Abstract

We demonstrate analytically and experimentally that a circular abruptly autofocusing (AAF) Airy beam can be generated by Fourier-transforming an appropriately apodized Bessel beam whose radial oscillations are chirped by a cubic phase term. Depending on the relation between the chirp rate and the focal distance of the Fourier- transforming lens, it is possible to generate AAF beams with one or two foci, the latter case leading to the formation of an elegant paraboloid optical bottle.

© 2011 Optical Society of America

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2011

2010

2009

2007

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Chen, Z.

P. Zhang, Z. Zhang, J. Prakash, S. Huang, D. Hernandez, M. Salazar, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 1491 (2011).
[CrossRef] [PubMed]

P. Zhang, J. Prakash, Ze Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 2883 (2011).
[CrossRef] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, Y. Hu, N. K. Efremidis, V. Kajorndejnukul, D. Christodoulides, and Z. Chen, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QThS7.

Chremmos, I.

Christodoulides, D.

P. Zhang, J. Prakash, Z. Zhang, Y. Hu, N. K. Efremidis, V. Kajorndejnukul, D. Christodoulides, and Z. Chen, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QThS7.

Christodoulides, D. N.

Desyatnikov, A. S.

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Efremidis, N. K.

Hernandez, D.

Hu, Y.

P. Zhang, J. Prakash, Z. Zhang, Y. Hu, N. K. Efremidis, V. Kajorndejnukul, D. Christodoulides, and Z. Chen, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QThS7.

Huang, S.

Hwang, C.-Y.

Kajorndejnukul, V.

P. Zhang, J. Prakash, Z. Zhang, Y. Hu, N. K. Efremidis, V. Kajorndejnukul, D. Christodoulides, and Z. Chen, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QThS7.

Kim, K.-Y.

Kivshar, Y. S.

Krolikowski, W.

Lee, B.

Mills, M. S.

Papazoglou, D. G.

Prakash, J.

P. Zhang, Z. Zhang, J. Prakash, S. Huang, D. Hernandez, M. Salazar, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 1491 (2011).
[CrossRef] [PubMed]

P. Zhang, J. Prakash, Ze Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 2883 (2011).
[CrossRef] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, Y. Hu, N. K. Efremidis, V. Kajorndejnukul, D. Christodoulides, and Z. Chen, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QThS7.

Rode, A. V.

Salazar, M.

Shvedov, V. G.

Siviloglou, G. A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Tzortzakis, S.

Zhang, P.

P. Zhang, Z. Zhang, J. Prakash, S. Huang, D. Hernandez, M. Salazar, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 1491 (2011).
[CrossRef] [PubMed]

P. Zhang, J. Prakash, Ze Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 2883 (2011).
[CrossRef] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, Y. Hu, N. K. Efremidis, V. Kajorndejnukul, D. Christodoulides, and Z. Chen, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QThS7.

Zhang, Z.

P. Zhang, Z. Zhang, J. Prakash, S. Huang, D. Hernandez, M. Salazar, D. N. Christodoulides, and Z. Chen, Opt. Lett. 36, 1491 (2011).
[CrossRef] [PubMed]

P. Zhang, J. Prakash, Z. Zhang, Y. Hu, N. K. Efremidis, V. Kajorndejnukul, D. Christodoulides, and Z. Chen, in Quantum Electronics and Laser Science Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QThS7.

Zhang, Ze

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Figures (3)

Fig. 1
Fig. 1

(a) FT of a CAB with r 0 = 10 , a = 0.05 , as given by Eq. (2) (blue line) and by Eq. (8) (red dots). (b),(c) Full-wave simulation of CABs generated by Fourier–transforming chirped Bessel beams. The dashed lines indicate the lens with f = 10 . c = 10 in (b) and C = 6 in (c), while a = 0.05 .

Fig. 2
Fig. 2

BPM simulation of optical bottle generation from a CAB. (a) Side-view of the bottle beam dynamics numerically retrieved from the computer−generated hologram (e); (b)–(d) Transverse intensity patterns taken at planes 1 3 marked in (a); (e) a typical off-axis hologram.

Fig. 3
Fig. 3

Experimental results of an optical bottle beam generated using the hologram of Fig. 2e. (a) Side-view photo of the bottle beam taken from scattered light; (b)–(d) transverse intensity snapshots at planes 1 3 marked in (a).

Equations (9)

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u ( r ) = A i ( r 0 r ) exp [ a ( r 0 r ) ] ,
U ( k ) = 0 u ( x ) J 0 ( k x ) x d x .
U ( k ) = 1 2 π G ( ω ) W ( ω , k ) e i ω r 0 d ω ,
G ( ω ) = [ r 0 + ( ω + i a ) 2 ] exp [ i ( ω + i a ) 3 / 3 ] , W ( ω ) = { 2 ( k 2 ω 2 ) 1 / 2 , | ω | < k 0 , | ω | > k .
U ( k ) = 0 π F ( φ ) e i Q ( φ ) d φ ,
π F ( φ ) = [ r 0 + ( k cos φ + i a ) 2 ] exp ( a 3 / 3 a k 2 cos 2 φ ) , Q ( φ ) = ( k 3 / 3 ) cos 3 φ + k ( r 0 a 2 ) cos φ .
U S P ( k ) = 2 π Q ( 0 ) Re [ F ( 0 ) exp ( i Q ( 0 ) i π / 4 ) ] ,
V ( k ) = ( r 0 + k 2 ) e a k 2 k r 0 + k 3 / 3 k r 0 + k 3 J 0 ( k r 0 + k 3 / 3 ) ,
w ( r , 2 f ) i ( c / f ) A i ( c c r / f ) exp [ a ( c c r / f ) ] ,

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