超穎透鏡具有輕薄、平坦、可控性高的優勢，藉由在金屬薄膜表面上建立奈米結構，可以調製電磁波的振幅、偏振與相位，並實現成像、聚焦等應用。本研究提出具有不同奈米孔洞陣列的表面電漿超穎透鏡，並透過實驗與數值模擬探討了其光束效應。我們先在玻璃基板上沉積銀薄膜，接著利用雙束型聚焦離子束在銀膜上製作出同心橢圓奈米孔陣列的結構。本次實驗中，我們使用紫外和可見光區域的線偏振光作為入射光，由於橢圓形奈米孔的雙折射效應，橢圓孔長軸的旋轉角度和銀膜的厚度會影響橢圓形奈米孔透射光的偏振態和大小，當內部橢圓孔陣列的長軸與外部橢圓孔陣列的長軸互相垂直時，會在透鏡上產生正交偏振，使得超穎透鏡產生具有強聚焦能力的透射光，因此我們可以透過旋轉超穎透鏡的橢圓長軸來控制光束的聚焦表現。

Metalens has the advantages of being thin, flat, and highly controllable. By building nanostructures on the surface of metal films, it can modulate the amplitude, polarization and phase of electromagnetic waves, and realize applications such as imaging and focusing. In this study, the plasmonic metalenses with different nanohole arrays are proposed, and their beam effects are discussed through experiments and numerical simulations. We deposited a thin silver film on a glass substrate and then milled concentric elliptical nanohole arrays by using a dual-beam focused ion beam. We use linearly polarized light with the ultraviolet and visible regions as the incident light. Due to the birefringence effect of the elliptical nanohole, the rotation angle of the major axis of the elliptical hole and the thickness of the silver film will affect the polarization state of the transmitted light. When the major axis of the inner elliptical hole array and the outer elliptical hole array are perpendicular to each other, orthogonal polarization will be generated on the lens. The metalens generates transmitted light with a strong focusing ability. We can rotate the major axis of the nanoholes on the metalens to control the focusing performance of the beam.

1. Rayleigh, XXXI. Investigations in optics, with special reference to the spectroscope. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1879. 8(49): p. 261-274.

2. Abbe, E., Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung. Archiv für Mikroskopische Anatomie, 1873. 9(1): p. 413-468.

3. Wood, R.W., On a remarkable case of uneven distribution of light in a diffraction grating spectrum. Philosophical Magazine, 1902. 4(19-24): p. 396-402.

4. Fano, U., The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld's waves). Journal of the Optical Society of America, 1941. 31(3): p. 213-222.

5. Hessel, A. and A.A. Oliner, A New Theory of Wood’s Anomalies on Optical Gratings. Applied Optics, 1965. 4(10): p. 1275-1297.

6. Garnett, J.C.M., Colours in metal glasses and in metallic films. Philosophical Transactions of the Royal Society of London Series a-Containing Papers of a Mathematical or Physical Character, 1904. 203: p. 385-420.

7. Mie, G., Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen. Annalen der Physik, 1908. 330(3): p. 377-445.

8. Ritchie, R.H., Plasma Losses by Fast Electrons in Thin Films. Physical Review, 1957. 106(5): p. 874-881.

9. Zhang, J., L. Zhang, and W. Xu, Surface plasmon polaritons: physics and applications. Journal of Physics D: Applied Physics, 2012. 45(11): p. 113001.
10. 吳民耀, 劉威志, 表面電漿子理論與模擬. 物理, 2006. 28:2 p. 486-496.

11. Kelly, K.L., et al., The Optical Properties of Metal Nanoparticles:  The Influence of Size, Shape, and Dielectric Environment. The Journal of Physical Chemistry B, 2003. 107(3): p. 668-677.

12. Mayer, K.M. and J.H. Hafner, Localized Surface Plasmon Resonance Sensors. Chemical Reviews, 2011. 111(6): p. 3828-3857.

13. Link, S. and M.A. El-Sayed, Size and Temperature Dependence of the Plasmon Absorption of Colloidal Gold Nanoparticles. The Journal of Physical Chemistry B, 1999. 103(21): p. 4212-4217.

14. Link, S. and M.A. El-Sayed, Simulation of the Optical Absorption Spectra of Gold Nanorods as a Function of Their Aspect Ratio and the Effect of the Medium Dielectric Constant. The Journal of Physical Chemistry B, 2005. 109(20): p. 10531-10532.

15. Lu, X., et al., Chemical Synthesis of Novel Plasmonic Nanoparticles. Annual Review of Physical Chemistry, 2009. 60(1): p. 167-192.

