Abstract

Accelerating waves have received significant attention of late, first in the optical domain and later in the form of electron matter waves, and have found numerous applications in non-linear optics, material processing, microscopy, particle manipulation and laser plasma interactions. Here we create angular accelerating light beams with a potentially unlimited acceleration rate. By employing wavelength independent digital holograms for the creation and propagation of white light beams, we are able to study the resulting propagation in real and virtual space. We find that dephasing occurs for real propagation and that this can be compensated for in a virtual propagation scheme when single plane dynamics are important. Our work offers new insights into the propagation dynamics of such beams and provides a versatile tool for further investigations into propagating structured light fields.

© 2017 Optical Society of America

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  1. H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
    [Crossref]
  2. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy airy beams,” J. Opt. 32, 979–981 (2007).
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
    [Crossref]
  4. M. A. Bandres, “Accelerating parabolic beams,” Opt. Lett. 33, 1678–1680 (2008).
    [Crossref] [PubMed]
  5. C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Generalized radially self-accelerating helicon beams,” Phys. Rev. Lett. 113, 183901 (2014).
    [Crossref] [PubMed]
  6. C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparre, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91, 043821 (2015).
    [Crossref]
  7. J. Webster, C. Rosales-Guzmán, and A. Forbes, “Radially dependent angular acceleration of twisted light,” Opt. Lett. 42, 675–678 (2017).
    [Crossref] [PubMed]
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  9. J. C. Gutíerrez-Vega, M. Iturbe-Castillo, G. Ramírez, E. Tepichín, R. Rodríguez-Dagnino, S. Chávez-Cerda, and G. New, “Experimental demonstration of optical mathieu beams,” Opt. Commun. 195, 35–40 (2001).
    [Crossref]
  10. P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
    [Crossref] [PubMed]
  11. J. Y. Lu and J. F. Greenleaf, “Nondiffracting x-waves - exact-solutions to free-space scalar wave-equation and their finite aperture realizations,” IEEE Transactions On Ultrasonics Ferroelectrics and Frequency Control 39, 19–31 (1992).
    [Crossref]
  12. Y. Lumer, Y. Liang, R. Schley, I. Kaminer, E. Greenfield, D. Song, X. Zhang, J. Xu, Z. Chen, and M. Segev, “Incoherent self-accelerating beams,” Optica 2, 886–892 (2015).
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  13. T. Eichelkraut, C. Vetter, A. Perez-Leija, and A. Szameit, “Coherent random walks in free space,” Optica 1, 268–271 (2014).
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  14. T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an airy beam,” Nat. Methods 11, 541–544 (2014).
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  15. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using airy wavepackets,” Nat. Photon. 2, 675–678 (2008).
    [Crossref]
  16. N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
    [Crossref] [PubMed]
  17. R. Steiger, S. Bernet, and M. Ritsch-Marte, “Slm-based off-axis fourier filtering in microscopy with white light illumination,” Opt. Express 20, 15377–15384 (2012).
    [Crossref] [PubMed]
  18. C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
    [Crossref]
  19. D. Grier and S. Lee, “Multi-color holographic optical traps,” (2010). US Patent 7,759,020.
  20. A. Mathis, L. Froehly, L. Furfaro, M. Jacquot, J. M. Dudley, and F. Courvoisier, “Direct machining of curved trenches in silicon with femtosecond accelerating beams,” J. Eur. Opt. Soc, Rapid Publ. 8, 13019 (2013).
    [Crossref]
  21. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense airy beams,” Science 324, 229–232 (2009).
    [Crossref] [PubMed]
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    [Crossref]
  24. C. Paterson and R. Smith, “Helicon waves: Propagation-invariant waves in a rotating coordinate system,” Opt. Commun. 124, 131–140 (1996).
    [Crossref]
  25. R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, “Generating superpositions of higher-order bessel beams,” Opt. Express 17, 23389–23395 (2009).
    [Crossref]
  26. R. Rop, I. A. Litvin, and A. Forbes, “Generation and propagation dynamics of obstructed and unobstructed rotating orbital angular momentum-carrying helicon beams,” J. Opt. 14, 035702 (2012).
    [Crossref]
  27. C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Optimization and control of two-component radially self-accelerating beams,” Appl. Phys. Lett. 107, 211104 (2015).
    [Crossref]
  28. A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200–227 (2016).
    [Crossref]
  29. J. L. Martinez, E. J. Fernandez, P. M. Prieto, and P. Artal, “Chromatic aberration control with liquid crystal spatial phase modulators,” Opt. Express 25, 9793–9801 (2017).
    [Crossref] [PubMed]
  30. D.-M. Spangenberg, A. Dudley, P. H. Neethling, E. G. Rohwer, and A. Forbes, “White light wavefront control with a spatial light modulator,” Opt. Express 22, 13870–13879 (2014).
    [Crossref] [PubMed]
  31. C. Schulze, D. Flamm, M. Duparre, and A. Forbes, “Beam-quality measurements using a spatial light modulator,” Opt. Lett. 37, 4687–4689 (2012).
    [Crossref] [PubMed]
  32. J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a fresnel diffraction algorithm,” Opt. Eng. 54, 103101 (2015).
    [Crossref]
  33. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [Crossref] [PubMed]
  34. J. Durnin, “Exact-solutions for nondiffracting beams 1 – the scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [Crossref]
  35. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
    [Crossref]

