Abstract

We simulate the propagation of the abruptly autofocusing chirped ring Pearcey Gaussian vortex (CRPGV) beams with caustics by modulating the phase of a circularly symmetric optical wavefront appropriately. The propagation characteristics of the CRPGV beams are explored in the Kerr medium. Different caustic surfaces of revolution which can be used as optical bottles are formed during the propagation. We also introduce the influence of the initial input power, the chirp factor and the stochastic type perturbations for the CRPGV beams during the propagation. Furthermore, the dynamics of the optical bottle and the breathers-like structures are explored in detail.

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

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2019 (3)

2018 (4)

H. X. Xu, Z. Y. Yang, L. C. Zhao, L. Duan, and W. L. Yang, “Breathers and solitons on two different backgrounds in a generalized coupled Hirota system with four wave mixing,” Phys. Lett. A 382(26), 1738–1744 (2018).
[Crossref]

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

X. Chen, J. Zhuang, D. Li, L. Zhang, X. Peng, F. Zhao, X. Yang, H. Liu, and D. Deng, “Spatiotemporal rapidly autofocused ring Pearcey Gaussian vortex wavepackets,” J. Opt. 20(7), 075607 (2018).
[Crossref]

X. Chen, D. Deng, J. Zhuang, X. Yang, H. Liu, and G. Wang, “Nonparaxial propagation of abruptly autofocusing circular pearcey gaussian beams,” Appl. Opt. 57(28), 8418–8423 (2018).
[Crossref]

2017 (1)

L. Medina, “On the existence of optical vortex solitons propagating in saturable nonlinear media,” J. Math. Phys. 58(1), 011505 (2017).
[Crossref]

2016 (3)

Y. Peng, C. Chen, B. Chen, X. Peng, M. Zhou, L. Zhang, D. Li, and D. Deng, “Propagation of a Pearcey-Gaussian-vortex beam in free space and Kerr media,” Laser Phys. 26(12), 125401 (2016).
[Crossref]

C. Chen, X. Peng, B. Chen, Y. Peng, M. Zhou, X. Yang, and D. Deng, “Propagation of an Airy-Gaussian vortex beam in linear and nonlinear media,” J. Opt. 18(5), 055505 (2016).
[Crossref]

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18(5), 055504 (2016).
[Crossref]

2015 (4)

C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17(3), 035504 (2015).
[Crossref]

P. M. Lushnikov and N. Vladimirova, “Modeling of nonlinear combining of multiple laser beams in Kerr medium,” Opt. Express 23(24), 31120–31125 (2015).
[Crossref]

A. A. Kovalev, V. V. Kotlyar, S. G. Zaskanov, and A. P. Porfirev, “Half Pearcey laser beams,” J. Opt. 17(3), 035604 (2015).
[Crossref]

Z. Ren, C. Ying, H. Jin, and B. Chen, “Generation of a family of Pearcey beams based on Fresnel diffraction catastrophes,” J. Opt. 17(10), 105608 (2015).
[Crossref]

2014 (2)

D. Deng, C. Chen, X. Zhao, B. Chen, X. Peng, and Y. Zheng, “Virtual source of a Pearcey beam,” Opt. Lett. 39(9), 2703–2706 (2014).
[Crossref]

G. Yang, Y. Wang, Z. Qin, B. A. Malomed, D. Mihalache, and L. Li, “Breatherlike solitons extracted from the Peregrine rogue beam,” Phys. Rev. E 90(6), 062909 (2014).
[Crossref]

2012 (2)

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

A. V. Ustinov and S. N. Khonina, “Calculating the complex transmission function of refractive axicons,” Opt. Mem. Neural Networks 21(3), 133–144 (2012).
[Crossref]

2011 (3)

2010 (1)

2008 (1)

2007 (1)

A. Biswa, H. Ren, and S. Konar, “Stochastic perturbation of non-kerr law optical solitons,” Optik 118(10), 471–480 (2007).
[Crossref]

2006 (2)

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73(1), 016608 (2006).
[Crossref]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. Fibich, G. W. Hooft, and E. R. Eliel, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref]

2005 (2)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

S. Medhekar and R. K. Sarkar, “All-optical passive transistor,” Opt. Lett. 30(8), 887–889 (2005).
[Crossref]

2001 (2)

2000 (4)

