We investigate the propagation of the Lommel beams in a gradient-index medium. Based on the ABCD transfer matrix and Collins diffraction integral formula, the analytical expressions of the complex amplitude of the Lommel beams through the gradient-index medium are derived. The intensity distribution and the Poynting vector of the Lommel beams are studied analytically and numerically. The results show that the Lommel beam is focused at the singularities and the corresponding periodic beam profile is induced by the symmetrical refractive index pattern during the beam propagating in the gradient-index medium. The effects of the asymmetry factor and the topological charge on the propagation characteristics of the Lommel beams in the gradient-index medium are discussed in detail. Especially, the propagation trajectories of the Lommel beams become visible as the topological charge increases and the symmetry of the Lommel beam’s transverse intensity pattern can be controlled by varying the asymmetry factor. It is expected that the results obtained in this paper may be useful for potential applications of optical control and trapping.

我们研究了洛梅尔光束在梯度折射率介质中的传播。基于ABCD传递矩阵和柯林斯衍射积分公式，推导了Lommel光束通过梯度折射率介质的复振幅解析表达式。洛默尔光束的强度分布和坡印廷矢量进行了分析和数值研究。结果表明，洛默尔光束聚焦在奇点处，并且在光束在梯度折射率介质中传播期间，对称的折射率图案会引起相应的周期性光束轮廓。详细讨论了不对称因子和拓扑电荷对洛美尔光束在梯度折射率介质中传播特性的影响。尤其，随着拓扑电荷的增加，洛默尔光束的传播轨迹变得可见，洛默尔光束横向强度模式的对称性可以通过改变不对称因子来控制。预计本文获得的结果可能对光学控制和捕获的潜在应用有用。