Abstract

A new family of finite-energy accelerating beams was constructed through misplacing the Hermite polynomial and Gaussian window function. The closed-form solution of k-space spectra and paraxial propagation of these beams are derived from the Fourier transform and the scalar angle spectra integral. These beams have similar propagation properties to finite Airy beams and parabolic beams, but the accelerating trajectory is hyperbola rather than parabola. The beam family can be experimentally generated by exponentially truncating the high-order Hermite–Gaussian beams in the spatial domain.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett. 32, 979–981 (2007).
    [CrossRef]
  2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
    [CrossRef]
  3. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2, 675–678 (2008).
    [CrossRef]
  4. 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]
  5. 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]
  6. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4, 103–106 (2010).
    [CrossRef]
  7. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
    [CrossRef]
  8. M. V. Berry and N. L. Balazs, “Nonspreading wave packets,” Am. J. Phys. 47, 264–267 (1979).
    [CrossRef]
  9. K. Unnikrishnan and A. R. P. Rau, “Uniqueness of the Airy packet in quantum mechanics,” Am. J. Phys. 64, 1034 (1996).
    [CrossRef]
  10. M. A. Bandres, “Accelerating parabolic beams,” Opt. Lett. 33, 1678–1680 (2008).
    [CrossRef]
  11. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef]
  12. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
    [CrossRef]
  13. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29, 44–46 (2004).
    [CrossRef]
  14. J. A. Davis, M. J. Mitry, M. A. Bandres, and D. M. Cottrell, “Observation of accelerating parabolic beams,” Opt. Express 16, 12866–12871 (2008).
    [CrossRef]
  15. E. Greenfield, M. Segev, W. Walasik, and O. Raz, “Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett. 106, 213902 (2011).
    [CrossRef]
  16. Y. F. Jiang, K. K. Huang, and X. H. Lu, “Airy-related beam generated from flat-topped Gaussian beams,” J. Opt. Soc. Am. A 29, 1412–1416 (2012).
    [CrossRef]
  17. I. D. Chremmos, Z. G. Chen, D. N. Christodoulides, and N. K. Efremidis, “Bessel-like optical beams with arbitrary trajectories,” Opt. Lett. 37, 5003–5005 (2012).
    [CrossRef]
  18. J. Y. Zhao, P. Zhang, D. M. Deng, J. J. Liu, Y. M. Gao, I. D. Chremmos, N. K. Efremidis, D. N. Christodoulides, and Z. G. Chen, “Observation of self-accelerating Bessel-like optical beams along arbitrary trajectories,” Opt. Lett. 38, 498–500 (2013).
    [CrossRef]

2013 (1)

2012 (2)

2011 (2)

2010 (2)

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

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

2009 (1)

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]

2008 (3)

2007 (2)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. 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]

2004 (1)

2000 (1)

1996 (1)

K. Unnikrishnan and A. R. P. Rau, “Uniqueness of the Airy packet in quantum mechanics,” Am. J. Phys. 64, 1034 (1996).
[CrossRef]

1987 (1)

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

1979 (1)

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

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Balazs, N. L.

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

Bandres, M. A.

Baumgartl, J.

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

Berry, M. V.

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

Broky, J.

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

Chávez-Cerda, S.

Chen, Z.

Chen, Z. G.

Chong, A.

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

Chremmos, I. D.

Christodoulides, D.

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

Christodoulides, D. N.

Cottrell, D. M.

Davis, J. A.

Deng, D. M.

Dholakia, K.

J. Baumgartl, M. Mazilu, and 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, and D. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Durnin, J.

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

Eberly, J. H.

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

Efremidis, N. K.

Gao, Y. M.

Greenfield, E.

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

Gutiérrez-Vega, J. C.

Huang, K. K.

Iturbe-Castillo, M. D.

Jiang, Y. F.

Kolesik, M.

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

Liu, J. J.

Lu, X. H.

Mazilu, M.

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

Miceli, J. J.

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

Mills, M. S.

Mitry, M. J.

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]

Papazoglou, D. G.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

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]

Prakash, J.