1999 (1)

D. Kaminski and R. B. Paris, “On the zeroes of the Pearcey integral,” J. Comput. Appl. Math. 107(1), 31–52 (1999).
[Crossref]

1998 (1)

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Multimode Incoherent Spatial Solitons in Logarithmically Saturable Nonlinear Media,” Phys. Rev. Lett. 80(11), 2310–2313 (1998).
[Crossref]

1997 (1)

1990 (1)

1974 (1)

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, “Relationship of self-focusing to spatial instability modes,” Appl. Phys. Lett. 24(4), 178–180 (1974).
[Crossref]

1946 (1)

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

Abdollahpour, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84(2), 021807 (2011).
[Crossref]

Afanasjev, V. V.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th edn. (Academic, 2007).

Aitchison, J. S.

Arlt, J.

Berry, M. V.

C. J. Howls and M. V. Berry, Integrals with Coalescing Saddles (Cambridge University, 2010).

Bigelow, N. P.

Biswa, A.

A. Biswa, H. Ren, and S. Konar, “Stochastic perturbation of non-kerr law optical solitons,” Optik 118(10), 471–480 (2007).
[Crossref]

Bryant, P.

Burvall, A.

A. Burvall, Axicon imaging by scalar diffraction theory (Microelectronics and Information Technology, 2004).

Campillo, A. J.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, “Relationship of self-focusing to spatial instability modes,” Appl. Phys. Lett. 24(4), 178–180 (1974).
[Crossref]

Chen, B.

Y. Peng, C. Chen, B. Chen, X. Peng, M. Zhou, L. Zhang, D. Li, and D. Deng, “Propagation of a Pearcey-Gaussian-vortex beam in free space and Kerr media,” Laser Phys. 26(12), 125401 (2016).
[Crossref]

C. Chen, X. Peng, B. Chen, Y. Peng, M. Zhou, X. Yang, and D. Deng, “Propagation of an Airy-Gaussian vortex beam in linear and nonlinear media,” J. Opt. 18(5), 055505 (2016).
[Crossref]

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18(5), 055504 (2016).
[Crossref]

Z. Ren, C. Ying, H. Jin, and B. Chen, “Generation of a family of Pearcey beams based on Fresnel diffraction catastrophes,” J. Opt. 17(10), 105608 (2015).
[Crossref]

C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17(3), 035504 (2015).
[Crossref]

D. Deng, C. Chen, X. Zhao, B. Chen, X. Peng, and Y. Zheng, “Virtual source of a Pearcey beam,” Opt. Lett. 39(9), 2703–2706 (2014).
[Crossref]

Chen, C.

Y. Peng, C. Chen, B. Chen, X. Peng, M. Zhou, L. Zhang, D. Li, and D. Deng, “Propagation of a Pearcey-Gaussian-vortex beam in free space and Kerr media,” Laser Phys. 26(12), 125401 (2016).
[Crossref]

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18(5), 055504 (2016).
[Crossref]

C. Chen, X. Peng, B. Chen, Y. Peng, M. Zhou, X. Yang, and D. Deng, “Propagation of an Airy-Gaussian vortex beam in linear and nonlinear media,” J. Opt. 18(5), 055505 (2016).
[Crossref]

C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17(3), 035504 (2015).
[Crossref]

D. Deng, C. Chen, X. Zhao, B. Chen, X. Peng, and Y. Zheng, “Virtual source of a Pearcey beam,” Opt. Lett. 39(9), 2703–2706 (2014).
[Crossref]

Chen, X.

Chen, Z.

Chremmos, I.

Christodoulides, D. N.

Chu, P. L.

Coskun, T. H.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Multimode Incoherent Spatial Solitons in Logarithmically Saturable Nonlinear Media,” Phys. Rev. Lett. 80(11), 2310–2313 (1998).
[Crossref]

Couairon, A.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84(2), 021807 (2011).
[Crossref]

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73(1), 016608 (2006).
[Crossref]

Deng, D.

