Abstract

It is understood from the conical wave picture that Bessel beams may self-heal after certain opaque obstructions, but the extrapolation to transparent phase screens is not self-evident. Here we consider the propagation of Bessel beams through aberrated obstacles and show that the self-healing is not guaranteed, but rather a function of the severity of the aberration. Paradoxically, we explain why strong aberrations may show self-healing while weak aberrations will not, and highlight the parameters that influence this. Finally, we combine aberrations to pass the Bessel beam through turbulence, and debunk the myth that Bessel beams are resilient to such perturbations.

© 2018 Optical Society of America

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2017 (4)

2016 (3)

S. Chen, S. Li, Y. Zhao, J. Liu, L. Zhu, A. Wang, J. Du, L. Shen, and J. Wang, “Demonstration of 20-Gbit/s high-speed Bessel beam encoding/decoding link with adaptive turbulence compensation,” Opt. Lett. 41, 4680–4683 (2016).
[Crossref]

T. Doster and A. T. Watnik, “Laguerre-Gauss and Bessel-Gauss beams propagation through turbulence: analysis of channel efficiency,” Appl. Opt. 55, 10239–10246 (2016).
[Crossref]

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref]

2015 (4)

2014 (7)

W. Nelson, J. Palastro, C. Davis, and P. Sprangle, “Propagation of Bessel and airy beams through atmospheric turbulence,” J. Opt. Soc. Am. A 31, 603–609 (2014).
[Crossref]

Y. Zhu, X. Liu, J. Gao, Y. Zhang, and F. Zhao, “Probability density of the orbital angular momentum mode of Hankel-Bessel beams in an atmospheric turbulence,” Opt. Express 22, 7765–7772 (2014).
[Crossref]

A. Trichili, T. Mhlanga, Y. Ismail, F. S. Roux, M. McLaren, M. Zghal, and A. Forbes, “Detection of Bessel beams with digital axicons,” Opt. Express 22, 17553–17560 (2014).
[Crossref]

A. Aiello and G. S. Agarwal, “Wave-optics description of self-healing mechanism in Bessel beams,” Opt. Lett. 39, 6819–6822 (2014).
[Crossref]

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref]

C. Ryu, K. Henderson, and M. Boshier, “Creation of matter wave Bessel beams and observation of quantized circulation in a Bose-Einstein condensate,” New J. Phys. 16, 013046 (2014).
[Crossref]

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
[Crossref]

2013 (4)

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photon. News 24(6), 22–29 (2013).
[Crossref]

M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of Bessel-Gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[Crossref]

A. Dudley, T. Mhlanga, M. Lavery, A. McDonald, F. S. Roux, M. Padgett, and A. Forbes, “Efficient sorting of Bessel beams,” Opt. Express 21, 165–171 (2013).
[Crossref]

A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett. 38, 3429–3432 (2013).
[Crossref]

2012 (3)

2010 (2)

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]

I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
[Crossref]

2008 (1)

L. Burger, I. A. Litvin, and A. Forbes, “Simulating atmospheric turbulence using a phase-only spatial light modulator,” South Afr. J. Sci. 104, 129–134 (2008).

2007 (3)

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46, 078001 (2007).
[Crossref]

H. T. Eyyuboğlu, “Propagation of higher order Bessel-Gaussian beams in turbulence,” Appl. Phys. B 88, 259–265 (2007).
[Crossref]

V. Kollarova, T. Medrik, R. Celechovsky, Z. Bouchal, O. Wilfert, and Z. Kolka, “Application of nondiffracting beams to wireless optical communications,” Proc. SPIE 6736, 67361C (2007).
[Crossref]

2006 (1)

S. Hacyan and R. Jáuregui, “A relativistic study of Bessel beams,” J. Phys. B 39, 1669–1676 (2006).
[Crossref]

2005 (2)

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

R. Jáuregui and S. Hacyan, “Quantum-mechanical properties of Bessel beams,” Phys. Rev. A 71, 033411 (2005).
[Crossref]

2004 (1)

