  2. D. Mugnai, A. Ranfagni, and R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
    [Crossref]
  3. I. Alexeev, K. Y. Kim, and H. M. Milchberg, “Measurement of the superluminal group velocity of an ultrashort Bessel beam pulse,” Phys. Rev. Lett. 88, 073901 (2002).
    [Crossref]
  4. P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, P. Saari, and R. Trebino, “Measuring the spatiotemporal field of ultrashort Bessel-X pulses,” Opt. Lett. 34, 2276–2278 (2009).
    [Crossref]
  5. H. Valtna-Lukner, P. Bowlan, M. Lõhmus, P. Piksarv, R. Trebino, and P. Saari, “Direct spatiotemporal measurements of accelerating ultrashort Bessel-type light bullets,” Opt. Express 17, 14948–14955 (2009).
    [Crossref]
  6. F. Bonaretti, D. Faccio, M. Clerici, J. Biegert, and P. D. Trapani, “Spatiotemporal amplitude and phase retrieval of Bessel-X pulses using a Hartmann–Shack sensor,” Opt. Express 17, 9804–9809 (2009).
    [Crossref]
  7. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
    [Crossref]
  8. M. Lõhmus, P. Bowlan, P. Piksarv, H. Valtna-Lukner, R. Trebino, and P. Saari, “Diffraction of ultrashort optical pulses from circularly symmetric binary phase gratings,” Opt. Lett. 37, 1238–1240 (2012).
    [Crossref]
  9. P. Piksarv, H. Valtna-Lukner, A. Valdmann, M. Lõhmus, R. Matt, and P. Saari, “Temporal focusing of ultrashort pulsed Bessel beams into Airy-Bessel light bullets,” Opt. Express 20, 17220–17229 (2012).
    [Crossref]
  10. D. Giovannini, J. Romero, V. Potoček, G. Ferenczi, F. Speirits, S. M. Barnett, D. Faccio, and M. J. Padgett, “Spatially structured photons that travel in free space slower than the speed of light,” Science 347, 857–860 (2015).
    [Crossref]
  11. M. Born, E. Wolf, and A. B. Bhatia, Principles of Optics (Cambridge University, 1999), Chap. 1, Eq. (56).
  12. F. Bouchard, J. Harris, H. Mand, R. W. Boyd, and E. Karimi, “Observation of subluminal twisted light in vacuum,” Optica 3, 351–354 (2016).
    [Crossref]
  13. N. D. Bareza and N. Hermosa, “Subluminal group velocity and dispersion of Laguerre–Gauss beams in free space,” Sci. Rep. 6, 26842 (2016).
    [Crossref]
  14. M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
    [Crossref]
  15. M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
    [Crossref]
  16. J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
    [Crossref]
  17. M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 62101 (2011).
    [Crossref]
  18. A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
    [Crossref]
  19. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
    [Crossref]
  20. S. Chelkowski, S. Hild, and A. Freise, “Prospects of higher-order Laguerre–Gauss modes in future gravitational wave detectors,” Phys. Rev. D 79, 122002 (2009).
    [Crossref]
  21. C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
    [Crossref]
  22. D. N. Schimpf, J. Schulte, W. P. Putnam, and F. X. Kärtner, “Generalizing higher-order Bessel–Gauss beams: analytical description and demonstration,” Opt. Express 20, 26852–26867 (2012).
    [Crossref]
  23. V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
    [Crossref]
  24. R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, “Generating superpositions of higher-order Bessel beams,” Opt. Express 17, 23389–23395 (2009).
    [Crossref]
  25. J. C. Gutiérrez-Vega and M. A. Bandres, “Helmholtz–Gauss waves,” J. Opt. Soc. Am. A 22, 289–298 (2005).
    [Crossref]
  26. J. Courtial and M. J. Padgett, “Limit to the orbital angular momentum per unit energy in a light beam that can be focussed onto a small particle,” Opt. Commun. 173, 269–274 (2000).
    [Crossref]
  27. J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).
    [Crossref]

2016 (2)

N. D. Bareza and N. Hermosa, “Subluminal group velocity and dispersion of Laguerre–Gauss beams in free space,” Sci. Rep. 6, 26842 (2016).
[Crossref]

