Abstract

We show that it is possible to generate non-paraxial optical beams with pre-engineered trajectories and designed maximum amplitude along these trajectories. The independent control of these two degrees of freedom is made possible by engineering both the amplitude and the phase of the optical wave on the input plane. Furthermore, we come to the elegant conclusion that the beam width depends solely on the local curvature of the trajectory. Thus, we can generate beams with pre-defined amplitude and beam-width by appropriately selecting the local curvature. Our theoretical results are in excellent agreement with numerical simulations. We discuss about methods that can be utilized to experimentally generate such beam. Our work might be useful in applications where precise beam control is important such as particle manipulation, filamentation, and micromachining.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4, 4817 (2018).
[Crossref]

2016 (1)

2015 (3)

R.-S. Penciu, V. Paltoglou, and N. K. Efremidis, “Closed-form expressions for nonparaxial accelerating beams with pre-engineered trajectories,” Opt. Lett. 40, 1444–1447 (2015).
[Crossref] [PubMed]

M. Clerici, Y. Hu, P. Lassonde, C. Milián, A. Couairon, D. N. Christodoulides, Z. Chen, L. Razzari, F. Vidal, F. Légaré, D. Faccio, and R. Morandotti, “Laser-assisted guiding of electric discharges around objects,” Sci. Adv. 1, e1400111 (2015).
[Crossref] [PubMed]

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5, 12086 (2015).
[Crossref] [PubMed]

2014 (5)

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photon. 8, 302–306 (2014).
[Crossref]

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, 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]

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

M. A. Preciado, K. Dholakia, and M. Mazilu, “Generation of attenuation-compensating Airy beams,” Opt. Lett. 39, 4950–4953 (2014).
[Crossref] [PubMed]

A. Libster-Hershko, I. Epstein, and A. Arie, “Rapidly accelerating Mathieu and Weber surface plasmon beams,” Phys. Rev. Lett. 113, 123902 (2014).
[Crossref] [PubMed]

2013 (4)

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Periodic self-accelerating beams by combined phase and amplitude modulation in the Fourier space,” Opt. Lett. 38, 3387–3389 (2013).
[Crossref] [PubMed]

M. A. Bandres and B. M. Rodríguez-Lara, “Nondiffracting accelerating waves: Weber waves and parabolic momentum,” New J. Phys. 15, 013054 (2013).
[Crossref]

P. Panagiotopoulos, D. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

J. Zhao, P. Zhang, D. Deng, J. Liu, Y. Gao, I. D. Chremmos, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Observation of self-accelerating Bessel-like optical beams along arbitrary trajectories,” Opt. Lett. 38, 498–500 (2013).
[Crossref] [PubMed]

2012 (6)

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Bessel-like optical beams with arbitrary trajectories,” Opt. Lett. 37, 5003–5005 (2012).
[Crossref] [PubMed]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37, 2820–2822 (2012).
[Crossref] [PubMed]

F. Courvoisier, A. Mathis, L. Froehly, R. Giust, L. Furfaro, P. A. Lacourt, M. Jacquot, and J. M. Dudley, “Sending femtosecond pulses in circles: highly nonparaxial accelerating beams,” Opt. Lett. 37, 1736–1738 (2012).
[Crossref] [PubMed]

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]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109, 203902 (2012).
[Crossref] [PubMed]

2011 (6)

2010 (1)

2009 (3)

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]

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of femtosecond laser Airy beams in water,” Phys. Rev. Lett. 103, 123902 (2009).
[Crossref] [PubMed]

T. Čižmár and K. Dholakia, “Tunable bessel light modes: engineering the axial propagation,” Opt. Express 17, 15558–15570 (2009).
[Crossref] [PubMed]

2008 (1)

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

2007 (2)

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[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]

2004 (1)

1999 (1)

1979 (1)

1978 (1)

W.-H. Lee, “Computer-generated holograms: Techniques and applications,” Prog. Opt. 16, 119–232 (1978).
[Crossref]

Aggarwal, S.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4, 4817 (2018).
[Crossref]

Aleahmad, P.

