Abstract

We have proposed a kind of modified circular Airy beam (MCAB) based upon a modification of the Fourier spectrum of circular Airy beams (CAB) in this paper. Unlike most abruptly autofocusing beams, the position of peak intensity of MCAB can be moved to any rings behind. Two apodization parameters are introduced to describe the propagation characteristics of MCAB. It is found that the focal position, focal trajectory and the size of focal spot do not change with the apodization parameters; but the abruptly autofocusing property will be greatly enhanced if appropriately apodization parameters are chosen. Comparing with the common CAB and the previous blocked CAB, the MCAB shows better abruptly autofocusing property. It may have more applications in various fields.

© 2015 Optical Society of America

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References

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  1. N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
    [Crossref] [PubMed]
  2. D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
    [Crossref] [PubMed]
  3. I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36(18), 3675–3677 (2011).
    [Crossref] [PubMed]
  4. S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013).
    [Crossref] [PubMed]
  5. F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” Appl. Phys. B 117(3), 905–913 (2014).
    [Crossref]
  6. W. Zhu and W. She, “Tightly focusing vector circular airy beam through a hard aperture,” Opt. Commun. 334(0), 303–307 (2015).
    [Crossref]
  7. 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(15), 2883–2885 (2011).
    [Crossref] [PubMed]
  8. Y. Jiang, K. Huang, and X. Lu, “Radiation force of abruptly autofocusing Airy beams on a Rayleigh particle,” Opt. Express 21(20), 24413–24421 (2013).
    [Crossref] [PubMed]
  9. P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
    [Crossref] [PubMed]
  10. N. K. Efremidis, V. Paltoglou, and W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87(4), 043637 (2013).
    [Crossref]
  11. J. A. Davis, D. M. Cottrell, and D. Sand, “Abruptly autofocusing vortex beams,” Opt. Express 20(12), 13302–13310 (2012).
    [Crossref] [PubMed]
  12. Y. Jiang, K. Huang, and X. Lu, “Propagation dynamics of abruptly autofocusing Airy beams with optical vortices,” Opt. Express 20(17), 18579–18584 (2012).
    [Crossref] [PubMed]
  13. P. Li, S. Liu, T. Peng, G. Xie, X. Gan, and J. Zhao, “Spiral autofocusing Airy beams carrying power-exponent-phase vortices,” Opt. Express 22(7), 7598–7606 (2014).
    [Crossref] [PubMed]
  14. N. Li, Y. Jiang, K. Huang, and X. Lu, “Abruptly autofocusing property of blocked circular Airy beams,” Opt. Express 22(19), 22847–22853 (2014).
    [Crossref] [PubMed]
  15. I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36(10), 1890–1892 (2011).
    [Crossref] [PubMed]
  16. I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85(2), 023828 (2012).
    [Crossref]
  17. P. Vaveliuk, A. Lencina, J. A. Rodrigo, and O. M. Matos, “Symmetric Airy beams,” Opt. Lett. 39(8), 2370–2373 (2014).
    [Crossref] [PubMed]
  18. S. Barwick, “Reduced side-lobe Airy beams,” Opt. Lett. 36(15), 2827–2829 (2011).
    [Crossref] [PubMed]
  19. I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Bessel-like optical beams with arbitrary trajectories,” Opt. Lett. 37(23), 5003–5005 (2012).
    [Crossref] [PubMed]
  20. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
    [Crossref] [PubMed]

2015 (1)

W. Zhu and W. She, “Tightly focusing vector circular airy beam through a hard aperture,” Opt. Commun. 334(0), 303–307 (2015).
[Crossref]

2014 (4)

2013 (4)

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013).
[Crossref] [PubMed]

Y. Jiang, K. Huang, and X. Lu, “Radiation force of abruptly autofocusing Airy beams on a Rayleigh particle,” Opt. Express 21(20), 24413–24421 (2013).
[Crossref] [PubMed]

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87(4), 043637 (2013).
[Crossref]

2012 (4)

2011 (5)

2010 (1)

2007 (1)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Barwick, S.

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Cai, Y.

F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” Appl. Phys. B 117(3), 905–913 (2014).
[Crossref]

Chen, Z.

Chremmos, I.

