Abstract:
<p>We calculate electromagnetic transmission through periodic gratings using a mode-matching method for solving Maxwell's equations. We record the derivation of the equations involved for several variations of the problem, including one- and two- dimensionally periodic films, one-sided films, films with complicated periodicity, and a simpler formula for the case of a single contributing waveguide mode. We demonstrate the effects of the Rayleigh anomaly, which causes energy transmission to be very low compared to nearby frequencies, and the associated transmission maxima which may be as high as 100% for certain energy frequencies. Finally we present further variations of the model to account for the effects of conductivity, finite hole arrays, and collimation. We find that assuming the film is perfectly conducting with infinite periodicity does not change the transmission sufficiently to explain the difference between experimental and theoretical results. However, removing the assumption that the incident radiation is in the form of a plane wave brings the transmission much more in agreement with experimental results.</p>
