Abstract

We introduce the circle Pearcey Gaussian vortex (CPGV) beams in a harmonic potential for the first time and investigate their abruptly autofocusing properties by theoretical analysis and numerical simulations in this paper. By varying the spatial distribution factors, one can effectively control the propagating dynamics of the beams, including the position of the focus, the radius of the focal light spot and the intensity contrast. Meanwhile, the magnitude of topological charges and the position of the vortex can alter the focal pattern and the intensity contrast. Furthermore, the position of the focus can be flexibly controlled in a tiny range by adjusting the scaled parameter of the incident beam properly.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

J. Chen, F. Zhang, K. Bian, C. Jiang, W. Hu, and D. Lu, “Dynamics of shape-invariant rotating beams in linear media with harmonic potentials,” Phys. Rev. A 99(3), 033808 (2019).
[Crossref]

2018 (2)

T. Han, H. Chen, C. Qin, W. Li, B. Wang, and P. Lu, “Airy pulse shaping using time-dependent power-law potentials,” Phys. Rev. A 97(6), 063815 (2018).
[Crossref]

X. Y. Chen, D. M. Deng, J. L. Zhuang, X. Peng, D. D. Li, L. P. Zhang, F. Zhao, X. B. Yang, H. Z. Liu, and G. H. Wang, “Focusing properties of circle Pearcey beams,” Opt. Lett. 43(15), 3626–3629 (2018).
[Crossref]

2017 (1)

2016 (2)

2015 (6)

2014 (3)

2013 (2)

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(1), 2622 (2013).
[Crossref]

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]

2012 (4)

2011 (5)

2010 (3)

2001 (1)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled Rotation of Optically Trapped Microscopic Particles,” Science 292(5518), 912–914 (2001).
[Crossref]

1946 (1)

T. Pearcey, “The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic,” Philos. Mag. Ser. 37(268), 311–317 (1946).
[Crossref]

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled Rotation of Optically Trapped Microscopic Particles,” Science 292(5518), 912–914 (2001).
[Crossref]

Belic, M. R.

Bian, K.

J. Chen, F. Zhang, K. Bian, C. Jiang, W. Hu, and D. Lu, “Dynamics of shape-invariant rotating beams in linear media with harmonic potentials,” Phys. Rev. A 99(3), 033808 (2019).
[Crossref]

Boyd, R.

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled Rotation of Optically Trapped Microscopic Particles,” Science 292(5518), 912–914 (2001).
[Crossref]

Cai, X. D.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Chen, B.

Chen, C.

Chen, H.

T. Han, H. Chen, C. Qin, W. Li, B. Wang, and P. Lu, “Airy pulse shaping using time-dependent power-law potentials,” Phys. Rev. A 97(6), 063815 (2018).
[Crossref]

Chen, J.

J. Chen, F. Zhang, K. Bian, C. Jiang, W. Hu, and D. Lu, “Dynamics of shape-invariant rotating beams in linear media with harmonic potentials,” Phys. Rev. A 99(3), 033808 (2019).
[Crossref]

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).
[Crossref]

Chen, M. C.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Chen, X. Y.

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]

Christodoulides, D. N.

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(1), 2622 (2013).
[Crossref]

Dai, H. T.

Davis, J. A.

Deng, D.

Deng, D. M.

Dennis, M. R.

Dholakia, K.

J. D. Ring, J. Lindberg, A. Mourka, M. Mazilu, K. Dholakia, and M. R. Dennis, “Auto-focusing and self-healing of Pearcey beams,” Opt. Express 20(17), 18955–18966 (2012).
[Crossref]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled Rotation of Optically Trapped Microscopic Particles,” Science 292(5518), 912–914 (2001).
[Crossref]

Ding, J.

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).
[Crossref]

Efremidis, N. K.

Gregg, P.

Guo, C. S.

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).
[Crossref]

Han, T.

T. Han, H. Chen, C. Qin, W. Li, B. Wang, and P. Lu, “Airy pulse shaping using time-dependent power-law potentials,” Phys. Rev. A 97(6), 063815 (2018).
[Crossref]

Hu, W.

J. Chen, F. Zhang, K. Bian, C. Jiang, W. Hu, and D. Lu, “Dynamics of shape-invariant rotating beams in linear media with harmonic potentials,” Phys. Rev. A 99(3), 033808 (2019).
[Crossref]

Huang, K.

Jiang, C.

J. Chen, F. Zhang, K. Bian, C. Jiang, W. Hu, and D. Lu, “Dynamics of shape-invariant rotating beams in linear media with harmonic potentials,” Phys. Rev. A 99(3), 033808 (2019).
[Crossref]

Jiang, Y.

Karimi, E.

Kim, T.

T.-C. Poon and T. Kim, Engineering Optics with MATLAB (Word Scientific, 2006).

Lencina, A.

Li, C.

Li, D. D.

Li, L.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Li, W.

