On The Gould’s Formula for Stirling Numbers of The Second Kind

We present an alternative deduction of the Gould’s relation for Stirling numbers of the second kind. Our approach is based in the Nörlund polynomials and in the duality property between the Stirling numbers

Shape resonances in nested diffraction gratings

The diffraction problem of a plane wave impinging on a grating formed by nested cavities is solved by means of the modal method, for $s$ and $p$ polarization modes. The cavities are formed by perfectly conducting sheets that describe rectangular profiles. The electromagnetic response of the grating is analyzed, paying particular attention to the generation of resonances within the structure. The dependence of the resonances on the geometrical parameters of the grating is studied, and results of far and near field are shown. The results are checked and compared with those available in the literature for certain limit cases.Comment: 18 pages, 8 figure