Abstract

Accelerating beams are wave packets that preserve their shape while propagating along curved trajectories. Their unique characteristics have opened the door to applications that range from optical micromanipulation and plasma-channel generation to laser micromachining. Here, we demonstrate, theoretically and experimentally, that accelerating beams can be generated with a variety of arbitrarily chosen transverse shapes. We present a general method to construct such beams in the paraxial and nonparaxial regime and demonstrate experimentally their propagation in the paraxial case. The key ingredient of our method is the use of the spectral representation of the accelerating beams, which offers a unique and compact description of these beams. The on-demand accelerating light patterns described here are likely to give rise to new applications and add versatility to the current ones.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2013

M. A. Bandres, B. M. Rodríguez-Lara, “Nondiffracting accelerating waves: Weber waves and parabolic momentum,” New Journal of Physics 15, 013054 (2013).
[CrossRef]

M. A. Bandres, M. A. Alonso, I. Kaminer, M. Segev, “Three-dimensional accelerating electromagnetic waves,” Opt. Express 21, 13917–13929 (2013).
[CrossRef] [PubMed]

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[CrossRef] [PubMed]

A. Mathis, F. Courvoisier, R. Giust, L. Furfaro, M. Jacquot, L. Froehly, J. M. Dudley, “Arbitrary nonparaxial accelerating periodic beams and spherical shaping of light,” Opt. Lett. 38, 2218–2220 (2013).
[CrossRef] [PubMed]

2012

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[CrossRef]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef] [PubMed]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, 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, D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef] [PubMed]

M. A. Alonso, M. A. Bandres, “Spherical fields as nonparaxial accelerating waves,” Opt. Lett. 37, 5175–5177 (2012).
[CrossRef] [PubMed]

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

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

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

2011

2010

2009

2008

2007

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

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

2005

2004

1999

1979

M. V. Berry, N.L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[CrossRef]

Aleahmad, P.

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

Alonso, M. A.

Arie, A.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[CrossRef] [PubMed]

I. Dolev, I. Kaminer, A. Shapira, M. Segev, A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef] [PubMed]

Balazs, N.L.

M. V. Berry, N.L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[CrossRef]

Bandres, M. A.

Baumgartl, J.

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

Bekenstein, R.

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

Berry, M. V.

M. V. Berry, N.L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[CrossRef]

Broky, J.

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

Campos, J.

Cannan, D.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, 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, X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[CrossRef] [PubMed]

Chávez-Cerda, S.

Chen, Z.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, 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, X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[CrossRef] [PubMed]

Christodoulides, D. N.

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

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, 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, D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

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

Cižmár, T.

Cottrell, D. M.

Courvoisier, F.

Davis, J. A.

Dholakia, K.

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

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

Dogariu, A.

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

Dolev, I.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef] [PubMed]

Dudley, J.

A. Mathis, L. Froehly, L. Furfaro, M. Jacquot, J. Dudley, F. Courvoisier, “Direct machining of curved trenches in silicon with femtosecond accelerating beams,” J. Euro. Opt. Soc. Rapid publications8(2013).
[CrossRef]

Dudley, J. M.

Froehly, L.

Furfaro, L.

Giust, R.

Gover, A.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[CrossRef] [PubMed]

Greenfield, E.

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

Guizar-Sicairos, M.

Gutiérrez-Vega, J. C.

Helmerson, K.

Hu, Y.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, 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, X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[CrossRef] [PubMed]

Jacquot, M.

Kaminer, I.

M. A. Bandres, M. A. Alonso, I. Kaminer, M. Segev, “Three-dimensional accelerating electromagnetic waves,” Opt. Express 21, 13917–13929 (2013).
[CrossRef] [PubMed]

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

I. Dolev, I. Kaminer, A. Shapira, M. Segev, A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef] [PubMed]

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

Kolesik, M.

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

Lacourt, P. A.

Lereah, Y.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[CrossRef] [PubMed]

Li, T.

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

Lilach, Y.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[CrossRef] [PubMed]

López-Mariscal, C.

Mathis, A.

Mazilu, M.

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

McAuley, K. P.

Mills, M. S.

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

Mintry, M. J.

Miri, M.-A.

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

Mitry, M. J.

Moloney, J. V.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, 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, 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, Z. Chen, “Generation of linear and nonlinear nonparaxial accelerating beams,” Opt. Lett. 37, 2820–2822 (2012).
[CrossRef] [PubMed]

Moreno, I.

Nemirovsky, J.

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

Polynkin, P.

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

Raz, O.

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

Rodríguez-Lara, B. M.

M. A. Bandres, B. M. Rodríguez-Lara, “Nondiffracting accelerating waves: Weber waves and parabolic momentum,” New Journal of Physics 15, 013054 (2013).
[CrossRef]

Ruiz, I.

Salandrino, A.

Segev, M.

M. A. Bandres, M. A. Alonso, I. Kaminer, M. Segev, “Three-dimensional accelerating electromagnetic waves,” Opt. Express 21, 13917–13929 (2013).
[CrossRef] [PubMed]

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

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

I. Dolev, I. Kaminer, A. Shapira, M. Segev, A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef] [PubMed]

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

Shapira, A.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef] [PubMed]

Siviloglou, G. A.

P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, 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, D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

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

Voloch-Bloch, N.

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[CrossRef] [PubMed]

Walasik, W.

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

Yin, X.

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

Zhang, X.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, 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, X. Zhang, “Nonparaxial Mathieu and Weber accelerating beams,” Phys. Rev. Lett. 109, 193901 (2012).
[CrossRef] [PubMed]

Am. J. Phys.