2017 (3)

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

J. Webster, C. Rosales-Guzmán, and A. Forbes, “Radially dependent angular acceleration of twisted light,” Opt. Lett. 42, 675–678 (2017).
[Crossref] [PubMed]

J. L. Martinez, E. J. Fernandez, P. M. Prieto, and P. Artal, “Chromatic aberration control with liquid crystal spatial phase modulators,” Opt. Express 25, 9793–9801 (2017).
[Crossref] [PubMed]

2016 (1)

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200–227 (2016).
[Crossref]

2015 (4)

C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Optimization and control of two-component radially self-accelerating beams,” Appl. Phys. Lett. 107, 211104 (2015).
[Crossref]

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparre, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91, 043821 (2015).
[Crossref]

Y. Lumer, Y. Liang, R. Schley, I. Kaminer, E. Greenfield, D. Song, X. Zhang, J. Xu, Z. Chen, and M. Segev, “Incoherent self-accelerating beams,” Optica 2, 886–892 (2015).
[Crossref]

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a fresnel diffraction algorithm,” Opt. Eng. 54, 103101 (2015).
[Crossref]

2014 (4)

D.-M. Spangenberg, A. Dudley, P. H. Neethling, E. G. Rohwer, and A. Forbes, “White light wavefront control with a spatial light modulator,” Opt. Express 22, 13870–13879 (2014).
[Crossref] [PubMed]

T. Eichelkraut, C. Vetter, A. Perez-Leija, and A. Szameit, “Coherent random walks in free space,” Optica 1, 268–271 (2014).
[Crossref]

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref] [PubMed]

C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Generalized radially self-accelerating helicon beams,” Phys. Rev. Lett. 113, 183901 (2014).
[Crossref] [PubMed]

2013 (1)

A. Mathis, L. Froehly, L. Furfaro, M. Jacquot, J. M. Dudley, and F. Courvoisier, “Direct machining of curved trenches in silicon with femtosecond accelerating beams,” J. Eur. Opt. Soc, Rapid Publ. 8, 13019 (2013).
[Crossref]

2012 (4)

R. Rop, I. A. Litvin, and A. Forbes, “Generation and propagation dynamics of obstructed and unobstructed rotating orbital angular momentum-carrying helicon beams,” J. Opt. 14, 035702 (2012).
[Crossref]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

R. Steiger, S. Bernet, and M. Ritsch-Marte, “Slm-based off-axis fourier filtering in microscopy with white light illumination,” Opt. Express 20, 15377–15384 (2012).
[Crossref] [PubMed]

