Abstract

Controlling the focal length and the intensity of the optical focus in the media is an important task. Here we investigate the propagation properties of the sharply autofocused ring Airy Gaussian vortex beams numerically and some numerical experiments are performed. We introduce the distribution factor b into the initial beams, and discuss the influences for the beams. With controlling the factor b, the beams that tend to a ring Airy vortex beam with the smaller value, or a hollow Gaussian vortex beam with the larger one. By a choice of initial launch condition, we find that the number of topological charge of the incident beams, as well as its size, greatly affect the focal intensity and the focal length of the autofocused ring Airy Gaussian vortex beams. Furthermore, we show that the off-axis autofocused ring Airy Gaussian beams with vortex pairs can be implemented.

© 2015 Optical Society of America

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References

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  1. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
    [Crossref]
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    [Crossref] [PubMed]
  3. M. A. Bandres and J. C. Gutirrez-Vega, “Airy-Gauss beams and their transformation by paraxial optical systems,” Opt. Express. 15, 16719–16728. (2007).
    [Crossref] [PubMed]
  4. D. Deng and H. Li, “Propagation properties of Airy-Gaussian beams,” Appl. Phys. B. 106677–681 (2012).
    [Crossref]
  5. C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17, 035504 (2015).
    [Crossref]
  6. F. Flossmann, U. T. Schwarz, and M. Maier, “Propagation dynamics of optical vortices in Laguerre-Gaussian beams,” Opt. Commun. 250, 218–230 (2005).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  10. D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B. 110433–436 (2013).
    [Crossref]
  11. B. Chen, C. Chen, X. Peng, and D. Deng, “Propagation of Airy Gaussian vortex beams through slabs of right-handed materials and left-handed materials,” J. Opt. Soc. Am. B. 32, 173–178 (2015).
    [Crossref]
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    [Crossref] [PubMed]
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  14. 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] [PubMed]
  15. 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, 023828 (2012).
    [Crossref]
  16. 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, 3675–3677 (2011).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  18. L. Froehly, F. Courvoisier, A. Mathis, M. Jacquot, L. Furfaro, R. Giust, P. A. Lacourt, and J. M. Dudley, “Arbitrary accelerating micron-scale caustic beams in two and three dimensions,” Opt. Express 19, 16455–16465 (2011).
    [Crossref] [PubMed]
  19. J. A. Davis, D. M. Cottrell, and D. Sand, “Abruptly autofocusing vortex beams,” Opt. Express 20, 13302–13310 (2012).
    [Crossref] [PubMed]
  20. Y. F. Jiang, K. K. Huang, and X. H. Lu, “Propagation dynamics of abruptly autofocusing Airy beams with optical vortices,” Opt. Express 20, 18579–18584 (2012).
    [Crossref] [PubMed]
  21. S. Liu, M. Wang, P. Li, P. Zhang, and J. Zhao, “Abrupt polarization transition of vector autofocusing Airy beams,” Opt. Lett. 38, 2416–2418 (2013).
    [Crossref] [PubMed]
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  23. Ting-Chung Poon and Taegeun Kim, Engineering Optics with MATLAB (World Scientific, 2006).

2015 (2)

C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17, 035504 (2015).
[Crossref]

B. Chen, C. Chen, X. Peng, and D. Deng, “Propagation of Airy Gaussian vortex beams through slabs of right-handed materials and left-handed materials,” J. Opt. Soc. Am. B. 32, 173–178 (2015).
[Crossref]

2014 (1)

2013 (3)

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

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1406 (2013).
[Crossref] [PubMed]

D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B. 110433–436 (2013).
[Crossref]

2012 (4)

D. Deng and H. Li, “Propagation properties of Airy-Gaussian beams,” Appl. Phys. B. 106677–681 (2012).
[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, 023828 (2012).
[Crossref]

J. A. Davis, D. M. Cottrell, and D. Sand, “Abruptly autofocusing vortex beams,” Opt. Express 20, 13302–13310 (2012).
[Crossref] [PubMed]

