大气湍流中光束束宽扩展和角扩展的比较研究

以厄米-双曲余弦-高斯（H-ChG）光束为例，对H-ChG光束通过大气湍流传输时的束宽扩展和角扩展做了详细研究.用相对束宽和相对角扩展代替束宽和角扩展来研究湍流对光束影响的灵敏程度.研究表明，折射率结构常数C²_n越小，光束束宽扩展和角扩展越小.有较大阶数m，n，较小参数Ω₀和束腰宽度w₀ H-ChG光束的角扩展受湍流影响较小.当传输距离足够远时，这一结论对H-ChG光束的束宽扩展也成立.当传输距离不长时，对H-ChG光束相对束宽随Ω₀和w₀的变化规律做了分析.用数值计算例做了说明，并对结果的正确性做了物理解释.厄米-高斯，双曲余弦高斯和高斯光束在大气湍流中的扩展可作为H-ChG光束的特例来处理. 关键词： 束宽扩展和角扩展 大气湍流 厄米-双曲余弦-高斯光束

A comparative study of the beam-width spreading and angular spread in atmospheric turbulence

Taking the Hermite cosh Gaussian（H ChG） beam as a typical example, the beam width spreading and angular spread of H ChG beams propagating through atmospheric turbulence are throughly studied. The relative beam width and relative angular spread instead of the beam width and angular spread have been used to study the sensitivity of a beam to the effect of turbulence. It is found that the smaller the refraction index structure constant C²_n is, the less the beam width spreading and angular spread of H ChG beams are. The angular spread of H ChG beams with larger beam orders m, n, smaller parameter Ω₀ and smaller waist width w₀ is less affected by turbulence. This conclusion also holds true for the beam width spreading of H ChG beams for the case of the propagation distance is sufficiently long. The variation of the relative beam width of H ChG beams versus Ω₀ and w₀ is analyzed if the propagation distance being not so long. The results are illustrated by numerical examples and the validity of the results is explained physically. The spreading of Hermite Gaussian, cosh Gaussian and Gaussian beams in atmospheric turbulence can be treated as special cases of H ChG beams.