L. Zhang, D. Deng, X. Yang, G. Wang, and H. Liu, “Effects of the modulated vortex and second-order chirp on the propagation dynamics of ring Pearcey Gaussian beams,” Opt. Lett. 44(19), 4654–4657 (2019).
[Crossref]

X. Chen, D. Deng, X. Yang, G. Wang, and H. Liu, “Abruptly autofocused and rotated circular chirp pearcey gaussian vortex beams,” Opt. Lett. 44(4), 955–958 (2019).
[Crossref]

L. Zhang, X. Chen, D. Deng, X. Yang, G. Wang, and H. Liu, “Dynamics of breathers-like circular Pearcey Gaussian waves in a Kerr medium,” Opt. Express 27(13), 17482–17492 (2019).
[Crossref]

X. Chen, D. Deng, J. Zhuang, X. Yang, H. Liu, and G. Wang, “Nonparaxial propagation of abruptly autofocusing circular pearcey gaussian beams,” Appl. Opt. 57(28), 8418–8423 (2018).
[Crossref]

X. Chen, J. Zhuang, D. Li, L. Zhang, X. Peng, F. Zhao, X. Yang, H. Liu, and D. Deng, “Spatiotemporal rapidly autofocused ring Pearcey Gaussian vortex wavepackets,” J. Opt. 20(7), 075607 (2018).
[Crossref]

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

Y. Peng, C. Chen, B. Chen, X. Peng, M. Zhou, L. Zhang, D. Li, and D. Deng, “Propagation of a Pearcey-Gaussian-vortex beam in free space and Kerr media,” Laser Phys. 26(12), 125401 (2016).
[Crossref]

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18(5), 055504 (2016).
[Crossref]

C. Chen, X. Peng, B. Chen, Y. Peng, M. Zhou, X. Yang, and D. Deng, “Propagation of an Airy-Gaussian vortex beam in linear and nonlinear media,” J. Opt. 18(5), 055505 (2016).
[Crossref]

C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17(3), 035504 (2015).
[Crossref]

D. Deng, C. Chen, X. Zhao, B. Chen, X. Peng, and Y. Zheng, “Virtual source of a Pearcey beam,” Opt. Lett. 39(9), 2703–2706 (2014).
[Crossref]

Dennis, M. R.

Dholakia, K.

Duan, L.

H. X. Xu, Z. Y. Yang, L. C. Zhao, L. Duan, and W. L. Yang, “Breathers and solitons on two different backgrounds in a generalized coupled Hirota system with four wave mixing,” Phys. Lett. A 382(26), 1738–1744 (2018).
[Crossref]

Dubietis, A.

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73(1), 016608 (2006).
[Crossref]

Efremidis, N. K.

Ejnisman, R.

Eliel, E. R.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. Fibich, G. W. Hooft, and E. R. Eliel, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref]

Faccio, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84(2), 021807 (2011).
[Crossref]

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73(1), 016608 (2006).
[Crossref]

Fibich, G.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. Fibich, G. W. Hooft, and E. R. Eliel, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref]

G. Fibich and A. L. Gaeta, “Critical Power for Self-Focusing in Bulk Media and in Hollow Waveguides,” Opt. Lett. 25(5), 335–337 (2000).
[Crossref]

Gaeta, A. L.

Gaižauskas, E.

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73(1), 016608 (2006).
[Crossref]

Grow, T. D.

A. A. Ishaaya, L. T. Vuong, T. D. Grow, and A. L. Gaeta, “Self-focusing dynamics of polarization vortices in Kerr media,” Opt. Lett. 33(1), 13–15 (2008).
[Crossref]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. Fibich, G. W. Hooft, and E. R. Eliel, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref]

Guo, H.

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18(5), 055504 (2016).
[Crossref]

Hooft, G. W.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. Fibich, G. W. Hooft, and E. R. Eliel, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref]

Howls, C. J.

C. J. Howls and M. V. Berry, Integrals with Coalescing Saddles (Cambridge University, 2010).

Ishaaya, A.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. Fibich, G. W. Hooft, and E. R. Eliel, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref]

Ishaaya, A. A.

Jackel, J. L.

Jin, H.

Z. Ren, C. Ying, H. Jin, and B. Chen, “Generation of a family of Pearcey beams based on Fresnel diffraction catastrophes,” J. Opt. 17(10), 105608 (2015).
[Crossref]

Kaminski, D.

D. Kaminski and R. B. Paris, “On the zeroes of the Pearcey integral,” J. Comput. Appl. Math. 107(1), 31–52 (1999).
[Crossref]

Khonina, S. N.

