Graphene oxide (GO) ultrathin flat lenses have provided a new and viable solution to achieve high resolution, high efficiency, ultra-light weight, integratable and flexible optical systems. Current GO lenses are designed based on the Fresnel diffraction model, which uses a paraxial approximation for low numerical aperture (NA) focusing process. Herein we develop a lens design method based on the Rayleigh-Sommerfeld (RS) diffraction theory that is able to unambiguously determine the radii of each ring without the optimization process for the first time. More importantly, the RS design method is able to accurately design GO lenses with arbitrary NA and focal length. Our design is experimentally confirmed by fabricating high NA GO lenses with both short and long focal lengths. Compared with the conventional Fresnel design methods, the differences in ring positions and the resulted focal length are up to 13.9% and 9.1%, respectively. Our method can be further applied to design high performance flat lenses of arbitrary materials given the NA and focal length requirements, including metasurfaces or other two-dimensional materials.
An accurate design of graphene oxide ultrathin flat lens based on Rayleigh-Sommerfeld theory
1 Mahajan V N. Aberration Theory Made Simple (SPIE Optical Engineering Press, Bellingham, WA, 1991).
2 Lu D, Lin Z W. Hyperlenses and metalenses for far-field super-resolution imaging. Nat Commun3, 1205 (2012). DOI:10.1038/ncomms2176
3 Liu Z W, Steele J M, Srituravanich W, Pikus Y, Sun C et al. Focusing surface plasmons with a plasmonic lens. Nano Lett5, 1726-1729 (2005). DOI:10.1021/nl051013j
4 Fang N, Lee H, Sun C, Zhang X. Sub-diffraction-limited optical imaging with a silver superlens. Science308, 534-537 (2005). DOI:10.1126/science.1108759
5 Verslegers L, Catrysse P B, Yu Z, White J S, Barnard E S et al. Planar lenses based on nanoscale slit arrays in a metallic film. Nano Lett9, 235-238 (2009). DOI:10.1021/nl802830y
6 Yu N F, Capasso F. Flat optics with designer metasurfaces. Nat Mater13, 139-150 (2014). DOI:10.1038/nmat3839
7 Kildishev A V, Boltasseva A, Shalaev V M. Planar photonics with metasurfaces. Science339, 1232009 (2013). DOI:10.1126/science.1232009
8 Aieta F, Genevet P, Kats M A, Yu N F, Blanchard R et al. Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces. Nano Lett12, 4932-4936 (2012). DOI:10.1021/nl302516v
9 Rogers E T F, Lindberg J, Roy T, Savo S, Chad J E et al. A super-oscillatory lens optical microscope for subwavelength imaging. Nat Mater11, 432-435 (2012). DOI:10.1038/nmat3280
10 Qin F, Huang K, Wu J F, Teng J H, Qiu C W et al. A supercritical lens optical label-free microscopy: Sub-diffraction resolution and ultra-long working distance. Adv Mater29, 1602721 (2017). DOI:10.1002/adma.201602721
11 Zheng X R, Jia B H, Lin H, Qiu L, Li D et al. Highly efficient and ultra-broadband graphene oxide ultrathin lenses with three-dimensional subwavelength focusing. Nat Commun6, 8433 (2015). DOI:10.1038/ncomms9433
12 Gao H W, Hyun J K, Lee M H, Yang J C, Lauhon L J et al. Broadband plasmonic microlenses based on patches of nanoholes. Nano Lett10, 4111-4116 (2010). DOI:10.1021/nl1022892
13 Wang Y X, Yun W B, Jacobsen C. Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging. Nature424, 50-53 (2003). DOI:10.1038/nature01756
14 Wang S C, Ouyang X Y, Feng Z W, Gao Y Y, Gu M et al. Diffractive photonic applications mediated by laser reduced graphene oxides. Opto-Electron Adv1, 170002 (2018).
