非傍轴对称高斯光束矢量和标量表征的比较研究

Study on comparison of vector and scalar representations of nonparaxial symmetrical Gaussian beam

微型激光源和衍射光学元件应用的不断增加激发了人们对非傍轴激光束的研究兴趣,导致非傍轴条件下高斯光束的表征受到格外的关注.迄今为止,人们已提出很多方法描述非傍轴条件下的高斯光束,既有标量表征,也有矢量表征.分别采用矢量和标量表征非傍轴对称高斯光束,通过引入比值T来度量光场的z分量对整个光场的贡献.结果表明,以x/W(z)和y/W(z)作为坐标时,T值的变化规律与z无关.对于光源半宽度w0≥0.5λ的非傍轴对称高斯光束,在传输轴附近,特别是沿xy平面45°对角线附近,可以采用标量表征;且随着传输距离的增大,适用范围同步增大.对于半宽度w0小于0.5λ的非傍轴对称高斯光束,由于在xy平面原点附近T值有较大的极值峰,因此标量表征完全失效.

Nonparaxial laser beam inspired by the incessant increase in applications of minitype laser sources and diffractive optics elements results in the representations of Gaussian beams beyond the paraxial approximation receive considerable attention. So far, many different approaches have been presented to describe Gaussian beam beyond the paraxial approximation. There are not only scalar descriptions, but also vector representations. The nonparaxial symmetrical Gaussian beam was described by vector and scalar descriptions. A ratio T was introduced to evaluate the contribution of z component of optical field to the whole optical field. The results showed the variational rule of T to be independent of z while choosing x/W（z） and y/W（z） as coordinates. When the half width of nonparaxial symmetrical Gaussian beam ω0 be larger than or equal to 0.5λ, the scalar description would applicable in the vicinity of propagating axis, especially in the vicinity of 45° diagonal in xy plane. Moreover, the applicable range was broadened as the propagating distance increased. When the half width ω0 be smaller than 0. 5λ, the scalar description would fail caused by extrema of T in the vicinity of origin in the xy plane.