Y. F. Jiang, K. K. Huang, and X. H. Lu, “Propagation dynamics of abruptly autofocusing Airy beams with optical vortices,” Opt. Express 20, 18579–18584 (2012).
[Crossref] [PubMed]

2011 (5)

2010 (2)

2007 (3)

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. 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] [PubMed]

M. A. Bandres and J. C. Gutirrez-Vega, “Airy-Gauss beams and their transformation by paraxial optical systems,” Opt. Express. 15, 16719–16728. (2007).
[Crossref] [PubMed]

2005 (1)

F. Flossmann, U. T. Schwarz, and M. Maier, “Propagation dynamics of optical vortices in Laguerre-Gaussian beams,” Opt. Commun. 250, 218–230 (2005).
[Crossref]

2001 (1)

S. A. Ponomarenko, “A class of partially coherent beams carrying optical vortices,” J. Opt. Soc. Am. A. 18, 150–156 (2001).
[Crossref]

Bandres, M. A.

M. A. Bandres and J. C. Gutirrez-Vega, “Airy-Gauss beams and their transformation by paraxial optical systems,” Opt. Express. 15, 16719–16728. (2007).
[Crossref] [PubMed]

Broky, J.

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

Chen, B.

B. Chen, C. Chen, X. Peng, and D. Deng, “Propagation of Airy Gaussian vortex beams through slabs of right-handed materials and left-handed materials,” J. Opt. Soc. Am. B. 32, 173–178 (2015).
[Crossref]

C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17, 035504 (2015).
[Crossref]

Chen, C.

C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17, 035504 (2015).
[Crossref]

B. Chen, C. Chen, X. Peng, and D. Deng, “Propagation of Airy Gaussian vortex beams through slabs of right-handed materials and left-handed materials,” J. Opt. Soc. Am. B. 32, 173–178 (2015).
[Crossref]

D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B. 110433–436 (2013).
[Crossref]

Chen, R. P.

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1406 (2013).
[Crossref] [PubMed]

Chen, Z.

Chew, K. H.

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1406 (2013).
[Crossref] [PubMed]

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, 023828 (2012).
[Crossref]

Christodoulides, D. N.

Cottrell, D. M.

Courvoisier, F.

Dai, H. T.

Davis, J. A.

Deng, D.

B. Chen, C. Chen, X. Peng, and D. Deng, “Propagation of Airy Gaussian vortex beams through slabs of right-handed materials and left-handed materials,” J. Opt. Soc. Am. B. 32, 173–178 (2015).
[Crossref]

C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17, 035504 (2015).
[Crossref]

D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B. 110433–436 (2013).
[Crossref]

D. Deng and H. Li, “Propagation properties of Airy-Gaussian beams,” Appl. Phys. B. 106677–681 (2012).
[Crossref]

Dogariu, A.

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.

Efremidis, N. K.

Flossmann, F.

F. Flossmann, U. T. Schwarz, and M. Maier, “Propagation dynamics of optical vortices in Laguerre-Gaussian beams,” Opt. Commun. 250, 218–230 (2005).
[Crossref]

Froehly, L.

Furfaro, L.

Giust, R.

Gutirrez-Vega, J. C.

M. A. Bandres and J. C. Gutirrez-Vega, “Airy-Gauss beams and their transformation by paraxial optical systems,” Opt. Express. 15, 16719–16728. (2007).
[Crossref] [PubMed]

He, S.

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1406 (2013).
[Crossref] [PubMed]

Huang, K. K.

Jacquot, M.

Jiang, Y. F.

Kim, Taegeun

Ting-Chung Poon and Taegeun Kim, Engineering Optics with MATLAB (World Scientific, 2006).

Lacourt, P. A.

Li, H.

