Abstract

A method is proposed for generating Bessel-like optical beams with arbitrary trajectories in free space. The method involves phase-modulating an optical wavefront so that conical bundles of rays are formed whose apexes write a continuous focal curve with pre-specified shape. These ray cones have circular bases on the input plane; thus their interference results in a Bessel-like transverse field profile that propagates along the specified trajectory with a remarkably invariant main lobe. Such beams can be useful as hybrids between non-accelerating and accelerating optical waves that share diffraction-resisting and self-healing properties.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Durnin, J. Opt. Soc. Am. A 4, 651 (1987).
    [CrossRef]
  2. D. Mcgloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
    [CrossRef]
  3. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, Opt. Lett. 25, 1493 (2000).
    [CrossRef]
  4. M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, Opt. Lett. 29, 44 (2004).
    [CrossRef]
  5. R. Piestun and J. Shamir, J. Opt. Soc. Am. A 15, 3039 (1998).
    [CrossRef]
  6. G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
    [CrossRef]
  7. M. Berry and N. Balazs, Am. J. Phys. 47, 264 (1979).
    [CrossRef]
  8. M. A. Bandres, Opt. Lett. 33, 1678 (2008).
    [CrossRef]
  9. Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, Self-Accelerating Airy Beams: Generation, Control, and Applications (Springer, 2012), pp. 1–46.
  10. V. Jarutis, A. Matijošius, P. D. Trapani, and A. Piskarskas, Opt. Lett. 34, 2129 (2009).
    [CrossRef]
  11. A. Matijošius, V. Jarutis, and A. Piskarskas, Opt. Express 18, 8767 (2010).
    [CrossRef]
  12. J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).
  13. S.-H. Lee, Y. Roichman, and D. G. Grier, Opt. Express 18, 6988 (2010).
    [CrossRef]
  14. V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
    [CrossRef]

2010

A. Matijošius, V. Jarutis, and A. Piskarskas, Opt. Express 18, 8767 (2010).
[CrossRef]

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).

S.-H. Lee, Y. Roichman, and D. G. Grier, Opt. Express 18, 6988 (2010).
[CrossRef]

2009

2008

2007

2005

D. Mcgloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

2004

2002

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

2000

1998

1987

1979

M. Berry and N. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Balazs, N.

M. Berry and N. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Bandres, M. A.

Berry, M.

M. Berry and N. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Chávez-Cerda, S.

Chen, Z.

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, Self-Accelerating Airy Beams: Generation, Control, and Applications (Springer, 2012), pp. 1–46.

Christodoulides, D.

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, Self-Accelerating Airy Beams: Generation, Control, and Applications (Springer, 2012), pp. 1–46.

Christodoulides, D. N.

Cizmar, T.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).

Dalgarno, H.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).

Dholakia, K.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).

D. Mcgloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Durnin, J.

Efremidis, N.

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, Self-Accelerating Airy Beams: Generation, Control, and Applications (Springer, 2012), pp. 1–46.

Garces-Chavez, V.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Grier, D. G.

Gunn-Moore, F.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).

Gutiérrez-Vega, J. C.

Hu, Y.

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, Self-Accelerating Airy Beams: Generation, Control, and Applications (Springer, 2012), pp. 1–46.

Iturbe-Castillo, M. D.

Jarutis, V.

Lee, S.-H.

Marchington, R.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).

Matijošius, A.

Mcgloin, D.

D. Mcgloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Melville, H.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Morris, J.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).

Piestun, R.

Piskarskas, A.

Roichman, Y.

Shamir, J.

Sibbett, W.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Siviloglou, G.

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, Self-Accelerating Airy Beams: Generation, Control, and Applications (Springer, 2012), pp. 1–46.

Siviloglou, G. A.

Trapani, P. D.

Zhang, P.

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, Self-Accelerating Airy Beams: Generation, Control, and Applications (Springer, 2012), pp. 1–46.

Am. J. Phys.

M. Berry and N. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Contemp. Phys.

D. Mcgloin and K. Dholakia, Contemp. Phys. 46, 15 (2005).
[CrossRef]

J. Opt.

J. Morris, T. Cizmar, H. Dalgarno, R. Marchington, F. Gunn-Moore, and K. Dholakia, J. Opt. 12, 124002 (2010).

J. Opt. Soc. Am. A

Nature

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Other

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, Self-Accelerating Airy Beams: Generation, Control, and Applications (Springer, 2012), pp. 1–46.

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.

Schematic of the principle: Rays emitted from expanding circles on the input plane intersect on the specified focal curve. The dots are the shifting circle centers.

Fig. 2.
Fig. 2.

(a) Modulo-2π input phase for a Bessel-like beam with trajectory f(Z)=Z2/40, g=0 and R(Z)=Z. (b) Evolution of amplitude on plane Y=0. Dashed curve is the analytic trajectory. Bottom row: Transverse amplitude profiles at different Z.

Fig. 3.
Fig. 3.

(a) Modulo-2π input phase; (b) amplitude evolution on Y=0; and (c) transverse profile at the indicated distance for a Bessel-like beam with a piecewise trajectory. The 10<Z<60 part of the trajectory is f(Z)=4[1cos(π(Z10)/50)]. (d)–(f) Corresponding results for the hyperbolic trajectory f(Z)=(0.64Z232Z+800)1/28001/2. R(Z)=Z for both beams.

Fig. 4.
Fig. 4.

(a)–(c) Self-healing evolution and transverse profiles of the hyperbolic beam of Fig. 3, when a disk with center (10,0) and radius 20 is obstructed on Z=0. (d)–(f) A beam with trajectory 8sech[0.05(Z45)] propagating around a cylindrical potential with strength 0.5 (dashed line).

Fig. 5.
Fig. 5.

Main lobe track and transverse profiles of a beam with trajectory f(Z)=5tanh[0.12(Z10)]+5, g(Z)=6sech[0.12(Z10)]. The dashed curves are the projection of the trajectory on the X-Y plane.

Equations (4)

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

u(X,Y,Z)=u(x,y,0)2πiZei(Xx)2+(Yy)22Zdxdy,
P(Z)=Q(x,y)+[(fx)2+(gy)2]/2Z
P(Z)=120Z{[f(ζ)]2+[g(ζ)]2[R(ζ)/ζ]2}dζ,
R(Z)>Z[f(Z)]2+[g(Z)]2.

Metrics