30 - Transmission of light through small elliptical apertures

Summary

The apertures of classical optics simply block those parts of an incident wavefront that fall outside the aperture, allowing everything else to go through intact. Moreover, multiple apertures act upon an incident beam independently of each other, polarization effects are usually negligible (i.e., scalar diffraction), and it is not necessary to keep track of both the electric- and the magnetic-field components of the beam.

All of the above assumptions break down when apertures shrink to dimensions comparable to or smaller than a wavelength. For example, transmission through two small adjacent apertures cannot be treated by assuming that only one aperture is open at a time, then adding the fields transmitted by the individual apertures. (This is because the electric charge and current distributions in the vicinity of one aperture are influenced by the radiation pattern of the other aperture.) Polarization effects are extremely important for small apertures, as exemplified by the case of a normally incident beam going through an elliptical aperture in a thin metal film; whereas in the case of polarization (i.e., E-field) parallel to the long axis of the ellipse there is negligible transmission, when the incident polarization is rotated 90° to point along the ellipse's minor axis, the aperture transmits a substantial fraction of the incident light. Finally, to analyze the interaction of light with small apertures, it is generally necessary to keep track of both E and B components of the electromagnetic wave, as the modification of one of these fields produces non-trivial changes in the other field's distribution.