A. V. Ustinov and S. N. Khonina, “Calculating the complex transmission function of refractive axicons,” Opt. Mem. Neural Networks 21(3), 133–144 (2012).
[Crossref]

Kivshar, Y. S.

Konar, S.

A. Biswa, H. Ren, and S. Konar, “Stochastic perturbation of non-kerr law optical solitons,” Optik 118(10), 471–480 (2007).
[Crossref]

Kotlyar, V. V.

A. A. Kovalev, V. V. Kotlyar, S. G. Zaskanov, and A. P. Porfirev, “Half Pearcey laser beams,” J. Opt. 17(3), 035604 (2015).
[Crossref]

Kovalev, A. A.

A. A. Kovalev, V. V. Kotlyar, S. G. Zaskanov, and A. P. Porfirev, “Half Pearcey laser beams,” J. Opt. 17(3), 035604 (2015).
[Crossref]

Leaird, D. E.

Lee, S.

Li, D.

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

X. Chen, J. Zhuang, D. Li, L. Zhang, X. Peng, F. Zhao, X. Yang, H. Liu, and D. Deng, “Spatiotemporal rapidly autofocused ring Pearcey Gaussian vortex wavepackets,” J. Opt. 20(7), 075607 (2018).
[Crossref]

Y. Peng, C. Chen, B. Chen, X. Peng, M. Zhou, L. Zhang, D. Li, and D. Deng, “Propagation of a Pearcey-Gaussian-vortex beam in free space and Kerr media,” Laser Phys. 26(12), 125401 (2016).
[Crossref]

Li, L.

G. Yang, Y. Wang, Z. Qin, B. A. Malomed, D. Mihalache, and L. Li, “Breatherlike solitons extracted from the Peregrine rogue beam,” Phys. Rev. E 90(6), 062909 (2014).
[Crossref]

Lindberg, J.

Liu, H.

Lotti, A.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84(2), 021807 (2011).
[Crossref]

Lushnikov, P. M.

MacDonald, M. P.

Malomed, B. A.

G. Yang, Y. Wang, Z. Qin, B. A. Malomed, D. Mihalache, and L. Li, “Breatherlike solitons extracted from the Peregrine rogue beam,” Phys. Rev. E 90(6), 062909 (2014).
[Crossref]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

Mazliu, M.

Medhekar, S.

Medina, L.

L. Medina, “On the existence of optical vortex solitons propagating in saturable nonlinear media,” J. Math. Phys. 58(1), 011505 (2017).
[Crossref]

Mihalache, D.

G. Yang, Y. Wang, Z. Qin, B. A. Malomed, D. Mihalache, and L. Li, “Breatherlike solitons extracted from the Peregrine rogue beam,” Phys. Rev. E 90(6), 062909 (2014).
[Crossref]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

Mitchell, M.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Multimode Incoherent Spatial Solitons in Logarithmically Saturable Nonlinear Media,” Phys. Rev. Lett. 80(11), 2310–2313 (1998).
[Crossref]

Mourka, A.

Oliver, M. K.

Ozeri, R.

Padgett, M. J.

Panagiotopoulos, P.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84(2), 021807 (2011).
[Crossref]

Papazoglou, D. G.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84(2), 021807 (2011).
[Crossref]

Paris, R. B.

D. Kaminski and R. B. Paris, “On the zeroes of the Pearcey integral,” J. Comput. Appl. Math. 107(1), 31–52 (1999).
[Crossref]

Paterson, L.

Pearcey, T.

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

Peng, X.

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

X. Chen, J. Zhuang, D. Li, L. Zhang, X. Peng, F. Zhao, X. Yang, H. Liu, and D. Deng, “Spatiotemporal rapidly autofocused ring Pearcey Gaussian vortex wavepackets,” J. Opt. 20(7), 075607 (2018).
[Crossref]

Y. Peng, C. Chen, B. Chen, X. Peng, M. Zhou, L. Zhang, D. Li, and D. Deng, “Propagation of a Pearcey-Gaussian-vortex beam in free space and Kerr media,” Laser Phys. 26(12), 125401 (2016).
[Crossref]

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18(5), 055504 (2016).
[Crossref]

C. Chen, X. Peng, B. Chen, Y. Peng, M. Zhou, X. Yang, and D. Deng, “Propagation of an Airy-Gaussian vortex beam in linear and nonlinear media,” J. Opt. 18(5), 055505 (2016).
[Crossref]

C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17(3), 035504 (2015).
[Crossref]

D. Deng, C. Chen, X. Zhao, B. Chen, X. Peng, and Y. Zheng, “Virtual source of a Pearcey beam,” Opt. Lett. 39(9), 2703–2706 (2014).
[Crossref]

Peng, Y.

