Abstract

We introduce the propagation properties of the circular Pearcey Gaussian (CPG) waves in Kerr medium for the first time. The breathers-like structure and breathers-like groups structure (filamentions) of CPG waves will form due to the interaction between the linear waves and the nonlinear medium. The focusing characteristics in Kerr medium can be adjusted by the deviation factor and the initial input power of the CPG waves. By choosing appropriate input power, the imaginary part of the CPG waves can split into some wavelets during the propagation. It is worth noting that the distinctive stepwise focusing of the imaginary part of the CPG waves which can be applied to wave modulation. Furthermore, the numerical experiment results show good agreement with the numerical simulation results.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (4)

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

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), 8418–8422 (2018).
[Crossref] [PubMed]

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, 075607 (2018).
[Crossref]

L. Medina, “On the existence of optical vortex solitons propagating in saturable nonlinear media,” J. Math. Phys. 58(1), 011505 (2018).
[Crossref]

2017 (2)

V. Gorder and A. Robert, “Breathers and nonlinear waves on open vortex filaments in the nonrelativistic Abelian Higgs model,” Phys. Rev. D 95(9), 096007 (2017).
[Crossref]

M. Chen, S. Huang, W. Shao, and X. Liu, “Experimental study on the propagation characteristics of ring Airy Gaussian vortex beams,” Appl. Phys. B 123(8), 215 (2017).
[Crossref]

2016 (4)

L Wang, S. Li, and F. Qi, “Breather-to-soliton and rogue wave-to-soliton transitions in a resonant erbium-doped fiber system with higher-order effects,” Nonlinear Dynam. 85(1), 389–398 (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]

Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (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]

2015 (2)

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

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

2014 (1)

2013 (2)

D. Deng, Y. Gao, J. Zhao, P. Zhang, and Z. Chen, “Three-dimensional nonparaxial beams in parabolic rotational coordinates,” Opt. Lett. 38(19), 3934–3936 (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]

2012 (1)

2011 (6)

2010 (1)

2006 (1)

T. L. Vuong, T. D. Grow, A. Ishaaya, and A. L. Gaeta, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref] [PubMed]

2005 (1)

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium (with Erratum),” Phys. Rev. A 71(16), 362–368 (2005).
[Crossref]

2002 (2)

V. Garcés-hávez, D. Mcgloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

T. Juhasz, F. Loesel, R. Kurtz, C. Horvath, J. Bille, and G. Mourou, “Corneal refractive surgery with femtosecond lasers,” IEEE J. Sel. Top. Quantum Electron. 5(4), 902–910 (2002).
[Crossref]

2000 (3)

1998 (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]

M. Segev, “Optical spatial solitons,” Opt. Quant. Electron 30(7–10), 503–533 (1998).
[Crossref]

1996 (1)

1990 (2)

1985 (1)

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32(4), 2287–2292 (1985).
[Crossref]

1980 (2)

P. D. Drummond and D. F. Walls, “Quantum theory of optical bistability. I. Nonlinear polarisability model,” J. Phys. A 13, 725 (1980).
[Crossref]

C. Flytzanis and C. L. Tang, “Light-Induced Critical Behavior in the Four-Wave Interaction in Nonlinear Systems,” Phys. Rev. Lett. 45(6), 441–445 (1980).
[Crossref]

1975 (1)

J. H. Marburger, “Self-focusing: Theory,” Prog. Quan. Electron. 4(1), 35–110 (1975).
[Crossref]

1946 (1)

T. Pearcey, “The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic,” Phil. Mag. Philos. 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]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th edn. (Academic2007).

Aitchison, J. S.

Berry, M. V.

M. V. Berry and C. J. Howls, Integrals with Coalescing Saddles (Cambridge University2012).

Bille, J.

T. Juhasz, F. Loesel, R. Kurtz, C. Horvath, J. Bille, and G. Mourou, “Corneal refractive surgery with femtosecond lasers,” IEEE J. Sel. Top. Quantum Electron. 5(4), 902–910 (2002).
[Crossref]

Centurion, M.

