**4. Tailoring the optical properties of artificial materials**

After studying the resonance effects in a small RGWN, we now investigate the dispersion characteristics of infinitely large 2D periodic RGWNs by modelling the structure unit cell in FDTD with Bloch boundary conditions. Through this analysis, we find that RGWNs exhibit wave dispersion and photonic bandgaps due to interference effects, and that their band structure can be controlled by modifying the network structural parameters. Two different length-scales control the network dispersion: the subwavelength width of the MIM gaps determines the phase shift at each X-junction, and the wavelength-order distance between the nodes along with network topology determine the interference scheme.

Fig. 6. Photonic band structure of infinitely large periodic RGWNs (Feigenbaum 2010).

The same interference dynamics that govern the energy storage in finite-size 2x2 RGWN resonators are the same that control the optical properties of artificially designed RGWN materials of infinite-size. If the network parameters are chosen such that a planewave excitation at a given incidence angle results in a resonance effect similar to the one demonstrated for the 2x2 network, then this would correspond to a forbidden state of propagation in the photonic band diagram. Examining the optical density of states (DOS) for different wave vectors over frequencies in the near infrared range, where the material (Au in this case) dispersion is small, we observe a photonic band structure which is only due to dispersion resulting from the network topology, as shown in Fig. 6a. The functionality of the infinitely large RGWN is not hindered by loss since its dispersion depends on the waveguide decay length being much larger than the size of the largest resonant feedback

Fig. 5. Q-factor of 2×2 RGWN resonator from simulation results compared with those

After studying the resonance effects in a small RGWN, we now investigate the dispersion characteristics of infinitely large 2D periodic RGWNs by modelling the structure unit cell in FDTD with Bloch boundary conditions. Through this analysis, we find that RGWNs exhibit wave dispersion and photonic bandgaps due to interference effects, and that their band structure can be controlled by modifying the network structural parameters. Two different length-scales control the network dispersion: the subwavelength width of the MIM gaps determines the phase shift at each X-junction, and the wavelength-order distance between

resulting from incoherent power splitting (Feigenbaum 2010).

**4. Tailoring the optical properties of artificial materials** 

the nodes along with network topology determine the interference scheme.

Fig. 6. Photonic band structure of infinitely large periodic RGWNs (Feigenbaum 2010).

The same interference dynamics that govern the energy storage in finite-size 2x2 RGWN resonators are the same that control the optical properties of artificially designed RGWN materials of infinite-size. If the network parameters are chosen such that a planewave excitation at a given incidence angle results in a resonance effect similar to the one demonstrated for the 2x2 network, then this would correspond to a forbidden state of propagation in the photonic band diagram. Examining the optical density of states (DOS) for different wave vectors over frequencies in the near infrared range, where the material (Au in this case) dispersion is small, we observe a photonic band structure which is only due to dispersion resulting from the network topology, as shown in Fig. 6a. The functionality of the infinitely large RGWN is not hindered by loss since its dispersion depends on the waveguide decay length being much larger than the size of the largest resonant feedback loop that has dominant contribution to the RGWN dispersion. Further possibilities for achieving band dispersion control are illustrated in Fig. 6b, showing a flat bands over a wide range of wavevectors at 130 and 170 THz, as well as the formation of a photonic bandgap between 140-160 THz, for appropriately chosen network parameters.

The infinitely large RGWN is illustrated in Fig. 6c along with a few schematic resonance orders that represent the resonances that could arise within the network. The operating mechanism of the RGWN is very different from that of photonic crystals composed of metaldielectric alternating materials. Although the schematic layout might look similar, the difference between the two classes of artificially designed optical materials becomes clear when considering the difference in the length scales of their composite elements. Whereas photonic crystals operate based on non-local interaction of Bloch waves with the entire array, RGWNs rely on the interference of local waves. Therefore RGWNs are not sensitive to the actual topology of waveguides between junctions but only to its trajectory length, whereas the properties of photonic crystals would greatly depend on the shape of the periodic metallic islands. Additionally, RGWNs do not necessarily have to be periodic to operate as resonant guided wave networks, and for the same reason, planting a defect in a RGWN would not have the same effect as it would in a photonic crystal.
