Spectral Collapse in Ensembles of Metamolecules

Abstract

We report on a new collective phenomenon in metamaterials: spectral line collapse with increasing number of the unit cell resonators (meta-molecules). Resembling the behaviour of exotic states of matter, such as Bose-Einstein condensates of excitons and magnons, this new effect is linked to the suppression of radiation losses in periodic arrays. We demonstrate experimentally spectral line collapse at microwave, terahertz and optical frequencies. It emerges as a universal and truly scalable effect underpinned by classical electromagnetic interactions between the excited meta-molecules.The burgeoning field of metamaterials provides unique opportunities to engineer the electromagnetic properties of artificial media and achieve exotic functionalities, such as negative refraction [1] and cloaking [2]. Similarly to natural crystals, which are created by arranging individual atoms and molecules in a regular grid, periodic ensembles of subwavelength electromagnetic resonators present an effective medium to an incident with properties not available in natural materials. Here, we study the dependence of the metamaterial properties on the number of meta-molecules in the microwave, THz and optical domain, and demonstrate a new collective phenomenon in metamaterials: in contrast to solid state crystals, where bulk arrangements result in broadening of the individual element spectral line, leading eventually to the formation of absorption bands, regular ensembles of meta-molecules can exhibit the opposite effect, i.e. spectral line collapse. The reported phenomenon is characteristic to a novel class of artificial media, which we call "coherent" metamaterials [3] and are characterized by very strong interactions between the electromagnetically excited metamolecules that provide for a low rate of energy loss due to scattering and lead to a high-quality resonant response. An example of a coherent metamaterial is an array of ASRs, where the meta-molecular excitation corresponds to an oscillating magnetic dipole perpendicular to the plane of the array that does not interact directly with the magnetic field of the incident wave, thus creating a nearly thermodynamically isolated ensemble of strongly interacting coherent "molecules" with interesting physical properties. To illustrate this behavior we present a comparison with an "incoherent" metamaterial: a twodimensional array formed by pairs of concentric conducting rings that also supports a high-quality resonant response. In this case, however, the response of the array is a sum of the individual meta-molecule responses, rather than a collective property.The coherent microwave metamaterial was manufactured as a regular planar array of asymmetric split rings (ASR) etched from a 35 µm thick copper layer on a 1.6 mm thick FR4 substrate. The diameter of the ASR was 6 mm with a line width of 0.4 mm and was split in two segments corresponding to 140 • and 160 • arcs. The unit cell of 7.5 × 7.5 mm 2 rendered the arrays nondiffracting at normal incidence for frequencies of up to 40 GHz. I...

All-dielectric metasurface analogue of electromagnetically induced transparency

“…The response of the dielectric metasurface is similar to the collective modes found in asymmetric double-gap split-ring resonators, in which the asymmetry in the rings yields a finite electric dipole moment that can couple the out-of-plane magnetic dipole mode to free space [27][28][29][30][31][32] . In our case, coupling to free space is provided by the bright-mode resonators, which are placed in close proximity to the symmetric dark-mode resonators.…”

“…3a. The array size thus becomes an important factor in the overall Q-factor of the metasurface due to the fact that lattice perturbations at the array's edge break the coherence 27,28 , leading to strong scattering of light into free space and broadening of the resonance peak. To characterize this effect, we fabricated arrays of five different sizes, consisting of 400 to 90,000 unit cells (SEM image of the test samples are shown in Fig.…”

“…The radiative damping term, g R2 , is minimized due to the collective oscillations of the array, mediated by near-field coupling between the unit cells. One consequence of utilizing collective modes is that the value of g R2 is inversely proportional to the size of the array due to the fact that the discontinuity at the edges of the array allows for light leakage to free space 27,28 . While collective modes have been utilized in past demonstrations of plasmonic EIT metamaterials to realize extremely small g R2 values, the Q-factors have intrinsically been limited by the ohmic loss in the metal.…”

Spectrally selective chiral silicon metasurfaces based on infrared Fano resonances

“…More details on the interaction between neighbouring unit cells can be found in Supplementary Note 1. Note 40 that the diffractive effects are unimportant in Fano-resonant metasurfaces, and the spectral position of the dark resonance is determined primarily by the unit cell's geometry (its physical dimensions R, L, g, d and w shown in Fig. 1) and not by the period P separating them.…”

“…Unfortunately, even for the most judicious engineering of the radiative loss, the total Q is limited 16,[40][41][42] by the non-radiative loss of the underlying material. A notable exception is the special class of diffraction-coupled plasmonic arrays 25,[43][44][45] , which rely on the geometric resonance that arises when the wavelength of light is commensurate with the array's periodicity 44 .…”