Given a time-harmonic electric-current distribution over a finite planar aperture situated in front of a dielectric half-space, the transmitted field in the dielectric half-space is calculated by the plane-wave-spectrum technique. We concentrate on the current distribution that focuses the electromagnetic energy into a small spot in the dielectric medium, such as in hyperthermia applications. Numerical results are given to illustrate the variation of spot size and of focal-point electric-field intensity as functions of polarization, scanning, and the permittivity of the half-space. We find that (1) the maximum electric-field intensity is not at the focal point but rather at a point closer to the aperture; for a small aperture, this focal shift may be more than one wavelength; (2) when the dielectric half-space is introduced, the 3-dB spot size changes according to the ratio of the wavelength in the half-space to that in the original aperture medium; and (3) the electric-field intensity at the focal point is greatest when the permittivity of the half-space is less than that of the aperture medium, not when the two media are electrically matched.
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