先前之研究中，對狹縫的漏斗效應已有較完整的了解，而孔洞的漏斗效應之特性仍待研究。因此，本研究主要探討三維孔洞之漏斗效應，並以我們定義的漏斗形狀進一步分析漏斗效應之特性。孔洞入口處之能量流與漏斗效應會隨時間改變，其週期為光週期的一半。我們發現孔洞邊界上會產生電流，造成金屬表面之電荷分佈與孔洞入口處之電磁場改變，影響漏斗效應的範圍。此外，漏斗效應的範圍會隨著孔洞z方向之長度而改變，我們發現在孔洞長度為1.5個波長時，孔洞中心區域沒有漏斗效應產生，而且孔洞入口處之能量反而往回流。本研究經由對孔洞入口處之能量流與漏斗形狀之分析更深入了解漏斗效應之特性，進一步增進我們對能量進入孔洞的機制之理解。

From previous studies, we already have a more complete understanding about the funneling effect of slit. However, there is no understanding the characteristics of the funneling effect of aperture. In this study, we mainly study the funneling effect into a three-dimensional sub-wavelength rectangular aperture and use the funnel shape we define to analyze the property of the funneling effect. The energy flow and the funneling effect near aperture entrance can change over time and the periods are half of the period of the light. We observe the current is generated on the boundary of the aperture. The current causes change to the charge distribution on the metal surface and the electromagnetic field. The change further influence the scope of the funneling effect. Furthermore, the scope of the funneling effect can change with the length of the aperture in z direction. In particular, when the length of the aperture in z direction is 1.5 times the wavelength, we find that there is no funneling effect at the region closing to the midst of aperture entrance. More interesting is that the energy flow at the region even flows back. This study is more understanding the funneling effect by way of analyzing the energy flow and the funnel shape at the aperture entrance, and it should give us a better understanding of the mechanism in the energy flowing into aperture.

1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
2. J. A. Porto, F. J. García-Vidal, and J. B. Pendry, "Transmission Resonances on Metallic Gratings with Very Narrow Slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
3. Y. Takakura, "Optical Resonance in a Narrow Slit in a Thick Metallic Screen," Phys. Rev. Lett. 86, 5601-5603 (2001).
4. F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, "Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit," Phys. Rev. Lett. 90, 213901 (2003).
5. F. J. Garcı́a-Vidal, L. Martı́n-Moreno, H. J. Lezec, and T. W. Ebbesen, "Focusing light with a single subwavelength aperture flanked by surface corrugations," Appl. Phys. Lett. 83, 4500 (2003).
6. D. A. Thomas, and H. P. Hughes, "Enhanced optical transmission through a subwavelength 1D aperture," Solid State Commun. 129, 519-524 (2004).
7. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, "Enhanced light transmission through a single subwavelength aperture," Opt. Lett. 26, 1972-1974 (2001).
8. F. J. García-Vidal, L. Martín-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, "Transmission of light through a single rectangular hole in a real metal," Physical Review B 74, 153411 (2006).
9. S. Astilean, P. Lalanne, and M. Palamaru, "Light transmission through metallic channels much smaller than the wavelength," Opt. Commun. 175, 265-273 (2000).
10. F. J. García-Vidal, and L. Martín-Moreno, "Transmission and focusing of light in one-dimensional periodically nanostructured metals," Physical Review B 66, 155412 (2002).
11. J. Bravo-Abad, L. Martín-Moreno, and F. J. García-Vidal, "Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit," Physical Review E 69, 026601 (2004).
12. B. Sturman, E. Podivilov, and M. Gorkunov, "Transmission and diffraction properties of a narrow slit in a perfect metal," Physical Review B 82, 115419 (2010).
13. Y. Zeng, Y. Fu, X. Chen, W. Lu, and H. Ågren, "Dynamics of the damping oscillator formed by the collective generation of surface polaritons for extraordinary light transmission through subwavelength hole arrays in thin metal films," Physical Review B 76, 125409 (2007).
14. D. C. Adams, S. Inampudi, T. Ribaudo, D. Slocum, S. Vangala, N. A. Kuhta, W. D. Goodhue, V. A. Podolskiy, and D. Wasserman, "Funneling Light through a Subwavelength Aperture with Epsilon-Near-Zero Materials," Phys. Rev. Lett. 107, 133901 (2011).
15. G. Subramania, S. Foteinopoulou, and I. Brener, "Nonresonant Broadband Funneling of Light via Ultrasubwavelength Channels," Phys. Rev. Lett. 107, 163902 (2011).
16. F. Pardo, P. Bouchon, R. Haïdar, and J.-L. Pelouard, "Light Funneling Mechanism Explained by Magnetoelectric Interference," Phys. Rev. Lett. 107, 093902 (2011).
17. P. Bouchon, F. Pardo, B. Portier, L. Ferlazzo, P. Ghenuche, G. Dagher, C. Dupuis, N. Bardou, R. Haïdar, and J.-L. Pelouard, "Total funneling of light in high aspect ratio plasmonic nanoresonators," Appl. Phys. Lett. 98, 191109 (2011).
18. P. Chevalier, P. Bouchon, R. Haïdar, and F. Pardo, Funneling of light in combinations of metal-insulator-metal resonators (2012).
19. P. Zhu, P. Jin, H. Shi, and L. J. Guo, "Funneling light into subwavelength grooves in metal/dielectric multilayer films," Opt. Express 21, 3595-3602 (2013).
20. D. L. Sounas, and A. Alù, "Color Separation through Spectrally-Selective Optical Funneling," ACS Photonics 3, 620-626 (2016).
21. R. Gordon, "Light in a subwavelength slit in a metal: Propagation and reflection," Physical Review B 73, 153405 (2006).
22. J. Wuenschell, and H. K. Kim, "Excitation and Propagation of Surface Plasmons in a Metallic Nanoslit Structure," IEEE Trans. Nanotechnol. 7, 229-236 (2008).
23. Y. Xi, Y. S. Jung, and H. K. Kim, "Interaction of light with a metal wedge: the role of diffraction in shaping energy flow," Opt. Express 18, 2588-2600 (2010).
24. S.-H. Chang, and Y.-L. Su, "Mapping of transmission spectrum between plasmonic and nonplasmonic single slits. I: resonant transmission," J. Opt. Soc. Am. B 32, 38-44 (2015).
25. J. W. Lee, "The characteristics of light funneling effect into a subwavelength metallic slit," National Cheng Kung University (2016).
26. K. S. Yee, Numerical Solution of Initial Boundary Value Problem Involving Maxwell's Equations in Isotropic Media (1966).
27. K. F. R. Courant, H. Lewy, "Über die partiellen Differenzengleichungen der mathematischen Physik," Mathematische Annalen (in German) 100 (1): 32–74 (1928).
28. G. L. Chen, "The correction of electromagnetic field updates in FDTD method at metal-dielectric boundary," National Cheng Kung University (2015).