V. Pyragaite, A. Piskarskas, K. Regelskis, V. Smilgevicius, A. Stabinis, and S. Mikalauskas, “Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium,” Opt. Commun. 240, 191–200 (2004).
[Crossref]

2003 (2)

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. 53, 537–578 (2003).
[Crossref]

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

2002 (2)

Z. Bouchal, “Resistance of nondiffracting vortex beam against amplitude and phase perturbations,” Opt. Commun. 210, 155–164 (2002).
[Crossref]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref]

2001 (3)

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

J. Rogel-Salazar, G. New, and S. Chávez-Cerda, “Bessel-Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
[Crossref]

A. N. Khilo, E. G. Katranji, and A. A. Ryzhevich, “Axicon-based Bessel resonator: analytical description and experiment,” J. Opt. Soc. Am. A 18, 1986–1992 (2001).
[Crossref]

2000 (2)

1999 (1)

C. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a “nondiffracting” light beam,” Am. J. Phys. 67, 912–915 (1999).
[Crossref]

1998 (2)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

P. Pääkkönen and J. Turunen, “Resonators with Bessel-Gauss modes,” Opt. Commun. 156, 359–366 (1998).
[Crossref]

1996 (1)

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[Crossref]

1989 (3)

1987 (3)

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

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[Crossref]

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

1976 (1)

1954 (1)

Agarwal, G. S.

Agnew, M.

Ahmed, N.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref]

Aiello, A.

Akturk, S.

T. Ersoy, B. Yalizay, and S. Akturk, “Self-reconstruction of diffraction-free and accelerating laser beams in scattering media,” J. Quantum Spectrosc. Radiat. Transfer 113, 2470–2475 (2012).
[Crossref]

Alfano, R. R.

G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17, 035617 (2015).
[Crossref]

Almaiman, A.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref]

Anguiano-Morales, M.

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46, 078001 (2007).
[Crossref]

Arlt, J.

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

C. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a “nondiffracting” light beam,” Am. J. Phys. 67, 912–915 (1999).
[Crossref]

Arroyo-Carrasco, M. L.

Ashrafi, S.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref]

Belyi, V. N.

Birch, P.

Bock, M.

M. Bock, A. Treffer, and R. Grunwald, “Nondiffracting self-imaging of ultrashort wavepackets,” Opt. Lett. 42, 2374–2377 (2017).
[Crossref]

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, “Self-reconstruction of pulsed optical x-waves,” in Localized Waves (Wiley, 2008), pp. 299–313.

Boshier, M.

C. Ryu, K. Henderson, and M. Boshier, “Creation of matter wave Bessel beams and observation of quantized circulation in a Bose-Einstein condensate,” New J. Phys. 16, 013046 (2014).
[Crossref]

Bouchal, Z.

V. Kollarova, T. Medrik, R. Celechovsky, Z. Bouchal, O. Wilfert, and Z. Kolka, “Application of nondiffracting beams to wireless optical communications,” Proc. SPIE 6736, 67361C (2007).
[Crossref]

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. 53, 537–578 (2003).
[Crossref]

Z. Bouchal, “Resistance of nondiffracting vortex beam against amplitude and phase perturbations,” Opt. Commun. 210, 155–164 (2002).
[Crossref]

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

Boyd, R.