16. Zhao, J., et al., Localized surface plasmon resonance biosensors. Nanomedicine, 2006. 1(2): p. 219-228.

17. Petryayeva, E. and U.J. Krull, Localized surface plasmon resonance: Nanostructures, bioassays and biosensing—A review. Analytica Chimica Acta, 2011. 706(1): p. 8-24.

18. Haes, A.J., et al., A Localized Surface Plasmon Resonance Biosensor:  First Steps toward an Assay for Alzheimer's Disease. Nano Letters, 2004. 4(6): p. 1029-1034.

19. Chen, J., et al., Optimization and application of reflective LSPR optical fiber biosensors based on silver nanoparticles. Sensors (Basel), 2015. 15(6): p. 12205-17.

20. Hossain, M.K., et al., Surface-enhanced Raman scattering: realization of localized surface plasmon resonance using unique substrates and methods. Anal Bioanal Chem, 2009. 394(7): p. 1747-60.

21. Zhang, S., et al., Metasurfaces for biomedical applications: imaging and sensing from a nanophotonics perspective. Nanophotonics, 2020. 10(1): p. 259-293.

22. Lin, Z., et al., On the role of localized surface plasmon resonance in UV-Vis light irradiated Au/TiO2 photocatalysis systems: pros and cons. Nanoscale, 2015. 7(9): p. 4114-4123.

23. Banholzer, M.J., et al., Rationally designed nanostructures for surface-enhanced Raman spectroscopy. Chemical Society Reviews, 2008. 37(5): p. 885.

24. Uddin, A. and X. Yang, Surface plasmonic effects on organic solar cells. J Nanosci Nanotechnol, 2014. 14(2): p. 1099-119.

25. Yu, N., et al., Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction. Science, 2011. 334(6054): p. 333-337.

26. Aieta, F., et al., Aberration-Free Ultrathin Flat Lenses and Axicons at Telecom Wavelengths Based on Plasmonic Metasurfaces. Nano Letters, 2012. 12(9): p. 4932-4936.

27. Huang, Y.-W., et al., Design of plasmonic toroidal metamaterials at optical frequencies. Optics Express, 2012. 20(2): p. 1760-1768.

28. Liu, M. and D.-Y. Choi, Extreme Huygens’ Metasurfaces Based on Quasi-Bound States in the Continuum. Nano Letters, 2018. 18(12): p. 8062-8069.

29. Yu, N., et al., A Broadband, Background-Free Quarter-Wave Plate Based on Plasmonic Metasurfaces. Nano Letters, 2012. 12(12): p. 6328-6333.

30. Zhang, X., et al., Broadband Terahertz Wave Deflection Based on C-shape Complex Metamaterials with Phase Discontinuities. Advanced Materials, 2013. 25(33): p. 4567-4572.

31. Aieta, F., et al., Out-of-Plane Reflection and Refraction of Light by Anisotropic Optical Antenna Metasurfaces with Phase Discontinuities. Nano Letters, 2012. 12(3): p. 1702-1706.

32. Liu, W., et al., Diffractive metalens: from fundamentals, practical applications to current trends. Advances in Physics: X, 2020. 5(1): p. 1742584.

33. Avayu, O., et al., Composite functional metasurfaces for multispectral achromatic optics. Nature Communications, 2017. 8(1): p. 14992.

34. Yang, Y., et al., Dielectric Meta-Reflectarray for Broadband Linear Polarization Conversion and Optical Vortex Generation. Nano Letters, 2014. 14(3): p. 1394-1399.

35. Khorasaninejad, M., et al., Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging. Science, 2016. 352(6290): p. 1190-1194.

36. Arbabi, A., et al., Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays. Nature Communications, 2015. 6(1): p. 7069.

37. Engelberg, J., et al., Near-IR wide-field-of-view Huygens metalens for outdoor imaging applications. Nanophotonics, 2020. 9(2): p. 361-370.

38. Sinton, D., R. Gordon, and A.G. Brolo, Nanohole arrays in metal films as optofluidic elements: progress and potential. Microfluidics and Nanofluidics, 2008. 4(1-2): p. 107-116.

39. Bethe, H.A., Theory of Diffraction by Small Holes. Physical Review, 1944. 66(7-8): p. 163-182.

40. Shin, H., P.B. Catrysse, and S. Fan, Effect of the plasmonic dispersion relation on the transmission properties of subwavelength cylindrical holes. Physical Review B, 2005. 72(8).

41. Martín-Moreno, L., et al., Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays. Physical Review Letters, 2001. 86(6): p. 1114-1117.

