2020/12/26 by Jiaxin Zhou, Zhou, Jiaxin, Wangtao Lu +1
Engineering · #35B34 #35B40 #35J05 #35P20 #FOS: Mathematics #FOS: Physical sciences #Microwave Engineering and Waveguides #Microwave and Dielectric Measurement Techniques #Numerical Analysis (math.NA) #Optics (physics.optics) #Plasmonic and Surface Plasmon Research
paper · pdf · doi:10.48550/arxiv.2012.13691
openalex publication_date 2020/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proposes a novel, rigorous and simple Fourier-transformation approach to study resonances in a perfectly conducting slab with finite number of subwavelength slits of width h≪ 1. Since regions outside the slits are variable separated, by Fourier transforming the governing equation, we could express field in the outer regions in terms of field derivatives on the aperture. Next, in each slit where variable separation is still available, wave field could be expressed as a Fourier series in terms of a countable basis functions with unknown Fourier coefficients. Finally, by matching field on the aperture, we establish a linear system of infinite number of equations governing the countable Fourier coefficients. By carefully asymptotic analysis of each entry of the coefficient matrix, we rigorously show that, by removing only a finite number of rows and columns, the resulting principle sub-matrix is diagonally dominant so that the infinite dimensional linear system can be reduced to a finite dimensional linear system. Resonance frequencies are exactly those frequencies making the linear system rank-deficient. This in turn provides a simple, asymptotic formula describing resonance frequencies with accuracy \cal O(h3log h). We emphasize that such a formula is more accurate than all existing results and is the first accurate result especially for slits of number more than two to our best knowledge. Moreover, this asymptotic formula rigorously confirms a fact that the imaginary part of resonance frequencies is always \cal O(h) no matter how we place the slits as long as they are spaced by distances independent of width h.