Sharp Trapped-Mode Resonances in Planar Metamaterials with a Broken Structural Symmetry

We report that a resonance response with a very high quality factor can be achieved in a planar metamaterial by introducing symmetry breaking in the shape of its structural elements, which enables excitation of trapped modes, i.e., modes that are weakly coupled to free space.

Figure 1

Fragments of planar metamaterials with asymmetrically split copper rings. The dashed boxes indicate elementary translation cells of the structures.

Figure 2

(a) Normal incidence reflection and transmission and absorption (linear scale) spectra of $A$-type metamaterial [presented in Fig. 1a] for $x$-polarization: solid line—experiment, filled circles—theory (method of moments), empty circles—theory for reference structure with symmetrically split rings. (b) $x$-Component of the instantaneous current distribution in the asymmetrically split rings corresponding to resonant features I, II, and III marked in section (a). Arrows indicate instantaneous directions of the current flow, while their length corresponds to the overall current strength, and the midpoint shows location of the current density maximum.

Figure 3

(a) Normal incidence reflection and transmission, and absorption (linear scale) spectra of $B$-type metamaterial [presented in Fig. 1b] for $y$-polarization: solid line—experiment, filled circles—theory (method of moments), empty circles—theory for reference structure with symmetrically split rings. (b) $y$-Component of the instantaneous current distribution in the asymmetrically split rings corresponding to resonant features I, II, and III marked in section (a). Arrows indicate instantaneous directions of the current flow, while their length corresponds to the current strength and the midpoint shows location of the current density maximum.

Figure 4

Quality factor of “trapped-mode” resonance in $A$-type metamaterial as a function the particle asymmetry $\gamma$, defined as the relative difference of the arcs’ lengths. Solid and dashed curves correspond to the cases of lossy ($\epsilon =4.07+i0.05$) and lossless ($\epsilon =4.07$) substrate. The inset shows the evolution of “trapped-mode” resonance in transmission at different $\gamma$ calculated for the lossy case.