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109, 203902 (2012).
[Crossref] [PubMed]

Arie, A.

A. Libster-Hershko, I. Epstein, and A. Arie, “Rapidly accelerating Mathieu and Weber surface plasmon beams,” Phys. Rev. Lett. 113, 123902 (2014).
[Crossref] [PubMed]

Bandres, M. A.

M. A. Bandres and B. M. Rodríguez-Lara, “Nondiffracting accelerating waves: Weber waves and parabolic momentum,” New J. Phys. 15, 013054 (2013).
[Crossref]

Baumgartl, J.

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

Bekenstein, R.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

Bongiovanni, D.

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]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37, 2820–2822 (2012).
[Crossref] [PubMed]

Chen, H.

Chen, Z.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5, 12086 (2015).
[Crossref] [PubMed]

M. Clerici, Y. Hu, P. Lassonde, C. Milián, A. Couairon, D. N. Christodoulides, Z. Chen, L. Razzari, F. Vidal, F. Légaré, D. Faccio, and R. Morandotti, “Laser-assisted guiding of electric discharges around objects,” Sci. Adv. 1, e1400111 (2015).
[Crossref] [PubMed]

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Periodic self-accelerating beams by combined phase and amplitude modulation in the Fourier space,” Opt. Lett. 38, 3387–3389 (2013).
[Crossref] [PubMed]

J. Zhao, P. Zhang, D. Deng, J. Liu, Y. Gao, I. D. Chremmos, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Observation of self-accelerating Bessel-like optical beams along arbitrary trajectories,” Opt. Lett. 38, 498–500 (2013).
[Crossref] [PubMed]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37, 2820–2822 (2012).
[Crossref] [PubMed]

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Bessel-like optical beams with arbitrary trajectories,” Opt. Lett. 37, 5003–5005 (2012).
[Crossref] [PubMed]

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]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[Crossref] [PubMed]

Chremmos, I.

Chremmos, I. D.

Christodoulides, D. N.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5, 12086 (2015).
[Crossref] [PubMed]

M. Clerici, Y. Hu, P. Lassonde, C. Milián, A. Couairon, D. N. Christodoulides, Z. Chen, L. Razzari, F. Vidal, F. Légaré, D. Faccio, and R. Morandotti, “Laser-assisted guiding of electric discharges around objects,” Sci. Adv. 1, e1400111 (2015).
[Crossref] [PubMed]

J. Zhao, P. Zhang, D. Deng, J. Liu, Y. Gao, I. D. Chremmos, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Observation of self-accelerating Bessel-like optical beams along arbitrary trajectories,” Opt. Lett. 38, 498–500 (2013).
[Crossref] [PubMed]

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Bessel-like optical beams with arbitrary trajectories,” Opt. Lett. 37, 5003–5005 (2012).
[Crossref] [PubMed]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109, 203902 (2012).
[Crossref] [PubMed]

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36, 1890–1892 (2011).
[Crossref] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
[Crossref] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[Crossref] [PubMed]

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

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[Crossref] [PubMed]

Cizmar, T.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, 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]

Cižmár, T.

Clerici, M.

M. Clerici, Y. Hu, P. Lassonde, C. Milián, A. Couairon, D. N. Christodoulides, Z. Chen, L. Razzari, F. Vidal, F. Légaré, D. Faccio, and R. Morandotti, “Laser-assisted guiding of electric discharges around objects,” Sci. Adv. 1, e1400111 (2015).
[Crossref] [PubMed]

Coll-Lladó, C.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, 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.

Couairon, A.

M. Clerici, Y. Hu, P. Lassonde, C. Milián, A. Couairon, D. N. Christodoulides, Z. Chen, L. Razzari, F. Vidal, F. Légaré, D. Faccio, and R. Morandotti, “Laser-assisted guiding of electric discharges around objects,” Sci. Adv. 1, e1400111 (2015).
[Crossref] [PubMed]

P. Panagiotopoulos, D. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

Courvoisier, F.

