空心光束在Non-Kolmogorov湍流中的角扩展及传播方向研究

Study on the Spread Angular and Transmission Direction of Hollow Beams in Non-Kolmogorov Turbulence

利用两束束宽不同的平顶光束,建立空心光束的理论模型;基于广义惠更斯-菲涅耳原理和积分变换技术,推导出空心光束在Non-Kolmogorov湍流中的二阶矩束宽、扩展角及相对扩展角表达式,定量地分析湍流对空心光束扩展角的影响。研究发现:当3<α<3.11时,扩展角θsp和相对扩展角θsp/θspfree随湍流广义指数α的增加而增加;而当3.11<α<4时,θsp和θsp/θspfree均随α的增加而减小。θsp/θspfree随遮拦比ε、光束阶数M(N)的增加而减少,即湍流对空心光束扩展角的影响随ε、M(N)的增加而减少。此外,给出不同参数的空心光束在Non-Kolmogorov湍流中二阶矩束宽随传输距离的变化图,研究指出不同参数的空心光束传输于Non-Kolmogorov湍流中可产生相同的传播方向,并对以上结论均作了相关的物理解释。

Theoretical model of hollow beam is established by using two Flat-topped beams with different beam widths. Based on generalized Huygens-Fresnel Principle and integral transform technology, the expressions of the mean-squared width, spread angular and relative spread angular of hollow beams in Non-Kolmogorov turbulence are derived, and the influence of turbulence on the spread angular is studied quantitatively by the relative angular spread. The results show that spread angular θ sp and relative spread angular θ sp /θ spfree increase with increasing turbulence generalized exponent parameter α, when 3<α<3.11;however, when 3.11<α<4,θ sp and θ sp /θ spfree decrease with increasing α.θ sp /θ spfree decreases with the increasing obscure ratio ε、 beam orders M(N), i.e., the effect of turbulence on the spread angular of hollow beams decreases with the increasing ε and M(N). In addition, the variation of mean-squared width with propagation distance of hollow beams with different parameters in Non- Kolmogorov turbulence is given, and it is pointed out that hollow beam with different parameters can have the same transmission direction in Non-Kolmogorov turbulence, and the results are explained physically.