C. Schulze, D. Flamm, M. Duparre, and A. Forbes, “Beam-quality measurements using a spatial light modulator,” Opt. Lett. 37, 4687–4689 (2012).
[Crossref] [PubMed]

2011 (1)

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

2010 (1)

2009 (2)

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

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

2008 (2)

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using airy wavepackets,” Nat. Photon. 2, 675–678 (2008).
[Crossref]

M. A. Bandres, “Accelerating parabolic beams,” Opt. Lett. 33, 1678–1680 (2008).
[Crossref] [PubMed]

2007 (2)

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy airy beams,” J. Opt. 32, 979–981 (2007).

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

2001 (1)

J. C. Gutíerrez-Vega, M. Iturbe-Castillo, G. Ramírez, E. Tepichín, R. Rodríguez-Dagnino, S. Chávez-Cerda, and G. New, “Experimental demonstration of optical mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

2000 (2)

1999 (1)

1996 (2)

Y. Y. Schechner, R. Piestun, and S. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996).
[Crossref]

C. Paterson and R. Smith, “Helicon waves: Propagation-invariant waves in a rotating coordinate system,” Opt. Commun. 124, 131–140 (1996).
[Crossref]

1992 (1)

J. Y. Lu and J. F. Greenleaf, “Nondiffracting x-waves - exact-solutions to free-space scalar wave-equation and their finite aperture realizations,” IEEE Transactions On Ultrasonics Ferroelectrics and Frequency Control 39, 19–31 (1992).
[Crossref]

1987 (2)

J. Durnin, “Exact-solutions for nondiffracting beams 1 – the scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[Crossref]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Alpmann, C.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Andrews, D. L.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Arlt, J.

Artal, P.

Baker, M.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Bandres, M. A.

Banzer, P.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Bauer, T.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using airy wavepackets,” Nat. Photon. 2, 675–678 (2008).
[Crossref]

Belmonte, A.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Berg, C. A.

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a fresnel diffraction algorithm,” Opt. Eng. 54, 103101 (2015).
[Crossref]

Bernet, S.

R. Steiger, S. Bernet, and M. Ritsch-Marte, “Slm-based off-axis fourier filtering in microscopy with white light illumination,” Opt. Express 20, 15377–15384 (2012).
[Crossref] [PubMed]

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Berry, M.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Bigelow, N. P.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Campos, J.

Cannan, D.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Carmona, A.

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a fresnel diffraction algorithm,” Opt. Eng. 54, 103101 (2015).
[Crossref]

Chávez-Cerda, S.

J. C. Gutíerrez-Vega, M. Iturbe-Castillo, G. Ramírez, E. Tepichín, R. Rodríguez-Dagnino, S. Chávez-Cerda, and G. New, “Experimental demonstration of optical mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Chen, Z.

Y. Lumer, Y. Liang, R. Schley, I. Kaminer, E. Greenfield, D. Song, X. Zhang, J. Xu, Z. Chen, and M. Segev, “Incoherent self-accelerating beams,” Optica 2, 886–892 (2015).
[Crossref]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Christodoulides, D. N.

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35, 4045–4047 (2010).
[Crossref] [PubMed]

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy airy beams,” J. Opt. 32, 979–981 (2007).

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Cizmar, T.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref] [PubMed]

Coll-Llado, C.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref] [PubMed]

Cottrell, D. M.

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a fresnel diffraction algorithm,” Opt. Eng. 54, 103101 (2015).
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J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
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Courvoisier, F.