F. Bouchard, J. Harris, H. Mand, R. W. Boyd, and E. Karimi, “Observation of subluminal twisted light in vacuum,” Optica 3, 351–354 (2016).
[Crossref]

2015 (2)

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

D. Giovannini, J. Romero, V. Potoček, G. Ferenczi, F. Speirits, S. M. Barnett, D. Faccio, and M. J. Padgett, “Spatially structured photons that travel in free space slower than the speed of light,” Science 347, 857–860 (2015).
[Crossref]

2013 (1)

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

2012 (3)

2011 (2)

M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 62101 (2011).
[Crossref]

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

2010 (2)

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[Crossref]

2009 (5)

2005 (1)

2004 (1)

2003 (1)

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).
[Crossref]

2002 (1)

I. Alexeev, K. Y. Kim, and H. M. Milchberg, “Measurement of the superluminal group velocity of an ultrashort Bessel beam pulse,” Phys. Rev. Lett. 88, 073901 (2002).
[Crossref]

2000 (2)

D. Mugnai, A. Ranfagni, and R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[Crossref]

J. Courtial and M. J. Padgett, “Limit to the orbital angular momentum per unit energy in a light beam that can be focussed onto a small particle,” Opt. Commun. 173, 269–274 (2000).
[Crossref]

1996 (2)

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[Crossref]

Z. L. Horváth, J. Vinkó, Z. Bor, and D. von der Linde, “Acceleration of femtosecond pulses to superluminal velocities by Gouy phase shift,” Appl. Phys. B 63, 481–484 (1996).
[Crossref]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[Crossref]

Agnew, M.

M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 62101 (2011).
[Crossref]

Alexeev, I.

I. Alexeev, K. Y. Kim, and H. M. Milchberg, “Measurement of the superluminal group velocity of an ultrashort Bessel beam pulse,” Phys. Rev. Lett. 88, 073901 (2002).
[Crossref]

Andersson, E.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Arlt, J.

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).
[Crossref]

Bagini, V.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[Crossref]

Bandres, M. A.

Bareza, N. D.

N. D. Bareza and N. Hermosa, “Subluminal group velocity and dispersion of Laguerre–Gauss beams in free space,” Sci. Rep. 6, 26842 (2016).
[Crossref]

Barnett, S. M.

D. Giovannini, J. Romero, V. Potoček, G. Ferenczi, F. Speirits, S. M. Barnett, D. Faccio, and M. J. Padgett, “Spatially structured photons that travel in free space slower than the speed of light,” Science 347, 857–860 (2015).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

Bhatia, A. B.

M. Born, E. Wolf, and A. B. Bhatia, Principles of Optics (Cambridge University, 1999), Chap. 1, Eq. (56).

Biegert, J.

Bonaretti, F.

Bor, Z.

Z. L. Horváth, J. Vinkó, Z. Bor, and D. von der Linde, “Acceleration of femtosecond pulses to superluminal velocities by Gouy phase shift,” Appl. Phys. B 63, 481–484 (1996).
[Crossref]

Born, M.

M. Born, E. Wolf, and A. B. Bhatia, Principles of Optics (Cambridge University, 1999), Chap. 1, Eq. (56).

Bouchard, F.

Bowlan, P.

Boyd, R. W.

F. Bouchard, J. Harris, H. Mand, R. W. Boyd, and E. Karimi, “Observation of subluminal twisted light in vacuum,” Optica 3, 351–354 (2016).
[Crossref]

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 62101 (2011).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

Buller, G. S.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Chelkowski, S.

S. Chelkowski, S. Hild, and A. Freise, “Prospects of higher-order Laguerre–Gauss modes in future gravitational wave detectors,” Phys. Rev. D 79, 122002 (2009).
[Crossref]

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[Crossref]

Christodoulides, D. N.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[Crossref]

Clerici, M.

Courtial, J.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

J. Courtial and M. J. Padgett, “Limit to the orbital angular momentum per unit energy in a light beam that can be focussed onto a small particle,” Opt. Commun. 173, 269–274 (2000).
[Crossref]

Dada, A. C.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

Dudley, A.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, “Generating superpositions of higher-order Bessel beams,” Opt. Express 17, 23389–23395 (2009).
[Crossref]

Faccio, D.

