Abstract

The abruptly autofocusing properties of partially coherent circular Airy beam (CAB) with different spatial coherent length are theoretically investigated in this paper. It is found that, as spatial coherent length decreases, the size of the focal spot would increase and the focal intensity would decrease. But the abruptly autofocusing property for partially coherent CAB is still quite obvious, when comparing with the common partially coherent Gaussian beam under the same conditions; and its autofocusing position is less easily influenced by coherence. The influences of initial radius r0 and decaying parameter a on the autofocusing property have also been investigated in the end.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

2017 (6)

2016 (3)

2015 (3)

2014 (5)

2013 (8)

2012 (5)

O. Korotkova, S. Sahin, and E. Shchepakina, “Multi-Gaussian Schell-model beams,” J. Opt. Soc. Am. A 29(10), 2159–2164 (2012).
[Crossref] [PubMed]

J. A. Davis, D. M. Cottrell, and D. Sand, “Abruptly autofocusing vortex beams,” Opt. Express 20(12), 13302–13310 (2012).
[Crossref] [PubMed]

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

Y. Jiang, K. Huang, and X. Lu, “Propagation dynamics of abruptly autofocusing Airy beams with optical vortices,” Opt. Express 20(17), 18579–18584 (2012).
[Crossref] [PubMed]

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100(5), 051108 (2012).
[Crossref]

2011 (6)

2010 (3)

2009 (2)

2008 (3)

B. Chen, Z. Chen, and J. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40(6), 820–827 (2008).
[Crossref]

H. T. Eyyuboğlu, “Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence,” Opt. Laser Technol. 40(1), 156–166 (2008).
[Crossref]

H. T. Eyyuboğlu and F. Hardalaç, “Propagation of modified Bessel-Gaussian beams in turbulence,” Opt. Laser Technol. 40(2), 343–351 (2008).
[Crossref]

2007 (2)

2006 (1)

2004 (1)

2002 (1)

1989 (1)

M. Zahid and M. S. Zubairy, “Directionality of partially coherent Bessel-Gauss beams,” Opt. Commun. 70(5), 361–364 (1989).
[Crossref]

1979 (1)

1978 (1)

Alonzo, M.

Auñón, J. M.

Baumgartl, J.

Baykal, Y.

F. Wang, Y. Cai, H. Eyyuboğlu, and Y. Baykal, “Partially coherent Elegant Hermite-Gaussian beams,” Appl. Phys. B 103(2), 461–469 (2010).
[Crossref]

Cai, Y.

Y. Chen, S. A. Ponomarenko, and Y. Cai, “Self-steering partially coherent beams,” Sci. Rep. 7(1), 39957 (2017).
[Crossref] [PubMed]

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

R. Chen, L. Liu, S. Zhu, G. Wu, F. Wang, and Y. Cai, “Statistical properties of a Laguerre-Gaussian Schell-model beam in turbulent atmosphere,” Opt. Express 22(2), 1871–1883 (2014).
[Crossref] [PubMed]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

F. Wang, X. Liu, Y. Yuan, and Y. Cai, “Experimental generation of partially coherent beams with different complex degrees of coherence,” Opt. Lett. 38(11), 1814–1816 (2013).
[Crossref] [PubMed]

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100(5), 051108 (2012).
[Crossref]

Y. Dong, Y. Cai, C. Zhao, and M. Yao, “Statistics properties of a cylindrical vector partially coherent beam,” Opt. Express 19(7), 5979–5992 (2011).
[Crossref] [PubMed]

F. Wang, Y. Cai, H. Eyyuboğlu, and Y. Baykal, “Partially coherent Elegant Hermite-Gaussian beams,” Appl. Phys. B 103(2), 461–469 (2010).
[Crossref]

F. Wang, Y. Cai, and O. Korotkova, “Partially coherent standard and elegant Laguerre-Gaussian beams of all orders,” Opt. Express 17(25), 22366–22379 (2009).
[Crossref] [PubMed]

F. Wang, Y. Cai, and S. He, “Experimental observation of coincidence fractional Fourier transform with a partially coherent beam,” Opt. Express 14(16), 6999–7004 (2006).
[Crossref] [PubMed]

D. Ge, Y. Cai, and Q. Lin, “Partially coherent flat-topped beam and its propagation,” Appl. Opt. 43(24), 4732–4738 (2004).
[Crossref] [PubMed]

Chen, B.

B. Chen, C. Chen, X. Peng, Y. Peng, M. Zhou, and D. Deng, “Propagation of sharply autofocused ring Airy Gaussian vortex beams,” Opt. Express 23(15), 19288–19298 (2015).
[Crossref] [PubMed]

B. Chen, Z. Chen, and J. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40(6), 820–827 (2008).
[Crossref]

Chen, C.

Chen, R.

Chen, Y.

