Light, sound, and electron transmission through a single hole in a screen of finite thickness

The hole has circular shape. For light, the film is made of perfect conductor and the transmission is calculated by solving Maxwell's equations. For sound, the film is made of a hard solid and we solve the Helmholz equation with vanishing normal derivative at the boundaries. For electrons, the film represents an infinite potential region and we solve the Helmholz equation with vanishing wave function at the boundaries. The transmission cross section is normalized to the area of the hole. For more details on light transmission through a single hole, see F. J. García de Abajo, Opt. Express 10, 1475 (2002) and F. J. García de Abajo, Rev. Mod. Phys. 79, 1267 (2007). For a comparison of light, sound, and electron transmission, see F. J. García de Abajo, H. Estrada, and F. Meseguer, New J. Phys. 11, 093013 (2009).

Geometry under consideration: a light, sound, or electron wave impinges normally on a plate perforated by a circular hole.
Geometrical parameters Type of incident wave: light sound electron Thickness/radius ratio = The calculation yields the transmission as a function of the radius/wavelength ratio in the following range: Lower value of radius/wavelength = Upper value of radius/wavelength = Convergence parameters: Number of hole-cavity modes n = (≤5)* Q =(≤5)* *The number of radial parallel wave vectors is ~ 2Q. The calculation must be checked for convergence with n and Q. A copy of the source code can be obtained from Prof. F. J. García de Abajo upon request if larger values of these parameters are needed. Warning: calculations for light can take up to one minute on this server for large n. Permittivity inside hole (only for light) = Permeability inside hole (only for light) =