Boyd, R. W.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
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V. Kollarova, T. Medrik, R. Celechovsky, Z. Bouchal, O. Wilfert, and Z. Kolka, “Application of nondiffracting beams to wireless optical communications,” Proc. SPIE 6736, 67361C (2007).
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G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17, 035617 (2015).
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J. Rogel-Salazar, G. New, and S. Chávez-Cerda, “Bessel-Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
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V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
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D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
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G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17, 035617 (2015).
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A. Trichili, T. Mhlanga, Y. Ismail, F. S. Roux, M. McLaren, M. Zghal, and A. Forbes, “Detection of Bessel beams with digital axicons,” Opt. Express 22, 17553–17560 (2014).
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M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of Bessel-Gaussian modes,” Phys. Rev. A 88, 033818 (2013).
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A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett. 38, 3429–3432 (2013).
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A. Dudley, T. Mhlanga, M. Lavery, A. McDonald, F. S. Roux, M. Padgett, and A. Forbes, “Efficient sorting of Bessel beams,” Opt. Express 21, 165–171 (2013).
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M. McLaren, M. Agnew, J. Leach, F. Roux, M. Padgett, R. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20, 23589–23597 (2012).
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I. A. Litvin, N. A. Khilo, A. Forbes, and V. N. Belyi, “Intra-cavity generation of Bessel-like beams with longitudinally dependent cone angles,” Opt. Express 18, 4701–4708 (2010).
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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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R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
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V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
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Gao, J.

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V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
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Gazzadi, G. C.

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
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R. Grunwald, U. Griebner, F. Tschirschwitz, E. T. J. Nibbering, T. Elsaesser, V. Kebbel, H.-J. Hartmann, and W. Jüptner, “Generation of femtosecond Bessel beams with microaxicon arrays,” Opt. Lett. 25, 981–983 (2000).
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R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, “Self-reconstruction of pulsed optical x-waves,” in Localized Waves (Wiley, 2008), pp. 299–313.

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V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
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R. Grunwald, U. Griebner, F. Tschirschwitz, E. T. J. Nibbering, T. Elsaesser, V. Kebbel, H.-J. Hartmann, and W. Jüptner, “Generation of femtosecond Bessel beams with microaxicon arrays,” Opt. Lett. 25, 981–983 (2000).
[Crossref]

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, “Self-reconstruction of pulsed optical x-waves,” in Localized Waves (Wiley, 2008), pp. 299–313.

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Hartmann, H.-J.

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Ismail, Y.

Ituen, I.

Iturbe-Castillo, M. D.

J. Mendoza-Hernández, M. L. Arroyo-Carrasco, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Laguerre-Gauss beams versus Bessel beams showdown: peer comparison,” Opt. Lett. 40, 3739–3742 (2015).
[Crossref]

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46, 078001 (2007).
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Jáuregui, R.

S. Hacyan and R. Jáuregui, “A relativistic study of Bessel beams,” J. Phys. B 39, 1669–1676 (2006).
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R. Jáuregui and S. Hacyan, “Quantum-mechanical properties of Bessel beams,” Phys. Rev. A 71, 033411 (2005).
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Jüptner, W.

Karimi, E.

G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17, 035617 (2015).
[Crossref]

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
[Crossref]

Katranji, E. G.

Kebbel, V.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

R. Grunwald, U. Griebner, F. Tschirschwitz, E. T. J. Nibbering, T. Elsaesser, V. Kebbel, H.-J. Hartmann, and W. Jüptner, “Generation of femtosecond Bessel beams with microaxicon arrays,” Opt. Lett. 25, 981–983 (2000).
[Crossref]

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, “Self-reconstruction of pulsed optical x-waves,” in Localized Waves (Wiley, 2008), pp. 299–313.

Khilo, A. N.

Khilo, N.

Khilo, N. A.

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V. Kollarova, T. Medrik, R. Celechovsky, Z. Bouchal, O. Wilfert, and Z. Kolka, “Application of nondiffracting beams to wireless optical communications,” Proc. SPIE 6736, 67361C (2007).
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V. Kollarova, T. Medrik, R. Celechovsky, Z. Bouchal, O. Wilfert, and Z. Kolka, “Application of nondiffracting beams to wireless optical communications,” Proc. SPIE 6736, 67361C (2007).
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Kummrow, A.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
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Lavery, M.

A. Dudley, T. Mhlanga, M. Lavery, A. McDonald, F. S. Roux, M. Padgett, and A. Forbes, “Efficient sorting of Bessel beams,” Opt. Express 21, 165–171 (2013).
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A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photon. News 24(6), 22–29 (2013).
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Lavery, M. P. J.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
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Leuchs, G.

