为了研究高斯涡旋光束在ABCD 光学系统的传输演化规律,基于广义惠更斯菲涅耳积分公式,推导了拓扑荷为+1 的高斯涡旋光束经ABCD 傍轴光学系统传输的解析表达式,并数值模拟和分析高斯涡旋光束在自由空间传输中4 个观察平面上的光强分布和相位分布的特点.结果表明:随着传输距离的增加,高斯涡旋光束的光斑尺度明显增大,但光强也随之减小;同时从相位奇异点发出的等相位线由射线变成弧线,最终形成螺旋线结构.
In order to study propagation of Gaussian vortex beams in an ABCD optical system, an analytical propagation equation of Gaussian vortex beams with a unit topological charge through a paraxial ABCD optical system is derived based on the generalized Huygens-fresnel integral formulae. According to the obtained analytical representation, the light intensity distributions and the phase distributions of a Gaussian vortex beam in several observation planes in the free space are illustrated and analyzed by numerical examples. The results show that with the increase of propagation distance, the beam spot is enlarged obviously, but its intensity decreases. Meanwhile, it is also found that the isophase line of a Gaussian vortex beam is a ray emanating from the singularity in the original input plane, but with the increase of the propagation distance, the isophase line changes from radial to arc and finally takes on a spiral shape.
[1] Bron M, Wolf E. Principle of optics[M]. 7th edition. New York: Cambridge University Press, 1999.
[2] Nye J F, Berry M V. Dislocations in wave trains[J]. Proceedings of the Royal Society of London Series A, 1974, 336: 165-190.
[3] Allen L, Beijersbergen M W, Spreeuw R J C, et al. Orbital angular momentum of light and the transformation of laguerre- gaussian laser modes[J]. Physical Review A, 1992, 45(11): 8185-8190.
[4] Barnett S M, Allen L. Orbital angular momentum and nonparaxial light beams[J]. Optics Communications, 1994, 110(5/6): 670-678.
[5] Curtis J E, Grier D G. Structure of optical vortices[J]. Physical Review Letters, 2003, 90(13): 133901(1-4).
[6] Simpson N B, Mcgloin D, Dholakia K, et al. Optical tweezers with increased axial trapping efficiency[J]. Journal of Modern Optics, 1998, 45(9): 1943-1949.
[7] Curtis J E, Koss B A, Grier D G. Dynamic holographic optical tweezers[J]. Optics Communications 2002, 207: 169-175.
[8] Gibson G, Courtical J, Padgett M, et al. Free-space information transfer using light beams carrying orbital angular momentum[J]. Optics Express, 2004, 12 (22): 5448-5456.
[9] Ladavac K, Grier D. Microoptomechanical pumps assembled and driven by holographic optical vortex arrays[J]. Optics Express, 2004, 12(6): 1144-1149.
[10] Ng J, Lin Z F, Chan C T. Theory of optical trapping by an optical vortex beam[J]. Physical Review Letters, 2010, 104(10): 103601(1-4).
[11] Bouchal Z, Celechovsky R. Mixed vortex states of light as information carriers[J]. New Journal of Physics. 2004(6): 131.
[12] Salgueiro J R, Carlsson A H, Ostrovskaya E, et al. Second-harmonic generation in vortex-induced waveguides[J]. Optics Letters, 2004, 29 (6): 593-595.
[13] Sato S, Harada Y, Waseda Y. Optical trapping of microscopic metal particles[J]. Optics Letters, 1994, 19(22): 1807-1809.
[14] Friese M E J, Rubinsztein-Dunlop H, Gold J, et al. Optically driven micromachine elements[J]. Applied Physics Letters, 2001, 78(4): 547- 549.
[15] Stuarta. A, Collins J R. Lens-System diffraction Integral written in terms of matrix optics[J]. Journal of the Optical Society of America A, 1970, 60(9): 1168-1177.