D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B. 110433–436 (2013).
[Crossref]

D. Deng and H. Li, “Propagation properties of Airy-Gaussian beams,” Appl. Phys. B. 106677–681 (2012).
[Crossref]

Li, P.

Liu, S.

Liu, Y. J.

Lu, X. H.

Lukin, I. P.

Luo, D.

Maier, M.

F. Flossmann, U. T. Schwarz, and M. Maier, “Propagation dynamics of optical vortices in Laguerre-Gaussian beams,” Opt. Commun. 250, 218–230 (2005).
[Crossref]

Mathis, A.

Mills, M. S.

Papazoglou, D. G.

Peng, X.

C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17, 035504 (2015).
[Crossref]

B. Chen, C. Chen, X. Peng, and D. Deng, “Propagation of Airy Gaussian vortex beams through slabs of right-handed materials and left-handed materials,” J. Opt. Soc. Am. B. 32, 173–178 (2015).
[Crossref]

Ponomarenko, S. A.

S. A. Ponomarenko, “A class of partially coherent beams carrying optical vortices,” J. Opt. Soc. Am. A. 18, 150–156 (2001).
[Crossref]

Poon, Ting-Chung

Ting-Chung Poon and Taegeun Kim, Engineering Optics with MATLAB (World Scientific, 2006).

Prakash, J.

Sand, D.

Schwarz, U. T.

F. Flossmann, U. T. Schwarz, and M. Maier, “Propagation dynamics of optical vortices in Laguerre-Gaussian beams,” Opt. Commun. 250, 218–230 (2005).
[Crossref]

Siviloglou, G. A.

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

Sun, X. W.

Tzortzakis, S.

Wang, M.

Zhang, P.

Zhang, Z.

Zhao, J.

Zhao, X.

D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B. 110433–436 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B. (2)

D. Deng and H. Li, “Propagation properties of Airy-Gaussian beams,” Appl. Phys. B. 106677–681 (2012).
[Crossref]

D. Deng, C. Chen, X. Zhao, and H. Li, “Propagation of an Airy vortex beam in uniaxial crystals,” Appl. Phys. B. 110433–436 (2013).
[Crossref]

J. Opt. (1)

C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17, 035504 (2015).
[Crossref]

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

S. A. Ponomarenko, “A class of partially coherent beams carrying optical vortices,” J. Opt. Soc. Am. A. 18, 150–156 (2001).
[Crossref]

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

B. Chen, C. Chen, X. Peng, and D. Deng, “Propagation of Airy Gaussian vortex beams through slabs of right-handed materials and left-handed materials,” J. Opt. Soc. Am. B. 32, 173–178 (2015).
[Crossref]

Opt. Commun. (1)

F. Flossmann, U. T. Schwarz, and M. Maier, “Propagation dynamics of optical vortices in Laguerre-Gaussian beams,” Opt. Commun. 250, 218–230 (2005).
[Crossref]

Opt. Express (3)

Opt. Express. (1)

M. A. Bandres and J. C. Gutirrez-Vega, “Airy-Gauss beams and their transformation by paraxial optical systems,” Opt. Express. 15, 16719–16728. (2007).
[Crossref] [PubMed]

Opt. Lett. (8)

Phys. Rev. A (1)

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, 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, 213901 (2007).
[Crossref]

Sci. Rep. (1)

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1406 (2013).
[Crossref] [PubMed]

Other (1)

Ting-Chung Poon and Taegeun Kim, Engineering Optics with MATLAB (World Scientific, 2006).

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Figures (12)

Fig. 1
Fig. 1 The influences of the distribution factor b for the initial input RAiGV beams.

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Fig. 2
Fig. 2 Intensity distribution of the RAiGV beams with one on-axis vortex propagation. (a) the detailed plot of the central part of the propagation dynamics. (b) the peak intensity distribution of the RAiGV beams versus propagation distance.

