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Based on the interference patterns of the speckle field and the reference beam recorded by the charge-coupled device, and the digital Fourier transform technique, the complex amplitudes and phases of speckle field produced at different scattering angles are extracted. The phase distribution and the statistical properties at the singular point, such as the angle between two zero-contour lines of real part and imaginary part of the complex amplitude, the eccentricity of the intensity contours, etc. are studied. We find that there are some special properties of phase singularity when the scattering angle is large enough. With the increase of the scattering angle, great changes have taken place in the spatial distributions of the amplitude and the phase, and the probability of the angle between two zero-contour lines of real part and imaginary part is close to a smaller value, and the average eccentricity of the intensity contours around the phase singularity gradually increase. Moreover, the most interesting thing is that the eccentricity is probably greater than 1 in large anger scattering. The phase singular line as a new kind of phase singularity is found at a large scattering angle; the phase mutation rules and the vortex distribution characteristics of the phase on both sides of the phase singular line are investigated, and the hyperbolic or parabolic shape intensity contour around the phase singular line is found.
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Keywords:
- phase singularity /
- speckle /
- eccentricity /
- statistical property
[1] Goodman J W 1965 Proc. IEEE 53 1688
[2] Dainty J C 1984 Laser Speckle and Related Phenomena (Berlin: Spring-Verlag) pp18, 29
[3] Coulet P, Gil L, Rocca F 1989 Opt. Commun. 73 403
[4] Ren J R, Zhu T, Duan Y S 2008 Commun. Theor. Phys. 50 345
[5] Xu Y, Miroshnichenko A E, Desyatnikov A S 2012 Opt. Lett. 37 4985
[6] Soskin M S, Vasnetsov M V 2001 Prog. Opt. 42 219
[7] Yang Y S, Zhang R F 2014 SIAM J. Math. Anal. 46 484
[8] Plyanskii P V 2004 Proc. SPIE 5477 31
[9] Neshev D N, Dreischuh A, Maleshkov G, Samoc M, Kivshar Y S 2010 Opt. Express 18 18368
[10] Foley J T, Wolf E J 2002 J. Opt. Soc. Am. A 19 2510
[11] Wang W, Yokozeki T, Ishijima R, Wada A, Miyamoto Y, Takeda M, Hanson S G 2006 Opt. Express 14 120
[12] Terhalle B, Richter T, Desyatnikov A S, Neshev D N, Krolikowski W, Kaiser F, Denz C, Kivshar Y S 2008 Phys. Rev. Lett. 101 013903
[13] Desyatnikov A S, Kivshar Y S 2005 Prog. Opt. 47 291
[14] Freund I 1994 J. Opt. Soc. Am. A 11 1644
[15] Berry M V 1978 J. Phys. A 11 27
[16] Baranova N B, Zel' dovich B Y, Mamaev A V, Pilipetslii N F, Shkukov V V 1981 Pis'ma Zh. Eksp. Teor. Fiz. 33 206
[17] Freund I, Shvartsman N, Freilikher V 1993 Opt. Commun. 101 247
[18] Shvartsman N, Freund I 1994 Phys. Rev. Lett. 72 1008