A. Mathis, L. Froehly, L. Furfaro, M. Jacquot, J. M. Dudley, and F. Courvoisier, “Direct machining of curved trenches in silicon with femtosecond accelerating beams,” J. Eur. Opt. Soc, Rapid Publ. 8, 13019 (2013).
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Dalgarno, H. I. C.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an airy beam,” Nat. Methods 11, 541–544 (2014).
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J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a fresnel diffraction algorithm,” Opt. Eng. 54, 103101 (2015).
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J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
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J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a fresnel diffraction algorithm,” Opt. Eng. 54, 103101 (2015).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
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T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an airy beam,” Nat. Methods 11, 541–544 (2014).
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J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using airy wavepackets,” Nat. Photon. 2, 675–678 (2008).
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G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
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A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200–227 (2016).
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C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparre, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91, 043821 (2015).
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D.-M. Spangenberg, A. Dudley, P. H. Neethling, E. G. Rohwer, and A. Forbes, “White light wavefront control with a spatial light modulator,” Opt. Express 22, 13870–13879 (2014).
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R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, “Generating superpositions of higher-order bessel beams,” Opt. Express 17, 23389–23395 (2009).
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Dudley, J. M.

A. Mathis, L. Froehly, L. Furfaro, M. Jacquot, J. M. Dudley, and F. Courvoisier, “Direct machining of curved trenches in silicon with femtosecond accelerating beams,” J. Eur. Opt. Soc, Rapid Publ. 8, 13019 (2013).
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Duparre, M.

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparre, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91, 043821 (2015).
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C. Schulze, D. Flamm, M. Duparre, and A. Forbes, “Beam-quality measurements using a spatial light modulator,” Opt. Lett. 37, 4687–4689 (2012).
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J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
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J. Durnin, “Exact-solutions for nondiffracting beams 1 – the scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
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J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
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Eichelkraut, T.

C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Optimization and control of two-component radially self-accelerating beams,” Appl. Phys. Lett. 107, 211104 (2015).
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C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Generalized radially self-accelerating helicon beams,” Phys. Rev. Lett. 113, 183901 (2014).
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T. Eichelkraut, C. Vetter, A. Perez-Leija, and A. Szameit, “Coherent random walks in free space,” Optica 1, 268–271 (2014).
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Ferrier, D. E. K.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an airy beam,” Nat. Methods 11, 541–544 (2014).
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Fickler, R.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
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Forbes, A.

J. Webster, C. Rosales-Guzmán, and A. Forbes, “Radially dependent angular acceleration of twisted light,” Opt. Lett. 42, 675–678 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200–227 (2016).
[Crossref]

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparre, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91, 043821 (2015).
[Crossref]

D.-M. Spangenberg, A. Dudley, P. H. Neethling, E. G. Rohwer, and A. Forbes, “White light wavefront control with a spatial light modulator,” Opt. Express 22, 13870–13879 (2014).
[Crossref] [PubMed]

R. Rop, I. A. Litvin, and A. Forbes, “Generation and propagation dynamics of obstructed and unobstructed rotating orbital angular momentum-carrying helicon beams,” J. Opt. 14, 035702 (2012).
[Crossref]

C. Schulze, D. Flamm, M. Duparre, and A. Forbes, “Beam-quality measurements using a spatial light modulator,” Opt. Lett. 37, 4687–4689 (2012).
[Crossref] [PubMed]

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

Freeman, C. L.

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a fresnel diffraction algorithm,” Opt. Eng. 54, 103101 (2015).
[Crossref]

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A. Mathis, L. Froehly, L. Furfaro, M. Jacquot, J. M. Dudley, and F. Courvoisier, “Direct machining of curved trenches in silicon with femtosecond accelerating beams,” J. Eur. Opt. Soc, Rapid Publ. 8, 13019 (2013).
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A. Mathis, L. Froehly, L. Furfaro, M. Jacquot, J. M. Dudley, and F. Courvoisier, “Direct machining of curved trenches in silicon with femtosecond accelerating beams,” J. Eur. Opt. Soc, Rapid Publ. 8, 13019 (2013).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
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Greenleaf, J. F.