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Fig. 3
Fig. 3 Numerical demonstrations of a RAiGV beam propagating in the linear media. (a) numerically simulated side-view propagation of the RAiGV beams; (b1)–(b4) snapshots of the transverse intensity patterns taken at the planes marked by the dashed lines in (a); (c1)–(c4) the corresponding phase distributions at different planes marked in (a).

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Fig. 4
Fig. 4 Numerical demonstrations of RAiGV beams propagating through the linear media. (a)–(c) the intensity of the initial incident 1D and 2D RAiGV beams for various parameters b = 0.1,0.2,0.4, respectively; (a1)–(c1) numerically simulated side-view propagation of the RAiGV beams for different parameters b = 0.1,0.2,0.4, respectively; (a2)–(c2) the peak intensity distribution of the RAiGV beams corresponding to (a1)–(c1).

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Fig. 5
Fig. 5 Numerical experimental demonstrations of the RAiGV beams propagating for different parameters b.(a1)–(c1) Computer-generated hologram for b = 0.1, 0.2, 0.4, respectively; (a2)–(c2) interference intensity of the initial generated beam and a plane wave for b = 0.1, 0.2, 0.4, respectively; (a3)–(c3) numerical experimentally recorded normalized transverse beam patterns at initial plane for different b = 0.1, 0.2, 0.4, respectively; (a2)–(c2)numerical experimentally recorded normalized transverse beam patterns at the focal plane for b = 0.1, 0.2, 0.4, respectively.

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Fig. 6
Fig. 6 (a)–(c) the intensity of the initial incident 1D and 2D RAiGV beams for m = 0, 1, 2 (m = 0, namely ring Airy Gaussian beams), respectively; (a1)–(c1) numerically simulated side-view propagation of the RAiGV beams for m = 0, 1, 2, respectively, the dashed line indicates the focal plane; (a2)–(c2) the intensity of the focal plane 1D and 2D for m = 0, 1, 2, respectively.

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Fig. 7
Fig. 7 Beam width of the RAiGV beams versus propagation distance for various topological charge m, (a) m = 0; (b) m = 1; (c) m = 2.

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Fig. 8
Fig. 8 Focus position versus the different topological charge in the medium.

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Fig. 9
Fig. 9 (a) the intensity of the focal plane for m = 0, 1, 2, respectively. (b) the peak intensity distribution of the RAiGV beams for m = 0, 1, 2, 3, 4, respectively.

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Fig. 10
Fig. 10 Peak intensity distribution of the RAiGV beams versus propagation distance for various topological charge m, (a) m = 0; (b) m = 1; (c) m = 2.

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Fig. 11
Fig. 11 Similar to Fig. 3 but with positive vortex pairs off-axis, and rk = 0.6mm.

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Fig. 12
Fig. 12 Numerical experimental demonstrations of the off-axis propagation of RAiG beams with positive vortex pairs.(a) Computer-generated hologram; (a1)–(a4) numerical experimentally recorded normalized transverse beam patterns at the planes marked by the dashed lines in Fig. 11(a).

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Equations (6)

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

∇ ⊥ 2 u + 2 i k ∂ u ∂ z = 0 ,
1 r ∂ u ∂ r + ∂ 2 u ∂ r 2 + 1 r 2 ∂ 2 u ∂ φ 2 + 2 i k ∂ u ∂ z = 0.
u ( r , φ , z ) = U ( r , z ) exp ( i m φ ) ,
1 r ∂ U ∂ r + ∂ 2 U ∂ r 2 − m 2 r 2 U + 2 i k ∂ U ∂ z = 0.
u ( r , φ , z = 0 ) = A 0 A i ( r 0 − r b w ) exp ( a r 0 − r b w ) exp [ − ( r 0 − r ) 2 w 2 ] ( r m e i m φ ) ,
u ( r , φ , z = 0 ) = A 0 A i ( r 0 − r b w ) exp ( a r 0 − r b w ) exp [ − ( r 0 − r ) 2 w 2 ] ( r e i φ + r k ) ( r e i φ − r k ) ,

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