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艾里变换是一种能实现高斯光束与艾里光束相互转换的神奇光学变换。一阶艾里导数光束，作为艾里光束的进阶型，在经过艾里变换后会产生怎样的光束？这就是本文所要研究的内容。当艾里系数大于负的横向比例因子时，一阶艾里导数光束的艾里变换在任意一个横向上的光场是偏心艾里光束和偏心一阶艾里导数光束之和。当艾里系数等于负的横向比例因子时，一阶艾里导数光束的艾里变换在任意一个横向上的光场是两个偏心优美厄米-高斯光束之和。此外，分别导出了一阶艾里导数光束经艾里变换后的质心和光束半宽在上述两种情形下的解析表达式。最后，实验上实现了一阶艾里导数光束的艾里变换，并测量了艾里系数对光强分布、质心和光束半宽的影响。一阶艾里导数光束艾里变换的研究拓宽了特殊形态分布光束的获取途径，有望应用于光通信和分束技术等领域。As a remarkable optical transformation enabling mutual conversion between Gaussian and Airy beams, the Airy transformation raises intriguing questions when applied to Airyprime beam—an advanced variant of conventional Airy beam. To address this inquiry, this study combines numerical simulations with experimental verification. Results reveal two distinct operational regimes: when the Airy coefficients exceed the negative transverse scale factor, the Airy-transformed optical field of Airyprime beam in any transverse direction becomes equivalent to the superposition of eccentric Airy beam and eccentric Airyprime beam. Conversely, when the Airy coefficients equal the negative transverse scale factor, the transformed optical field equivalently corresponds to the sum of two displaced elegant Hermite-Gaussian beams. Analytical expressions for centroids and beam half width under both regimes have been rigorously derived. Experimental validation through Airy transformation of Airyprime beams systematically measures the Airy coefficients’ influence on intensity distribution, centroid displacement, and beam half width. This investigation establishes a novel methodology for generating complex beam profiles while enhancing the potential application value of such beams in optical communication and beam-splitting technology.
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Keywords:
- Airyprime beam /
- Airy transformation /
- Airy coefficients /
- centroid /
- beam half width
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