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium (with Erratum),” Phys. Rev. A 71(16), 362–368 (2005).
[Crossref]

Chen, B.

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]

Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (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. J. Ren, C. F. Ying, H. Z. Jin, and B. Chen, “Generation of a family of Pearcey beams based on Fresnel diffraction catastrophes,” J. Opt. 17, 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. M. Deng, C. D. Chen, X. Zhao, B. Chen, and Y. S. Zheng, “Virtual source of a Pearcey beam,” Opt. Lett. 39(9), 2703–2706 (2014).
[Crossref] [PubMed]

Chen, C.

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]

Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (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, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17(3), 035504 (2015).
[Crossref]

Chen, C. D.

Chen, M.

M. Chen, S. Huang, W. Shao, and X. Liu, “Experimental study on the propagation characteristics of ring Airy Gaussian vortex beams,” Appl. Phys. B 123(8), 215 (2017).
[Crossref]

Chen, R. P.

R. P. Chen, H. P. Zheng, and X. X. Chu, “Propagation properties of a sinh-Gaussian beam in a Kerr medium,” Appl. Phys. B 102(3), 695–698 (2011).
[Crossref]

Chen, X.

Chen, Z.

Chremmos, I.

Christodoulides, D.

Christodoulides, D. N.

Chu, X. X.

R. P. Chen, H. P. Zheng, and X. X. Chu, “Propagation properties of a sinh-Gaussian beam in a Kerr medium,” Appl. Phys. B 102(3), 695–698 (2011).
[Crossref]

Cornolti, F.

F. Cornolti, M. Lucchesi, and B. Zambon, “Elliptic gaussian beam self-focusing in nonlinear media,” Opt. Commun. 75(2), 129–135 (1990).
[Crossref]

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]

D. N. Christodoulides and T. H. Coskun, “Self-bouncing optical beams in photorefractive waveguides,” Opt. Lett. 21(16), 1220–1222 (1996).
[Crossref] [PubMed]

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]

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]

Deng, D.

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, 075607 (2018).
[Crossref]

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

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), 8418–8422 (2018).
[Crossref] [PubMed]

Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (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]

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, Y. Gao, J. Zhao, P. Zhang, and Z. Chen, “Three-dimensional nonparaxial beams in parabolic rotational coordinates,” Opt. Lett. 38(19), 3934–3936 (2013).
[Crossref] [PubMed]

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] [PubMed]

V. Garcés-hávez, D. Mcgloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

Drummond, P. D.

P. D. Drummond and D. F. Walls, “Quantum theory of optical bistability. I. Nonlinear polarisability model,” J. Phys. A 13, 725 (1980).
[Crossref]

Efremidis, N.

Efremidis, N. K.

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]

Fibich, G.

Flytzanis, C.

C. Flytzanis and C. L. Tang, “Light-Induced Critical Behavior in the Four-Wave Interaction in Nonlinear Systems,” Phys. Rev. Lett. 45(6), 441–445 (1980).
[Crossref]

Gaeta, A. L.

T. L. Vuong, T. D. Grow, A. Ishaaya, and A. L. Gaeta, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref] [PubMed]

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]

Gao, Y.

Garcés-hávez, V.

V. Garcés-hávez, D. Mcgloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

Gorder, V.

V. Gorder and A. Robert, “Breathers and nonlinear waves on open vortex filaments in the nonrelativistic Abelian Higgs model,” Phys. Rev. D 95(9), 096007 (2017).
[Crossref]

Grow, T. D.

T. L. Vuong, T. D. Grow, A. Ishaaya, and A. L. Gaeta, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref] [PubMed]

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]

Haus, H. A.

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32(4), 2287–2292 (1985).
[Crossref]

Horvath, C.