Li, L.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
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Li, S.

Li, Y.

Liao, P.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
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I. A. Litvin, N. A. Khilo, A. Forbes, and V. N. Belyi, “Intra-cavity generation of Bessel-like beams with longitudinally dependent cone angles,” Opt. Express 18, 4701–4708 (2010).
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I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
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L. Burger, I. A. Litvin, and A. Forbes, “Simulating atmospheric turbulence using a phase-only spatial light modulator,” South Afr. J. Sci. 104, 129–134 (2008).

Liu, J.

Liu, S.

Liu, X.

Margiewicz, J.

McDonald, A.

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
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V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
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McLaren, M.

A. Trichili, T. Mhlanga, Y. Ismail, F. S. Roux, M. McLaren, M. Zghal, and A. Forbes, “Detection of Bessel beams with digital axicons,” Opt. Express 22, 17553–17560 (2014).
[Crossref]

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref]

M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of Bessel-Gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[Crossref]

M. McLaren, M. Agnew, J. Leach, F. Roux, M. Padgett, R. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20, 23589–23597 (2012).
[Crossref]

McLaren, M. G.

I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
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McLeod, J. H.

McQueen, C.

C. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a “nondiffracting” light beam,” Am. J. Phys. 67, 912–915 (1999).
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Medrik, T.

V. Kollarova, T. Medrik, R. Celechovsky, Z. Bouchal, O. Wilfert, and Z. Kolka, “Application of nondiffracting beams to wireless optical communications,” Proc. SPIE 6736, 67361C (2007).
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Melville, H.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
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M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46, 078001 (2007).
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Mhlanga, T.

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J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
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G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17, 035617 (2015).
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Molisch, A. F.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
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Neumann, U.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
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R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, “Self-reconstruction of pulsed optical x-waves,” in Localized Waves (Wiley, 2008), pp. 299–313.

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J. Rogel-Salazar, G. New, and S. Chávez-Cerda, “Bessel-Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
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G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17, 035617 (2015).
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R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
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R. Grunwald, U. Griebner, F. Tschirschwitz, E. T. J. Nibbering, T. Elsaesser, V. Kebbel, H.-J. Hartmann, and W. Jüptner, “Generation of femtosecond Bessel beams with microaxicon arrays,” Opt. Lett. 25, 981–983 (2000).
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Padgett, M. J.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
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M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of Bessel-Gaussian modes,” Phys. Rev. A 88, 033818 (2013).
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F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
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Piestun, R.

Piskarskas, A.

V. Pyragaite, A. Piskarskas, K. Regelskis, V. Smilgevicius, A. Stabinis, and S. Mikalauskas, “Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium,” Opt. Commun. 240, 191–200 (2004).
[Crossref]

Pyragaite, V.

V. Pyragaite, A. Piskarskas, K. Regelskis, V. Smilgevicius, A. Stabinis, and S. Mikalauskas, “Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium,” Opt. Commun. 240, 191–200 (2004).
[Crossref]

Regelskis, K.

V. Pyragaite, A. Piskarskas, K. Regelskis, V. Smilgevicius, A. Stabinis, and S. Mikalauskas, “Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium,” Opt. Commun. 240, 191–200 (2004).
[Crossref]

Rehácek, J.

Ren, Y.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref]

Rini, M.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

Rogel-Salazar, J.

J. Rogel-Salazar, G. New, and S. Chávez-Cerda, “Bessel-Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
[Crossref]

Rohrbach, A.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

Romero, J.

M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of Bessel-Gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[Crossref]

Rousseau, G.

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
[Crossref]

Roux, F.

Roux, F. S.

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref]

A. Trichili, T. Mhlanga, Y. Ismail, F. S. Roux, M. McLaren, M. Zghal, and A. Forbes, “Detection of Bessel beams with digital axicons,” Opt. Express 22, 17553–17560 (2014).
[Crossref]

A. Dudley, T. Mhlanga, M. Lavery, A. McDonald, F. S. Roux, M. Padgett, and A. Forbes, “Efficient sorting of Bessel beams,” Opt. Express 21, 165–171 (2013).
[Crossref]

M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of Bessel-Gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[Crossref]

Ryu, C.

