Bethe’s aperture theory for arrays

Bethe’s theory is applied to the optical transmission through an array of apertures in an infinitely thin perfect electric conductor. This method shows that, in the small-aperture limit, the lowest-order TM evanescent mode governs the transmission process, allowing for both 100% transmission at the passband wavelength and zero transmission at the Wood’s anomaly. The applicability of this theory to total transmission in other systems is discussed, and a specific example of a single aperture in a transverse screen of a rectangular waveguide is given.

Figure 1

(a) Geometry of aperture array for the case of circular holes. (b) Schematic of transverse electric field distribution for $y=z=0$. The PEC is shown with a thick black line, the constant electric field of the transmitted plane wave is shown with a dashed line, and the nonconstant field is shown with a gray line. The constant and nonconstant field components cancel each other out over the PEC. (c) Schematic of aperture in transverse PEC screen in a rectangular waveguide.

Figure 2

Transmittivity for arrays of circles, holes, and rectangles, each with the apertures covering 2% of the total area. Rectangle $A$ is half as wide in the direction of the electric polarization, and rectangle $B$ is twice as wide in that direction.