H H Wills Physics Laboratory, University of Bristol, Bristol, UK.
Opt Lett. 2013 May 15;38(10):1639-41. doi: 10.1364/OL.38.001639.
We present a mathematical analysis of the finite-energy Airy beam with a sharply truncated spectrum, which can be generated by a uniformly illuminated, finite-sized spatial light modulator, or windowed cubic phase mask. The resulting "incomplete Airy beam" is tractable mathematically, and differs from an infinite-energy Airy beam by an additional oscillating modulation and the decay of its fringes. Its propagation can be described explicitly using an incomplete Airy function, from which we derive simple expressions for the beam's total power and mean position. Asymptotic analysis reveals a simple connection between the cutoff and the region of the beam with Airy-like behavior.
我们提出了一种对有限能量 Airy 光束的数学分析，该光束具有急剧截断的光谱，可通过均匀照明的有限尺寸空间光调制器或窗状立方位相掩模生成。所得的“不完全 Airy 光束”在数学上是可处理的，与无限能量 Airy 光束的区别在于附加的振荡调制和条纹的衰减。它的传播可以使用不完全 Airy 函数显式描述，从中我们得出了光束总功率和平均位置的简单表达式。渐近分析揭示了截止与具有类似 Airy 行为的光束区域之间的简单关系。