T. Han, H. Chen, C. Qin, W. Li, B. Wang, and P. Lu, “Airy pulse shaping using time-dependent power-law potentials,” Phys. Rev. A 97(6), 063815 (2018).
[Crossref]

Li, Y.

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).
[Crossref]

Lindberg, J.

Liu, H. Z.

Liu, N. L.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Liu, X.

Liu, Y. J.

Lu, C. Y.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Lu, D.

J. Chen, F. Zhang, K. Bian, C. Jiang, W. Hu, and D. Lu, “Dynamics of shape-invariant rotating beams in linear media with harmonic potentials,” Phys. Rev. A 99(3), 033808 (2019).
[Crossref]

Lu, P.

T. Han, H. Chen, C. Qin, W. Li, B. Wang, and P. Lu, “Airy pulse shaping using time-dependent power-law potentials,” Phys. Rev. A 97(6), 063815 (2018).
[Crossref]

Lu, X.

Luo, D.

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled Rotation of Optically Trapped Microscopic Particles,” Science 292(5518), 912–914 (2001).
[Crossref]

Makris, K. G.

Marrucci, L.

Martinez Matos, O.

Mazilu, M.

Mills, M. S.

Mourka, A.

Padgett, Miles J.

Alison M. Yao and Miles J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Pan, J. W.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[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(1), 2622 (2013).
[Crossref]

Pang, Z.

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(1), 2622 (2013).
[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]

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled Rotation of Optically Trapped Microscopic Particles,” Science 292(5518), 912–914 (2001).
[Crossref]

Pearcey, T.

T. Pearcey, “The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic,” Philos. Mag. Ser. 37(268), 311–317 (1946).
[Crossref]

Penciu, R. S.

Peng, X.

Peng, Y.

Poon, T.-C.

T.-C. Poon and T. Kim, Engineering Optics with MATLAB (Word Scientific, 2006).

Prakash, J.

Qin, C.

T. Han, H. Chen, C. Qin, W. Li, B. Wang, and P. Lu, “Airy pulse shaping using time-dependent power-law potentials,” Phys. Rev. A 97(6), 063815 (2018).
[Crossref]

Ramachandran, S.

Ring, J. D.

Rodrigo, J. A.

Rubano, A.

Sand, D.

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, “Controlled Rotation of Optically Trapped Microscopic Particles,” Science 292(5518), 912–914 (2001).
[Crossref]

Su, Z. E.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Sun, X. W.

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(1), 2622 (2013).
[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]

Vaveliuk, P.

Wang, B.

T. Han, H. Chen, C. Qin, W. Li, B. Wang, and P. Lu, “Airy pulse shaping using time-dependent power-law potentials,” Phys. Rev. A 97(6), 063815 (2018).
[Crossref]

Wang, G. H.

Wang, H. T.

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).
[Crossref]

Wang, R.

Wang, X. L.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

X. L. Wang, J. Chen, Y. Li, J. Ding, C. S. Guo, and H. T. Wang, “Optical orbital angular momentum from the curl of polarization,” Phys. Rev. Lett. 105(25), 253602 (2010).
[Crossref]

Wen, F.

Wu, D.

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Yan, L.

Yang, X. B.

Yao, Alison M.

Alison M. Yao and Miles J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

Zhang, F.

J. Chen, F. Zhang, K. Bian, C. Jiang, W. Hu, and D. Lu, “Dynamics of shape-invariant rotating beams in linear media with harmonic potentials,” Phys. Rev. A 99(3), 033808 (2019).
[Crossref]

Zhang, L.

Zhang, L. P.

Zhang, P.

Zhang, Y.

H. Zhong, Y. Zhang, M. R. Belić, C. Li, F. Wen, Z. Zhang, and Y. Zhang, “Controllable circular Airy beams via dynamic linear potential,” Opt. Express 24(7), 7495–7506 (2016).
[Crossref]

H. Zhong, Y. Zhang, M. R. Belić, C. Li, F. Wen, Z. Zhang, and Y. Zhang, “Controllable circular Airy beams via dynamic linear potential,” Opt. Express 24(7), 7495–7506 (2016).
[Crossref]

Y. Zhang, M. R. Belić, L. Zhang, W. Zhong, D. Zhu, R. Wang, and Y. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23(8), 10467–10480 (2015).
[Crossref]

Y. Zhang, M. R. Belić, L. Zhang, W. Zhong, D. Zhu, R. Wang, and Y. Zhang, “Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential,” Opt. Express 23(8), 10467–10480 (2015).
[Crossref]

Y. Zhang, X. Liu, M. R. Belić, W. Zhong, F. Wen, and Y. Zhang, “Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential,” Opt. Lett. 40(16), 3786–3789 (2015).
[Crossref]

Y. Zhang, X. Liu, M. R. Belić, W. Zhong, F. Wen, and Y. Zhang, “Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential,” Opt. Lett. 40(16), 3786–3789 (2015).
[Crossref]

Y. Zhang, X. Liu, M. R. Belić, W. Zhong, F. Wen, and Y. Zhang, “Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential,” Opt. Lett. 40(16), 3786–3789 (2015).
[Crossref]

Y. Zhang, X. Liu, M. R. Belić, W. Zhong, F. Wen, and Y. Zhang, “Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential,” Opt. Lett. 40(16), 3786–3789 (2015).
[Crossref]

Zhang, Z.