J. Y. Lu and J. F. Greenleaf, “Nondiffracting x-waves - exact-solutions to free-space scalar wave-equation and their finite aperture realizations,” IEEE Transactions On Ultrasonics Ferroelectrics and Frequency Control 39, 19–31 (1992).
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T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an airy beam,” Nat. Methods 11, 541–544 (2014).
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J. C. Gutíerrez-Vega, M. Iturbe-Castillo, G. Ramírez, E. Tepichín, R. Rodríguez-Dagnino, S. Chávez-Cerda, and G. New, “Experimental demonstration of optical mathieu beams,” Opt. Commun. 195, 35–40 (2001).
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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
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J. C. Gutíerrez-Vega, M. Iturbe-Castillo, G. Ramírez, E. Tepichín, R. Rodríguez-Dagnino, S. Chávez-Cerda, and G. New, “Experimental demonstration of optical mathieu beams,” Opt. Commun. 195, 35–40 (2001).
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A. Mathis, L. Froehly, L. Furfaro, M. Jacquot, J. M. Dudley, and F. Courvoisier, “Direct machining of curved trenches in silicon with femtosecond accelerating beams,” J. Eur. Opt. Soc, Rapid Publ. 8, 13019 (2013).
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C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
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Karimi, E.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
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Kolesik, M.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense airy beams,” Science 324, 229–232 (2009).
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D. Grier and S. Lee, “Multi-color holographic optical traps,” (2010). US Patent 7,759,020.

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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
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Litchinitser, N. M.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
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Litvin, I. A.

R. Rop, I. A. Litvin, and A. Forbes, “Generation and propagation dynamics of obstructed and unobstructed rotating orbital angular momentum-carrying helicon beams,” J. Opt. 14, 035702 (2012).
[Crossref]

Lu, J. Y.

J. Y. Lu and J. F. Greenleaf, “Nondiffracting x-waves - exact-solutions to free-space scalar wave-equation and their finite aperture realizations,” IEEE Transactions On Ultrasonics Ferroelectrics and Frequency Control 39, 19–31 (1992).
[Crossref]

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Mansuripur, M.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
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Mathis, A.

A. Mathis, L. Froehly, L. Furfaro, M. Jacquot, J. M. Dudley, and F. Courvoisier, “Direct machining of curved trenches in silicon with femtosecond accelerating beams,” J. Eur. Opt. Soc, Rapid Publ. 8, 13019 (2013).
[Crossref]

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C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Mazilu, M.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using airy wavepackets,” Nat. Photon. 2, 675–678 (2008).
[Crossref]

McLaren, M.

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200–227 (2016).
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McMorran, B.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
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J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
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Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

Morandotti, R.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Moreno, I.

J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a fresnel diffraction algorithm,” Opt. Eng. 54, 103101 (2015).
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J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
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New, G.

J. C. Gutíerrez-Vega, M. Iturbe-Castillo, G. Ramírez, E. Tepichín, R. Rodríguez-Dagnino, S. Chávez-Cerda, and G. New, “Experimental demonstration of optical mathieu beams,” Opt. Commun. 195, 35–40 (2001).
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T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an airy beam,” Nat. Methods 11, 541–544 (2014).
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C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Optimization and control of two-component radially self-accelerating beams,” Appl. Phys. Lett. 107, 211104 (2015).
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C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Generalized radially self-accelerating helicon beams,” Phys. Rev. Lett. 113, 183901 (2014).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
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J. C. Gutíerrez-Vega, M. Iturbe-Castillo, G. Ramírez, E. Tepichín, R. Rodríguez-Dagnino, S. Chávez-Cerda, and G. New, “Experimental demonstration of optical mathieu beams,” Opt. Commun. 195, 35–40 (2001).
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H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
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J. C. Gutíerrez-Vega, M. Iturbe-Castillo, G. Ramírez, E. Tepichín, R. Rodríguez-Dagnino, S. Chávez-Cerda, and G. New, “Experimental demonstration of optical mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Rohwer, E. G.

Romero, J.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Rop, R.