Rau, A. R. P.

K. Unnikrishnan and A. R. P. Rau, “Uniqueness of the Airy packet in quantum mechanics,” Am. J. Phys. 64, 1034 (1996).
[CrossRef]

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]

Renninger, W. H.

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

Segev, M.

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

Siviloglou, G. A.

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

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

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

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Tzortzakis, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Unnikrishnan, K.

K. Unnikrishnan and A. R. P. Rau, “Uniqueness of the Airy packet in quantum mechanics,” Am. J. Phys. 64, 1034 (1996).
[CrossRef]

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]

Wise, F. W.

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

Zhang, P.

Zhang, Z.

Zhao, J. Y.

Am. J. Phys. (2)

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

K. Unnikrishnan and A. R. P. Rau, “Uniqueness of the Airy packet in quantum mechanics,” Am. J. Phys. 64, 1034 (1996).
[CrossRef]

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

Nat. Photonics (2)

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

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

Opt. Express (1)

Opt. Lett. (7)

Phys. Rev. Lett. (4)

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

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

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal Airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

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

Science (1)

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]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Propagation contour diagrams of 1D HG20 beam with λ=1.06μm, ω0=0.5mm, and its “hard” truncation version.

Fig. 2.
Fig. 2.

Variation of k-space spectra of 1D exponentially truncated HG beams with truncation factor a (λ=1.06μm, ω0=0.5mm, and m=20).

Fig. 3.
Fig. 3.

Propagation characteristics of 1D misplaced HG beams with different parameters (m=20, 40, and 60 for the first, second, and third rows, respectively; a/ω0=0.15, 0.25, and 0.35 for the first, second, and third columns, respectively).

Fig. 4.
Fig. 4.

Propagation characteristics of 1D misplaced HG beams (HG20, HG40, and HG60) with a/ω0=0.15. (a), (b), and (c) Show the intensity distributions at z=0, 0.5, and 1 m for beams with m=20, 40, and 60, respectively. (d) Shows the propagation trajectories of the main lobes of these beams.

Fig. 5.
Fig. 5.

Propagation characteristics of 2D exponentially HG beams with different parameters (m=20, n=0, a/ω0=0.15, and b/ω0=0 for the first row; m=n=20 and a/ω0=b/ω0=0.15 for the second row; m=20, n=1, a/ω0=0.15, and b/ω0=0 for the third row; and z=0, 0.3, and 0.6 m for the first, second, and third columns).

Equations (12)

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

U(x)=Hm(2ω0x)exp(x2ω02)·exp(2axω02),
U(x)=exp(a2ω02)Hm(2ω0x)exp((xa)2ω02).
U(kx)=(i)mω0πHm[ω02(kx+i2aω02)]·exp[ω024(kx+i2aω02)2].
U(x,z)=12π+U(kx)exp(ikxx)exp(izk2kx2)dkx.
U(x,z)=(ω0ω)1/2exp(a2ω2)Hm[2ω(x+izf0a)]·exp[(xa)2ω2]·exp(ikz)·exp[ik(xa)22Ri(m+1/2)arctgzf0],
f0=πω02λ,ω=ω01+(zf0)2,R=z[1+(f0z)2].
x=x01+(zf0)2.
U(x,y)=Hm(2ω0x)Hn(2ω0y)·exp(x2+y2ω02)exp(2ax+2byω02),
U(x,y)=exp(a2+b2ω02)Hm(2ω0x)Hn(2ω0y)·exp[(xa)2+(yb)2ω02].
U(kx,ky)=(i)m+nω02π·Hm[ω02(kx+i2aω02)]exp[ω024(kx+i2aω02)2]·Hn[ω02(ky+i2bω02)]exp[ω024(ky+i2bω02)2],
U(x,y,z)=Hm[2ω(x+izaf0)]Hn[2ω(y+izbf0)]·ω0ωexp(a2+b2ω2)exp((xa)2+(yb)2ω2)exp(ikz)·exp[ik(xa)2+(yb)22Ri(m+n+1)arctgzf0],
r=r01+(zf0)2,

Metrics