42. Martín-Moreno, L. and F.J. García-Vidal, Optical transmission through circular hole arrays in optically thick metal films. Optics Express, 2004. 12(16): p. 3619-3628.

43. Zhang, Q., et al., Vector beam generation based on the nanometer-scale rectangular holes. Optics Express, 2017. 25(26): p. 33480-33486.

44. Liu, X., et al., Highly sensitive deep-silver-nanowell arrays (d-AgNWAs) for refractometric sensing. Nano Research, 2017. 10(3): p. 908-921.

45. Rodrigo, S.G., F.J. García-Vidal, and L. Martín-Moreno, Influence of material properties on extraordinary optical transmission through hole arrays. Physical Review B, 2008. 77(7).

46. Sun, J., et al., Spinning Light on the Nanoscale. Nano Letters, 2014. 14(5): p. 2726-2729.

47. Zhang, M., et al., Theory of extraordinary light transmission through sub-wavelength circular hole arrays. Journal of Optics, 2010. 12(1): p. 015004.

48. Zhang, X., et al., Near-field plasmon effects in extraordinary optical transmission through periodic triangular hole arrays. Optical Engineering, 2014. 53(10): p. 107108.

49. Liu, L., et al., Color filtering and displaying based on hole array. Optics Communications, 2019. 436: p. 96-100.

50. Berry, M.V. and M. Wilkinson, Diabolical Points in the Spectra of Triangles. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1984. 392(1802): p. 15-43.

51. Han, Y., et al., Multi-wavelength focusing based on nanoholes. New Journal of Physics, 2020. 22(7): p. 073021.

52. Hasman, E., et al., Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics. Applied Physics Letters, 2003. 82(3): p. 328-330.

53. Overvig, A.C., S.C. Malek, and N. Yu, Multifunctional Nonlocal Metasurfaces. Physical Review Letters, 2020. 125(1).

54. Shi, J., et al., Coherent control of Snell’s law at metasurfaces. Optics Express, 2014. 22(17): p. 21051-21060.

55. Pu, M., et al., Catenary optics for achromatic generation of perfect optical angular momentum. Science Advances, 2015. 1(9): p. e1500396.

56. Ni, X., et al., Ultra-thin, planar, Babinet-inverted plasmonic metalenses. Light: Science & Applications, 2013. 2(4): p. e72-e72.

57. Zhou, C., et al., Optical Singularity Built on Tiny Holes. Annalen der Physik, 2021. 533(12): p. 2100147.

58. Zhang, Q., et al., Generation of vector beams using spatial variation nanoslits with linearly polarized light illumination. Optics Express, 2018. 26(18): p. 24145-24153.

59. Wang, H., et al., Spatial multiplexing plasmonic metalenses based on nanometer cross holes. New Journal of Physics, 2018. 20(12): p. 123009.

60. Wang, Y., et al., Broadband Ultrathin Transmission Quarter Waveplate with Rectangular Hole Array Based on Plasmonic Resonances. Nanoscale Research Letters, 2019. 14(1).

61. Yang, H., et al., Annihilating optical angular momentum and realizing a meta-waveplate with anomalous functionalities. Optics Express, 2017. 25(15): p. 16907-16915.

62. Yu, P., et al., Controllable optical activity with non-chiral plasmonic metasurfaces. Light: Science & Applications, 2016. 5(7): p. e16096-e16096.

63. Zhang, Q., et al., Optical vortex generator with linearly polarized light illumination. Journal of Nanophotonics, 2018. 12(1): p. 016011.

64. Wang, H., et al., Plasmonic vortex generator without polarization dependence. New Journal of Physics, 2018. 20(3): p. 033024.

65. Xu, Q., et al., Coupling‐Mediated Selective Spin‐to‐Plasmonic‐Orbital Angular Momentum Conversion. Advanced Optical Materials, 2019. 7(20): p. 1900713.

66. Mou, Z., et al., Uniform theory of plasmonic vortex generation based on nanoholes. Nanotechnology, 2020. 31(45): p. 455301.

67. Chen, C.-F., et al., Creating Optical Near-Field Orbital Angular Momentum in a Gold Metasurface. Nano Letters, 2015. 15(4): p. 2746-2750.

68. Mehmood, M.Q., et al., Visible-Frequency Metasurface for Structuring and Spatially Multiplexing Optical Vortices. Advanced Materials, 2016. 28(13): p. 2533-2539.

69. Bao, R., et al., Generation of diffraction-free beams using resonant metasurfaces. New Journal of Physics, 2020. 22(10): p. 103064.