M. V. Berry, N.L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. 101, 071110 (2012).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photonics

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

Nature

N. Voloch-Bloch, Y. Lereah, Y. Lilach, A. Gover, A. Arie, “Generation of electron Airy beams,” Nature 494, 331–335 (2013).
[CrossRef] [PubMed]

New Journal of Physics

M. A. Bandres, B. M. Rodríguez-Lara, “Nondiffracting accelerating waves: Weber waves and parabolic momentum,” New Journal of Physics 15, 013054 (2013).
[CrossRef]

Opt. Express

Opt. Lett.

A. Mathis, F. Courvoisier, R. Giust, L. Furfaro, M. Jacquot, L. Froehly, J. M. Dudley, “Arbitrary nonparaxial accelerating periodic beams and spherical shaping of light,” Opt. Lett. 38, 2218–2220 (2013).
[CrossRef] [PubMed]

M. A. Bandres, M. Guizar-Sicairos, “Paraxial group,” Opt. Lett. 34, 13–15 (2009).
[CrossRef]

M. A. Bandres, J. C. Gutiérrez-Vega, S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29, 44–46 (2004).
[CrossRef] [PubMed]

C. López-Mariscal, K. Helmerson, “Shaped nondiffracting beams,” Opt. Lett. 35, 1215–1217 (2010).
[CrossRef] [PubMed]

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

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

M. A. Bandres, “Accelerating beams,” Opt. Lett. 34, 3791–3793 (2009).
[CrossRef] [PubMed]

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

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

M. A. Alonso, M. A. Bandres, “Spherical fields as nonparaxial accelerating waves,” Opt. Lett. 37, 5175–5177 (2012).
[CrossRef] [PubMed]

Phys. Rev. Lett.

I. Dolev, I. Kaminer, A. Shapira, M. Segev, A. Arie, “Experimental observation of self-accelerating beams in quadratic nonlinear media,” Phys. Rev. Lett. 108, 113903 (2012).
[CrossRef] [PubMed]

P. Zhang, Y. Hu, T. Li, D. Cannan, X. Yin, R. Morandotti, Z. Chen, 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, D. N. Christodoulides, “Fully vectorial accelerating diffraction-free Helmholtz beams,” Phys. Rev. Lett. 109, 203902 (2012).
[CrossRef] [PubMed]

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

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

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

Science

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

Other

A. Mathis, L. Froehly, L. Furfaro, M. Jacquot, J. Dudley, F. Courvoisier, “Direct machining of curved trenches in silicon with femtosecond accelerating beams,” J. Euro. Opt. Soc. Rapid publications8(2013).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Accelerating beams with on-demand transverse shapes: (a) triangle, (b) cosine-Gauss and (c) triangle+i cosine-Gauss. First row, desired target modulation Y (v), blue/red line are the real/imaginary parts and the black line is the vertical y-line profile of the beam at the local maxima of the horizontal x-modulation. Second row, line spectrum of the desired beam. Third row, intensity of the engineered accelerating beams. Last row, propagation of the accelerating beams with no apodization, exponential apodization and Gaussian apodization.

Fig. 2
Fig. 2

The behavior of our method to shape accelerating beams as a function of the extent of the spectrum of the desired modulation Y (y/α), for (a) Mexican hat and (b) random function modulation. The red line is the desired target modulation; the blue lines are the beam y-line profile at different local x-maxima of the beam invariant structure. The darkest tone of blue stands for the first x-maximum. Each row represents a different extent of the desired modulation.

Fig. 3
Fig. 3

Experimental realization of accelerating beams with on-demand transverse structures. The first row depicts the simulated optical intensity distributions of accelerating beams with different transverse patterns; the blue line shows the desired y-modulation. The second to fifth row show the experimental intensity distribution propagation of the generated beams at z =0, 15, 30 and 45 cm. Each rectangle depicts a 3.46 cm × 4.76 cm portion of the image. The last column shows an Airy beam for comparison.

Fig. 4
Fig. 4

Experimental transverse x-location of the maximum intensity as a function of the axial distance z (modulo transverse constant shift) for all six beams in Fig. 3.

Fig. 5
Fig. 5

Nonparaxial accelerating beams with on-demand transverse shapes: (a) Mexican hat shape (m = 50), (b) transverse apodized Bessel shape (m = 100), and (c) saw shape (m = 200). First row, desired target modulation Y (y/k) (red line) and the vertical line profile of the beam at the first 5 local maxima of the horizontal modulation (black lines). Second row, angular spectrum of the desired beam. Third row, intensity of the engineered nonparaxial accelerating beams. Last row, propagation of the accelerating waves.

Equations (6)

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AipwB ( u , v , s ; γ , k v ) = exp ( i s ( u γ s 2 ) + i s 3 / 3 ) Ai ( u + k v 2 γ s 2 ) exp ( i k v v ) ,
AipwB * ( γ , k v ) AipwB ( γ , k v ) d u d v = 2 π δ ( k v k v ) δ ( γ γ ) .
ψ ( u , v , 0 ) = 1 4 π 2 L ( k v ) A i ( u + k v 2 ) exp ( i k v v ) d k v = 1 [ L ( k v ) exp ( i k u k v 2 + i k u 3 / 3 ) ] ,
0.95 = k 95 % k 95 % | L ( k v ) | d k v / | L ( k v ) | d k v .
ψ ( r ) = 0 π π / 2 π / 2 g ( θ ) exp ( i m ϕ ) exp ( i k r u ) sin θ d ϕ d θ ,
g ( θ ) = L ( k sin θ ) cos θ ,

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