AI 中文总结
该研究探讨有效各向异性背景下结构化标量光束的传播，采用格林函数方法，以拉盖尔-高斯、贝塞尔-高斯光束为对象，揭示各向异性对径向强度分布等的调控作用。
AI 中文摘要
我们研究受标准模型扩展标量部分启发、由单一无量纲参数λ控制的有效各向异性背景中结构化标量光束的传播。物理上相关的构型为横向径向指向矢场，其修改亥姆霍兹算子的径向部分同时保持轴对称性。从格林函数表示出发，我们将传播问题转化为z=0处给定有限孔径入射轮廓的初值谱重建问题，并验证在分析所用的λ值范围内，该轮廓在发射平面上可被恢复，且数值误差很小。我们选用拉盖尔-高斯模式L₃作为无涡旋拉盖尔情况的代表，仅保留L₄作为径向阶依赖的定量基准，并将两者与输入阶m=0的贝塞尔-高斯光束进行比较。有效各向异性会系统性地重新分布径向强度，决定传播过程中中心峰值是否保持主导地位或被离轴最大值超越，还会控制主导旁瓣的径向位移。对于有限孔径的贝塞尔-高斯光束，同一参数可量化近似抗衍射的环形结构在传播期间如何随λ为负而展宽、随λ为正而压缩。
英文摘要
We investigate the propagation of structured scalar optical beams in an effective anisotropic background inspired by the scalar sector of the Standard-Model Extension and controlled by a single dimensionless parameter $λ$. The physically relevant configuration is a transverse radial director field that modifies the radial part of the Helmholtz operator while preserving axial symmetry. Starting from the Green-function representation, we cast the propagation problem as an initial-value spectral reconstruction of a prescribed finite-aperture entrance profile at $z=0$ and verify that this profile is recovered at the launch plane across the values of $λ$ used in the analysis, within small numerical error. We use the Laguerre--Gaussian mode $L_3$ as the representative vortex-free Laguerre case, retain $L_4$ only as a quantitative benchmark for radial-order dependence, and compare both with a Bessel--Gaussian beam of input order $m=0$. The effective anisotropy produces a systematic redistribution of radial intensity, determines whether the central peak remains dominant or is overtaken by off-axis maxima as propagation advances, and controls the radial displacement of the dominant side lobes. For the finite-aperture Bessel--Gaussian beam, the same parameter quantifies how the approximately diffraction-resistant ring structure broadens for negative $λ$ and compresses for positive $λ$ during propagation.
Comments15 pages, 6 figures
Journal refJournal of Physics Communications, 10 085005 (2026)
