利用Debye积分，研究了三个相互正交的轨道角动量（包括两个正交的横向轨道角动量以及一个纵向轨道角动量）光场在紧聚焦条件下的复杂耦合现象，并演示了焦场中相位奇点在三维时空间中的演化。此外，还研究了具有不同拓扑荷数的纵向轨道角动量对聚焦波包整体轨道角动量指向的影响。数值结果表明，聚焦波包的整体轨道角动量指向可由纵向轨道角动量的拓扑荷数进行调控，进而实现紧聚焦时空波包的轨道角动量指向可控。这种角动量指向可控的时空波包在光学微操作、微纳加工、自旋-轨道耦合以及量子通信等领域具有潜在的应用价值。

We numerically demonstrate that the tight focusing of Bessel beams can generate focal fields with an ultra-long depth of focus (DOF). The ultra-long focal field can be controlled by appropriately regulating the order of the Bessel function and the polarization. An optical needle and an optical dark channel with nearly 100λ DOF are generated. The optical needle has a DOF of ∼104.9λ and a super-diffraction-limited focal spot with the size of 0.19λ2. The dark channel has a full-width at half-maximum of ∼0.346λ and a DOF of ∼103.8λ. Furthermore, the oscillating focal field with an ultra-long DOF can be also generated by merely changing the order of the input Bessel beam. Our results are expected to contribute to potential applications in optical tweezers, atom guidance and capture, and laser processing.

携带横向轨道角动量的时空光涡旋是一种新型光脉冲波包，受到越来越多的关注。本文报道一种经过高数值孔径透镜聚焦，在透镜焦平面上产生偏振态可控的线偏振时空光涡旋的方法。为克服聚焦透镜对入射时空涡旋产生的时空像散效应，需对入射时空波包作预劈裂处理。基于Richards Wolf矢量衍射公式仿真了不同偏振态下的高度局域时空涡旋的三维时空场分布，并对其强度和相位特性进行了分析。生成的水平偏振、垂直偏振以及45°偏振高度局域时空涡旋证明了本文所提方法的有效性。