Y. Peng, C. Chen, B. Chen, X. Peng, M. Zhou, L. Zhang, D. Li, and D. Deng, “Propagation of a Pearcey-Gaussian-vortex beam in free space and Kerr media,” Laser Phys. 26(12), 125401 (2016).
[Crossref]

C. Chen, X. Peng, B. Chen, Y. Peng, M. Zhou, X. Yang, and D. Deng, “Propagation of an Airy-Gaussian vortex beam in linear and nonlinear media,” J. Opt. 18(5), 055505 (2016).
[Crossref]

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18(5), 055504 (2016).
[Crossref]

Porfirev, A. P.

A. A. Kovalev, V. V. Kotlyar, S. G. Zaskanov, and A. P. Porfirev, “Half Pearcey laser beams,” J. Opt. 17(3), 035604 (2015).
[Crossref]

Prakash, J.

Qin, Z.

G. Yang, Y. Wang, Z. Qin, B. A. Malomed, D. Mihalache, and L. Li, “Breatherlike solitons extracted from the Peregrine rogue beam,” Phys. Rev. E 90(6), 062909 (2014).
[Crossref]

Rahman, A.

Ren, H.

A. Biswa, H. Ren, and S. Konar, “Stochastic perturbation of non-kerr law optical solitons,” Optik 118(10), 471–480 (2007).
[Crossref]

Ren, Z.

Z. Ren, C. Ying, H. Jin, and B. Chen, “Generation of a family of Pearcey beams based on Fresnel diffraction catastrophes,” J. Opt. 17(10), 105608 (2015).
[Crossref]

Ring, J. D.

Rudy, P.

Sarkar, R. K.

Segev, M.

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Multimode Incoherent Spatial Solitons in Logarithmically Saturable Nonlinear Media,” Phys. Rev. Lett. 80(11), 2310–2313 (1998).
[Crossref]

Shapiro, S. L.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, “Relationship of self-focusing to spatial instability modes,” Appl. Phys. Lett. 24(4), 178–180 (1974).
[Crossref]

Sibbett, W.

Silberberg, Y.

Smith, P. W. E.

Suydam, B. R.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, “Relationship of self-focusing to spatial instability modes,” Appl. Phys. Lett. 24(4), 178–180 (1974).
[Crossref]

Torner, L.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

Trapani, P. D.

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73(1), 016608 (2006).
[Crossref]

Tzortzakis, S.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84(2), 021807 (2011).
[Crossref]

Ustinov, A. V.

A. V. Ustinov and S. N. Khonina, “Calculating the complex transmission function of refractive axicons,” Opt. Mem. Neural Networks 21(3), 133–144 (2012).
[Crossref]

Vladimirova, N.

Vogel, E. M.

Vuong, L. T.

A. A. Ishaaya, L. T. Vuong, T. D. Grow, and A. L. Gaeta, “Self-focusing dynamics of polarization vortices in Kerr media,” Opt. Lett. 33(1), 13–15 (2008).
[Crossref]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. Fibich, G. W. Hooft, and E. R. Eliel, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref]

Wang, G.

Wang, Y.

G. Yang, Y. Wang, Z. Qin, B. A. Malomed, D. Mihalache, and L. Li, “Breatherlike solitons extracted from the Peregrine rogue beam,” Phys. Rev. E 90(6), 062909 (2014).
[Crossref]

Weiner, A. M.

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

Xu, H. X.

H. X. Xu, Z. Y. Yang, L. C. Zhao, L. Duan, and W. L. Yang, “Breathers and solitons on two different backgrounds in a generalized coupled Hirota system with four wave mixing,” Phys. Lett. A 382(26), 1738–1744 (2018).
[Crossref]

Yang, G.

G. Yang, Y. Wang, Z. Qin, B. A. Malomed, D. Mihalache, and L. Li, “Breatherlike solitons extracted from the Peregrine rogue beam,” Phys. Rev. E 90(6), 062909 (2014).
[Crossref]

Yang, W. L.

