Nonlinear Nanofocusing in Tapered Plasmonic Waveguides

We suggest using tapered waveguides for compensating losses of surface plasmon-polaritons in order to enhance nonlinear effects at the nanoscale. We study nonlinear plasmon self-focusing in tapered metal-dielectric-metal slot waveguides and demonstrate that, by an appropriate choice of the taper angle, we can effectively suppress the mode attenuation achieving stable propagation of a spatial plasmon soliton. For larger tapering angles we observe plasmon-beam nanofocusing in both spatial dimensions.

Figure 1

Schematic of the three-dimensional plasmon focusing in a tapered slot waveguide. Focusing occurs in the horizontal plane, due to a taper, and in the vertical plane, due to the nonlinear self-focusing effect. Inset shows the waveguide cross section with the magnetic field distribution of a symmetric plasmon mode.

Figure 2

Variation of (a) normalized amplitude at the beam center and (b) normalized beam width (along $y$ axis) for three different values of the tapering angle $\alpha$: (1) 0.8°, (2) 1.2°, and (3) 1.6°, respectively.

Figure 3

Variation of the magnetic field in the nonlinear slot waveguide for two values of the tapering angle: (a) $\alpha =0.8°$ and (b) $\alpha =1.2°$. (c) Magnetic field profiles at the input and after $20\mu \mathrm{m}$ of propagation. Curves 1–3 correspond to the same tapering angles as discussed in Fig. 2. Dotted curve corresponds to the input soliton profile.

Figure 4

(a,b) Variation of the magnetic field in the slot plasmonic waveguide for the tapering angle $\alpha =1.6°$, shown for two cross sections. The mode tapering with the beam focusing in the lateral dimension $y$ are clearly observed.