Abstract

In this paper, we have developed an analytic method for describing Airy-type beams truncated by finite apertures. This new approach is based on suitable superposition of exponentially decaying Airy beams. Regarding both theoretical and numerical aspects, the results here shown are interesting because they have been quickly evaluated through a simple analytic solution, whose propagation characteristics agree with those already published in literature through the use of numerical methods. To demonstrate the method’s potentiality three different truncated beams have been analyzed: ideal Airy, Airy-Gauss and Airy-Exponential.

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  1. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams,” Opt. Lett.32, 979–981 (2007); and references therein.
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99, 213901 (2007).
    [CrossRef]
  4. I. M. Besieris and A. M. Shaarawi, “A note on an accelerating finite energy Airy beam,” Opt. Lett.32, 2447–2449 (2007).
    [CrossRef] [PubMed]
  5. J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express16, 12880–12891 (2008).
    [CrossRef] [PubMed]
  6. X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A85, 013815 (2012).
    [CrossRef]
  7. D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. (Accepted for publication).
  8. Y. Kaganovsky and E. Heyman, “Wave analysis of Airy beams,” Opt. Express18, 8440–8452 (2010).
    [CrossRef] [PubMed]
  9. Y. Kaganovsky and E. Heyman, Nonparaxial wave analysis of three-dimensional Airy beams, J. Opt. Soc. Am. A29, 671–688 (2012).
    [CrossRef]
  10. E. Greenfield, M. Segev, W. Wallasik, and O. Raz, Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett.106, 213903 (2011).
    [CrossRef]
  11. 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]

2012 (3)

2011 (1)

E. Greenfield, M. Segev, W. Wallasik, and O. Raz, Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett.106, 213903 (2011).
[CrossRef]

2010 (2)

2008 (1)

2007 (3)

Besieris, I. M.

Broky, J.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express16, 12880–12891 (2008).
[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]

Carvalho, M. I.

Chen, R.

X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A85, 013815 (2012).
[CrossRef]

Choi, D.

D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. (Accepted for publication).

Christodoulides, D. N.

Chu, X.

X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A85, 013815 (2012).
[CrossRef]

Courvoisier, F.

Dogariu, A.

J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, “Self-healing properties of optical Airy beams,” Opt. Express16, 12880–12891 (2008).
[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]

Dudley, J. M.

Faco, M.

Froehly, L.

Furfaro, L.

Giust, R.

Greenfield, E.

E. Greenfield, M. Segev, W. Wallasik, and O. Raz, Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett.106, 213903 (2011).
[CrossRef]

Heyman, E.

Jacquot, M.

Kaganovsky, Y.

Lacourt, P. A.

Lee, B.

D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. (Accepted for publication).

Lee, I.-M.

D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. (Accepted for publication).

Lim, Y.

D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. (Accepted for publication).

Mathis, A.

Raz, O.

E. Greenfield, M. Segev, W. Wallasik, and O. Raz, Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett.106, 213903 (2011).
[CrossRef]

Roh, S.

D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. (Accepted for publication).

Segev, M.

E. Greenfield, M. Segev, W. Wallasik, and O. Raz, Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett.106, 213903 (2011).
[CrossRef]

Shaarawi, A. M.

Siviloglou, G. A.

Wallasik, W.

E. Greenfield, M. Segev, W. Wallasik, and O. Raz, Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett.106, 213903 (2011).
[CrossRef]

Zhou, G.

X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A85, 013815 (2012).
[CrossRef]

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

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. A (1)

X. Chu, G. Zhou, and R. Chen, “Analytical study of the self-healing property of Airy beams,” Phys. Rev. A85, 013815 (2012).
[CrossRef]

Phys. Rev. Lett. (2)

E. Greenfield, M. Segev, W. Wallasik, and O. Raz, Accelerating light beams along arbitrary convex trajectories,” Phys. Rev. Lett.106, 213903 (2011).
[CrossRef]

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

Other (1)

D. Choi, Y. Lim, I.-M. Lee, S. Roh, and B. Lee, “Airy beam excitation using a subwavelength metallic slit array,” IEEE Photon. Technol. Lett. (Accepted for publication).

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Figures (6)

Fig. 1
Fig. 1

Field intensity profile, at z = 0, of a truncated Ideal Airy beam described by Eq. (3), with an and Bn are given by Eqs. (5) and (9) and m(s) = 1.

Fig. 2
Fig. 2

(a)Intensity of an Ideal Airy beam truncated by a finite aperture, as given by Eq. (4).(b) The same result depicted in orthogonal projection

Fig. 3
Fig. 3

Field intensity profile, at z = 0, of a truncated Airy-Exponential beam described by Eq. (3), with an and Bn given by Eqs. (5) and (9), m(s) = exp(qs) and q = 0.05.

Fig. 4
Fig. 4

(a)Intensity of an Airy-Exponential beam truncated by a finite aperture, as given by solution (4).(b) The same result depicted in orthogonal projection

Fig. 5
Fig. 5

Field intensity profile, at z = 0, of a truncated Airy-Gauss beam described by Eq. (3), with an and Bn given by Eqs. (5) and (9), m(s) = exp(−qs2) and q = 5 x 0 2 / X 2 = 0.018.

Fig. 6
Fig. 6

(a)Intensity of an Airy-Gauss beam truncated by a finite aperture, as given by solution (4).(b) The same result depicted in orthogonal projection

Equations (10)

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ψ ( s , ζ = 0 ) = A i ( s ) exp ( a s )
ψ ( s , ζ ) = A i ( s ( ζ / 2 ) 2 + i a ζ ) exp ( a s ( a ζ 2 / 2 ) i ζ 3 / 12 + i a 2 ζ / 2 + i s ζ / 2 ) ,
Ψ ( s , ζ = 0 ) = n = B n A i ( s ) exp ( a n s ) ,
Ψ ( s , ζ ) = n = B n A i ( s ( ζ / 2 ) 2 + i a n ζ ) exp ( a n s ( a n ζ 2 / 2 ) i ζ 3 / 12 + i a n 2 ζ / 2 + i s ζ / 2 ) .
a n = a R + i 2 π n / L ,
Ψ ( s , ζ = 0 ) = A i ( s ) exp ( a R s ) n = B n exp ( i 2 π L n s )
I ( s ) = n = B n exp ( i 2 π L n s ) ,
I ( s ) = { exp ( a R s ) m ( s ) ; for S s S 0 ; for L / 2 s < S and S < s L / 2
B n = 1 L S S exp ( a R s ) m ( s ) exp ( i 2 π L n s ) d s .
Ψ ( s , 0 ) = A i ( s ) exp ( a R s ) n = B n exp ( i 2 π L n s ) = { A i ( s ) m ( s ) for | s | S 0 for S < | s | L / 2 A i ( s ) exp ( a R s ) I ( s ) 0 for | s | > L / 2

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