T. Juhasz, F. Loesel, R. Kurtz, C. Horvath, J. Bille, and G. Mourou, “Corneal refractive surgery with femtosecond lasers,” IEEE J. Sel. Top. Quantum Electron. 5(4), 902–910 (2002).
[Crossref]

Howls, C. J.

M. V. Berry and C. J. Howls, Integrals with Coalescing Saddles (Cambridge University2012).

Huang, S.

M. Chen, S. Huang, W. Shao, and X. Liu, “Experimental study on the propagation characteristics of ring Airy Gaussian vortex beams,” Appl. Phys. B 123(8), 215 (2017).
[Crossref]

Imoto, N.

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32(4), 2287–2292 (1985).
[Crossref]

Ishaaya, A.

T. L. Vuong, T. D. Grow, A. Ishaaya, and A. L. Gaeta, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref] [PubMed]

Jackel, J. L.

Jin, H. Z.

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

Juhasz, T.

T. Juhasz, F. Loesel, R. Kurtz, C. Horvath, J. Bille, and G. Mourou, “Corneal refractive surgery with femtosecond lasers,” IEEE J. Sel. Top. Quantum Electron. 5(4), 902–910 (2002).
[Crossref]

Kaul, S. S.

T. Singh, N. S. Saini, and S. S. Kaul, “Dynamics of self-focusing and self-phase modulation of elliptic Gaussian laser beam in a Kerr-medium,” Pramana J. Phys. 55(3), 423–431 (2000).
[Crossref]

Kurtz, R.

T. Juhasz, F. Loesel, R. Kurtz, C. Horvath, J. Bille, and G. Mourou, “Corneal refractive surgery with femtosecond lasers,” IEEE J. Sel. Top. Quantum Electron. 5(4), 902–910 (2002).
[Crossref]

Leaird, D. E.

Li, D.

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

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, 075607 (2018).
[Crossref]

Li, S.

L Wang, S. Li, and F. Qi, “Breather-to-soliton and rogue wave-to-soliton transitions in a resonant erbium-doped fiber system with higher-order effects,” Nonlinear Dynam. 85(1), 389–398 (2016).
[Crossref]

Li, Y.

Lindberg, J.

Liu, H.

Liu, X.

M. Chen, S. Huang, W. Shao, and X. Liu, “Experimental study on the propagation characteristics of ring Airy Gaussian vortex beams,” Appl. Phys. B 123(8), 215 (2017).
[Crossref]

Loesel, F.

T. Juhasz, F. Loesel, R. Kurtz, C. Horvath, J. Bille, and G. Mourou, “Corneal refractive surgery with femtosecond lasers,” IEEE J. Sel. Top. Quantum Electron. 5(4), 902–910 (2002).
[Crossref]

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]

Lucchesi, M.

F. Cornolti, M. Lucchesi, and B. Zambon, “Elliptic gaussian beam self-focusing in nonlinear media,” Opt. Commun. 75(2), 129–135 (1990).
[Crossref]

Marburger, J. H.

J. H. Marburger, “Self-focusing: Theory,” Prog. Quan. Electron. 4(1), 35–110 (1975).
[Crossref]

Mazilu, M.

Mcgloin, D.

V. Garcés-hávez, D. Mcgloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

Medina, L.

L. Medina, “On the existence of optical vortex solitons propagating in saturable nonlinear media,” J. Math. Phys. 58(1), 011505 (2018).
[Crossref]

Melville, H.

V. Garcés-hávez, D. Mcgloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

Mills, M. S.

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.

Mourou, G.

T. Juhasz, F. Loesel, R. Kurtz, C. Horvath, J. Bille, and G. Mourou, “Corneal refractive surgery with femtosecond lasers,” IEEE J. Sel. Top. Quantum Electron. 5(4), 902–910 (2002).
[Crossref]

Oliver, M. K.

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]

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.

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]

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]

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]

Pearcey, T.

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

Peng, X.

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

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, 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]

Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (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]

Peng, Y.

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]

Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (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]

Prakash, J.

