为了研究光束的光谱传输特性, 根据广义惠更斯-菲涅耳原理, 推导了高斯光束光谱经自由空间和湍流大气传输的表达式, 并以中心频率为1.78×1015rad/s、谱宽为8.39×1013rad/s的高斯光束为例进行了数值分析。结果表明, 高斯光束传输过程中, z轴附近光谱存在少量蓝移, 离轴距离增大到约为0.5w(z)时, 光谱由蓝移变为红移, 湍流效应对离轴较远点的谱移现象有比较明显的抑制作用, 而增大源光谱的带宽, 则会使谱移现象更显著; 计算1.78×1015rad/s和1.75×1015rad/s两束单色光传输5000m时传输截面上的光强分布发现, 对于某个横向位置, 源光谱中心频率激光的强度会比某个其它频率激光的强度小, 产生传输截面上的谱移现象, 谱移现象随各参量的变化规律可由高斯光束的束腰变化规律和湍流效应对光束的展宽效应进行解释。

In order to analyze the spectral propagating properties of laser beam, spectral propagation equations of Gaussian beam propagating through free space and turbulent atmosphere were derived according to the extended Huygens-Fresnel formula, and then numerical simulation was carried out for the beam with center frequency 1.78×1015rad/s and bandwidth 8.39×1013rad/s. Results indicate that when Gaussian beam propagating through free space and turbulent atmosphere, spectrum blue-shifted exists at the scopes of near-axis and red-shifted happens if the distance from z-axis increases to a critical value. Turbulent atmosphere has the ability to reduce spectrum shift for off-axis scope, and increase of spectrum bandwidth in source can make spectrum shift phenomena more obvious. Intensity distribution vertical to z-axis at 5000m for Gaussian beams with frequency 1.78×1015rad/s and 1.75×1015rad/s shows that, for a fixed position light intensity of center frequency becomes weaker than intensity of some other frequency, and this can leads to spectral shift, besides, the phenomena of spectral changing with some parameters can be explained with the theories of Gaussian beam propagation and turbulent atmosphere beam width-spreading effect.