李保平,陈健,王静

• 1:天津科学技术馆
• 2:天津市耀华中学

摘要(Abstract)：

波带片在X射线与光学领域中发挥着重要作用。本文提出了一种广义斐波那契波带片(generalized Fibonacci zone plate, GFiZP)设计，该设计能够实现对X射线与光线聚焦特性的调控。与传统斐波那契波带片(Fibonacci zone plate, FiZP)及康托型分形波带片(Cantor-type fractal zone plate, FraZP)相比，该器件为调控聚焦性能提供了更多自由度。相较于康托型分形波带片，广义斐波那契波带片采用膨胀规则而非提取规则构建而成，因此可避免在高递归阶数下形成稀疏结构——而这类稀疏结构往往会给制备工艺带来难题。值得注意的是，数值模拟结果表明，与康托型分形波带片类似，广义斐波那契波带片同样具备两项关键功能：多焦点特性与自相似强度分布。此外，本文还针对不同结构参数下广义斐波那契波带片的轴向辐照度分布展开了详细研究。凭借这些优良特性，这种新型波带片设计在光学制造、微粒子光学操控等领域具有广阔的拓展应用前景。

关键词(KeyWords)： 波带片;斐波那契数列;焦点调控;分形自相似

Abstract:

Keywords:

基金项目(Foundation):

作者(Author): 李保平,陈健,王静

参考文献(References)：

• [1] WANG S,ZHANG X.Terahertz tomographic imaging with a Fresnel lens[J].Chinese Optics Letters,2003,1(1):53-55.
• [2] WANG Y,YUN W,JACOBSEN C.Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging[J].Nature,2003,424(6944):50-53.
• [3] CAO Q,JAHNS J.Modified Fresnel zone plates that produce sharp Gaussian focal spots[J].Journal of the Optical Society of America A-Optics Image Science and Vision,2003,20(8):1576-1581.
• [4] SAAVEDRA G,FURLAN W D,MONSORIU J A.Fractal zone plates[J].Optics Letters,2003,28(12):971-973.
• [5] DAVIS J A,RAMIREZ L,MARTíN-ROMO J A R,et al.Focusing properties of fractal zone plates:experimental implementation with a liquid-crystal display[J].Optics Letters,2004,29(12):1321-1323.
• [6] MONSORIU J A,SAAVEDRA G,FURLAN W D.Fractal zone plates with variable lacunarity[J].Optics Express,2004,12(18):4227-4234.
• [7] DAI H T,WANG X,XU K S.Focusing properties of fractal zone plates with variable lacunarity:experimental studies based on liquid crystal on silicon[J].Chinese Physics Letters,2005,22(11):2851-2854.
• [8] MUNOZ-PEREZO F M,FERRAND V,FURLAN W D,et al.Optical multi-trapping by Kinoform m-Bonacci lenses[J].Optics Express,2022,30(19):34378-34384.
• [9] CANDELAS P,PEREZ-LOPEZ S,FUSTER J M.On the Design of Soret Zone Plates Based on Binary Sequences Using Directional Transducers[J].Sensors,2021,21(18):6086.
• [10] XIA T,CHENG S B,YU W X,et al.Extended bifocal depth imaging with modified generalized composite kinoform Fibonacci lenses[J].Optics and Laser Technology,2022,152:108162.
• [11] XIA T,CHENG S B,TAO S H.A general n-fractal aperiodic zone plate[J].Journal of Modern Optics,2019,66(11):1179-1189.
• [12] LIU S,LIU X J,XIONG Y,et al.Multi-helix beams generated with binary helico-conical phase patterns[J].Journal of the Optical Society of America A-Optics Image Science and Vision,2023,40(9):1706-1713.
• [13] LIU Y J,DAI H T,SUN X W,et al.Electrically switchable phase-type fractal zone plates and fractal photon sieves[J].Optics Express,2009,17(15):12418-12423 .
• [14] DAI H T,LIU J H,SUN X C,et al.Programmable fractal zone plates (FraZPs) with foci finely tuned[J].Optics Communications,2008(22),281:5515-5519.
• [15] FURLAN W D,SAAVEDRA G,MONSORIU J A.White light imaging with fractal zone plates[J].Optics Letters 2007,32(15):2109-2111.
• [16] BRUNO-ALFONSO A,REYES-GóMEZ E,CAVALCANTI S B,Oliveria L E.Band edge states of the 〈n〉=0 gap of Fibonacci photonic lattices[J].Physical Review A,2008,78(3):035801.
• [17] GELLERMANN W,KOHMOTO M,SUTHERLAND B.Localization of light waves in Fibonacci dielectric multilayers[J].Physical Review Letters,1994,72(5):633-636.
• [18] DAI H T,LIU Y J,SUN X W.The focusing property of the spiral Fibonacci zone plates[J].2012,Proceedings SPIE 8257,82570T.
• [19] GAO N,ZHANG Y C,XIE C Q.Circular Fibonacci gratings[J].Applied Optics,2011,50(31):G142-G148.
• [20] OH G Y,LEE M H.Band-structural and Fourier-spectral properties of one-dimensional generalized Fibonacci lattices[J].Physical Review B,1993,48(17):465-477.