The penetration of electromagnetic fields through small apertures has been a problem of enduring interests. For instance, Load Rayleigh proposed a solution expressed in a power expansion with respect to the wave number, k. According to Bethe's theory. the transmitted field of the small aperture maybe represented approximately by the fields of an electric and magnetic dipoles located at the center of aperture. The magnitude of magnetic dipole moments can be expressed as a multiplication of a polarizability and the magnetic field which lies in the plane of the aperture. As results of the analysis on the magnetic potential penetration through apertures, in chapter 2 ~ 5, magnetic polarizabilities are easily calculated.
In chapter 2, the magnetostatic potential penetration through a circular aperture in a thick conducting plane is considered. The space is divided into three regions, upper half space, lower half space, and a circular hole region. The incident, scattered and transmitted potential are represented in each region. The Hankel transform and the mode-matching technigue are utilized to obtain the simultaneous equations for the model coefficients. The solution of the simultaneous equations is represented in rapidly-convergent series form which is numerically very efficient. Numerical computations are performed to illustrate the behaviors of the magnetic polarizabilities with respect to aperture thickness d.
In chapter 3 ~ 5, the magnetostatic potential penetration through multiple rectangular apertures (2D, 3D) in a thick conducting plane are studied using the Fourier transform and the mode-matching technique. In the multiply-connected structure, the magnetic scalar potential is a multi-valued function. In order to make the magnetic scalar potential a single-valued function, arbitrary constants are included in the representation of the incident potential. The magnetic polarizabilities for multiple slits are presented to show the interaction between slits as a function of the period T and the thickness d. Our computed results of the longitudinal and the transverse magnetic polarizabilities for a rectangular aperture show good agreement with the known experimental and numerical results.
In chapter 6, the fast method to predict the shielding effectiveness of enclosures with thick multiple apertures is derived. To verify the theoretical assumption, a series of measurements are performed with two different setups. Numerical results for multiple rectangular apertures are also shown to illustrate the behavior of the magnetic polarizabilities and the shielding effectiveness of enclosure with different aperture thickness, shapes and the spacing between the apertures. Numerical result also shows that this method is reasonably accurate to the cutoff frequency of the longest aperture.
