拉盖尔-高斯光照射下Cu₂O中的 paraexciton（仲激子）激发
Paraexciton Excitation in Cu$_2$O under Laguerre--Gaussian Illumination
AI总结：
本研究探究拉盖尔-高斯光照射下Cu₂O中仲激子的激发，发现需结合OAM通道的对称性与光场空间局域性，为其结构光激发提供了设计规则。
AI中文摘要：
在Cu₂O中，最低的黄色激子Γ₂⁺ paraexciton（仲激子）在常规光谱学中是光学不可达的，因为向该态的跃迁在电偶极和电四极近似中都是禁戒的。我们研究携带轨道角动量（OAM）的光场是否能克服这一限制。微观对称性分析表明，梯度辅助的l=5和直接的l=6 OAM通道是耦合到仲激子的主要贡献，且与光场的详细径向分布无关。然而，对有限束腰的拉盖尔-高斯光束的计算显示，由于光场在激子玻尔半径上变化极弱，对应的矩阵元被强烈抑制。因此，仅满足OAM选择规则是不够的：高效激发不仅需要正确的角对称性，还需要光场在激子的空间尺度上变化。这一条件可通过局域化的OAM场实现。用物理强度环半径表示耦合，可直接比较光和激子的长度尺度，并揭示最优局域化主要由目标立方谐波的多项式阶数决定。对于六阶Γ₂⁺仲激子，最强耦合发生在强度环半径约为6a_B–7a_B处。这些结果表明，仲激子激发由对称性和空间局域性共同决定：立方对称性选择允许的OAM通道，而多项式阶数设定高效耦合的特征径向尺度。本工作为设计Cu₂O中仲激子的结构光激发提供了对称性框架和实用设计规则。
英文摘要：
In Cu$_2$O the lowest yellow exciton, the $Γ_2^+$ paraexciton, is optically inaccessible in conventional spectroscopy because transitions to this state are forbidden in both electric-dipole and electric-quadrupole approximations. We investigate whether optical fields carrying orbital angular momentum (OAM) can overcome this restriction. A microscopic symmetry analysis identifies the gradient-assisted $l=5$ and direct $l=6$ OAM channels as the leading contributions that couple to the paraexciton, independent of the detailed radial profile of the optical field. Calculations for finite-waist Laguerre--Gaussian beams, however, show that the corresponding matrix elements are strongly suppressed because the optical field varies only weakly over the exciton Bohr radius. Thus, satisfying the OAM selection rule alone is insufficient: efficient excitation requires not only the correct angular symmetry but also optical-field variations on the spatial scale of the exciton. This second condition is achieved by localized OAM fields. Expressing the coupling in terms of the physical intensity-ring radius provides a direct comparison between the optical and excitonic length scales and reveals that the optimal localization is determined primarily by the polynomial degree of the target cubic harmonic. For the degree-six $Γ_2^+$ paraexciton the strongest coupling occurs for an intensity-ring radius of approximately $6a_B$--$7a_B$. These results establish that paraexciton excitation is governed jointly by symmetry and spatial localization: cubic symmetry selects the allowed OAM channels, whereas the polynomial degree sets the characteristic radial scale for efficient coupling. This work provides both the symmetry framework and a practical design rule for engineering structured-light excitation of paraexcitons in Cu$_2$O.
