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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 microwave transmission through hole arrays in thick metal plates for both large holes (cut-off below onset of diffraction) and small holes (cut-off above onset of diffraction) have been compared through both experiment and modelling. Enhanced transmission is in part mediated by the excitation of diffractively coupled surface waves. Large holes, with cut-off below the onset of diffraction (due to the hole periodicity), are able to support multiple modes in transmission when the depth of the holes is sufficient to support quantisation in the propagation direction. Small holes, with cut-off above the onset of diffraction however only support two coupled surface modes (symmetric and anti-symmetric) below diffraction.
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