Psaltis, D.

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium (with Erratum),” Phys. Rev. A 71(16), 362–368 (2005).
[Crossref]

Pu, Y.

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium (with Erratum),” Phys. Rev. A 71(16), 362–368 (2005).
[Crossref]

Qi, F.

L Wang, S. Li, and F. Qi, “Breather-to-soliton and rogue wave-to-soliton transitions in a resonant erbium-doped fiber system with higher-order effects,” Nonlinear Dynam. 85(1), 389–398 (2016).
[Crossref]

Ren, Z. J.

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

Ring, J. D.

Robert, A.

V. Gorder and A. Robert, “Breathers and nonlinear waves on open vortex filaments in the nonrelativistic Abelian Higgs model,” Phys. Rev. D 95(9), 096007 (2017).
[Crossref]

Saini, N. S.

T. Singh, N. S. Saini, and S. S. Kaul, “Dynamics of self-focusing and self-phase modulation of elliptic Gaussian laser beam in a Kerr-medium,” Pramana J. Phys. 55(3), 423–431 (2000).
[Crossref]

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]

M. Segev, “Optical spatial solitons,” Opt. Quant. Electron 30(7–10), 503–533 (1998).
[Crossref]

Shao, W.

M. Chen, S. Huang, W. Shao, and X. Liu, “Experimental study on the propagation characteristics of ring Airy Gaussian vortex beams,” Appl. Phys. B 123(8), 215 (2017).
[Crossref]

Sibbett, W.

V. Garcés-hávez, D. Mcgloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

Silberberg, Y.

Singh, T.

T. Singh, N. S. Saini, and S. S. Kaul, “Dynamics of self-focusing and self-phase modulation of elliptic Gaussian laser beam in a Kerr-medium,” Pramana J. Phys. 55(3), 423–431 (2000).
[Crossref]

Smith, P. W E.

Tang, C. L.

C. Flytzanis and C. L. Tang, “Light-Induced Critical Behavior in the Four-Wave Interaction in Nonlinear Systems,” Phys. Rev. Lett. 45(6), 441–445 (1980).
[Crossref]

Tsang, M.

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium (with Erratum),” Phys. Rev. A 71(16), 362–368 (2005).
[Crossref]

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]

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]

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]

Vogel, E. M.

Vuong, T. L.

T. L. Vuong, T. D. Grow, A. Ishaaya, and A. L. Gaeta, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref] [PubMed]

Walls, D. F.

P. D. Drummond and D. F. Walls, “Quantum theory of optical bistability. I. Nonlinear polarisability model,” J. Phys. A 13, 725 (1980).
[Crossref]

Wang, G.

Wang, L

L Wang, S. Li, and F. Qi, “Breather-to-soliton and rogue wave-to-soliton transitions in a resonant erbium-doped fiber system with higher-order effects,” Nonlinear Dynam. 85(1), 389–398 (2016).
[Crossref]

Weiner, A. M.

Yamamoto, Y.

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32(4), 2287–2292 (1985).
[Crossref]

Yang, X.

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, 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), 8418–8422 (2018).
[Crossref] [PubMed]

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

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]

Ying, C. F.

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

Zambon, B.

F. Cornolti, M. Lucchesi, and B. Zambon, “Elliptic gaussian beam self-focusing in nonlinear media,” Opt. Commun. 75(2), 129–135 (1990).
[Crossref]

Zhang, L.

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

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, 075607 (2018).
[Crossref]

Zhang, P.

Zhang, Z.

Zhao, F.

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

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, 075607 (2018).
[Crossref]

Zhao, J.

Zhao, X.

Zheng, H. P.

R. P. Chen, H. P. Zheng, and X. X. Chu, “Propagation properties of a sinh-Gaussian beam in a Kerr medium,” Appl. Phys. B 102(3), 695–698 (2011).
[Crossref]

Zheng, Y. S.

Zhou, M.