C. Ryu, K. Henderson, and M. Boshier, “Creation of matter wave Bessel beams and observation of quantized circulation in a Bose-Einstein condensate,” New J. Phys. 16, 013046 (2014).
[Crossref]

Ryzhevich, A. A.

Sánchez-Soto, L. L.

Schechner, Y. Y.

Shamir, J.

Shen, L.

Shi, Z.

Sibbett, W.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

Smilgevicius, V.

V. Pyragaite, A. Piskarskas, K. Regelskis, V. Smilgevicius, A. Stabinis, and S. Mikalauskas, “Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium,” Opt. Commun. 240, 191–200 (2004).
[Crossref]

Smith, R.

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[Crossref]

Sprangle, P.

Stabinis, A.

V. Pyragaite, A. Piskarskas, K. Regelskis, V. Smilgevicius, A. Stabinis, and S. Mikalauskas, “Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium,” Opt. Commun. 240, 191–200 (2004).
[Crossref]

Steinmeyer, G.

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, “Self-reconstruction of pulsed optical x-waves,” in Localized Waves (Wiley, 2008), pp. 299–313.

Stibenz, G.

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, “Self-reconstruction of pulsed optical x-waves,” in Localized Waves (Wiley, 2008), pp. 299–313.

Stoklasa, B.

Tang, H.

Tang, Y.

Treffer, A.

Trichili, A.

Tschirschwitz, F.

Tur, M.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref]

Turunen, J.

Uehara, K.

K. Uehara and H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1989).
[Crossref]

Vasara, A.

Vasilyeu, R.

Wagner, J.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

Wang, A.

Wang, J.

Wang, Z.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref]

Watnik, A. T.

Wilfert, O.

V. Kollarova, T. Medrik, R. Celechovsky, Z. Bouchal, O. Wilfert, and Z. Kolka, “Application of nondiffracting beams to wireless optical communications,” Proc. SPIE 6736, 67361C (2007).
[Crossref]

Willner, A. E.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref]

Willner, A. J.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref]

Wu, D.

Xie, G.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref]

Yalizay, B.

T. Ersoy, B. Yalizay, and S. Akturk, “Self-reconstruction of diffraction-free and accelerating laser beams in scattering media,” J. Quantum Spectrosc. Radiat. Transfer 113, 2470–2475 (2012).
[Crossref]

Yan, Y.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref]

Young, R.

Yu, Y.

Zghal, M.

Zhang, Y.

Zhao, F.

Zhao, J.

Zhao, Y.

Zhao, Z.

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
[Crossref]

Zhu, K.

Zhu, L.

Zhu, Y.

Zhu, Z.

Zhuang, F.

Am. J. Phys. (1)

C. McQueen, J. Arlt, and K. Dholakia, “An experiment to study a “nondiffracting” light beam,” Am. J. Phys. 67, 912–915 (1999).
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Appl. Opt. (1)

Appl. Phys. B (2)

K. Uehara and H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1989).
[Crossref]

H. T. Eyyuboğlu, “Propagation of higher order Bessel-Gaussian beams in turbulence,” Appl. Phys. B 88, 259–265 (2007).
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Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
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Czech. J. Phys. (1)

Z. Bouchal, “Nondiffracting optical beams: physical properties, experiments, and applications,” Czech. J. Phys. 53, 537–578 (2003).
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J. Opt. (1)

G. Milione, A. Dudley, T. A. Nguyen, O. Chakraborty, E. Karimi, A. Forbes, and R. R. Alfano, “Measuring the self-healing of the spatially inhomogeneous states of polarization of vector Bessel beams,” J. Opt. 17, 035617 (2015).
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J. Opt. Soc. Am. (2)

