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Generation of optical skyrmions formed by electromagnetic field vectors under 4π focal configurations
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摘要:
光学斯格明子为实现结构光场以及时空光场的拓扑属性提供了新的研究方法与研究思路。本文在4π聚焦系统中，通过对两对入射柱矢量光束进行偏振与相位调控，实现了聚焦光场纵向分量与横向分量的独立控制，在焦平面上得到了Néel型与Bloch型的电磁矢量光学斯格明子。在4π聚焦系统内调控两对反向传播的径向偏振光时，焦平面处将产生Néel型的电场矢量斯格明子。将其中一对替换为角向偏振光时，焦平面处将同时产生Bloch型的电场矢量斯格明子与相位超前π/2的磁场矢量斯格明子。本工作为进一步研究自由空间中微纳尺度电磁矢量光学斯格明子与物质的相互作用提供了理论基础。
Abstract:Optical skyrmions provide a new idea and approach to endow structured light and spatial-temporal light with topological properties. In this paper, the longitudinal and transversal components of the focused light field are decoupled and can be controlled independently by modulating the polarizations and phases of two pairs of counter-propagating incident cylindrical vector beams under 4π focal configuration. Under this condition, Néel-type and Bloch-type optical skyrmions formed by electromagnetic field vectors are constructed in the focal plane. When one pair of the incident beams is radially polarized with a phase difference of π and the other pair is radially polarized in phase, a Néel-type optical skyrmion formed by electric field vectors can be constructed in the focal plane of the 4π focal system. The corresponding focal magnetic field is purely azimuthally polarized. If we substitute the other pair of the incident beams with azimuthally polarized beams, Bloch-type optical skyrmions formed by electromagnetic field vectors can be constructed in the focal plane, where the one formed by magnetic field vectors has a π/2 phase lead compared with the that formed by electric field vectors. This work provides a theoretical basis for further research on the interactions between matter and optical skyrmions formed by electromagnetic field vectors at micro and nano scales in free space.
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Key words:
- vector beams /
- 4π focal configurations /
- optical skyrmions
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Overview: Topological photonics inspired by the discovery of photonic topological insulators opens a path towards the discovery of fundamentally new states of light and potentially revolutionary applications, such as slow light, photonic circuitry, and topologically protected lasing. Recently, optical skyrmions, emerging as fire-new objects of study in topological photonics, were first proposed by Shai Tsesses and Luping Du et al. and may provide a new idea and approach to endow structured light and spatial-temporal light with topological properties. Resorting to vector field manipulations, different types of optical skyrmions have been generated in free space or by controlling the evanescent waves propagating along the surface of metal films. One of the most significant potential applications of optical skyrmions is the realization of the novel phenomena excited by the skyrmion-matter interactions at micro and nano scales, which could be applied to optical storage, high-resolution imaging, and precision metrology. However, there always exists a π/2 phase difference between the longitudinal and the transversal components of the focused light field under traditional tightly focusing systems in free space, and hence the generation of micro- or nano-scale optical skyrmions formed by electromagnetic field vectors in free space is still a challenge in this flourishing field.