H. X. Xu, Z. Y. Yang, L. C. Zhao, L. Duan, and W. L. Yang, “Breathers and solitons on two different backgrounds in a generalized coupled Hirota system with four wave mixing,” Phys. Lett. A 382(26), 1738–1744 (2018).
[Crossref]

Yang, X.

Yang, Z. Y.

H. X. Xu, Z. Y. Yang, L. C. Zhao, L. Duan, and W. L. Yang, “Breathers and solitons on two different backgrounds in a generalized coupled Hirota system with four wave mixing,” Phys. Lett. A 382(26), 1738–1744 (2018).
[Crossref]

Ying, C.

Z. Ren, C. Ying, H. Jin, and B. Chen, “Generation of a family of Pearcey beams based on Fresnel diffraction catastrophes,” J. Opt. 17(10), 105608 (2015).
[Crossref]

Zaskanov, S. G.

A. A. Kovalev, V. V. Kotlyar, S. G. Zaskanov, and A. P. Porfirev, “Half Pearcey laser beams,” J. Opt. 17(3), 035604 (2015).
[Crossref]

Zhang, L.

Zhang, P.

Zhao, F.

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

X. Chen, J. Zhuang, D. Li, L. Zhang, X. Peng, F. Zhao, X. Yang, H. Liu, and D. Deng, “Spatiotemporal rapidly autofocused ring Pearcey Gaussian vortex wavepackets,” J. Opt. 20(7), 075607 (2018).
[Crossref]

Zhao, L. C.

H. X. Xu, Z. Y. Yang, L. C. Zhao, L. Duan, and W. L. Yang, “Breathers and solitons on two different backgrounds in a generalized coupled Hirota system with four wave mixing,” Phys. Lett. A 382(26), 1738–1744 (2018).
[Crossref]

Zhao, X.

Zheng, Y.

Zhou, M.

Y. Peng, C. Chen, B. Chen, X. Peng, M. Zhou, L. Zhang, D. Li, and D. Deng, “Propagation of a Pearcey-Gaussian-vortex beam in free space and Kerr media,” Laser Phys. 26(12), 125401 (2016).
[Crossref]

C. Chen, X. Peng, B. Chen, Y. Peng, M. Zhou, X. Yang, and D. Deng, “Propagation of an Airy-Gaussian vortex beam in linear and nonlinear media,” J. Opt. 18(5), 055505 (2016).
[Crossref]

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18(5), 055504 (2016).
[Crossref]

Zhuang, J.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, “Relationship of self-focusing to spatial instability modes,” Appl. Phys. Lett. 24(4), 178–180 (1974).
[Crossref]

J. Comput. Appl. Math. (1)

D. Kaminski and R. B. Paris, “On the zeroes of the Pearcey integral,” J. Comput. Appl. Math. 107(1), 31–52 (1999).
[Crossref]

J. Math. Phys. (1)

L. Medina, “On the existence of optical vortex solitons propagating in saturable nonlinear media,” J. Math. Phys. 58(1), 011505 (2017).
[Crossref]

J. Opt. (6)

C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17(3), 035504 (2015).
[Crossref]

C. Chen, X. Peng, B. Chen, Y. Peng, M. Zhou, X. Yang, and D. Deng, “Propagation of an Airy-Gaussian vortex beam in linear and nonlinear media,” J. Opt. 18(5), 055505 (2016).
[Crossref]

Z. Ren, C. Ying, H. Jin, and B. Chen, “Generation of a family of Pearcey beams based on Fresnel diffraction catastrophes,” J. Opt. 17(10), 105608 (2015).
[Crossref]

A. A. Kovalev, V. V. Kotlyar, S. G. Zaskanov, and A. P. Porfirev, “Half Pearcey laser beams,” J. Opt. 17(3), 035604 (2015).
[Crossref]

X. Chen, J. Zhuang, D. Li, L. Zhang, X. Peng, F. Zhao, X. Yang, H. Liu, and D. Deng, “Spatiotemporal rapidly autofocused ring Pearcey Gaussian vortex wavepackets,” J. Opt. 20(7), 075607 (2018).
[Crossref]