Y. Chen, S. A. Ponomarenko, and Y. Cai, “Self-steering partially coherent beams,” Sci. Rep. 7(1), 39957 (2017).
[Crossref] [PubMed]

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

Y. Chen and Y. Cai, “Generation of a controllable optical cage by focusing a Laguerre-Gaussian correlated Schell-model beam,” Opt. Lett. 39(9), 2549–2552 (2014).
[Crossref] [PubMed]

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.

Cizmár, T.

Collett, E.

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] [PubMed]

Courvoisier, F.

Cui, S.

Davidson, F. M.

Davis, J. A.

de Sande, J. C.

de Sande, J. C. G.

Deng, D.

Dholakia, K.

Dong, Y.

F. Wang, Y. Cai, Y. Dong, and O. Korotkova, “Experimental generation of a radially polarized beam with controllable spatial coherence,” Appl. Phys. Lett. 100(5), 051108 (2012).
[Crossref]

Y. Dong, Y. Cai, C. Zhao, and M. Yao, “Statistics properties of a cylindrical vector partially coherent beam,” Opt. Express 19(7), 5979–5992 (2011).
[Crossref] [PubMed]

Efremidis, N. K.

Eyyuboglu, H.

F. Wang, Y. Cai, H. Eyyuboğlu, and Y. Baykal, “Partially coherent Elegant Hermite-Gaussian beams,” Appl. Phys. B 103(2), 461–469 (2010).
[Crossref]

Eyyuboglu, H. T.

H. T. Eyyuboğlu, “Propagation and coherence properties of higher order partially coherent dark hollow beams in turbulence,” Opt. Laser Technol. 40(1), 156–166 (2008).
[Crossref]

H. T. Eyyuboğlu and F. Hardalaç, “Propagation of modified Bessel-Gaussian beams in turbulence,” Opt. Laser Technol. 40(2), 343–351 (2008).
[Crossref]

Farsari, M.

Fedorov, V. Y.

A. D. Koulouklidis, D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Phase Memory Preserving Harmonics from Abruptly Autofocusing Beams,” Phys. Rev. Lett. 119(22), 223901 (2017).
[Crossref] [PubMed]

D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Janus waves,” Opt. Lett. 41(20), 4656–4659 (2016).
[Crossref] [PubMed]

Gan, X.

García-García, J.

Ge, D.

Gori, F.

Gu, J.

Y. Chen, J. Gu, F. Wang, and Y. Cai, “Self-splitting properties of a Hermite-Gaussian correlated Schell-model beam,” Phys. Rev. A 91(1), 013823 (2015).
[Crossref]

Hardalaç, F.

H. T. Eyyuboğlu and F. Hardalaç, “Propagation of modified Bessel-Gaussian beams in turbulence,” Opt. Laser Technol. 40(2), 343–351 (2008).
[Crossref]

He, S.

Hu, M.

Huang, K.

Jiang, Y.

Korotkova, O.

Koulouklidis, A. D.

A. D. Koulouklidis, D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Phase Memory Preserving Harmonics from Abruptly Autofocusing Beams,” Phys. Rev. Lett. 119(22), 223901 (2017).
[Crossref] [PubMed]

Lajunen, H.

Lencina, A.

Li, N.

Li, P.

Li, Y.

Lin, Q.

Liu, L.

Liu, S.

Liu, X.

Lu, X.

Lu, X. H.

Makris, K. G.

Maluenda, D.

Manousidaki, M.

Martinez Matos, O.

Martínez-Herrero, R.

Mazilu, M.

Mei, Z.

Mills, M. S.

Morris, J. E.

Ni, D.

Nieto-Vesperinas, M.

Olvera-Santamaría, M. A.

Ostrovsky, A. S.

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] [PubMed]

Papazoglou, D. G.

A. D. Koulouklidis, D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Phase Memory Preserving Harmonics from Abruptly Autofocusing Beams,” Phys. Rev. Lett. 119(22), 223901 (2017).
[Crossref] [PubMed]

D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Janus waves,” Opt. Lett. 41(20), 4656–4659 (2016).
[Crossref] [PubMed]

M. Manousidaki, D. G. Papazoglou, M. Farsari, and S. Tzortzakis, “Abruptly autofocusing beams enable advanced multiscale photo-polymerization,” Optica 3(5), 525–530 (2016).
[Crossref]

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] [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]

Penciu, R. S.

Peng, T.

Peng, X.

Peng, Y.

Piquero, G.

Plonus, M.

Ponomarenko, S. A.

Y. Chen, S. A. Ponomarenko, and Y. Cai, “Self-steering partially coherent beams,” Sci. Rep. 7(1), 39957 (2017).
[Crossref] [PubMed]

Prakash, J.

Pu, J.

S. Cui, Z. Chen, L. Zhang, and J. Pu, “Experimental generation of nonuniformly correlated partially coherent light beams,” Opt. Lett. 38(22), 4821–4824 (2013).
[Crossref] [PubMed]

B. Chen, Z. Chen, and J. Pu, “Propagation of partially coherent Bessel-Gaussian beams in turbulent atmosphere,” Opt. Laser Technol. 40(6), 820–827 (2008).
[Crossref]

Rickenstorff-Parrao, C.