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]

Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (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. B (2)

M. Chen, S. Huang, W. Shao, and X. Liu, “Experimental study on the propagation characteristics of ring Airy Gaussian vortex beams,” Appl. Phys. B 123(8), 215 (2017).
[Crossref]

R. P. Chen, H. P. Zheng, and X. X. Chu, “Propagation properties of a sinh-Gaussian beam in a Kerr medium,” Appl. Phys. B 102(3), 695–698 (2011).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

T. Juhasz, F. Loesel, R. Kurtz, C. Horvath, J. Bille, and G. Mourou, “Corneal refractive surgery with femtosecond lasers,” IEEE J. Sel. Top. Quantum Electron. 5(4), 902–910 (2002).
[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 (2018).
[Crossref]

J. Opt. (5)

C. Chen, B. Chen, X. Peng, and D. Deng, “Propagation of Airy-Gaussian beam in Kerr medium,” J. Opt. 17(3), 035504 (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, 075607 (2018).
[Crossref]

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

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

J. Phys. A (1)

P. D. Drummond and D. F. Walls, “Quantum theory of optical bistability. I. Nonlinear polarisability model,” J. Phys. A 13, 725 (1980).
[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]

Nature (1)

V. Garcés-hávez, D. Mcgloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

Nonlinear Dynam. (1)

L Wang, S. Li, and F. Qi, “Breather-to-soliton and rogue wave-to-soliton transitions in a resonant erbium-doped fiber system with higher-order effects,” Nonlinear Dynam. 85(1), 389–398 (2016).
[Crossref]

Opt. Commun. (2)

F. Cornolti, M. Lucchesi, and B. Zambon, “Elliptic gaussian beam self-focusing in nonlinear media,” Opt. Commun. 75(2), 129–135 (1990).
[Crossref]

Y. Peng, X. Peng, B. Chen, M. Zhou, C. Chen, and D. Deng, “Interaction of Airy-Gaussian beams in Kerr media,” Opt. Commun. 359, 116–122 (2016).
[Crossref]

Opt. Express (1)

Opt. Lett. (11)

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

D. N. Christodoulides and T. H. Coskun, “Self-bouncing optical beams in photorefractive waveguides,” Opt. Lett. 21(16), 1220–1222 (1996).
[Crossref] [PubMed]

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

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] [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]

P. Zhang, J. Prakash, Z. Zhang, M. S. Mills, N. Efremidis, D. 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]

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]

D. Deng, Y. Gao, J. Zhao, P. Zhang, and Z. Chen, “Three-dimensional nonparaxial beams in parabolic rotational coordinates,” Opt. Lett. 38(19), 3934–3936 (2013).
[Crossref] [PubMed]

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

Opt. Quant. Electron (1)

M. Segev, “Optical spatial solitons,” Opt. Quant. Electron 30(7–10), 503–533 (1998).
[Crossref]

Phil. Mag. Philos. Mag. (1)

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

Phys. Rev. A (3)

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]

N. Imoto, H. A. Haus, and Y. Yamamoto, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32(4), 2287–2292 (1985).
[Crossref]

M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, “Dynamics of filament formation in a Kerr medium (with Erratum),” Phys. Rev. A 71(16), 362–368 (2005).
[Crossref]

Phys. Rev. D (1)

V. Gorder and A. Robert, “Breathers and nonlinear waves on open vortex filaments in the nonrelativistic Abelian Higgs model,” Phys. Rev. D 95(9), 096007 (2017).
[Crossref]

Phys. Rev. Lett. (3)

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]

C. Flytzanis and C. L. Tang, “Light-Induced Critical Behavior in the Four-Wave Interaction in Nonlinear Systems,” Phys. Rev. Lett. 45(6), 441–445 (1980).
[Crossref]

T. L. Vuong, T. D. Grow, A. Ishaaya, and A. L. Gaeta, “Collapse of Optical Vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref] [PubMed]

Pramana J. Phys. (1)

