Light Funneling Mechanism Explained by Magnetoelectric Interference

We investigate the mechanisms involved in the funneling of optical energy into subwavelength grooves etched on a metallic surface. The key phenomenon is unveiled thanks to the decomposition of the electromagnetic field into its propagative and evanescent parts. We unambiguously show that the funneling is not due to plasmonic waves flowing toward the grooves, but rather to the magnetoelectric interference of the incident wave with the evanescent field, this field being mainly due to the resonant wave escaping from the groove.

Figure 1

(a) Poynting-vector streamlines are drawn on a grating of grooves of height $h=640\mathrm{nm}$, width $w=56\mathrm{nm}$ and period $d=2\mu \mathrm{m}$. The incident energy is funneled inside the grooves. (b) Vector streamlines inside a groove. The dissipation of the energy is computed in the metallic region, it clearly appears that this dissipation occurs on the sidewalls of the grooves (orange [dark gray] volume), see 22 for detailed field maps. (c) Reflectivity spectra for various values of the grating period $d=1.618\mu \mathrm{m}$, $d=2\mu \mathrm{m}$, and $d=2.472\mu \mathrm{m}$. The geometry of the groove is the same as before. The period has almost no influence on the resonance since it is due to the Fabry-Perot resonator inside the grooves.

Figure 2

Poynting-vector streamlines in one period of the slit grating for two angles of incidence $\theta =0°$ (left column) and $\theta =30°$ (right column) at $\lambda =4000\mathrm{nm}$. Streamlines of the incident wave are shown in (a) and (b). Streamlines of the interference between the incident wave and the evanescent field are shown in (c) and (d). The energy flux of the evanescent waves is negligible in this structure for $\theta =0°$; refer to Fig. 3a for an illustration at $\theta =30°$. Streamlines of the total Poynting vector are shown in (e) and (f). In both cases, the incident energy is funneled inside the groove where it is fully absorbed inside the metal.

Figure 3

Poynting-vector streamlines of the evanescent field for two angles of incidence (a) 30° and (b) 50° at $\lambda =4000\mathrm{nm}$. $S_e$ does not play a role in funneling but redistributes the energy in the grating.

Figure 4

Isolated single interface analysis of the metallic grating optimized to absorb all the incident light. (a) Unit plane wave from air: ${\rho }_1$ is the amplitude of the reflected plane wave, ${\eta }_1$ is the vector of evanescent field amplitudes. (b) Unit modal wave from bottom of grooves: ${\tau }_2$ is the amplitude of the plane wave escaping in the air, ${\eta }_2$ is the vector of evanescent field amplitudes. (c) Same as (b), but with the modal wave having the amplitude $A$. (d) Superposition of (a) and (c), showing the field amplitudes in the grating excited by a unit plane wave: the reflectivity is null and the evanescent field is dominated by the term escaping from the resonator.