Chremmos, I. D.

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85(2), 023828 (2012).
[Crossref]

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Bessel-like optical beams with arbitrary trajectories,” Opt. Lett. 37(23), 5003–5005 (2012).
[Crossref] [PubMed]

Christodoulides, D. N.

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Bessel-like optical beams with arbitrary trajectories,” Opt. Lett. 37(23), 5003–5005 (2012).
[Crossref] [PubMed]

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85(2), 023828 (2012).
[Crossref]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[Crossref] [PubMed]

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36(10), 1890–1892 (2011).
[Crossref] [PubMed]

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(15), 2883–2885 (2011).
[Crossref] [PubMed]

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36(18), 3675–3677 (2011).
[Crossref] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
[Crossref] [PubMed]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Cottrell, D. M.

Couairon, A.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

Davis, J. A.

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Dong, Y.

F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” Appl. Phys. B 117(3), 905–913 (2014).
[Crossref]

F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” Appl. Phys. B 117(3), 905–913 (2014).
[Crossref]

Efremidis, N. K.

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87(4), 043637 (2013).
[Crossref]

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85(2), 023828 (2012).
[Crossref]

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Bessel-like optical beams with arbitrary trajectories,” Opt. Lett. 37(23), 5003–5005 (2012).
[Crossref] [PubMed]

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36(18), 3675–3677 (2011).
[Crossref] [PubMed]

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(15), 2883–2885 (2011).
[Crossref] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[Crossref] [PubMed]

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36(10), 1890–1892 (2011).
[Crossref] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
[Crossref] [PubMed]

Gan, X.

Huang, K.

Jiang, Y.

Lencina, A.

Li, N.

Li, P.

Liu, S.

Lu, X.

Matos, O. M.

Mills, M. S.

Paltoglou, V.

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87(4), 043637 (2013).
[Crossref]

Panagiotopoulos, P.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

Papazoglou, D. G.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[Crossref] [PubMed]

Peng, T.

Prakash, J.

Rodrigo, J. A.

Sand, D.

She, W.

W. Zhu and W. She, “Tightly focusing vector circular airy beam through a hard aperture,” Opt. Commun. 334(0), 303–307 (2015).
[Crossref]

Siviloglou, G. A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

Tzortzakis, S.

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[Crossref] [PubMed]

Vaveliuk, P.

von Klitzing, W.

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87(4), 043637 (2013).
[Crossref]

Wang, F.

F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” Appl. Phys. B 117(3), 905–913 (2014).
[Crossref]

Wang, M.

Xie, G.

Zhang, P.

Zhang, Z.

Zhao, C.

F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” Appl. Phys. B 117(3), 905–913 (2014).
[Crossref]

Zhao, J.

Zhu, W.

W. Zhu and W. She, “Tightly focusing vector circular airy beam through a hard aperture,” Opt. Commun. 334(0), 303–307 (2015).
[Crossref]

Appl. Phys. B (1)

F. Wang, C. Zhao, Y. Dong, Y. Dong, and Y. Cai, “Generation and tight-focusing properties of cylindrical vector circular Airy beams,” Appl. Phys. B 117(3), 905–913 (2014).
[Crossref]

Nat. Commun. (1)

P. Panagiotopoulos, D. G. Papazoglou, A. Couairon, and S. Tzortzakis, “Sharply autofocused ring-Airy beams transforming into non-linear intense light bullets,” Nat. Commun. 4, 2622 (2013).
[Crossref] [PubMed]

Opt. Commun. (1)

W. Zhu and W. She, “Tightly focusing vector circular airy beam through a hard aperture,” Opt. Commun. 334(0), 303–307 (2015).
[Crossref]

Opt. Express (5)

Opt. Lett. (9)

I. Chremmos, N. K. Efremidis, and D. N. Christodoulides, “Pre-engineered abruptly autofocusing beams,” Opt. Lett. 36(10), 1890–1892 (2011).
[Crossref] [PubMed]

P. Vaveliuk, A. Lencina, J. A. Rodrigo, and O. M. Matos, “Symmetric Airy beams,” Opt. Lett. 39(8), 2370–2373 (2014).
[Crossref] [PubMed]

