Theoretical investigation of electromagnetic diffraction focusing in the near zone of a sub-wavelength aperture

Diffraction of a Plane Electromagnetic Wave by a Circular Aperture in a Conducting Screen of Finite Thickness

“…However, below we will be interested in the electric field only in a thin dielectric film, which plays a part of a radiation detector or an object under study in optical spectroscopy. For evaluation of the focusing properties of a circular aperture, we will use the same technique, as for the case of a rectangular slot [7].…”

“…where ∆(ρ) is the weight function. By analogy with the case of a simple slot [7], we set ∆(ρ) = W 2 (ρ) for it. Then the effective amplitude is equal to:…”

“…This expression approximately characterizes the effective area of the diffraction image of a circular hole in a dielectric film. Then the index of focusing, or the index of the relative reduction of the aperture image, introduced in [7], can be defined as the ratio of the real aperture area to the effective area of the aperture image:…”

“…The classical problem of electromagnetic wave diffraction by a slot or a circular aperture in a conducting screen is of great interest in the context of the recent discovery of two interesting phenomena: the occurrence of an anomalously high local intensity of the transmitted radiation [1][2][3] and the appearance of lensless focusing of the diffraction slot image, when the effective width of this image turns out to be several times smaller than the transverse dimensions of the aperture [4,5]. An effective theoretical method for searching the region of existence of the latter effect was proposed in [6,7] † . It is obvious that these two phenomena are interconnected, since a high local intensity of the field can take place when it is concentrated in a small region, and these phenomena are noticeably manifested only for microapertures in the near zone, when the aperture dimensions, the screen thickness, and the distance from it to the plane of the diffraction pattern observation have dimensions on the order of one to several wavelengths of radiation.…”

“…Therefore, in order to elaborate an adequate picture of anomalous phenomena in the near zone of microapertures, it is necessary to utilize a rigorous solution of the Maxwell equations that would completely satisfy all the exact boundary conditions at the aperture boundaries and on the surfaces of the conducting screen, in which this aperture is cut. For a slot aperture of rectangular geometry in a perfectly conducting screen, such a solution by the eigenwave technique was presented in [10,11], and on its basis, in [7], the study of anomalous high-intensity phenomena and lensless diffraction focusing of radiation near microsized slots was carried out. It turned out that the focusing effect takes place only for TE polarization of the incident plane wave, for which the electric vector is parallel to the edges of the slot, while for orthogonal TM polarization, it practically does not manifest itself.…”