Zhao, F.

Zhao, X.

Zheng, Y.

Zhong, H.

Zhong, W.

Zhou, M.

Zhu, D.

Zhuang, J. L.

Adv. Opt. Photonics (1)

Alison M. Yao and Miles J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[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(1), 2622 (2013).
[Crossref]

Nature (1)

X. L. Wang, X. D. Cai, Z. E. Su, M. C. Chen, D. Wu, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, “Quantum teleportation of multiple degrees of freedom of a single photon,” Nature 518(7540), 516–519 (2015).
[Crossref]

Opt. Express (8)

Opt. Lett. (12)

X. Y. Chen, D. M. Deng, J. L. Zhuang, X. Peng, D. D. Li, L. P. Zhang, F. Zhao, X. B. Yang, H. Z. Liu, and G. H. Wang, “Focusing properties of circle Pearcey beams,” Opt. Lett. 43(15), 3626–3629 (2018).
[Crossref]

Y. Zhang, X. Liu, M. R. Belić, W. Zhong, F. Wen, and Y. Zhang, “Anharmonic propagation of two-dimensional beams carrying orbital angular momentum in a harmonic potential,” Opt. Lett. 40(16), 3786–3789 (2015).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. The intensity profiles of the CPGV beams propagating at different propagation distances. The transverse intensity profiles and the corresponding cross lines of the CPGV beams (a) at the initial plane ($z=0$), (b) before the focal plane ($z=L_{s}/2$), (c) at the focal plane ($z=L_{s}$), the detailed intensity distribution of the propagation dynamics for (d) $a=0.1$ and (e) $a=0.5$, (f) the phase pattern at the initial plane.
Fig. 2.
Fig. 2. The intensity profiles of CPGV beams propagating at different propagation distances. (a) The numerically simulated side-view propagation of the CPGV beams, (b1) - (b6) snapshots of the transverse intensity patterns are taken at the planes marked by the dashed lines in (a); (c1) - (c6) the corresponding phase distributions at different planes marked in (a). Other parameters are the same as those in Fig. 1 except $m=1$, $r_{k}=0$ and $\varphi _{k}=0$.
Fig. 3.
Fig. 3. The evolutions of the intensity distributions of the CPGV beams with the different spatial distribution factor (a1) and (b1) $p_{s}=0.1$; (a2) and (b2) $p_{s}=0.13$, (a3) and (b3) $p_{s}=0.15$. The corresponding cross line of the intensity distribution on $y=0$ (c1) at the initial plane, (c2) at the focal plane. (c3) The peak intensity distribution of the CPGV beams versus the propagation distance. Other parameters are the same as those in Fig. 2 except $a=0.6$.
Fig. 4.
Fig. 4. The transverse intensity profiles of the CPGV beams (a1)–(c1) at the initial plane (z = 0), (a2)–(c2) at the the focal plane (z = Ls), (a3)–(c3) the phase pattern at the initial plane. Comparison of $(I/I_{0})_{max}$ of the CPGV beams with different m as a function of z for (d1) on-axis vortices and (d2) off-axis vortices. Other parameters are the same as those in Fig. 3(a1), except $r_{k}=0.5$ and $\varphi _{k}=\pi /3$ in (a1)–(c1), m=2 in (a2)–(c2), and m=2, $r_{k}=0.5$ and $\varphi _{k}=\pi /3$ in (a3)–(c3).
Fig. 5.
Fig. 5. The transverse intensity profiles and the phase patterns of the CPGV beams with an off-axis vortex pair at different propagation distances. Other parameters are the same as those in Fig. 4(a1), except l=1 in (a1)–(a5); l=1 and $r_{k}=0.7$ in (b1)–(b5); l$=1$ and $p_{s}=0.13$ in (c1)–(c5).
Fig. 6.
Fig. 6. (a) The peak intensity contrast of the CPG beams versus the propagation distance for (a) different $\xi$, (b) different $a$. Other parameters are the same as those in Fig. 1.

Equations (5)

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2 E + 2 i E z α 2 ( x 2 + y 2 ) E = 0 ,
2 E r 2 + r 1 E r + r 2 2 E φ 2 + 2 i E z α 2 r 2 E = 0 ,
E ( r , φ , 0 ) = A 0 P e ( r p s , r ξ ) exp ( r 2 ) q ( r ) × ( r e i φ + r k e i φ k ) m ( r e i φ r k e i φ k ) l ,
q ( r ) = { C e a r β , r < r 0 0 , r r 0 ,
E ( r , φ , z ) = 0 2 π 0 E ( ρ , θ , 0 ) 2 π i z e i ρ 2 + r 2 2 ρ r c o s ( φ θ ) 2 z ρ d ρ d θ .

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