像散幺正变换中复杂结构光的塔尔博特类似图案演化
Talbot-like pattern evolution in complex structured light from unitary transformation
AI总结：
本研究通过像散幺正变换，揭示了复杂结构化高斯光束中类似塔尔博特效应的模态演化机制，并提出了通用模态转换理论，为空间模态塑造提供了新方法。
摘要：
像散幺正变换允许在同一个模态球上绝热连接近轴高斯光束的所有可行态，即厄米-拉盖尔-高斯（HLG）模式。在这里，我们通过像散变换，对由来自不同模态球的HLG模式组成的复杂结构化高斯光束的幺正模态演化进行了全面研究。在循环变换中，非同步的高阶几何相位在叠加态中引发了类似塔尔博特效应的模态演化，导致在特定测地线回路的变换中出现图案变化和复原。以因斯-高斯模式为例，我们系统地分析并实验验证了图案演化背后的波束成形机制。我们的结果概述了通过像散幺正变换实现结构化高斯光束的通用模态转换理论，为塑造空间模态结构提供了一种新方法。这些发现可能激发基于结构化光的广泛应用。
英文摘要：
Astigmatic unitary transformations allow for the adiabatic connections of all feasible states of paraxial Gaussian beams on the same modal sphere, i.e., Hermite-Laguerre-Gaussian (HLG) modes. Here, we present a comprehensive investigation into the unitary modal evolution of complex structured Gaussian beams, comprised by HLG modes from disparate modal spheres, via astigmatic transformation. The non-synchronized higher-order geometric phases in cyclic transformations originates a Talbot-effect-like modal evolution in the superposition state of these HLG modes, resulting in pattern variations and revivals in transformations with specific geodesic loops. Using Ince-Gaussian modes as an illustrative example, we systematically analyze and experimentally corroborate the beamforming mechanism behind the pattern evolution. Our results outline a generic modal conversion theory of structured Gaussian beams via astigmatic unitary transformation, offering a new approach for shaping spatial modal structure. These findings may inspire a wide variety of applications based on structured light.
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