T. Singh, N. S. Saini, and S. S. Kaul, “Dynamics of self-focusing and self-phase modulation of elliptic Gaussian laser beam in a Kerr-medium,” Pramana J. Phys. 55(3), 423–431 (2000).
[Crossref]

Prog. Quan. Electron. (1)

J. H. Marburger, “Self-focusing: Theory,” Prog. Quan. Electron. 4(1), 35–110 (1975).
[Crossref]

Other (2)

M. V. Berry and C. J. Howls, Integrals with Coalescing Saddles (Cambridge University2012).

G. P. Agrawal, Nonlinear Fiber Optics, 4th edn. (Academic2007).

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Figures (7)

Fig. 1
Fig. 1 The initial intensity distribution of the Pearcey waves (a), the CPG waves of (a1)–(a3) corresponding to u1 rotate a circle along the dotted lines (1):c=0, (2):c=2, (3):c=5; (a4)–(a6) corresponding to u2 rotate a circle along the dotted lines (4):c=0, (5):c=2, (6):c=5, respectively.
Fig. 2
Fig. 2 (a), (b) Optical transmission diagrams with different input power within 10ZR relating to u1. (a1) and (b1) are initial intensity distribution of the CPG waves; (a2)–(a4), (b2)–(b4): Intensity distribution of the CPG waves at normalized propagation distances Z = 2, 3.9, 5.8 (as dotted lines), respectively; Other parameter: c = 0.
Fig. 3
Fig. 3 (a1)–(b1) Initial intensity distribution of the CPG waves of u1 at Z = 0; (c1)–(d1): Initial intensity distribution of the CPG waves of u2 at Z = 0, respectively; (a2)–(b2), (c2)–(d2) Numerical simulated transverse intensity and propagation with different deviation factors c of the CPG waves of the CPG waves of u1 and u2 within 10ZR.
Fig. 4
Fig. 4 Numerical experiments demonstrations of the CPG waves evolution in Kerr medium. The parameters in (a1)–(a5) and (b1)–(b5) are the same as those in Figs. 1(a1) and (a2); The parameters in (c) are the same as those in Fig. 3(a2).
Fig. 5
Fig. 5 (a1) The propagation of the CPG waves (u1) for Pin = 0.7Pcr in Kerr medium within 10ZR, (b1) the real part of the CPG waves, and (c1) the imaginary part of the CPG waves; (a2)–(c2) Intensity distribution of the CPG waves at normalized propagation distance Z = 2 (the dotted line); (b1s) and (c1s) are the enlarged parts of dotted circle of (b1) and (c1); Other parameter: c = 0.
Fig. 6
Fig. 6 The real part (a1), (b1) and imaginary part (c1), (d1) of the CPG waves (u1) transmit in Kerr medium for big input power within 10ZR. (a2)–(d2) Intensity distribution of the CPG waves at normalized propagation distance Z = 6 (the dotted line); Other parameter: c = 0.
Fig. 7
Fig. 7 The CPG waves of u2 transmit in Kerr medium for big input power within 10ZR. (a2)–(d2) Intensity distribution of the CPG waves at normalized propagation distance Z = 6 (the dotted line); Other parameter: c = 0.

Equations (6)

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2 i u Z + 2 u X 2 + 2 u Y 2 + 2 n 2 n 0 σ 2 | u | 2 u = 0 ,
2 i u Z + 2 u r 2 + r 1 u r + r 2 2 u θ 2 + 2 n 2 n 0 σ 2 | u | 2 u = 0 ,
u 1 ( r , θ , 0 ) = A 0 P e ( r , c ) e α 2 r 2 ,
u 2 ( r , θ , 0 ) = A 0 P e ( c , r ) e α 2 r 2 ,
Pe ( c , r ) = exp [ i ( s 4 + cs 2 + rs ) ] ds ,
P in = n 2 k 2 2 π n 0 0 2 π 0 P cr | u ( r , θ , 0 ) | 2 r d r d θ .

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