D. Giovannini, J. Romero, V. Potoček, G. Ferenczi, F. Speirits, S. M. Barnett, D. Faccio, and M. J. Padgett, “Spatially structured photons that travel in free space slower than the speed of light,” Science 347, 857–860 (2015).
[Crossref]

F. Bonaretti, D. Faccio, M. Clerici, J. Biegert, and P. D. Trapani, “Spatiotemporal amplitude and phase retrieval of Bessel-X pulses using a Hartmann–Shack sensor,” Opt. Express 17, 9804–9809 (2009).
[Crossref]

Ferenczi, G.

D. Giovannini, J. Romero, V. Potoček, G. Ferenczi, F. Speirits, S. M. Barnett, D. Faccio, and M. J. Padgett, “Spatially structured photons that travel in free space slower than the speed of light,” Science 347, 857–860 (2015).
[Crossref]

Forbes, A.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, “Generating superpositions of higher-order Bessel beams,” Opt. Express 17, 23389–23395 (2009).
[Crossref]

Franke-Arnold, S.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

Freise, A.

S. Chelkowski, S. Hild, and A. Freise, “Prospects of higher-order Laguerre–Gauss modes in future gravitational wave detectors,” Phys. Rev. D 79, 122002 (2009).
[Crossref]

Frezza, F.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[Crossref]

Gauthier, D. J.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Gibson, G.

Giovannini, D.

D. Giovannini, J. Romero, V. Potoček, G. Ferenczi, F. Speirits, S. M. Barnett, D. Faccio, and M. J. Padgett, “Spatially structured photons that travel in free space slower than the speed of light,” Science 347, 857–860 (2015).
[Crossref]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Goyal, S.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Gutiérrez-Vega, J. C.

Harris, J.

Hermosa, N.

N. D. Bareza and N. Hermosa, “Subluminal group velocity and dispersion of Laguerre–Gauss beams in free space,” Sci. Rep. 6, 26842 (2016).
[Crossref]

Hild, S.

S. Chelkowski, S. Hild, and A. Freise, “Prospects of higher-order Laguerre–Gauss modes in future gravitational wave detectors,” Phys. Rev. D 79, 122002 (2009).
[Crossref]

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[Crossref]

Horváth, Z. L.

Z. L. Horváth, J. Vinkó, Z. Bor, and D. von der Linde, “Acceleration of femtosecond pulses to superluminal velocities by Gouy phase shift,” Appl. Phys. B 63, 481–484 (1996).
[Crossref]

Ireland, D. G.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

Jack, B.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

Jha, A. K.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

Karimi, E.

Kärtner, F. X.

Khilo, N.

Kim, K. Y.

I. Alexeev, K. Y. Kim, and H. M. Milchberg, “Measurement of the superluminal group velocity of an ultrashort Bessel beam pulse,” Phys. Rev. Lett. 88, 073901 (2002).
[Crossref]

Konrad, T.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Lavery, M. P. J.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Leach, J.

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 62101 (2011).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

Lõhmus, M.

Lütkenhaus, N.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Mafu, M.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Magaña-Loaiza, O. S.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Malik, M.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Mand, H.

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[Crossref]

Matt, R.

McLaren, M.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 62101 (2011).
[Crossref]

Milchberg, H. M.

I. Alexeev, K. Y. Kim, and H. M. Milchberg, “Measurement of the superluminal group velocity of an ultrashort Bessel beam pulse,” Phys. Rev. Lett. 88, 073901 (2002).
[Crossref]

Mirhosseini, M.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Mugnai, D.

D. Mugnai, A. Ranfagni, and R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[Crossref]

O’Sullivan, M. N.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[Crossref]

Padgett, M. J.

D. Giovannini, J. Romero, V. Potoček, G. Ferenczi, F. Speirits, S. M. Barnett, D. Faccio, and M. J. Padgett, “Spatially structured photons that travel in free space slower than the speed of light,” Science 347, 857–860 (2015).
[Crossref]

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12, 5448–5456 (2004).
[Crossref]

J. Courtial and M. J. Padgett, “Limit to the orbital angular momentum per unit energy in a light beam that can be focussed onto a small particle,” Opt. Commun. 173, 269–274 (2000).
[Crossref]

Pas’ko, V.

Petruccione, F.

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

Piksarv, P.

Potocek, V.