15 Zheng X R, Lin H, Yang T S, Jia B H. Laser trimming of graphene oxide for functional photonic applications. J Phys D: Appl Phys50, 074003 (2017). DOI:10.1088/1361-6463/aa54e9
16 Ojeda-Casta eda J, Gómez-Reino C. Selected Papers on Zone Plates (SPIE Press, Bellingham, WA, 1996).
17 Cao Q, Jahns J. Modified Fresnel zone plates that produce sharp Gaussian focal spots. J Opt Soc Am A20, 1576-1581 (2003). DOI:10.1364/JOSAA.20.001576
18 Yu Y H, Tian Z N, Jiang T, Niu L G, Gao B R. Fabrication of large-scale multilevel phase-type Fresnel zone plate arrays by femtosecond laser direct writing. Opt Commun362, 69-72 (2016). DOI:10.1016/j.optcom.2015.08.039
19 Wang X K, Xie Z W, Sun W F, Feng S F, Cui Y et al. Focusing and imaging of a virtual all-optical tunable terahertz Fresnel zone plate. Opt Lett38, 4731-4734 (2013). DOI:10.1364/OL.38.004731
20 Saavedra G, Furlan W D, Monsoriu J A. Fractal zone plates. Opt Lett28, 971-973 (2003). DOI:10.1364/OL.28.000971
21 Solak H H, David C, Gobrecht J. Fabrication of high-resolution zone plates with wideband extreme-ultraviolet holography. Appl Phys Lett85, 2700-2702 (2004). DOI:10.1063/1.1803937
22 Kunz K S, Luebbers R J. The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Roca Raton, FL, 1993).
23 Taflove A. Review of the formulation and applications of the finite-difference time-domain method for numerical modeling of electromagnetic wave interactions with arbitrary structures. Wave Motion10, 547-582 (1988). DOI:10.1016/0165-2125(88)90012-1
24 Zhang H R, Zhang F C, Liang Y, Huang X G, Jia B H. Diodelike asymmetric transmission in hybrid plasmonic waveguides via breaking polarization symmetry. J Phys D: Appl Phys50, 165104 (2017). DOI:10.1088/1361-6463/aa613a
25 Byrnes S J, Lenef A, Aieta F, Capasso F. Designing large, high-efficiency, high-numerical-aperture, transmissive meta-lenses for visible light. Opt Express24, 5110-5124 (2016). DOI:10.1364/OE.24.005110
26 Zhuang Z F, Yu F H. Optimization design of hybrid Fresnel-based concentrator for generating uniformity irradiance with the broad solar spectrum. Opt Laser Technol60, 27-33 (2014). DOI:10.1016/j.optlastec.2013.12.021
27 Huang K, Shi P, Kang X L, Zhang X B, Li Y P. Design of DOE for generating a needle of a strong longitudinally polarized field. Opt Lett35, 965-967(2010). DOI:10.1364/OL.35.000965
28 Gu M. Advanced Optical Imaging Theory (Springer, Berlin Heidelberg, 2000).
29 Goodman J W. Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
30 Hecht E. Optics 4th ed (Addison-Wesley, Boston, 2002).
31 Zheng X R, Jia B H, Chen X, Gu M. In situ third-order non-linear responses during laser reduction of graphene oxide thin films towards on-chip non-linear photonic devices. Adv Mater26, 2699-2703 (2014). DOI:10.1002/adma.201304681
32 Li X P, Zhang Q M, Chen X, Gu M. Giant refractive-index modulation by two-photon reduction of fluorescent graphene oxides for multimode optical recording. Sci Rep3, 2819 (2013). DOI:10.1038/srep02819
33 Yang T S, Lin H, Jia B H. Two-dimensional material functional devices enabled by direct laser fabrication. Front Optoelectron11, 2-22 (2018). DOI:10.1007/s12200-017-0753-1
引用本文： Cao G Y, Gan X S, Lin H, Jia B H. An accurate design of graphene oxide ultrathin flat lens based on Rayleigh-Sommerfeld theory. Opto-Electron Adv 1, 180012 (2018).
Extraordinary optical fields in nanostructures: from sub-diffraction-limited optics to sensing and energy conversion
Chemical Society Reviews, 2019