Abstract
The tightly focused field of an incident light beam through cubic phase modulation has been investigated by vectorial diffraction theory. For different modulation index of cubic phase and polarization states of the incident light, the focused fields have been presented. The results show that the Airy-like field can be produced by cubic phase modulation under high numerical aperture (NA) optical system. Intensity pattern and length of the main lobe are depended on modulation index for the spatial uniform polarization, and the Airy-like field is affected by polarization state for the spatial nonuniform polarization. It is helpful to structure new optical fields in optical manipulation, optical imaging, and surface plasma controlling.
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References
Berry M V, Balazs N L. Nonspreading wave packets. American Journal of Physics, 1979, 47(3): 264–267
Siviloglou G A, Broky J, Dogariu A, Christodoulides D N. Observation of accelerating Airy beams. Physical Review Letters, 2007, 99(21): 213901
Jia S, Vaughan J C, Zhuang X. Isotropic three-dimensional super-resolution imaging with a self-bending point spread function. Nature Photonics, 2014, 8(4): 302–306
Vettenburg T, Dalgarno H I C, Nylk J, Coll-Lladó C, Ferrier D E K, Čižmár T, Gunn-Moore F J, Dholakia K. Light-sheet microscopy using an Airy beam. Nature Methods, 2014, 11(5): 541–544
Chong A, Renninger W H, Christodoulides D N, Wise F W. Airy-Bessel wave packets as versatile linear light bullets. Nature Photonics, 2010, 4(2): 103–106
Abdollahpour D, Suntsov S, Papazoglou D G, Tzortzakis S. Spatiotemporal airy light bullets in the linear and nonlinear regimes. Physical Review Letters, 2010, 105(25): 253901
Baumgartl J, Mazilu M, Dholakia K. Optically mediated particle clearing using Airy wavepackets. Nature Photonics, 2008, 2(11): 675–678
Zhang P, Prakash J, Zhang Z, Mills M S, Efremidis N K, Christodoulides D N, Chen Z. Trapping and guiding microparticles with morphing autofocusing Airy beams. Optics Letters, 2011, 36 (15): 2883–2885
Liu W, Neshev D N, Shadrivov I V, Miroshnichenko A E, Kivshar Y S. Plasmonic Airy beam manipulation in linear optical potentials. Optics Letters, 2011, 36(7): 1164–1166
Belafhal A, Ez-Zariy L, Hennani S, Nebdi H. Theoretical introduction and generation method of a novel nondiffracting waves: Olver beams. Optics and Photonics Journal, 2015, 5(7): 234–246
Khonina S N, Ustinov A V. Fractional Airy beams. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2017, 34(11): 1991–1999
Efremidis N K, Christodoulides D N. Abruptly autofocusing waves. Optics Letters, 2010, 35(23): 4045–4047
Khonina S N, Porfirev A P, Ustinov A V. Sudden autofocusing of superlinear chirp beams. Journal of Optics, 2018, 20(2): 025605
Siviloglou G A, Christodoulides D N. Accelerating finite energy Airy beams. Optics Letters, 2007, 32(8): 979–981
Ellenbogen T, Voloch-Bloch N, Ganany-Padowicz A, Arie A. Nonlinear generation and manipulation of Airy beams. Nature Photonics, 2009, 3(7): 395–398
Dolev I, Ellenbogen T, Voloch-Bloch N, Arie A. Control of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals. Applied Physics Letters, 2009, 95(20): 201112
Dai H T, Sun X W, Luo D, Liu Y J. Airy beams generated by a binary phase element made of polymer-dispersed liquid crystals. Optics Express, 2009, 17(22): 19365–19370
Luo D, Dai H T, Sun X W, Demir H V. Electrically switchable finite energy Airy beams generated by a liquid crystal cell with patterned electrode. Optics Communications, 2010, 283(20): 3846–3849
Gecevicius M, Beresna M, Kazansky P G. Accelerating Airy beams generated by ultrafast laser induced space-variant nanostructures in glass. In: Proceedings of 2012 Conference on Lasers and Electro-Optics (CLEO). San Jose, CA: IEEE, 2012
