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Nowadays, methods for analyzing light transmission through subwavelengthstructures are typically based on the mode expansion with Fourier series.However, these methods require sophisticated techniques and the solutions arein $k$-space, where the coupling physics that associates the boundary field inreal space and the structure geometry becomes obscure. Moreover, the typicalmethods for the analysis of multi-layered hybrid configurations can beexhaustive due to the complex mode couplings at the interfaces of the layers.In contrast, an early method can analyze the single-slit transmission forsolutions entirely in real space [F. L. Neerhoff and G. Mur, Appl. Sci. Res.28, 73 (1973)] by rigorously formulating the field based on Green's theorem andobtaining two types of the Green's function for the cylindrical wave mode infree space and the symmetric waveguide modes inside the slit, respectively. Inthis article, we advance the method by developing a new type of Green'sfunction for the asymmetric waveguide modes inside a groove. Since these wavemodes are independent in real space, the coupling physics from the methodbecomes straightforward and the solutions are intuitive. With this meticulousmethod, we show that complex and multi-layered hybrid configurations can beeasily analyzed with excellent accuracy. In addition, the method demonstratesthe capability of translating the wave interaction problems to analyticalphysical models for further interpretation and study.

Advanced analytical method based on Green's theorem for light  transmission through subwavelength structures of multiple configurations in  metal films