Transmission of an inhomogeneous plane wave through an electrically small aperture in a perfectly conducting plane screen

Abstract

Most solutions for electromagnetic diffraction by a circular aperture in a perfectly conducting plane screen are for an incident homogeneous (propagating) plane wave. When the aperture is electrically small (dimensions small compared to the wavelength), the well-known transmission coefficient behaves as the fourth power of the diameter/wavelength. We consider the case in which the incident field is an inhomogeneous (evanescent) plane wave. Numerical calculations for the electrically small circular aperture show that the transmission coefficient for an inhomogeneous plane wave can be substantially greater than for a homogeneous plane wave at the same frequency. This observation may be helpful in explaining the increased transmission recently reported for electrically small apertures in plane screens with modifications. The numerical calculations for the electrically small aperture are in agreement with results from approximate analytical expressions that are based on the equivalent electric and magnetic dipole moments for the electrically small complementary disk.

Analysis of a Plane Wave-Excited Subwavelength Circular Aperture in a Planar Conducting Screen Illuminating a Multilayer Uniaxial Sample

“…5(a), we first note the large enhancement of the transmitted field, which is related to the increase in the magnitude of the incident aperture field when κ xi > 1, as is evident from (1). This phenomenon, which is consistent with the findings of Petersson and Smith [2], also confirms the crucial role played by the evanescent fields, such as surface waves and surface plasmons [58], in the extraordinary optical transmission (EOT) by subwavelength apertures in (real) metallic screens [1]. Hence, one way to achieve the EOT is to excite strongly evanescent fields at the input face, e.g., by texturing the metal surface in the vicinity of the aperture [59], which facilitates the coupling of the incident wave to a surface plasmon.…”

“…2 Without loss of generality, the amplitude of E i is set to unity. We assume the e jωt time convention and SI units.…”

Complex Image Method Analysis of a Plane Wave-Excited Subwavelength Circular Aperture in a Planar Screen

“…The magnetic field plots exhibit a distinct intermediate zone with a drop off rate of 1/z 2 . Comparing the homogeneous and evanescent illumination results, we note a significant near-zone electric field enhancement in the latter case, with a concomitant enhancement in transmission efficiency [17]. For the evanescent TM wave, we note a null in the axial plot of |E x |, which is a near-field phenomenon also predicted by the quasi-static analysis.…”

“…For generality, we also allow for an inhomogeneous plane wave, evanescent along the z axis [17], where κ xi may be any real number with the corresponding κ zi given as…”