Babinet’s principle for optical frequency metamaterials and nanoantennas

We consider Babinet’s principle for metamaterials at optical frequencies and include realistic conditions which deviate from the theoretical assumptions of the classic principle such as an infinitely thin and perfectly conducting metal layer. It is shown that Babinet’s principle associates not only transmission and reflection between a structure and its complement but also the field modal profiles of the electromagnetic resonances as well as effective material parameters—a critical concept for metamaterials. Also playing an important role in antenna design, Babinet’s principle is particularly interesting to consider in this case where the metasurfaces and their complements can be regarded as variations on a folded dipole antenna array and patch antenna array, respectively.

Figure 1

(Color online) Schematic view of (a) the fabricated gold SRRs and (b) their complementary structure. Both structures have a height of $15\mathrm{nm}$ and are deposited on a $2\text{−}\mathrm{mm}$-thick Infrasil glass substrate.

Figure 2

(Color online) Measured transmittance (blue, dotted) and reflectance (red, solid) of [(a) and (d)] SRRs and [(b) and (c)] C-SRRs for the two polarization configurations. The numbers mark the eigenmodes described in the text.

Figure 3

(Color online) Calculated transmittance (blue, dotted) and reflectance (red, solid) of [(a) and (d)] SRRs and [(b) and (c)] C-SRRs for the two polarization configurations. The numbers mark the eigenmodes described in the text.

Figure 4

(Color online) Calculated field distribution for the first- and third-order eigenmodes of the [(a) and (c)] SRR and [(b) and (d)] C-SRR. The plot shows the field component ($\mid {\mathbf{E}}_z\mid$ and $\mid {\mathbf{B}}_z\mid$) normal to the structure plane $7.5\mathrm{nm}$ above the surface. The fields are normalized to the illuminating electric and magnetic fields, respectively.

Figure 5

(Color online) Retrieved real part (solid line) and imaginary part (dotted line) for the permittivity of the SRR and C-SRR slab structures from the calculated spectra. The vertical dotted lines together with the numbers mark the transmission and/or reflection resonance positions in the spectra. $\mathrm{Im}\left(ϵ\right)$ in (b) is shown with a $1∕3$ magnitude scale.