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparre, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91, 043821 (2015).
[Crossref]

R. Rop, I. A. Litvin, and A. Forbes, “Generation and propagation dynamics of obstructed and unobstructed rotating orbital angular momentum-carrying helicon beams,” J. Opt. 14, 035702 (2012).
[Crossref]

Rosales-Guzmán, C.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

J. Webster, C. Rosales-Guzmán, and A. Forbes, “Radially dependent angular acceleration of twisted light,” Opt. Lett. 42, 675–678 (2017).
[Crossref] [PubMed]

Roux, F. S.

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparre, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91, 043821 (2015).
[Crossref]

Rubinsztein-Dunlop, H.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

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[Crossref]

Y. Y. Schechner, R. Piestun, and S. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996).
[Crossref]

Schley, R.

Schulze, C.

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparre, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91, 043821 (2015).
[Crossref]

C. Schulze, D. Flamm, M. Duparre, and A. Forbes, “Beam-quality measurements using a spatial light modulator,” Opt. Lett. 37, 4687–4689 (2012).
[Crossref] [PubMed]

Segev, M.

Shamir, J.

Shamir, S.

Y. Y. Schechner, R. Piestun, and S. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996).
[Crossref]

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense airy beams,” Science 324, 229–232 (2009).
[Crossref] [PubMed]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy airy beams,” J. Opt. 32, 979–981 (2007).

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Smith, R.

C. Paterson and R. Smith, “Helicon waves: Propagation-invariant waves in a rotating coordinate system,” Opt. Commun. 124, 131–140 (1996).
[Crossref]

Song, D.

Spangenberg, D.-M.

Steiger, R.

Stilgoe, A. B.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Szameit, A.

C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Optimization and control of two-component radially self-accelerating beams,” Appl. Phys. Lett. 107, 211104 (2015).
[Crossref]

C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Generalized radially self-accelerating helicon beams,” Phys. Rev. Lett. 113, 183901 (2014).
[Crossref] [PubMed]

T. Eichelkraut, C. Vetter, A. Perez-Leija, and A. Szameit, “Coherent random walks in free space,” Optica 1, 268–271 (2014).
[Crossref]

Tepichín, E.

J. C. Gutíerrez-Vega, M. Iturbe-Castillo, G. Ramírez, E. Tepichín, R. Rodríguez-Dagnino, S. Chávez-Cerda, and G. New, “Experimental demonstration of optical mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

Torres, J. P.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Vasilyeu, R.

Vettenburg, T.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an airy beam,” Nat. Methods 11, 541–544 (2014).
[Crossref] [PubMed]

Vetter, C.

C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Optimization and control of two-component radially self-accelerating beams,” Appl. Phys. Lett. 107, 211104 (2015).
[Crossref]

C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Generalized radially self-accelerating helicon beams,” Phys. Rev. Lett. 113, 183901 (2014).
[Crossref] [PubMed]

T. Eichelkraut, C. Vetter, A. Perez-Leija, and A. Szameit, “Coherent random walks in free space,” Optica 1, 268–271 (2014).
[Crossref]

Webster, J.

Weiner, A. M.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

White, A. G.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Willner, A. E.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Xie, G.

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

Xu, J.

Yin, X.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Yzuel, M. J.

Zhang, P.

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Zhang, X.

Y. Lumer, Y. Liang, R. Schley, I. Kaminer, E. Greenfield, D. Song, X. Zhang, J. Xu, Z. Chen, and M. Segev, “Incoherent self-accelerating beams,” Optica 2, 886–892 (2015).
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P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200–227 (2016).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Optimization and control of two-component radially self-accelerating beams,” Appl. Phys. Lett. 107, 211104 (2015).
[Crossref]

IEEE Transactions On Ultrasonics Ferroelectrics and Frequency Control (1)

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[Crossref]