S. Barwick, “Reduced side-lobe Airy beams,” Opt. Lett. 36(15), 2827–2829 (2011).
[Crossref] [PubMed]

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Bessel-like optical beams with arbitrary trajectories,” Opt. Lett. 37(23), 5003–5005 (2012).
[Crossref] [PubMed]

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(15), 2883–2885 (2011).
[Crossref] [PubMed]

N. K. Efremidis and D. N. Christodoulides, “Abruptly autofocusing waves,” Opt. Lett. 35(23), 4045–4047 (2010).
[Crossref] [PubMed]

D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. 36(10), 1842–1844 (2011).
[Crossref] [PubMed]

I. Chremmos, P. Zhang, J. Prakash, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, “Fourier-space generation of abruptly autofocusing beams and optical bottle beams,” Opt. Lett. 36(18), 3675–3677 (2011).
[Crossref] [PubMed]

S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38(14), 2416–2418 (2013).
[Crossref] [PubMed]

Phys. Rev. A (2)

N. K. Efremidis, V. Paltoglou, and W. von Klitzing, “Accelerating and abruptly autofocusing matter waves,” Phys. Rev. A 87(4), 043637 (2013).
[Crossref]

I. D. Chremmos, Z. Chen, D. N. Christodoulides, and N. K. Efremidis, “Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics,” Phys. Rev. A 85(2), 023828 (2012).
[Crossref]

Phys. Rev. Lett. (1)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of Accelerating Airy Beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1 Fourier transform of the modified circular Airy beam (MCAB). (a) Fourier spectrum with different β when kc = 5mm−1;(b) Fourier spectrum with different kc when β = 0.3mm. “β=0” is actually the common CAB.
Fig. 2
Fig. 2 Intensity patterns of MCAB at the initial plane. The first row is MCAB with different β when kc = 5mm−1: (a) β = 0; (b) β = 0.3mm; (c) β = 0.6mm. The second row is MCAB with different kc when β = 0.3mm: (d) kc = 5mm−1; (e) kc = 10mm−1; (f) kc = 17mm−1.
Fig. 3
Fig. 3 Intensity distributions of MCAB at the initial plane. (a) MCAB with different β when kc = 5mm−1; (b) MCAB with different kc when β = 0.3mm.
Fig. 4
Fig. 4 Propagation dynamics of MCAB in free space. The first row is MCAB with different β when kc = 5mm−1: (a) β = 0; (b) β = 0.3mm; (c) β = 0.6mm. The second row is MCAB with different kc when β = 0.3mm: (d) kc = 5mm−1; (e) kc = 10mm−1; (f) kc = 17mm−1.
Fig. 5
Fig. 5 Trajectories of the radii of MCAB. (a) MCAB with different β when kc = 5mm−1; (b) MCAB with different kc when β = 0.3mm.
Fig. 6
Fig. 6 Intensity distributions of MCAB at the focal plane. (a) MCAB with different β when kc = 5mm−1; (b) MCAB with different kc when β = 0.3mm.
Fig. 7
Fig. 7 Abruptly autofocusing property of MCAB. (a) MCAB with different β when kc = 5mm−1; (b) MCAB with different kc when β = 0.3mm.
Fig. 8
Fig. 8 Maximum value of Im/I0 that MCAB can reach during propagation with different apodization parameters: (a) change with β when kc is different; (b) change with kc when β is different.
Fig. 9
Fig. 9 Comparison of the MCAB with BCAB. (a) Intensity profile at the initial plane; (b) distribution of Im/I0 during propagation.CAB is the original circular Airy beams; the apodization parameters for MCAB are β = 0.3mm, kc = 17mm−1.

Equations (5)

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

u(r)= C 0 Ai( r 0 r w )exp( a r 0 r w ),
U(k)= C 0 w 2 ( r 0 w + k 2 w 2 )exp( a k 2 w 2 ) 3k r 0 + k 3 w 3 3k r 0 +3 k 3 w 3 J 0 ( k r 0 + k 3 w 3 3 ),
M(k)= 1 1+ e β(k k c ) ,
U M (k)=M(k)U(k).
u M (r,z)= 0 M(k)U(k) J 0 (kr) e 2iπz λ 2 k 2 kdk,

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