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, D. Deng, and H. Guo, “Evolution of the ring Airy Gaussian beams with a spiral phase in the Kerr medium,” J. Opt. 18(5), 055504 (2016).
[Crossref]

J. Opt. B: Quantum Semiclassical Opt. (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

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

Laser Phys. (1)

Y. Peng, C. Chen, B. Chen, X. Peng, M. Zhou, L. Zhang, D. Li, and D. Deng, “Propagation of a Pearcey-Gaussian-vortex beam in free space and Kerr media,” Laser Phys. 26(12), 125401 (2016).
[Crossref]

Opt. Express (4)

Opt. Lett. (15)

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

S. Medhekar and R. K. Sarkar, “All-optical passive transistor,” Opt. Lett. 30(8), 887–889 (2005).
[Crossref]

J. Arlt and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25(4), 191–193 (2000).
[Crossref]

J. Arlt and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25(4), 191–193 (2000).
[Crossref]

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

J. S. Aitchison, Y. Silberberg, A. M. Weiner, D. E. Leaird, M. K. Oliver, J. L. Jackel, E. M. Vogel, and P. W. E. Smith, “Observation of spatial optical solitons in a nonlinear glass waveguide,” Opt. Lett. 15(9), 471–473 (1990).
[Crossref]

M. P. MacDonald, L. Paterson, W. Sibbett, P. Bryant, and K. Dholakia, “Trapping and manipulation of low-index particles in a two-dimensional interferometric optical trap,” Opt. Lett. 26(12), 863–865 (2001).
[Crossref]

A. A. Ishaaya, L. T. Vuong, T. D. Grow, and A. L. Gaeta, “Self-focusing dynamics of polarization vortices in Kerr media,” Opt. Lett. 33(1), 13–15 (2008).
[Crossref]

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

D. Deng, C. Chen, X. Zhao, B. Chen, X. Peng, and Y. Zheng, “Virtual source of a Pearcey beam,” Opt. Lett. 39(9), 2703–2706 (2014).
[Crossref]

L. Zhang, D. Deng, X. Yang, G. Wang, and H. Liu, “Effects of the modulated vortex and second-order chirp on the propagation dynamics of ring Pearcey Gaussian beams,” Opt. Lett. 44(19), 4654–4657 (2019).
[Crossref]

V. V. Afanasjev, P. L. Chu, and Y. S. Kivshar, “Breathing spatial solitons in non-Kerr media,” Opt. Lett. 22(18), 1388–1390 (1997).
[Crossref]

G. Fibich and A. L. Gaeta, “Critical Power for Self-Focusing in Bulk Media and in Hollow Waveguides,” Opt. Lett. 25(5), 335–337 (2000).
[Crossref]

X. Chen, D. Deng, X. Yang, G. Wang, and H. Liu, “Abruptly autofocused and rotated circular chirp pearcey gaussian vortex beams,” Opt. Lett. 44(4), 955–958 (2019).
[Crossref]

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]

Opt. Mem. Neural Networks (1)

A. V. Ustinov and S. N. Khonina, “Calculating the complex transmission function of refractive axicons,” Opt. Mem. Neural Networks 21(3), 133–144 (2012).
[Crossref]

Optik (1)

A. Biswa, H. Ren, and S. Konar, “Stochastic perturbation of non-kerr law optical solitons,” Optik 118(10), 471–480 (2007).
[Crossref]

Phil. Mag. (1)

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

Phys. Lett. A (1)

H. X. Xu, Z. Y. Yang, L. C. Zhao, L. Duan, and W. L. Yang, “Breathers and solitons on two different backgrounds in a generalized coupled Hirota system with four wave mixing,” Phys. Lett. A 382(26), 1738–1744 (2018).
[Crossref]

Phys. Rev. A (1)

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84(2), 021807 (2011).
[Crossref]

Phys. Rev. E (2)

A. Couairon, E. Gaižauskas, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear X-wave formation by femtosecond filamentation in Kerr media,” Phys. Rev. E 73(1), 016608 (2006).
[Crossref]

G. Yang, Y. Wang, Z. Qin, B. A. Malomed, D. Mihalache, and L. Li, “Breatherlike solitons extracted from the Peregrine rogue beam,” Phys. Rev. E 90(6), 062909 (2014).
[Crossref]

Phys. Rev. Lett. (2)