J. Eur. Opt. Soc, Rapid Publ. (1)

A. Mathis, L. Froehly, L. Furfaro, M. Jacquot, J. M. Dudley, and F. Courvoisier, “Direct machining of curved trenches in silicon with femtosecond accelerating beams,” J. Eur. Opt. Soc, Rapid Publ. 8, 13019 (2013).
[Crossref]

J. Opt. (3)

R. Rop, I. A. Litvin, and A. Forbes, “Generation and propagation dynamics of obstructed and unobstructed rotating orbital angular momentum-carrying helicon beams,” J. Opt. 14, 035702 (2012).
[Crossref]

H. Rubinsztein-Dunlop, A. Forbes, M. Berry, M. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2017).
[Crossref]

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy airy beams,” J. Opt. 32, 979–981 (2007).

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

Laser Photon. Rev. (1)

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Nat. Methods (1)

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Llado, D. E. K. Ferrier, T. Cizmar, F. J. Gunn-Moore, and K. Dholakia, “Light-sheet microscopy using an airy beam,” Nat. Methods 11, 541–544 (2014).
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J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using airy wavepackets,” Nat. Photon. 2, 675–678 (2008).
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J. C. Gutíerrez-Vega, M. Iturbe-Castillo, G. Ramírez, E. Tepichín, R. Rodríguez-Dagnino, S. Chávez-Cerda, and G. New, “Experimental demonstration of optical mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[Crossref]

C. Paterson and R. Smith, “Helicon waves: Propagation-invariant waves in a rotating coordinate system,” Opt. Commun. 124, 131–140 (1996).
[Crossref]

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J. A. Davis, I. Moreno, D. M. Cottrell, C. A. Berg, C. L. Freeman, A. Carmona, and W. Debenham, “Experimental implementation of a virtual optical beam propagator system based on a fresnel diffraction algorithm,” Opt. Eng. 54, 103101 (2015).
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Opt. Express (4)

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Optica (2)

Phys. Rev. A (1)

C. Schulze, F. S. Roux, A. Dudley, R. Rop, M. Duparre, and A. Forbes, “Accelerated rotation with orbital angular momentum modes,” Phys. Rev. A 91, 043821 (2015).
[Crossref]

Phys. Rev. E (1)

Y. Y. Schechner, R. Piestun, and S. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E 54, R50–R53 (1996).
[Crossref]

Phys. Rev. Lett. (4)

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, and X. Zhang, “Nonparaxial mathieu and weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

C. Vetter, T. Eichelkraut, M. Ornigotti, and A. Szameit, “Generalized radially self-accelerating helicon beams,” Phys. Rev. Lett. 113, 183901 (2014).
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P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense airy beams,” Science 324, 229–232 (2009).
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Other (1)

D. Grier and S. Lee, “Multi-color holographic optical traps,” (2010). US Patent 7,759,020.

Supplementary Material (1)

NameDescription
» Visualization 1       Scan with a commercial RGB webcam over the beam shown in Fig. 5

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Figures (5)

Fig. 1
Fig. 1 The concept of the experiment requires the Fourier transform of the desired field u(x, y, 0) to be encoded on the SLM in conjunction with a blazed grating. This procedure can be understood as follows: (a) With no grating present, all light remains on-axis and the CCD-image dark. (b) With a uniform grating, all light is redirected into the first diffraction order. (c) Local modulation of the grating enables amplitude modulation. In addition a slowly varying phase can be added to the grating whereby, for example, angular accelerating beams can be achieved. (d) When adding the phase given by the free-space transfer function exp(ikz z), the output plane is shifted with respect to z whereby the beam is digitally propagated without moving the CCD-camera.

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Fig. 2
Fig. 2 Experimental implementation with (a) layout of our setup [L:Lens, SLM: Spatial Light Modulator, f1 = 15 mm, f2 = 125 mm, f3 = f4 = 500 mm, f5 = 200 mm], (b) hologram on SLM1 showing the amplitude-modulated annular apertures [R1 = 1.24 mm, R2 = 1.56 mm], (c) hologram on SLM2 with inverted grating to SLM1.