Ricklin, J. C.

Rodrigo, J. A.

Saastamoinen, T.

Sahin, S.

Sand, D.

Santarsiero, M.

Shao, H.

Shchepakina, E.

Song, M.

Tzortzakis, S.

A. D. Koulouklidis, D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Phase Memory Preserving Harmonics from Abruptly Autofocusing Beams,” Phys. Rev. Lett. 119(22), 223901 (2017).
[Crossref] [PubMed]

D. G. Papazoglou, V. Y. Fedorov, and S. Tzortzakis, “Janus waves,” Opt. Lett. 41(20), 4656–4659 (2016).
[Crossref] [PubMed]

M. Manousidaki, D. G. Papazoglou, M. Farsari, and S. Tzortzakis, “Abruptly autofocusing beams enable advanced multiscale photo-polymerization,” Optica 3(5), 525–530 (2016).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Propagation dynamics of partially coherent CAB in xz plane: (a) incoherent case, δc = ∞; (b) δc = 20mm; (c) δc = 10mm; (d) δc = 5mm.
Fig. 2
Fig. 2 Intensity distributions of incoherent CAB and partially coherent CAB at different z planes: (a) initial plane; (b) z = 40m; (c) z = 50m; (d) focal plane, zf = 65.5m; (e) z = 80m; (f) z = 100m.
Fig. 3
Fig. 3 Comparison of autofocusing property of GB and CAB with different spatial coherent length: (a) incoherent case, δc = ∞; (b) δc = 20mm; (c) δc = 10mm; (d) δc = 5mm.
Fig. 4
Fig. 4 Change of autofocusing property of partially coherent CAB with different initial radius r0: (a) focal intensity; (b) focal position.
Fig. 5
Fig. 5 Change of autofocusing property of partially coherent CAB with different decaying parameter a: (a) focal intensity; (b) focal position.

Equations (11)

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E( r )=CAi( r 0 r w )exp( a r 0 r w ),
W( r 1 , r 2 )=E( r 1 ) E ( r 2 )μ(| r 1 r 2 |),
μ(| r 1 r 2 |)=exp[ ( r 1 r 2 ) 2 2 δ c 2 ]=exp( r 1 2 + r 2 2 2 δ c 2 )exp[ r 1 r 2 cos( θ 1 θ 2 ) δ c 2 ],
W( ρ 1 , φ 1 , ρ 2 , φ 2 ,z )= k 2 4 π 2 z 2 - + W( r 1 , θ 1 , r 2 , θ 2 )exp[ ik 2z ( r 1 2 + ρ 1 2 )+ ik 2z ( r 2 2 + ρ 2 2 ) ] ×exp[ ik z r 1 ρ 1 cos( θ 1 φ 1 ) ik z r 2 ρ 2 cos( θ 2 φ 2 ) ] r 1 r 2 d r 1 d r 2 d θ 1 d θ 2 ,
P θ 1 = 0 2π exp[ r 1 r 2 δ c 2 cos( θ 1 θ 2 ) ]exp[ ik z r 1 ρ 1 cos( θ 1 φ 1 ) ]d θ 1 .
P θ 1 = l= i l J l ( k r 1 ρ 1 z )2πexp[ il( θ 2 φ 1 ) ] I l ( r 1 r 2 δ c 2 ).
P θ 2 = 0 2π exp[ il( θ 2 φ 1 ) ]exp[ ik z r 2 ρ 2 cos( θ 2 φ 2 ) ]d θ 2 = i l 2πexp[ il( φ 2 φ 1 ) ] J l ( k r 2 ρ 2 z ),
0 2π 0 2π exp[ r 1 r 2 δ c 2 cos( θ 1 θ 2 ) ] exp[ ik r 1 ρ 1 z cos( θ 1 φ 1 ) ik r 2 ρ 2 z cos( θ 2 φ 2 ) ]d θ 1 d θ 2 =4 π 2 k= J l ( k r 1 ρ 1 z ) J l ( k r 2 ρ 2 z ) I l ( r 1 r 2 δ c 2 ) .
W( ρ 1 , φ 1 , ρ 2 , φ 2 ,z )= k 2 z 2 l= 0 0 E( r 1 ) E * ( r 2 ) J l ( k r 1 ρ 1 z ) J l ( k r 2 ρ 2 z ) I l ( r 1 r 2 δ c 2 ) exp( r 1 2 + r 2 2 2 δ c 2 ) ×exp[ ik 2z ( r 1 2 + ρ 1 2 )+ ik 2z ( r 2 2 + ρ 2 2 ) ] r 1 r 2 d r 1 d r 2 ,
I(ρ,φ,z)=W(ρ,φ,ρ,φ,z).
E( r )=Cexp( ik r 2 2q ),

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