Vortex is one of the most common phenomena in nature. In 1992, Allen et al. proposed that such vortex beams carry orbital angular momentum (OAM), which has furthered the development of vortex beams in various fields, including optical tweezer, quantum communication and bio-image.

Optical beam usually has a phase term denoted by exp(impφ),where m is an integer so-called topological charge and φ is the azimuthal angle. For conventional optical beam, the main vortex near the optical axis forms an optical vortex line, which shows stable evolution during propagation. More complex light fields usually have more special evolution trajectories of vortex lines which determine the topology of the light fields. Previous studies have developed some methods to characterize and visualize optical vortex lines, including the interference method, the saturation-intensity method and the numerical search algorithm. But the mentioned methods still have some disadvantages such as complex measurement configuration, low accuracy, less visualization, and so on. Also, these methods only focus on the measurement and visualization of the optical lines in free space propagation. However, there are no relevant studies on visualizing the optical lines in nanoscale tightly focused light beam.

To address this problem as well as realization of high efficiency laser fabrication of three-dimensional chiral nanostructures, the research group led by Prof. Xu Liu and Prof. Cui-fang Kuang from the Zhejiang Lab and Zhejiang University, reveals the evolution properties of the tightly focused multi-vortex beams (MVBs) at the nanoscale based on two-photon polymerization direct laser writing (2PP-DLW). Meanwhile, by combining the MVBs and single exposure direct laser writing, high efficiency fabrication of three-dimensional chiral nanostructures can be realized.

The relevant research results are published in Photonics Research, Volume. 12, Issue 1, 2024 (Mengdi Luo, Jisen Wen, Pengcheng Ma, Qiuyuan Sun, Xianmeng Xia, Gangyao Zhan, Zhenyao Yang, Liang Xu, Dazhao Zhu, Cuifang Kuang, Xu Liu. Three-dimensional nanoscale vortex line visualization and chiral nanostructure fabrication of tightly focused multi-vortex beams via direct laser writing[J]. Photonics Research, 2024, 12(1): 70).

For breaking the donut-like intensity distribution of vortex beams and possessing more complex and intriguing vortex structure, the MVBs are proposed in this work. The MVBs at the entrance can be expressed as:

$$E_i(u,v)=\exp (-\frac{u^2+v^2}{w_0^2})\mathrm{\Phi }(u,v)$$

where (u, v) are the Cartesian coordiantes, w₀ is the waist radius of the incident Gassian beam, and

$$\Phi (u,v)=\prod _{n\prime =1}^{\left|m\right|}{\left[\frac{(u+a{cos\phi }_{n\prime })+i(v+a{sin\phi }_{n\prime })}{\sqrt{{(u+a{cos\phi }_{n\prime })}^2+{(v+a{sin\phi }_{n\prime })}^2}}\right]}^{\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\left[m\right]}.$$

a represents the initial off-axis distance of each vortex. According to the Richards-Wolf vectorial diffraction integration, the evolution properties of the wave front of the MVBs near the foci can be obtained. Fig. 1(a) and Fig. 1(b) exhibit the spiral-forward property of the two vortices during tightly focusing process. Therefore, the intensity distribution of the MVBs also rotates as shown in Fig. 1(c). For directly recording the spiral-forward vortex line through single exposure of 2PP-DLW, the high NA oil-immersion type objective is utilized to tightly focus the MVBs on positive photoresist. Thus, the vortex lines are visualized by the positive photoresist and the SEM photo is demonstrated in Fig. 1(d).

Fig. 1 (a) Visualization of numerically determined 3D evolution of phase vortices. The intensity and phase distributions at the focal plane are also shown. (b) Top view of (a). (c) Numerical results for the evolution of the MVBs at different propagation distance z with m = 2 and a= 0.375 mm. (d) SEM photo of the nanostructure of the positive photoresist fabricated by single exposure 2PP-DLW, recording the evolution of the phase vortices.

Fig. 2 (a) Propagation evolution and 3D intensity distributions of MVBs with a = 0.5 mm and m = 5. (b) SEM photos of the fabricated 3D chiral nanostructures and (c) the corresponding arrays via tightly focused MVBs. (d) Optical vortical dichroism measurements of the chiral nanostructure versus topological charge. (e) SEM photo of the nanostructure with different chiral properties in the inner area and outer area.

The phase vortices rotate during the tightly focusing process, forming the shaped three-dimensional light field. Thus, three-dimensional chiral nanostructures can be fabricated by tightly focusing the MVBs onto a negative photoresist. Compared with the point-to-point scanning strategy, the method of single exposure 2PP-DLW highly improve the fabrication efficiency. Fig. 2(b), 2(c) and 2(e) show the fabricated nanostructures. Fig. 2(e) show the optical response named vortex dichroism (VD) which is defined as:

$$\mathrm{V}\mathrm{D}=2\times \frac{I_{+l}-I_{-l}}{I_{+l}+I_{-l}}\times \mathrm{100\%}$$

where I_+l and I_-l are the reflection intensity of chiral nanostructure under the topological charge of +l and -l. Moreover, the response of the nanostructure to the spiral phase excited by the vortex beams is shown in Fig. 2(d).

Fabrication of three-dimensional chiral nanostructure through single exposure 2PP-DLW combing with light modulation effectively improves the manufacturing efficiency, which can be widely applied in the field of optical sensing, advanced functional devices and so on. Meanwhile, 2PP-DLW is also an excellent tool to reveal the properties of optical beams at the nanoscale like the visualization of the evolution of the vortex lines and intensity distributions.