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Fig. 3
Fig. 3 Experimental results and simulations in real- and digital propagation for the spectral components of an angular accelerating white light beam with ℓ = +1, m = −1 and η = π/5. Panels (a–b) show experiment (left) and simulation (right) of the rotation angle for real propagation. Panels (c–h) show experiment (left column) and simulations (right column) for digital propagation. Panels (e, g) are obtained from Panel (c) via numerical differentiation. Panels (d, f, h) are directly obtained from Eqs. (5) to (7) with k = 2π/632.8 nm.

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Fig. 4
Fig. 4 Measured rotation period for real (blue) and digital (orange) propagation. Error bars refer to half the distance between two consecutive data points in Figs. 3 (a) and (c), respectively.

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Fig. 5
Fig. 5 Recorded behaviour for a white light angular accelerating beam with ℓ = +1 and −1, and η = π/3. Top: Beam profiles recorded with a commercial rgb-webcam. Bottom: Iso-intensity plot obtained from beam profiles recorded with a high-quality monochromatic CCD. The iso-surface corresponds to two-thirds of the peak intensity. All wavelength components were set to contribute equally to the overall exposure.

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Equations (14)

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u ( r , φ , z ) = 𝒥 m ( k r | 1 r ) e im φ e i z k z | 1 + 𝒥 ℓ ( k r | 2 r ) e i ℓ φ e i z k z | 2 ,
| u ( r , φ , z ) | 2 = | 𝒥 m ( k r | 1 r ) | 2 + | 𝒥 ℓ ( k r | 2 r ) | 2 + 2 𝒥 m ( k r | 1 r ) 𝒥 ℓ ( k r | 2 r ) cos ( Δ m ℓ φ + Δ k z z ) .
φ ( z ) = φ 0 − Δ k z z Δ m ℓ               ω ( z ) = d φ ( z ) d z = − Δ k z Δ m ℓ                       α ( z ) = d 2 φ ( z ) d z 2 = 0
g m ( r , φ , z , η ) = 𝒥 m ( k r r ) [ cos ( η 2 ) e i m φ + sin ( η 2 ) e i m φ ] e i k z z .
u ( r , φ , z ) = 𝒥 m ( k r | 1 r ) [ cos ( η 2 ) e i m φ + sin ( η 2 ) e − i m φ ] e i k z | 1 z + 𝒥 − m ( k r | 2 r ) [ cos ( η 2 ) e − i m φ + sin ( η 2 ) e i m φ ] e i k z | 2 z .
φ ( z ) = 1 2 | m | arctan [ cos ( η ) sin ( Δ k z z ) sin ( η ) + cos ( Δ k z z ) ]
ω ( z ) = Δ k z 2 | m | cos ( η ) 1 + sin ( η ) cos ( Δ k z z )
α ( z ) = Δ k z 2 4 | m | sin ( 2 η ) sin ( Δ k z z ) [ 1 + sin ( η ) cos ( Δ k z z ) ] 2
u ( x , y ) = | u ( x , y ) | exp ( i θ ( x , y ) + i k x x ) ,
exp ( i k x λ 0 λ x ) rect ( 2 p x x ) ⊗ ∑ n = − ∞ ∞ δ ( x − n p x )         = ∑ n = − ∞ ∞ sinc ( π [ n − ( λ 0 / λ ) ] ) exp ( i n k x x ) .
u ^ λ ( x , y ) = ∑ n = − ∞ ∞ sinc ( π [ n − ( λ 0 / λ ) ] )     | u ( x , y ) | exp ( i n θ ( x , y ) + i n k x x ) .
u ^ λ ( x , y ) = A λ | u ( x , y ) | exp ( i θ ( x , y ) + i k x x ) = A λ u ( x , y ) .
u ( x , y , z ) = ℱ − 1 { ℱ [ u ( x , y , 0 ) ] exp ( i k z z ) } ,
k z | n = k ( λ ) 1 − R n 2 f 2 ,

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