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S. Hacyan and R. Jáuregui, “A relativistic study of Bessel beams,” J. Phys. B 39, 1669–1676 (2006).
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J. Quantum Spectrosc. Radiat. Transfer (1)

T. Ersoy, B. Yalizay, and S. Akturk, “Self-reconstruction of diffraction-free and accelerating laser beams in scattering media,” J. Quantum Spectrosc. Radiat. Transfer 113, 2470–2475 (2012).
[Crossref]

Nat. Commun. (1)

M. McLaren, T. Mhlanga, M. J. Padgett, F. S. Roux, and A. Forbes, “Self-healing of quantum entanglement after an obstruction,” Nat. Commun. 5, 3248 (2014).
[Crossref]

Nat. Photonics (1)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

Nature (1)

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419, 145–147 (2002).
[Crossref]

New J. Phys. (1)

C. Ryu, K. Henderson, and M. Boshier, “Creation of matter wave Bessel beams and observation of quantized circulation in a Bose-Einstein condensate,” New J. Phys. 16, 013046 (2014).
[Crossref]

Opt. Commun. (9)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

V. Pyragaite, A. Piskarskas, K. Regelskis, V. Smilgevicius, A. Stabinis, and S. Mikalauskas, “Parametric down-conversion of higher-order Bessel optical beams in quadratic nonlinear medium,” Opt. Commun. 240, 191–200 (2004).
[Crossref]

I. A. Litvin, M. G. McLaren, and A. Forbes, “A conical wave approach to calculating Bessel-Gauss beam reconstruction after complex obstacles,” Opt. Commun. 282, 1078–1082 (2009).
[Crossref]

Z. Bouchal, “Resistance of nondiffracting vortex beam against amplitude and phase perturbations,” Opt. Commun. 210, 155–164 (2002).
[Crossref]

J. Arlt, V. Garces-Chavez, W. Sibbett, and K. Dholakia, “Optical micromanipulation using a Bessel light beam,” Opt. Commun. 197, 239–245 (2001).
[Crossref]

C. Paterson and R. Smith, “Higher-order Bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[Crossref]

P. Pääkkönen and J. Turunen, “Resonators with Bessel-Gauss modes,” Opt. Commun. 156, 359–366 (1998).
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F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun. 64, 491–495 (1987).
[Crossref]

J. Rogel-Salazar, G. New, and S. Chávez-Cerda, “Bessel-Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
[Crossref]

Opt. Eng. (1)

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Conical dynamics of Bessel beams,” Opt. Eng. 46, 078001 (2007).
[Crossref]

Opt. Express (8)

Y. Zhu, X. Liu, J. Gao, Y. Zhang, and F. Zhao, “Probability density of the orbital angular momentum mode of Hankel-Bessel beams in an atmospheric turbulence,” Opt. Express 22, 7765–7772 (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).
[Crossref]

I. A. Litvin, N. A. Khilo, A. Forbes, and V. N. Belyi, “Intra-cavity generation of Bessel-like beams with longitudinally dependent cone angles,” Opt. Express 18, 4701–4708 (2010).
[Crossref]

A. Dudley, T. Mhlanga, M. Lavery, A. McDonald, F. S. Roux, M. Padgett, and A. Forbes, “Efficient sorting of Bessel beams,” Opt. Express 21, 165–171 (2013).
[Crossref]

A. Trichili, T. Mhlanga, Y. Ismail, F. S. Roux, M. McLaren, M. Zghal, and A. Forbes, “Detection of Bessel beams with digital axicons,” Opt. Express 22, 17553–17560 (2014).
[Crossref]

A. Aiello, G. S. Agarwal, M. Paúr, B. Stoklasa, Z. Hradil, J. Řeháček, P. de la Hoz, G. Leuchs, and L. L. Sánchez-Soto, “Unraveling beam self-healing,” Opt. Express 25, 19147–19157 (2017).
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P. Li, Y. Zhang, S. Liu, H. Cheng, L. Han, D. Wu, and J. Zhao, “Generation and self-healing of vector Bessel-Gauss beams with variant state of polarizations upon propagation,” Opt. Express 25, 5821–5831 (2017).
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M. McLaren, M. Agnew, J. Leach, F. Roux, M. Padgett, R. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20, 23589–23597 (2012).
[Crossref]

