Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides

We predict theoretically that surface plasmon polaritons propagating toward the tip of a tapered plasmonic waveguide are slowed down and asymptotically stopped when they tend to the tip, never actually reaching it (the travel time to the tip is logarithmically divergent). This phenomenon causes accumulation of energy and giant local fields at the tip. There are various prospective applications in nano-optics and nanotechnology.

Figure 1

(a) Geometry of the nanoplasmonic waveguide. The propagation direction of the SPP’s is indicated by the arrow. Intensity $I(\mathbf{r})=|\mathbf{E}(\mathbf{r}){|}^2$ of the local fields relative to the excitation field is shown by color. The scale of the intensities is indicated by the color bar in the center. (b) Local electric field intensity $I(\mathbf{r})$ is shown in the longitudinal cross section of the system. The coordinates are indicated in the units of the reduced radiation wavelength in vacuum, $\mathrm{\lambda ̵}=100\mathrm{n}\mathrm{m}$. The radius of the waveguide gradually decreases from 50 to 2 nm.

Figure 2

(a) Phase velocity $v_p$, group velocity $v_g$, and adiabatic parameter $\delta$ (scaled by a factor of 10) are shown as functions of the coordinate along the nanoplasmonic waveguide. (b) Radial optical electric field at the surface of the metal-nanowire waveguide in the units of the excitation field against the coordinate (in the propagation direction).

Figure 3

Snapshot of instanteneous fields (at some arbitrary moment $t=0$): Normal component $E_x$ (a) and longitudinal component $E_z$ (b) of the local optical electric field are shown in the longitudinal cross section ($xz$) plane of the system. The fields are in the units of the far-zone (excitation) field.

Figure 4

Mean (time averaged) intensity $I(\mathbf{r})$ (a) and the energy density $W(\mathbf{r})$ (b) of the local optical electric field in the $xy$ plane of the system. The magnitudes are relative to those of the excitation wave.