Dalgarno, H. I. C.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, 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]

Davis, J. A.

Deng, D.

Dholakia, K.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4, 4817 (2018).
[Crossref]

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, 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]

M. A. Preciado, K. Dholakia, and M. Mazilu, “Generation of attenuation-compensating Airy beams,” Opt. Lett. 39, 4950–4953 (2014).
[Crossref] [PubMed]

T. Čižmár and K. Dholakia, “Tunable bessel light modes: engineering the axial propagation,” Opt. Express 17, 15558–15570 (2009).
[Crossref] [PubMed]

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

Ding, J.

Dogariu, A.

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

Dudley, J. M.

Efremidis, N. K.

R.-S. Penciu, K. G. Makris, and N. K. Efremidis, “Nonparaxial abruptly autofocusing beams,” Opt. Lett. 41, 1042–1045 (2016).
[Crossref] [PubMed]

R.-S. Penciu, V. Paltoglou, and N. K. Efremidis, “Closed-form expressions for nonparaxial accelerating beams with pre-engineered trajectories,” Opt. Lett. 40, 1444–1447 (2015).
[Crossref] [PubMed]

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5, 12086 (2015).
[Crossref] [PubMed]

J. Zhao, P. Zhang, D. Deng, J. Liu, Y. Gao, I. D. Chremmos, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Observation of self-accelerating Bessel-like optical beams along arbitrary trajectories,” Opt. Lett. 38, 498–500 (2013).
[Crossref] [PubMed]

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Bessel-like optical beams with arbitrary trajectories,” Opt. Lett. 37, 5003–5005 (2012).
[Crossref] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[Crossref] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
[Crossref] [PubMed]

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36, 1890–1892 (2011).
[Crossref] [PubMed]

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

Epstein, I.

A. Libster-Hershko, I. Epstein, and A. Arie, “Rapidly accelerating Mathieu and Weber surface plasmon beams,” Phys. Rev. Lett. 113, 123902 (2014).
[Crossref] [PubMed]

Faccio, D.

M. Clerici, Y. Hu, P. Lassonde, C. Milián, A. Couairon, D. N. Christodoulides, Z. Chen, L. Razzari, F. Vidal, F. Légaré, D. Faccio, and R. Morandotti, “Laser-assisted guiding of electric discharges around objects,” Sci. Adv. 1, e1400111 (2015).
[Crossref] [PubMed]

Ferrier, D. E.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4, 4817 (2018).
[Crossref]

Ferrier, D. E. K.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, 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]

Froehly, L.

Furfaro, L.

Gao, Y.

Giust, R.

Greenfield, E.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106, 213902 (2011).
[Crossref] [PubMed]

Gunn-Moore, F. J.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4, 4817 (2018).
[Crossref]

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, 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]

Hu, Y.

M. Clerici, Y. Hu, P. Lassonde, C. Milián, A. Couairon, D. N. Christodoulides, Z. Chen, L. Razzari, F. Vidal, F. Légaré, D. Faccio, and R. Morandotti, “Laser-assisted guiding of electric discharges around objects,” Sci. Adv. 1, e1400111 (2015).
[Crossref] [PubMed]

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Periodic self-accelerating beams by combined phase and amplitude modulation in the Fourier space,” Opt. Lett. 38, 3387–3389 (2013).
[Crossref] [PubMed]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37, 2820–2822 (2012).
[Crossref] [PubMed]

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]

Jacquot, M.

Jia, S.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photon. 8, 302–306 (2014).
[Crossref]

Kaminer, I.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109, 203902 (2012).
[Crossref] [PubMed]

Kolesik, M.

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of femtosecond laser Airy beams in water,” Phys. Rev. Lett. 103, 123902 (2009).
[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]

Lacourt, P. A.

Lassonde, P.