Opt. Lett. (7)

Opt. Photon. News (1)

A. Dudley, M. Lavery, M. Padgett, and A. Forbes, “Unraveling Bessel beams,” Opt. Photon. News 24(6), 22–29 (2013).
[Crossref]

Phys. Rev. A (3)

R. Jáuregui and S. Hacyan, “Quantum-mechanical properties of Bessel beams,” Phys. Rev. A 71, 033411 (2005).
[Crossref]

M. McLaren, J. Romero, M. J. Padgett, F. S. Roux, and A. Forbes, “Two-photon optics of Bessel-Gaussian modes,” Phys. Rev. A 88, 033818 (2013).
[Crossref]

R. Grunwald, V. Kebbel, U. Griebner, U. Neumann, A. Kummrow, M. Rini, E. T. J. Nibbering, M. Piché, G. Rousseau, and M. Fortin, “Generation and characterization of spatially and temporally localized few-cycle optical wave packets,” Phys. Rev. A 67, 063820 (2003).
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Phys. Rev. Lett. (1)

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
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Phys. Rev. X (1)

V. Grillo, E. Karimi, G. C. Gazzadi, S. Frabboni, M. R. Dennis, and R. W. Boyd, “Generation of nondiffracting electron Bessel beams,” Phys. Rev. X 4, 011013 (2014).
[Crossref]

Proc. SPIE (1)

V. Kollarova, T. Medrik, R. Celechovsky, Z. Bouchal, O. Wilfert, and Z. Kolka, “Application of nondiffracting beams to wireless optical communications,” Proc. SPIE 6736, 67361C (2007).
[Crossref]

Sci. Rep. (2)

S. Li and J. Wang, “Adaptive free-space optical communications through turbulence using self-healing Bessel beams,” Sci. Rep. 7, 43233 (2017).
[Crossref]

N. Ahmed, Z. Zhao, L. Li, H. G. Huang, M. P. J. Lavery, P. Liao, Y. Yan, Z. Wang, G. Xie, Y. Ren, A. Almaiman, A. J. Willner, S. Ashrafi, A. F. Molisch, M. Tur, and A. E. Willner, “Mode-division-multiplexing of multiple Bessel-Gaussian beams carrying orbital-angular-momentum for obstruction-tolerant free-space optical and millimetre-wave communication links,” Sci. Rep. 6, 22082 (2016).
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South Afr. J. Sci. (1)

L. Burger, I. A. Litvin, and A. Forbes, “Simulating atmospheric turbulence using a phase-only spatial light modulator,” South Afr. J. Sci. 104, 129–134 (2008).

Other (3)

R. Grunwald, U. Neumann, U. Griebner, G. Steinmeyer, G. Stibenz, M. Bock, and V. Kebbel, “Self-reconstruction of pulsed optical x-waves,” in Localized Waves (Wiley, 2008), pp. 299–313.

J. E. Durnin and J. H. Eberly, “Diffraction free arrangement,” U.S. patent4,887,885 (Dec.19, 1989).

A. Aiello and G. S. Agarwal, “Self-healing of Gaussian and Bessel beams: a critical comparison,” arXiv:1501.05722 (2015).

