The microwave response of an array of square metal patches and its complementary structure, an array of square holes, has been experimentally studied. The resonant phenomena, which yield either enhanced transmission or reflection, are attributed to the excitation of diffractively coupled surface waves. The band structure of these surface modes has been quantified for both p-͑transverse magnetic͒ and s-͑transverse electric͒ polarized radiation and is found to be dependent on the periodicity of the electric and magnetic fields on resonance. The results are in excellent accord with predictions from finite element method modeling and the electromagnetic form of Babinet's principle ͓Babinet, C. R. Acad. Sci. 4, 638 ͑1837͔͒.
The electromagnetic response of two-dimensional square arrays of perfectly conducting square patches, and their complementary structures, is modeled utilizing a modal matching technique and employing Babinet's principle. This method allows for the introduction of progressively higher diffracted orders and waveguide modes to be included in the calculation, hence aiding understanding of the underlying causal mechanism for the observed response. At frequencies close to, but below, the onset of diffraction, a near-complete reflection condition is predicted, even for low filling fractions: conversely, for high filling fractions a near-complete transmission condition results. These resonance phenomena are associated with evanescent diffraction, which is sufficiently strong to reverse the step change in transmission upon establishment of electrical continuity; i.e., the connected structure demonstrates increased transmission with increasing filling fraction.
It is shown theoretically that a one-dimensional crystal with time-reversal and particle-hole symmetries is characterized by a topological invariant that predicts the existence or otherwise of edge states. This is confirmed experimentally through the construction and simulation of a photonic crystal analog in the microwave regime. It is shown that the edge mode couples to modes external to the photonic crystal via a Fano resonance.
The electromagnetic transmittance of a double layer of identical square arrays of square holes (mesh) in a perfectly conducting sheet is analytically modeled using a modal matching technique. The structure supports families of standing-wave modes together with surface modes that, close to the onset of diffraction, interact with each other. For frequencies below the onset of diffraction, it is the strength of this interaction mediated by evanescent diffraction in the near fields that dictates the electromagnetic response, which is studied as a function of mesh separation and the lateral misalignment between the meshes.
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