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图 1 4π聚焦条件下，两对相向传播的柱矢量入射光在聚焦空间中产生电磁矢量光学斯格明子示意图。PP1、PP2：相位延迟为π/2的均匀相位板，BS1、BS2：分束器，L1、L2：聚焦物镜
Figure 1. Schematic of the generation of optical skyrmions formed by electromagnetic field vectors in the focal region of two pairs of counter-propagating cylindrical vector beams under 4π focal condition. PP1, PP2: homogeneous phase plate with a phase delay of π/2; BS1, BS2: beam splitter; L1, L2: objectives
图 2 Néel型电场矢量斯格明子各分量在焦平面上的归一化分布。(a)~(b) 聚焦电场径向分量和纵向分量在焦平面上的归一化分布；(c) 聚焦磁场角向分量在焦平面上的归一化分布；(d) 聚焦电磁场各分量的归一化截面曲线分布
Figure 2. Normalized distributions of the components of the Néel-type optical skyrmion formed by electric field vectors in the focal plane. (a)~(b) Radial and longitudinal components of the focused electric field in the focal plane; (c) Angular component of the focused magnetic field in the focal plane; (d) The cross sections of the individual components of the focused electromagnetic field
图 3 Néel型电场矢量斯格明子在焦平面上的矢量分布。(a)~(b) 聚焦电场和聚焦磁场在焦平面上的归一化能量密度分布，黑色箭头表示电场或磁场单位矢量在焦平面上的投影；(c) 由(a)中红色圆圈内的单位矢量构成的电场斯格明子的三维矢量结构；(d) 由(b)中中心区域的磁场单位矢量形成的二维角向分布；(e) 电场单位矢量沿斯格明子结构径向的取向变化；(f) 电场矢量相对于x-y平面的方向角θxy随r的变化；(g) 电场矢量斯格明子在焦平面上的斯格明子数密度分布
Figure 3. Vectorial distributions of the Néel-type optical skyrmion formed by electric field vectors in the focal plane. (a)~(b) Normalized energy density distributions of the focused electric field and magnetic field in the focal plane. The black arrows represent the projections of the electric or magnetic field unit vectors on the focal plane; (c) Three-dimensional vectorial structure of the optical skyrmion formed by electric field vectors within the red circle in (a); (d) Two-dimensional vectorial structure of the focal magnetic field in the central region of (b); (e) Orientations of the electric field unit vectors along the radial direction of the constructed Néel-type optical skyrmion; (f) Variation of θxy versus r; (g) Skyrmion numberdensity distribution of the constructed optical skyrmion in the focal plane
图 4 Bloch型电磁矢量斯格明子各分量在焦平面上的归一化分布。(a)~(b) 聚焦电场矢量角向分量和纵向分量在焦平面上的归一化分布；(c)~(d) 聚焦磁场矢量角向分量和纵向分量在焦平面上的归一化分布；(e) 聚焦电磁场各分量的归一化截面曲线分布
Figure 4. Normalized distributions of the components of the Bloch-type optical skyrmions formed by electromagnetic field vectors in the focal plane. (a)~(b) Angular and the longitudinal components of the focused electric field in the focal plane; (c)~(d) Angular and longitudinal components of the focused magnetic field in the focal plane; (e) Cross sections of the individual components of the focused electromagnetic field
图 5 Bloch型电磁矢量斯格明子在焦平面上的矢量分布。(a)~(b) 聚焦电场和聚焦磁场在焦平面上的归一化能量密度分布，黑色箭头表示电场或磁场单位矢量在焦平面上的投影；(c)~(d) 由(a)和(b)中红色圆圈内的单位矢量构成的电场与磁场斯格明子的三维矢量结构；(e)~(f) 电场与磁场的单位矢量沿斯格明子结构径向的取向变化；(g)~(h) 电场与磁场矢量相对于x-y平面的方向角θxy随r的变化；(i) ~(j) 电场与磁场矢量斯格明子在焦平面上的斯格明子数密度分布
Figure 5. Vectorial distributions of the Bloch-type optical skyrmions formed by electromagnetic field vectors in the focal plane. (a)~(b) Normalized energy density distributions of the focused electric field and magnetic field in the focal plane. The black arrows represent the projections of the electric or magnetic field unit vectors on the focal plane; (c)~(d) Three-dimensional vectorial structures of the optical skyrmions formed by electromagnetic field vectors within the red circles in (a) and (b); (e)~(f) Orientations of the electric field unit vectors and the magnetic field unit vectors along the radial directions of the constructed Bloch-type optical skyrmions; (g)~(h) Variations of θxy versus r; (i)~(j) Skyrmion number density distributions of the constructed optical skyrmions in the focal plane
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