M. Clerici, Y. Hu, P. Lassonde, C. Milián, A. Couairon, D. N. Christodoulides, Z. Chen, L. Razzari, F. Vidal, F. Légaré, D. Faccio, and R. Morandotti, “Laser-assisted guiding of electric discharges around objects,” Sci. Adv. 1, e1400111 (2015).
[Crossref] [PubMed]

Lee, W.-H.

W.-H. Lee, “Binary computer-generated holograms,” Appl. Opt. 18, 3661–3669 (1979).
[Crossref] [PubMed]

W.-H. Lee, “Computer-generated holograms: Techniques and applications,” Prog. Opt. 16, 119–232 (1978).
[Crossref]

Légaré, F.

M. Clerici, Y. Hu, P. Lassonde, C. Milián, A. Couairon, D. N. Christodoulides, Z. Chen, L. Razzari, F. Vidal, F. Légaré, D. Faccio, and R. Morandotti, “Laser-assisted guiding of electric discharges around objects,” Sci. Adv. 1, e1400111 (2015).
[Crossref] [PubMed]

Li, T.

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]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37, 2820–2822 (2012).
[Crossref] [PubMed]

Libster-Hershko, A.

A. Libster-Hershko, I. Epstein, and A. Arie, “Rapidly accelerating Mathieu and Weber surface plasmon beams,” Phys. Rev. Lett. 113, 123902 (2014).
[Crossref] [PubMed]

Liu, J.

Lumer, Y.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

Makris, K. G.

Mathis, A.

Mazilu, M.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4, 4817 (2018).
[Crossref]

M. A. Preciado, K. Dholakia, and M. Mazilu, “Generation of attenuation-compensating Airy beams,” Opt. Lett. 39, 4950–4953 (2014).
[Crossref] [PubMed]

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

McCluskey, K.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4, 4817 (2018).
[Crossref]

Milián, C.

M. Clerici, Y. Hu, P. Lassonde, C. Milián, A. Couairon, D. N. Christodoulides, Z. Chen, L. Razzari, F. Vidal, F. Légaré, D. Faccio, and R. Morandotti, “Laser-assisted guiding of electric discharges around objects,” Sci. Adv. 1, e1400111 (2015).
[Crossref] [PubMed]

Mills, M. S.

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109, 203902 (2012).
[Crossref] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Trapping and guiding microparticles with morphing autofocusing Airy beams,” Opt. Lett. 36, 2883–2885 (2011).
[Crossref] [PubMed]

Miri, M.-A.

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109, 203902 (2012).
[Crossref] [PubMed]

Moloney, J.

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of femtosecond laser Airy beams in water,” Phys. Rev. Lett. 103, 123902 (2009).
[Crossref] [PubMed]

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.

M. Clerici, Y. Hu, P. Lassonde, C. Milián, A. Couairon, D. N. Christodoulides, Z. Chen, L. Razzari, F. Vidal, F. Légaré, D. Faccio, and R. Morandotti, “Laser-assisted guiding of electric discharges around objects,” Sci. Adv. 1, e1400111 (2015).
[Crossref] [PubMed]

Y. Hu, D. Bongiovanni, Z. Chen, and R. Morandotti, “Periodic self-accelerating beams by combined phase and amplitude modulation in the Fourier space,” Opt. Lett. 38, 3387–3389 (2013).
[Crossref] [PubMed]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37, 2820–2822 (2012).
[Crossref] [PubMed]

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.

Nemirovsky, J.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

Nylk, J.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4, 4817 (2018).
[Crossref]

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, 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]

Paltoglou, V.

Panagiotopoulos, P.

P. Panagiotopoulos, D. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

Papazoglou, D.

P. Panagiotopoulos, D. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

Papazoglou, D. G.

Penciu, R.-S.

Polynkin, P.

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]

P. Polynkin, M. Kolesik, and J. Moloney, “Filamentation of femtosecond laser Airy beams in water,” Phys. Rev. Lett. 103, 123902 (2009).
[Crossref] [PubMed]

Prakash, J.