[19] Berry M V, Dennis M R 2000 Proc. R. Soc. Lond. A 456 2059
[20] Wang W, Hanson S G, Miyamoto Y, Takeda M 2005 Phys. Rev. Lett. 94 103902
[21] Wang W, Duan Z, Hanson S G, Miyamoto Y, Takeda M 2006 Phys. Rev. Lett. 96 073902
[22] Dennis M R 2007 Eur. Phys. J. Spec. Top. 145 191
[23] Zhang S, Genack A Z 2007 Phys. Rev. Lett. 99 203901
[24] Egorow R I, Soskin M S, Kessler D A, Freund I 2008 Phys. Rev. Lett. 100 103901
[25] Song H S, Cheng C F, Liu M, Teng S Y, Zhang N Y 2009 Acta Phys. Sin. 58 291 (in Chinese) [宋洪胜, 程传福, 刘曼, 滕树云, 张宁玉 2009 58 291]
[26] Song H S, Cheng C F, Teng S Y, Liu M, Liu G Y, Zhang N Y 2009 Acta Phys. Sin. 58 7654 (in Chinese) [宋洪胜, 程传福, 滕树云, 刘曼, 刘桂媛, 张宁玉 2009 58 7654]
[27] Song H S, Cheng C F, Liu Y Y, Liu G Y, Teng S Y 2010 Chin. Phys. B 19 074204
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[1] Goodman J W 1965 Proc. IEEE 53 1688
[2] Dainty J C 1984 Laser Speckle and Related Phenomena (Berlin: Spring-Verlag) pp18, 29
[3] Coulet P, Gil L, Rocca F 1989 Opt. Commun. 73 403
[4] Ren J R, Zhu T, Duan Y S 2008 Commun. Theor. Phys. 50 345
[5] Xu Y, Miroshnichenko A E, Desyatnikov A S 2012 Opt. Lett. 37 4985
[6] Soskin M S, Vasnetsov M V 2001 Prog. Opt. 42 219
[7] Yang Y S, Zhang R F 2014 SIAM J. Math. Anal. 46 484
[8] Plyanskii P V 2004 Proc. SPIE 5477 31
[9] Neshev D N, Dreischuh A, Maleshkov G, Samoc M, Kivshar Y S 2010 Opt. Express 18 18368
[10] Foley J T, Wolf E J 2002 J. Opt. Soc. Am. A 19 2510
[11] Wang W, Yokozeki T, Ishijima R, Wada A, Miyamoto Y, Takeda M, Hanson S G 2006 Opt. Express 14 120
[12] Terhalle B, Richter T, Desyatnikov A S, Neshev D N, Krolikowski W, Kaiser F, Denz C, Kivshar Y S 2008 Phys. Rev. Lett. 101 013903
[13] Desyatnikov A S, Kivshar Y S 2005 Prog. Opt. 47 291
[14] Freund I 1994 J. Opt. Soc. Am. A 11 1644
[15] Berry M V 1978 J. Phys. A 11 27
[16] Baranova N B, Zel' dovich B Y, Mamaev A V, Pilipetslii N F, Shkukov V V 1981 Pis'ma Zh. Eksp. Teor. Fiz. 33 206
[17] Freund I, Shvartsman N, Freilikher V 1993 Opt. Commun. 101 247
[18] Shvartsman N, Freund I 1994 Phys. Rev. Lett. 72 1008
[19] Berry M V, Dennis M R 2000 Proc. R. Soc. Lond. A 456 2059
[20] Wang W, Hanson S G, Miyamoto Y, Takeda M 2005 Phys. Rev. Lett. 94 103902
[21] Wang W, Duan Z, Hanson S G, Miyamoto Y, Takeda M 2006 Phys. Rev. Lett. 96 073902
[22] Dennis M R 2007 Eur. Phys. J. Spec. Top. 145 191
[23] Zhang S, Genack A Z 2007 Phys. Rev. Lett. 99 203901
[24] Egorow R I, Soskin M S, Kessler D A, Freund I 2008 Phys. Rev. Lett. 100 103901
[25] Song H S, Cheng C F, Liu M, Teng S Y, Zhang N Y 2009 Acta Phys. Sin. 58 291 (in Chinese) [宋洪胜, 程传福, 刘曼, 滕树云, 张宁玉 2009 58 291]
[26] Song H S, Cheng C F, Teng S Y, Liu M, Liu G Y, Zhang N Y 2009 Acta Phys. Sin. 58 7654 (in Chinese) [宋洪胜, 程传福, 滕树云, 刘曼, 刘桂媛, 张宁玉 2009 58 7654]
[27] Song H S, Cheng C F, Liu Y Y, Liu G Y, Teng S Y 2010 Chin. Phys. B 19 074204
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