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, “Multimode Incoherent Spatial Solitons in Logarithmically Saturable Nonlinear Media,” Phys. Rev. Lett. 80(11), 2310–2313 (1998).
[Crossref]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. Fibich, G. W. Hooft, and E. R. Eliel, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref]

Other (3)

C. J. Howls and M. V. Berry, Integrals with Coalescing Saddles (Cambridge University, 2010).

G. P. Agrawal, Nonlinear Fiber Optics, 4th edn. (Academic, 2007).

A. Burvall, Axicon imaging by scalar diffraction theory (Microelectronics and Information Technology, 2004).

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Figures (5)

Fig. 1.
Fig. 1. (a): The initial intensity distribution of the Pearcey beam; (a1)-(a4),(b) and (c): the initial intensity distribution of the CRPGV beams; (b1) and (c1): the propagation process of the CRPGV beams in the nonlinear medium within $Z=0.2$ ; (b2)-(b3) and (c2)-(c3): the intensity distributions of the CRPGV beams at various locations [as the dotted lines in (b1) and (c1)]. The parameters are chosen as $\chi =1,c=0$ in (a1), $\chi =0,c=0$ in (a2), $\chi =-1,c=0$ in (a3), $\chi$ doesn’t exist, $c_2$ =0 in (a4), $\chi$ doesn’t exist, $c_2$ =−2 in (c), (b) corresponding to the cusp function integral, and other parameters, $P_{in}=20.1P_{cr}, m=n=0, R=0.$
Fig. 2.
Fig. 2. (a), (b): The optical transmission diagrams of the CRPGV beams relating two cases functions within $Z=0.1$ . (a0), (b0) the normalized intensity diagrams; (a1)-(a3) and (b1)-(b3): the intensity distributions of the CRPGV beams at normalized propagation distances; other parameters as follows, $m=n=0, \beta _1=5, \beta _2=0, R=0.$
Fig. 3.
Fig. 3. (a), (b): Optical transmission diagrams with different initial input power of the CRPGV beam in the nonlinear medium within $Z=0.08$ . (a0), (b0): the three-dimensional normalized intensity; (a1)-(a3) and (b1)-(b3): the transverse intensity distributions of the CRPGV beams at $Z=0.01, 0.015, 0.022$ ; other parameters as follows, $c=0, \chi$ doesn’t exist, $\beta _1=1, \beta _2=-35, m=n=1, r_s=0.5, R=0$ .
Fig. 4.
Fig. 4. (a1)-(c1): The propagation progress of the CRPGV beam for $P_{in}=10.5P_{cr}$ in the Kerr medium with different chirp factors $\beta _1,\beta _2$ ; (a2)-(c2): the three-dimensional transverse distributions; (d) the relationship presentation between the normalized distance of two intensity peaks and $\beta _1$ , $\beta _2$ ; the other parameters as follows, $c=0, \chi$ doesn’t exist, $m=n=1, r_s=0.5, R=0$ .
Fig. 5.
Fig. 5. (a), (b): Initial intensity distributions of the CRPGV beam with different $R$ ; (a), (b): optical transmission progress; (a2), (b2): the normalized intensity diagrams; other parameters as follows, $P_{in}=10.5P_{cr}$ , $c=0, \chi$ doesn’t exist, $\beta _1=1, \beta _2=-35, m=n=1, r_s=0.5$ .

Equations (5)

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Ψ 0 ( r , θ , 0 ) = A 0 P e ( r / p , χ r / p + c ) exp ( α 2 r 2 + i β 1 r + i β 2 r 2 ) ( r e i θ + r s e i φ ) m ( r e i θ r s e i φ ) n ,
P e ( r / p , χ r / p + c ) = exp [ i ( s 4 + ( χ r / p + c ) s 2 + r s / p ) ] d s .
2 i Ψ Z + 2 Ψ X 2 + 2 Ψ Y 2 + 2 n 2 n 0 σ 2 Ψ 2 Ψ = 0 ,
2 i Ψ Z + 2 Ψ r 2 + r 1 Ψ r + r 2 2 Ψ θ 2 + 2 n 2 n 0 σ 2 Ψ 2 Ψ = 0.
P i n = n 2 k 2 2 π n 0 0 2 π 0 P c r | u ( r , θ , 0 ) | 2 r d r d θ .

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