[1] HELSETH L H. Optical vortices in focal regions［J］. Opt Commun, 2004,229: 85-91.
[2] BEKSHAEV A Y, SOSKIN M S,VASNETSOV M V. Transformation of higher-order optical vortices upon focusing by an astigmatic lens［J］.Opt Commun,2004,241: 237-247.
[3] SOSKIN M S, VASNETSOV M V. A comprehensive review of optical vortices［M］//WOLF E. Progress in optics.Amsterdam:Elsevier,2001:219-276.
[4] TAO S H, YUAN X C, LIN J, et al. Residue orbital angular momentum in interferenced double vortex beams with unequal topological charges［J］. Opt Express,2006,14(2): 535-541.
[5] SCHMITZ C H J, UHRIG K, SPATZ J P, et al. Tuning the orbital angular momentum in optical vortex beams［J］. Opt Express,2006,14 (15): 6604-6612.
[6] FEIZULIN Z I, KRAVTSOV Y A. Broadening of a laser beam in a turbulent medium［J］. Radio Quantum Electron,1967,10(1): 33-35.
[7] YOUNG C Y, GILCHREST Y V,MACON B R. Turbulence-induced beam spreading of higher-order mode optical waves［J］. Opt Eng,2002,41(5): 1097-1103
[8] JI Xiao-ling, HUANG Tai-xing,LU Bai-da. Spreading of partially coherent cosh-Gaussian beams propagating through turbulent atmosphere［J］. Acta Physica Sinica, 2006, 55(2): 978-982.
[9] JI Xiao-ling, TANG Ming-yue. Propagation properties of one-dimensional off-axis Gaussian beams through the turbulent atmosphere［J］. Acta Physica Sinica, 2006, 55(9): 4986-4973.
[10] ZHANG Yi-xin, TANG Min-xia,TAO Chun-kan. Partially coherent vortex beams propagation in a turbulent atmosphere［J］.Chin Opt Lett, 2005,3(10): 559-561.
[11] ZHANG Yi-xin, ZHU Tuo. Propagation of Helmholtz-Gauss beams in weak turbulent atmosphere［J］. Chin Opt Lett 2008,6(2): 79-81.
[12] GOODMAN J W. Introduction to Fourier optics［M］. 2nd ed. New York: McGraw-Hill, 1996.
[13] BORN M, WOLF E. Principles of optics［M］.Cambridge: Cambridge University Press, 1999.
[14] ANDREWS L C, PHILLIPS R L. Laser beam propagation through random media［M］. Bellingham: SPIE Press, 1998.
[15] GRADSHTEYN I S, RYZHIK I M. Table of integrals, series and products［M］. NewYork: Academic Press, 2000.
