PyFocus – A Python package for vectorial calculations of focused optical fields under realistic conditions. Application to toroidal foci

Focused optical fields are key to a multitude of applications involving light-matter interactions, such as optical microscopy, single-molecule spectroscopy, optical tweezers, lithography, or quantum coherent control. A detailed vectorial characterization of the focused optical fields that includes a description beyond the paraxial approximation is key to optimize technological performance as well as for the design of meaningful experiments and interpret properly their results. Here, we present PyFocus, an open-source Python software package to perform fully vectorial calculations of focused electromagnetic fields after modulation by an arbitrary phase mask and in the presence of a multilayer system. We provide a graphical user interface and high-level functions to easily integrate PyFocus into custom scripts. Furthermore, to demonstrate the potential of PyFocus, we apply it to extensively characterize the generation of toroidal foci with a high numerical aperture objective, as it is commonly done in super-resolution fluorescence microscopy methods such as STED or MINFLUX. We provide examples of the effects of different experimental factors such as polarization, aberrations, and misalignments of key optical elements. Finally, we present calculations of toroidal foci through an interface of different mediums, and, to our knowledge, the first calculations of toroidal foci generated in total internal reflection conditions.

聚焦光场是诸多涉及光与物质相互作用应用的核心，例如光学显微、单分子光谱学、光镊、光刻或量子相干调控。对聚焦光场进行包含超越近轴近似描述的详细矢量表征，是优化技术性能、设计合理实验并正确解读实验结果的关键。本文介绍PyFocus——一款开源Python软件包，可对经任意相位掩模调制且存在多层系统时的聚焦电磁场进行全矢量计算。本软件提供图形用户界面与高级函数，可便捷地将PyFocus集成至自定义脚本中。此外，为验证PyFocus的应用潜力，我们利用其对高数值孔径物镜产生的环形焦斑生成过程进行了全面表征——这类操作常见于STED、MINFLUX等超分辨荧光显微技术中。我们还提供了不同实验因素（如偏振、像差与关键光学元件失准）所产生影响的示例。最后，我们给出了通过不同介质界面产生的环形焦斑的计算结果，且据我们所知，这是首次对全内反射条件下产生的环形焦斑进行的计算。