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Figures (8)

Fig. 1.
Fig. 1. Self-healing principle of BG beams. Plane waves incident on an axicon of apex angle α are refracted to form conical waves, which interfere to form a BG beam in the region zmax. An opaque obstruction placed at 12zmax blocks the waves while allowing unblocked waves to interfere at a short distance behind the obstruction, i.e., after zmin. The inset depicts the theoretical profiles (top row) of the beam at different distances before and after the obstruction together with corresponding experimental images (bottom row). The plane z0 is the region where the beam is expected to self-heal completely.
Fig. 2.
Fig. 2. (a) Phase maps of Zernike aberrations representing tilt (Z11), defocus (Z20), astigmatism (Z22), coma (Z31), trefoil (Z33), and spherical (Z40). (b) An example turbulence phase mask generated from the summation of appropriately weighted Zernike polynomials [56,57].
Fig. 3.
Fig. 3. (a) Schematic of the experimental setup used to study the self-healing of BG beams after encountering a phase-changing obstruction. A collimated argon-ion laser source was used to generate a BG from an axicon encoded on one half of the SLM screen (labeled 1) while the second half (labeled 2) was encoded with the obstruction. The distance between SLM1 and SLM2 was 12zmax, thereby placing the obstruction in the middle of zmax. (b) A conceptual illustration of the core optical planes, showing the position of the two phase screens of the SLM.
Fig. 4.
Fig. 4. Theoretical and experimental images depicting the evolution of the BG beam after encountering different aberrations. Columns (a)–(g) represent different obstructions, while the rows represent different observation planes within zmax. Column (a) depicts the reference case of an opaque obstruction, while columns (b), (c), (d), (e), (f), and (g) depict tilt, defocus, astigmatism, coma, trefoil, and spherical aberrations, respectively, with a magnitude coefficient of unity (an,m=1). Rows 1 (experimental) and 2 (theoretical) illustrate the influence of the obstruction at the shadow region (zmin), while row 3 (experimental) and 4 (theoretical) illustrate how the beam has evolved at the self-healing region (z0).
Fig. 5.
Fig. 5. Correlation of the perturbed beam against a reference unperturbed beam at the plane z=z0, plotted as a function of aberration strength, for odd and even aberrations as well as aberrations with no azimuthal dependence (i.e., m=0).
Fig. 6.
Fig. 6. Relationship between beam energy and aberration strength. The measurements are shown for astigmatism, trefoil, and spherical aberrations for the same aberration strengths as in Fig. 5. It is clear that energy decreases with an increase in aberration strength for all the displayed aberrations. The dotted lines are estimated based on a least-squared fit on the measurements.
Fig. 7.
Fig. 7. Theoretical and experimental (insets) images of Bessel beams at the self-healing plane after encountering trefoil of magnitude, a3,3, of (a) 1, (b) 5, (c) 10, and (d) 20. The circles indicate the region of the beam visible to the detector. Self-healing is seen to improve with increasing aberration strength around the center of the beam.
Fig. 8.
Fig. 8. Experimental images of the BG beams after encountering turbulence. (a)–(c) show the BG beam immediately behind the turbulence screen while (d)–(f) show the BG beam at z=z0. In all plots the turbulence increases from left to right with D/r0 values of 3, 10, and 20.

Equations (11)

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

U(r,ϕ,z=0)=Jl(krr)exp(r2w02)exp(ilϕ),
Znm(ρ,θ)={Unm(ρ,θ):m<0;|mn|=evenVnm(ρ,θ):m0;|mn|=oddRn0(ρ):m=0,
Unm(ρ,θ)=Rnm(ρ)cos(mθ),Vnm(ρ,θ)=Rnm(ρ)sin(mθ),
Rnm(ρ)=s=0(nm)/2(1)s(ns)!s(n+m2s)!(nm2s)!ρn2s.
ψ(ρ,θ)=n=0m=0nanmUnm(ρ,θ)+bnmVnm(ρ,θ),
anm=K(m)(n+1π)02π01ψ(ρ,θ)Unm(ρ,θ)ρdρdθ,
bnm=K(m)(n+1π)02π01ψ(ρ,θ)Vnm(ρ,θ)ρdρdθ.
K(m)={2:for  m=0,n01:otherwise.
σnm2=Inm(D/r0)5/3,
Inm=0.15337(1)nm(n+1)Γ(14/3)Γ(n5/6))Γ2(17/6)Γ(n+23/6)
r0=1.68(Cn2k2L)3/5,

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