**7. Possible Implementations**

The underlying physics and the working principles of the RGWNs were demonstrated in the previous sections with an idealized 2D implementation using MIM waveguides. However, for the same 2D network topology as shown in Fig. 4, but implemented with 3D high aspect ratio Au-air channel plasmon waveguides (Bozhevolnyi 2006), the observed wave dynamics are found to closely resemble that of the 2D MIM waveguide network, as studied with 3D full-field simulations. If the aspect ratio of the channel plasmon waveguide is high enough, the propagating mode within the channels strongly resembles the MIM gap plasmonic mode. This can for instance be seen in the measured quality factors of RGWNs comprised of channel plasmon waveguides (3D simulations) and MIM slot waveguides (2D simulations) which have Q-factor values of 82 and 83, respectively, at a wavelength of 1.5µm. Furthermore, the two power splitting events that define the RGWN resonant state are similar for both the channel and MIM waveguides (Fig. 4).

Fig. 11. 3D RGWN: (a) rendering of a 3D RGWN building block (6-arm junction). (b, c) Optical DOS of an infinite 3D network spaced periodically with cubic periodic unit cell with different spacing (Feigenbaum 2010-1).

The dispersion design in a volume can be addressed by 3D-RGWN topologies, for example, constructing an array of orthogonally intersecting 3D networks of coaxial Au-air waveguides aligned in a Cartesian grid (Fig. 11a). In this case, the four-arm X-junction

Vertical center-bottom (C-B) 0.45 13.25

Horizontal Top 0.29 12.8

The underlying physics and the working principles of the RGWNs were demonstrated in the previous sections with an idealized 2D implementation using MIM waveguides. However, for the same 2D network topology as shown in Fig. 4, but implemented with 3D high aspect ratio Au-air channel plasmon waveguides (Bozhevolnyi 2006), the observed wave dynamics are found to closely resemble that of the 2D MIM waveguide network, as studied with 3D full-field simulations. If the aspect ratio of the channel plasmon waveguide is high enough, the propagating mode within the channels strongly resembles the MIM gap plasmonic mode. This can for instance be seen in the measured quality factors of RGWNs comprised of channel plasmon waveguides (3D simulations) and MIM slot waveguides (2D simulations) which have Q-factor values of 82 and 83, respectively, at a wavelength of 1.5µm. Furthermore, the two power splitting events that define the RGWN resonant state

Fig. 11. 3D RGWN: (a) rendering of a 3D RGWN building block (6-arm junction). (b, c) Optical DOS of an infinite 3D network spaced periodically with cubic periodic unit cell with

The dispersion design in a volume can be addressed by 3D-RGWN topologies, for example, constructing an array of orthogonally intersecting 3D networks of coaxial Au-air waveguides aligned in a Cartesian grid (Fig. 11a). In this case, the four-arm X-junction

Table 2. Set of optimized parameters for a 3x3 RGWN trichroic router operating at

are similar for both the channel and MIM waveguides (Fig. 4).

*λ1*=1.59µm, *λ2*=1.97µm, and *λ3*=1.23µm.

different spacing (Feigenbaum 2010-1).

**7. Possible Implementations** 

(µm)

side-bottom (S-B) 0.1 8.15 center-top (C-T) 0.45 3.55 side-top (S-T) 0.1 4

> Middle 0.26 7.3 Down 0.3 11.95

Length (µm)

Waveguides Width

element of the 2D network is replaced by a six-arm 3D junction element. Using 3D FDTD, we have verified that six-way equal power splitting occurs for pulsed excitation in a coaxial Au-air waveguide junction. Like for the 2D-RGWN, the dispersion of the infinitely large periodic 3D-RGWN is predominantly determined by the network parameters rather than the waveguide dispersion. This is demonstrated by the noticeable difference in the band diagrams (Fig. 5b and 5c) obtained for two networks comprised of the same waveguides but with different inter-node spacing.