D. Giovannini, J. Romero, V. Potoček, G. Ferenczi, F. Speirits, S. M. Barnett, D. Faccio, and M. J. Padgett, “Spatially structured photons that travel in free space slower than the speed of light,” Science 347, 857–860 (2015).
[Crossref]

Putnam, W. P.

Ranfagni, A.

D. Mugnai, A. Ranfagni, and R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[Crossref]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[Crossref]

Rodenburg, B.

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Romero, J.

D. Giovannini, J. Romero, V. Potoček, G. Ferenczi, F. Speirits, S. M. Barnett, D. Faccio, and M. J. Padgett, “Spatially structured photons that travel in free space slower than the speed of light,” Science 347, 857–860 (2015).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

Roux, F. S.

M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 62101 (2011).
[Crossref]

Ruggeri, R.

D. Mugnai, A. Ranfagni, and R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[Crossref]

Saari, P.

Santarsiero, M.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[Crossref]

Schettini, G.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[Crossref]

Schimpf, D. N.

Schulte, J.

Spagnolo, G. S.

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[Crossref]

Speirits, F.

D. Giovannini, J. Romero, V. Potoček, G. Ferenczi, F. Speirits, S. M. Barnett, D. Faccio, and M. J. Padgett, “Spatially structured photons that travel in free space slower than the speed of light,” Science 347, 857–860 (2015).
[Crossref]

Trapani, P. D.

Trebino, R.

Valdmann, A.

Valtna-Lukner, H.

Vasilyeu, R.

Vasnetsov, M.

Vinkó, J.

Z. L. Horváth, J. Vinkó, Z. Bor, and D. von der Linde, “Acceleration of femtosecond pulses to superluminal velocities by Gouy phase shift,” Appl. Phys. B 63, 481–484 (1996).
[Crossref]

von der Linde, D.

Z. L. Horváth, J. Vinkó, Z. Bor, and D. von der Linde, “Acceleration of femtosecond pulses to superluminal velocities by Gouy phase shift,” Appl. Phys. B 63, 481–484 (1996).
[Crossref]

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[Crossref]

Wolf, E.

M. Born, E. Wolf, and A. B. Bhatia, Principles of Optics (Cambridge University, 1999), Chap. 1, Eq. (56).

Yao, A. M.

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

Appl. Phys. B (1)

Z. L. Horváth, J. Vinkó, Z. Bor, and D. von der Linde, “Acceleration of femtosecond pulses to superluminal velocities by Gouy phase shift,” Appl. Phys. B 63, 481–484 (1996).
[Crossref]

J. Mod. Opt. (2)

V. Bagini, F. Frezza, M. Santarsiero, G. Schettini, and G. S. Spagnolo, “Generalized Bessel–Gauss beams,” J. Mod. Opt. 43, 1155–1166 (1996).
[Crossref]

J. Arlt, “Handedness and azimuthal energy flow of optical vortex beams,” J. Mod. Opt. 50, 1573–1580 (2003).
[Crossref]

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

Nat. Photonics (1)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
[Crossref]

Nat. Phys. (1)

A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
[Crossref]

New J. Phys. (1)

M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O’Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, “High-dimensional quantum cryptography with twisted light,” New J. Phys. 17, 033033 (2015).
[Crossref]

Opt. Commun. (1)

J. Courtial and M. J. Padgett, “Limit to the orbital angular momentum per unit energy in a light beam that can be focussed onto a small particle,” Opt. Commun. 173, 269–274 (2000).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Optica (1)

Phys. Rev. A (2)

M. Mafu, A. Dudley, S. Goyal, D. Giovannini, M. McLaren, M. J. Padgett, T. Konrad, F. Petruccione, N. Lütkenhaus, and A. Forbes, “Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases,” Phys. Rev. A 88, 032305 (2013).
[Crossref]

M. Agnew, J. Leach, M. McLaren, F. S. Roux, and R. W. Boyd, “Tomography of the quantum state of photons entangled in high dimensions,” Phys. Rev. A 84, 62101 (2011).
[Crossref]

Phys. Rev. D (1)

S. Chelkowski, S. Hild, and A. Freise, “Prospects of higher-order Laguerre–Gauss modes in future gravitational wave detectors,” Phys. Rev. D 79, 122002 (2009).
[Crossref]