Preciado, M. A.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4, 4817 (2018).
[Crossref]

M. A. Preciado, K. Dholakia, and M. Mazilu, “Generation of attenuation-compensating Airy beams,” Opt. Lett. 39, 4950–4953 (2014).
[Crossref] [PubMed]

Raz, O.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106, 213902 (2011).
[Crossref] [PubMed]

Razzari, L.

M. Clerici, Y. Hu, P. Lassonde, C. Milián, A. Couairon, D. N. Christodoulides, Z. Chen, L. Razzari, F. Vidal, F. Légaré, D. Faccio, and R. Morandotti, “Laser-assisted guiding of electric discharges around objects,” Sci. Adv. 1, e1400111 (2015).
[Crossref] [PubMed]

Rodríguez-Lara, B. M.

M. A. Bandres and B. M. Rodríguez-Lara, “Nondiffracting accelerating waves: Weber waves and parabolic momentum,” New J. Phys. 15, 013054 (2013).
[Crossref]

Salandrino, A.

Schley, R.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

Segev, M.

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, “Nondiffracting accelerating wave packets of Maxwell’s equations,” Phys. Rev. Lett. 108, 163901 (2012).
[Crossref]

P. Aleahmad, M.-A. Miri, M. S. Mills, I. Kaminer, M. Segev, and D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109, 203902 (2012).
[Crossref] [PubMed]

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106, 213902 (2011).
[Crossref] [PubMed]

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

G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
[Crossref] [PubMed]

Song, D.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5, 12086 (2015).
[Crossref] [PubMed]

Tello, J. A.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4, 4817 (2018).
[Crossref]

Tzortzakis, S.

P. Panagiotopoulos, D. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36, 1842–1844 (2011).
[Crossref] [PubMed]

Vaughan, J. C.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photon. 8, 302–306 (2014).
[Crossref]

Vettenburg, T.

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, 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]

Vidal, F.

M. Clerici, Y. Hu, P. Lassonde, C. Milián, A. Couairon, D. N. Christodoulides, Z. Chen, L. Razzari, F. Vidal, F. Légaré, D. Faccio, and R. Morandotti, “Laser-assisted guiding of electric discharges around objects,” Sci. Adv. 1, e1400111 (2015).
[Crossref] [PubMed]

Walasik, W.

E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106, 213902 (2011).
[Crossref] [PubMed]

Wang, H.-T.

Yang, Z.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4, 4817 (2018).
[Crossref]

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.

Zamboni-Rached, M.

Zhang, B.-F.

Zhang, P.

Zhang, 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]

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37, 2820–2822 (2012).
[Crossref] [PubMed]

Zhang, Z.

Zhao, J.

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5, 12086 (2015).
[Crossref] [PubMed]

J. Zhao, P. Zhang, D. Deng, J. Liu, Y. Gao, I. D. Chremmos, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Observation of self-accelerating Bessel-like optical beams along arbitrary trajectories,” Opt. Lett. 38, 498–500 (2013).
[Crossref] [PubMed]

Zheng, Z.

Zhuang, X.

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photon. 8, 302–306 (2014).
[Crossref]

Appl. Opt. (3)

Nat. Commun. (2)

P. Panagiotopoulos, D. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

R. Schley, I. Kaminer, E. Greenfield, R. Bekenstein, Y. Lumer, and M. Segev, “Loss-proof self-accelerating beams and their use in non-paraxial manipulation of particles’ trajectories,” Nat. Commun. 5, 5189 (2014).
[Crossref]

Nat. Methods (1)

T. Vettenburg, H. I. C. Dalgarno, J. Nylk, C. Coll-Lladó, 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]

Nat. Photon. (2)

S. Jia, J. C. Vaughan, and X. Zhuang, “Isotropic three-dimensional super-resolution imaging with a self-bending point spread function,” Nat. Photon. 8, 302–306 (2014).
[Crossref]

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

New J. Phys. (1)

