Babinet’s principle and the band structure of surface waves on patterned metal arrays

Abstract

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 Effect of Rotational Disorder on the Microwave Transmission of Checkerboard Metal Square Arrays

“…When σ = 0° (solid black lines) all arrays exhibit a broad resonance just below the 50 GHz onset of diffraction, manifesting as a transmission minimum for electrically disconnected arrays and a maximum for connected ones. This behaviour is much the same as the Fano-type resonant transmission observed in similar studies 16 17 18 . These resonances are due to diffractive coupling between the bound surface mode of each patch/hole array and the incident radiation.…”

“…Following this observation there has been a substantial body of work exploring the response of sub-wavelength metallic patches and holes to optical frequency radiation 8 9 . A number of similar studies have been undertaken in the microwave regime exploring a range of element geometries including circular 10 11 , ring 12 13 , dipole 14 , triangular 15 and square 16 17 .…”

“…Due to this theoretical phenomenon, the checkerboard array has received much attention. Transmission features associated with connected and disconnected checkerboard arrays have been studied experimentally in the microwave 16 , terahertz 21 , and optical 22 regimes. Frequency-independent transmission has been observed in disordered systems where the square size is varied 21 , and by using resistive sheets to join the metallic elements 23 24 .…”

“…To draw a limited analogy with plasmonics, these are often termed ‘spoof surface plasmons’, but the key difference should be noted: that the character of these surface waves is not dictated by the metal’s conductivity. In connected arrays, the holes are coupled together by conventional electric current, and hence the resulting collective resonance of the holes is transverse magnetic (TM) in nature 16 . Conversely, disconnected arrays (patches) support transverse electric (TE) surface waves, with neighbouring patches interacting via displacement currents.…”

Geometric Structure behind Duality and Manifestation of Self-Duality from Electrical Circuits to Metamaterials

“…Over the past few decades, duality has been assuming an important role in the research and development of metamaterials. To name a few such cases, duality has been leveraged to design complementary metasurfaces [32][33][34][35], self-complementary metasurfaces [36][37][38][39][40][41][42], critical metasurfaces [43][44][45][46][47][48][49][50][51][52], maximally chiral metamaterials [53], and self-dual metamaterials with zero backscattering [54] or helicity conservation [55][56][57]. In such situations, the extensive target frequencies of metamaterials require a comprehensive understanding of duality in a unified manner.…”