洛伦兹光束的传输特性研究

运用光束传输的二阶矩理论，对洛伦兹光束的传输特性进行了研究，给出了束腰、横向发散角和光束传输因子的表达式.横向束腰仅取决于对应方向上的光束参数；而横向发散角和光束传输因子却取决于两横向上的光束参数.给出了光束传输因子随两横向光束参数的变化关系曲线.结果表明，两横向上的光束传输因子随两光束参数的变化规律是不相同的，而整体的光束传输因子随两光束参数的变化是前两者的综合体现；但在傍轴情形下，光束传输因子趋向于常数141，因此，对于相同束腰，其傍轴条件下的发散性为对应高斯光束的141倍.所以，洛伦兹光束适合用于描述某些发散程度较大的激光光源. 关键词： 洛伦兹光束 光束传输 二阶矩

Study on the propagation properties of Lorentz beam

Based on the second-order moment theory of beam propagation，the properties of Lorentz beam have been investigated. The expressions of the beam waists，the transverse divergence angle and the beam propagation factor have been presented. The transverse beam waist only depends on the corresponding beam parameter. However，the transverse divergence angle and the beam propagation factor are both determined by the two transverse beam parameters. The curves of the beam propagation factor versus the two transverse beam parameters are also given. The numerical results show that variational laws of the beam propagation factor in the x-and y-directions versus the two transverse beam parameters are apparently different，while the variational rule of the integrated beam propagation factor versus the two transverse beam parameters is the composite manifestation of the above cases. In the paraxial case，the beam propagation factor trends to a constant value of 141. With the beam waist being the same，therefore，the divergence of Lorentz beam is 1.41 times that of the Gaussian beam in the paraxial case. Accordingly，Lorentz beam is an appropriate model to describe certain laser sources with high divergence.