M. A. Bandres and B. M. Rodríguez-Lara, “Nondiffracting accelerating waves: Weber waves and parabolic momentum,” New J. Phys. 15, 013054 (2013).
[Crossref]

Opt. Express (3)

Opt. Lett. (13)

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Bessel-like optical beams with arbitrary trajectories,” Opt. Lett. 37, 5003–5005 (2012).
[Crossref] [PubMed]

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Prog. Opt. (1)

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[Crossref]

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Sci. Rep. (1)

J. Zhao, I. D. Chremmos, D. Song, D. N. Christodoulides, N. K. Efremidis, and Z. Chen, “Curved singular beams for three-dimensional particle manipulation,” Sci. Rep. 5, 12086 (2015).
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Science (1)

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Figures (2)

Fig. 1
Fig. 1 Accelerating beams with circular (first three columns) and elliptic (last three columns) trajectories. In the two subfigures we depict in the first column the amplitude dynamics and the theoretical prediction for the trajectory (white-red dashed curve), in the second column the maximum amplitude as a function of the propagation distance, and in the third column the intensity profile at the cross section shown in the first column (white dashed line). In the second and third columns the theoretical predictions are shown with circles. For the circular trajectory x c = ( R 0 2 z c 2 ) 1 / 2, R0 = 5000λ, and the engineered amplitude profile in the three rows is U = 1, U = [2 − exp(−(zR0/2)2/(1500λ)2)], U = [0.5 + 0.5 tanh(0.001(zR0/2)/λ)], respectively. For the elliptic trajectory x c = f ( z c ) = ( R 0 2 ( z c / α ) 2 ) 1 / 2, R0 = 3000λ, α = 3/2 and the amplitude profile in the three rows is U = 1, U = exp(−(z − 3R0/4)2/(1500λ)2), U = [3 − 2 tanh(0.002(z − 3R0/4)/λ)], respectively. In all the figures F(ξ) = sig[(ξR0)/(5λ)].
Fig. 2
Fig. 2 Same as in Fig. 1. In the left subfigure we show accelerating beams with a parabolic trajectory x c = f ( z c ) = α z c 2 and α = 10−4/λ. The engineered amplitude profile in the three rows is U = 1, U = [4 − 3 exp(−(z − 5000λ)2/(3000λ)2)], U = [0.75z/λ + 750 sin2(0.001z/λ)]/2000. In the right subfigure we show accelerating beams with with a cubic trajectory x c = f ( z c ) = α z c 3 and α = 10−8/λ2. The engineered amplitude profile in the three rows is U = 1, U = [0.5 + 1.5 exp(−(z − 5000λ)2/(1500λ)2)], U = [1 + sin2(0.0007(z − 5000λ))], respectively. In all the figures F(ξ) = sig(−ξ/(5λ)).

Equations (7)

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ψ ( x , z ) = 2 ψ 0 ( ξ ) G ( x , z ; ξ ) z d ξ .
ϕ ( ξ ) = k ( d f / d z c ) / ( 1 + ( d f / d z c ) 2 ) 1 / 2
ψ = 2 A ( ξ ) ( π 4 R c 3 κ 2 / λ ) 1 / 6 e i Ξ Ai ( s ( z c / R c ) [ 2 k 2 κ ( z c ) ] 1 / 3 δ x )
κ ( z c ) = | d 2 f ( z z ) / d z c 2 | / [ 1 + ( d f ( z c ) / d z c ) 2 ] 3 / 2 = z c 2 / [ R c 3 | z c ( ξ ) | ] ,
A ( ξ ) = F ( ξ ) ( U ( ξ ) / 2.3 ) ( λ R c 3 κ 2 ( z c ) / R c 3 ) 1 / 6 ,
ψ = 2 A ( ξ ) ( π 4 R c 3 κ 2 / λ ) 1 / 6 e i Ξ Ai ( s [ 2 k 2 κ ( z c ) ] 1 / 3 δ l ) .
sig ( x ) = max ( tanh ( x ) , 0 )

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