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The singular plasmonic metasurfaces differ from the conventional metasurface, as they are featured with singular points, like sharp corners or small gaps. Even though these singularities are tiny for the whole structure, they totally change the optical response of the metasurface. Instead of a discrete nature of conventional metasurface, the singular metasurface possesses a continuous spectrum. This continuous nature comes from the hidden dimensions at the singular point, making the mode of singular metasurface excited at whatever incident angle or frequency. This continuous nature of a singular metasurface leads to a broadband absorption, forming a grey or even black surface. For instance, a shining flat gold surface becomes a black surface after structuring the surface with sharp tips. These sharp singular points have a broadband absorption such that the light with different colors are all absorbed, leading to a black surface. This thesis is devoted to the analytic study of the singular metasurface. By transforming the complex singular metasurface into the simple slab geometry, the analytic solution is obtained. In the slab frame, we acquire the source excitation, the dispersion relation and the absorption. This absorption is then modeled as the surface conductivity in the metasurface frame, largely simplifying the calculation. However, the sharp vertex in the singular metasurface can go down to the screening length that the spatial dispersion should be considered. After introducing the nonlocal effect into the calculation, the continuous spectrum becomes discrete for the singular metasurface. The role of spatial dispersion is to smear the singular point such that the field enhancement there is reduced. Also, we point out that the degree of nonlocality can be measured from the discrete spectrum by observing the spacing between the peaks. In addition, we also apply our calculation in the field of electron energy loss spectroscopy (EELS), where the optical response of the singular metasurface in time domain is investigated. Finally, we have also implemented transformation optics to facilitate the calculation of the coaxial aperture array in the field of extraordinary optical transmission (EOT), for which the calculation efficiency has been increased at least tenfold. Open Access |
