[1] INDEBETOUW G. Optical vortices and their propagation[J]. Journal of Modern Optics, 1993, 40(1): 73-87. doi: 10.1080/09500349314550101
[2] FREUND I. Saddle point wave fields[J]. Optics Communications, 1999, 163(4/6): 230-242.
[3] ROUX F. Paraxial modal analysis technique for optical vortex trajectories[J]. Journal of the Optical Society of America, 2003, B20(6): 1575-1580.
[4] ROUX F. Spatial evolution of the morphology of an optical vortex dipole[J]. Optics Communications, 2004, 236(4/6): 433-440.
[5] YAN H W, LV B D. Transformation of the optical vortex dipole by an astigmatic lens[J]. Journal of Optics, 2009, A11(6): 065706.
[6] GAO Z H, HE D, LV B D. Evolution of an optical vortex dipole diffracted by a half screen[J]. Acta Physica Sinica, 2011, 60(7): 074209 (in Chinese). doi: 10.7498/aps.60.074209
[7] BERRY M, DENNIS M. Polarization singularities in isotropic random vector waves[J]. Proceedings of the Royal Society, 2001, A457(1): 141-155.
[8] RAJPUT R, SENTHILKUMARAN P, PAL S K. Phase singularities to polarization singularities[J]. International Journal of Optics, 2020, 1605 (1): 1-33.
[9] PAL S K, SENTHILKUMARAN P. Hexagonal vector field of polarization singularities with a gradient basis structure[J]. Optics Letters, 2019, 44(8): 2093-2096. doi: 10.1364/OL.44.002093
[10] FREUND I. Polarization singularity indices in Gaussian laser beams[J]. Optics Communications, 2002, 201(4): 251-270.
[11] YAN H W, LV B D. Evolution of emergent C-points, L-lines, and C-lines in free space[J]. Chinese Physics, 2012, B21(5): 054202.
[12] HE D, GAO Z H, LIAN X X, et al. Composite stokes singularities in coherently and incoherently superimposed vector optical fields[J]. Optics Communications, 2012, 285(21/22): 4215-4222.
[13] YE D H. Analysis of characteristics of Gaussian beam and its application[J]. Laser Technology, 2019, 43(1): 146-150 (in Chinese).
[14] LI H M, ZUO J W, XU J, et al. Study on incoherent combining technology of pulsed laser beams[J]. Laser Technology, 2015, 39(2): 237-241 (in Chinese).
[15] DUAN K L, WANG B Z, LV B D. Propagation of Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation[J]. Journal of the Optical Society of America, 2005, A22(9): 1976-80.
[16] LI D, PENG X, PENG Y L, et al. Nonparaxial evolution of the Airy-Gaussian vortex beam in uniaxial crystal[J]. Journal of the Optical Society of America, 2017, B34(4): 891-898.
[17] ZHANG J B, ZHOU K Z, LIANG M, et al. Nonparaxial propagation of the chirped Airy vortex beams in uniaxial crystal orthogonal to the optical axis[J]. Optics Express, 2018, 26(2): 1290-1304. doi: 10.1364/OE.26.001290
[18] SUN C, LV X, DENG D M, et al. Nonparaxial propagation of the radially polarized Airy-Gaussian beams with different initial launch angles in uniaxial crystals[J]. Optics Communications, 2019, 445(1): 147-157.
[19] FREUND I, MOKHUN A I, SOSKIN M S, et al. Stokes singularity relations[J]. Optics Letters, 2002, 27(7): 545-547. doi: 10.1364/OL.27.000545
[20] FREUND I, SHVARTSMAN N. Wave-field phase singularities: The sign principle[J]. Physical Review, 1995, A50(6): 5164-5172.
[21] YAN H W, LV B D. Spectral Stokes singularities of stochastic electromagnetic beams[J]. Optics Letters, 2009, 34(13): 1933-1935. doi: 10.1364/OL.34.001933
[22] FREUND I. Bichromatic optical Lissajous fields[J]. Optics Communications, 2003, 226(1/6): 351-376.