[论文解读] Structured-light propagation in a medium with uniform torsion: polarization textures, geometric birefringence, and beam-resolved optical activity

Edilberto O. Silva|arXiv (Cornell University)|Mar 23, 2026

Orbital Angular Momentum in Optics被引用 0

一句话总结

论文表明在螺旋几何背景下的均匀扭 визion-induced helicity splitting of circular polarizations, leading to radius-dependent polarization rotation and polarization-texture formation in finite-width beams, analyzed via a minimal paraxial model and Stokes parameters.

ABSTRACT

We investigate finite-width optical-beam propagation in a medium with uniform torsion described by the geometric theory of a continuous distribution of screw dislocations. Starting from the Riemann--Cartan framework that yields torsion-induced circular birefringence for local plane waves, we construct a minimal paraxial beam model in which the same contortion-driven helicity splitting remains explicit. We show that uniform torsion breaks the degeneracy between the two circular-polarization sectors and induces a geometric rotation of the polarization that scales with both the propagation distance and the radial position in the beam. As a consequence, a finite-width beam develops spatially varying polarization textures across its transverse profile, naturally described by the Stokes parameters. We introduce beam-level observables based on the integrated Stokes vector, the transverse inhomogeneity of the polarization texture, and the number of resolved radial polarization domains, thereby connecting the torsion parameter to experimentally accessible beam diagnostics. The paper combines two complementary levels of description: an analytic short-distance regime, used to isolate the geometric mechanism, and full paraxial propagation including diffraction, used to test the robustness of the predicted textures. Within the cylindrically symmetric minimal model, the most robust structured-light signature of uniform torsion is beam-resolved polarization structuring, whereas strong orbital-angular-momentum conversion is not expected without additional azimuthal structure. We also identify the geometric ingredient required for genuine torsion-assisted spin--orbit conversion beyond the minimal radial model: an effective azimuthal geometric connection.

研究动机与目标

• 使用 Riemann–Cartan 几何学对具有均匀扭 vison的介质进行建模，以研究光学活性，而不需要现象学性 gyrotropy 的假设。
• 通过以扭 Vishon 诱导的手性分裂为基础的最小准轴向模型，将局部圆偏振性与有限宽度波束动力学联系起来。
• 通过 Stokes 参数表征由此产生的偏振纹理，并定义用于扭 vison诊断的波束层观测量。

提出的方法

• 推导具有均匀扭 vison 的 Riemann–Cartan 时空中的协变 Maxwell 波动方程。
• 计算前向传播支的局部圆特征模和色散，得到 k_z^(±) 和 Δk_z=2Ωρ。
• 给出最小准轴向波束方程 i∂_z Ψ = [- (1/2k_0) ∇_⊥^2 I + Ωρ σ_3] Ψ。
• 转写为 Stokes 参数以描述径向偏振纹理 S_0、S_1、S_2、S_3，以及局部旋转 Δθ(ρ,L)=ΩρL。
• 讨论几何相位解释及扭 vison 辅助自旋–轨道转换的条件。
• 扩展至带有方位几何连接的扭 vis q-plate，并推导 OAM 耦合的选择规则。

实验结果

研究问题

• RQ1 均匀扭 vision 是否打破有限宽度波束中圆偏振扇区之间的简并性并引入半径相关的偏振旋转？
• RQ2 扭 vison 诱导的双折射的可观测光束级标志（如偏振纹理和 Stokes 映射）有哪些？
• RQ3 最小径向模型是否能捕捉鲁棒的偏振结构化，进一步需要哪些几何要素来实现自旋–轨道转换？
• RQ4 在 q-plate 扩展中引入方位偏振框架旋转如何在扭 vision 下实现 OAM 侧带？
• RQ5 哪些运行观测量最能诊断结构化光实验中的扭 vision？

主要发现

• 均匀扭 vision 打破圆偏振简并性并引入半径相关的偏振旋转，Δθ(ρ,L)=ΩρL。
• 有限宽度光束呈现随空间变化的偏振纹理，可用 Stokes 参数 S_0、S_1、S_2 表示，在最小模型下 S_3=0。
• 均匀扭 vision 的鲁棒结构化光学标志是光束分辨的偏振结构化，而非在圆柱对称模型中的强轨道角动量转换。
• 真正的扭 vision 辅助自旋–轨道转换所需的几何要素是方位几何连接（如扭 vis q-plate）。
• 在 q-plate 扩展中的方位调和选择规则为 m → m ± q，使得在扭 vision 出现时实现受控的 OAM 耦合。