Phys. Rev. Lett. (3)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[Crossref]

D. Mugnai, A. Ranfagni, and R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[Crossref]

I. Alexeev, K. Y. Kim, and H. M. Milchberg, “Measurement of the superluminal group velocity of an ultrashort Bessel beam pulse,” Phys. Rev. Lett. 88, 073901 (2002).
[Crossref]

Sci. Rep. (1)

N. D. Bareza and N. Hermosa, “Subluminal group velocity and dispersion of Laguerre–Gauss beams in free space,” Sci. Rep. 6, 26842 (2016).
[Crossref]

Science (2)

D. Giovannini, J. Romero, V. Potoček, G. Ferenczi, F. Speirits, S. M. Barnett, D. Faccio, and M. J. Padgett, “Spatially structured photons that travel in free space slower than the speed of light,” Science 347, 857–860 (2015).
[Crossref]

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle-orbital angular momentum variables,” Science 329, 662–665 (2010).
[Crossref]

Other (1)

M. Born, E. Wolf, and A. B. Bhatia, Principles of Optics (Cambridge University, 1999), Chap. 1, Eq. (56).

Supplementary Material (1)

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» Supplement 1       Supplemental document.

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Figures (4)

Fig. 1.
Fig. 1. Experimental setup to study the path length traveled by a structured photon. Pulses of light with a central wavelength of 404 nm are produced by frequency-doubling a Ti:sapphire laser in a type-I beta-barium borate (BBO) crystal. Photon pairs at 808 nm are generated in a type-II BBO crystal. The photons are polarized orthogonally and are split on a polarizing beam splitter. One photon is spatially structured via an SLM, whereas the other photon (reference) is coupled to a polarization-maintaining fiber (PMF) with the input end mounted on a stepper motor so as to finely control the length of free-space propagation before the fiber and, therefore, the optical delay (delay line). The phase structure of the structured photon is returned to a Gaussian beam by a second SLM and coupled into a PMF and recombined with the reference photon on a 50:50 beam splitter where the photons undergo HOM interference. Single-photon detectors are used to coincidence count the output photons. The position of the HOM interference dip measures the transit time of the signal photon.
Fig. 2.
Fig. 2. Experimental results. Photon path delay, measured relative to a Gaussian (m=0) beam, for photons with a ring aperture for the cases with (red squares) and without (blue circles) OAM. The ring diameter of the photons is D(m)=2w|m|/2. The lines show the theoretical predictions based on Eq. (5).
Fig. 3.
Fig. 3. Effect of adding OAM to beams with a ring aperture. (a) We show the difference in path length between ring-shaped photons with and without OAM, Δ[δz]=δzm>0δzm=0. The solid black line is the error-weighted, linear regression of the data. The dark (light) shaded area shows the 1σ(3σ) confidence bound. The null hypothesis (Δ[δz]=0) is shown as a dashed red line: this cannot explain the data with a confidence better than 3σ. (b) The data are fit using the full theoretical description of the group velocity for Bessel–Gauss modes Eq. (5) (solid line) and the ray-tracing approach using Eq. (6) (dashed line). The insets show transverse profiles of the m=0, 5 intensity profiles measured using a continuous-wave source. A wedge is removed from the ring to illustrate that adding OAM rotates the intensity profile by an angle measured to be α=155° for all values of m.
Fig. 4.
Fig. 4. Ray picture of the plane-wave trajectories in the case of a fixed-diameter ring-shaped beam passing through the focus of a telescope formed between lenses placed at positions A and B (separated by a distance of L=2f). In the zero-OAM m=0 case (indicated as “lens ray”), images are inverted, corresponding to a rotation of the ray by an angle of α=180°. Introducing OAM (indicated as “OAM ray”) necessarily leads to a smaller rotation angle of α and thus to a shorter path length covered by the respective Gaussian beam, i.e., to an acceleration of the photon.

Equations (6)

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vg(z)=(2ϕ(r)ωz)ω01,
vg¯=Lz1z2dzvg(z)1,
δz=ctL=[k(argψ(r,k0)|ψ(r,k))|k0z]z1z2,
vg¯=c1+k2z12k02c(1k2z12k02)
δz=L2k02k2z1,
δzRayTracing=(121cosα4)D2L,

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