Cao R, Yang Y, Wang J G, Bu J, Wang M W, Yuan X C. Microfabricated continuous cubic phase plate induced Airy beams for optical manipulation with high power efficiency. Applied Physics Letters, 2011, 99(26): 261106
Cottrell D M, Davis J A, Hazard T M. Direct generation of accelerating Airy beams using a 3/2 phase-only pattern. Optics Letters, 2009, 34(17): 2634–2636
Froehly L, Courvoisier F, Mathis A, Jacquot M, Furfaro L, Giust R, Lacourt P A, Dudley J M. Arbitrary accelerating micron-scale caustic beams in two and three dimensions. Optics Express, 2011, 19(17): 16455–16465
Singh B K, Remez R, Tsur Y, Arie A. Super-Airy beam: self-accelerating beam with intensified main lobe. Optics Letters, 2015, 40(20): 4703–4706
Torre A. Airy beams beyond the paraxial approximation. Optics Communications, 2010, 283(21): 4146–4165
Carretero L, Acebal P, Blaya S, Garcia C, Fimia A, Madrigal R, Murciano A. Nonparaxial diffraction analysis of Airy and SAiry beams. Optics Express, 2009, 17(25): 22432–22441
Bar-David J, Voloch-Bloch N, Mazurski N, Levy U. Unveiling the propagation dynamics of self-accelerating vector beams. Scientific Reports, 2016, 6(1): 34272
Weng X, Song Q, Li X, Gao X, Guo H, Qu J, Zhuang S. Free-space creation of ultralong anti-diffracting beam with multiple energy oscillations adjusted using optical pen. Nature Communications, 2018, 9(1): 5035
Cohen N, Yang S, Andalman A, Broxton M, Grosenick L, Deisseroth K, Horowitz M, Levoy M. Enhancing the performance of the light field microscope using wavefront coding. Optics Express, 2014, 22(20): 24817–24839
King S V, Doblas A, Patwary N, Saavedra G, Martínez-Corral M, Preza C. Spatial light modulator phase mask implementation of wavefront encoded 3D computational-optical microscopy. Applied Optics, 2015, 54(29): 8587–8595
Richards B, Wolf E. Electromagnetic diffraction in optical systems. 2. Structure of the image field in an aplanatic system. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1959, 253(1274): 358–379
Hao X, Kuang C F, Wang T T, Liu X. Effects of polarization on the de-excitation dark focal spot in STED microscopy. Journal of Optics, 2010, 12(11): 115707
Acknowledgements
This work was supported in part by the National Key Research and Development Program of China (Nos. 2017YFC0110303 and 2016YFF0101400); the National Basic Research Program of China (973 Program) (No. 2015CB352003); the Natural Science Foundation of Zhejiang province (No. LR16F050001); the Fundamental Research Funds for the Central Universities (No. 2017FZA5004); and the Natural Science Foundation of Shanghai (No. 16ZR1412900).
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Yong Liu obtained his Ph.D. degree from University of Shanghai for Science and Technology, Shanghai, China, in 2007. Currently, he is an associate professor at Shanghai University of Electric Power, Shanghai, China. His research interests are point spread function engineering and new imaging method. He focuses on optical microscopy imaging and optical coherence tomography.
Zhifeng Zhang received his Ph.D. degree in optical engineering from Beijing Jiaotong University. He is an associate professor and a Master tutor at the Zhengzhou University of Light Industry. His research interests are mainly in research and design of novel optical instruments and computer imaging technique.
Cuifang Kuang obtained his Ph.D. degree from Beijing Jiaotong University, Beijing, China, in 2007. Currently, he is a professor at Zhejiang University, Hangzhou, China. He recently focuses on optical superresolution and optical microscopy imaging.
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Liu, Y., Zhang, Z. & Kuang, C. Airy-like field under high numerical aperture optical system. Front. Optoelectron. 12, 397–404 (2019). https://doi.org/10.1007/s12200-019-0866-9
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DOI: https://doi.org/10.1007/s12200-019-0866-9