## 3 Results and Discussion  
Figure 1a represents a sketch of a ITO:TiO\({}_{2}\):air/SiO\({}_{2}\):air multilayer structure and a magnification of an ITO:TiO\({}_{2}\):air layer. The blue dots indicate the ITO nanoparticles, while the grey dots indicate the TiO\({}_{2}\) nanoparticles. The white interstitial volume depicts the air voids between the nanoparticles. To determine the effective refractive index of the layer we used a generalized Rayleigh Equation for a three-phase mixture (Equation (5)). In Figure 1b, the dashed curve represents the real (black) and imaginary (red) part of the dielectric function of an ITO:air two-phase mixture, which is a dispersion of ITO nanoparticles, with a filling factor of 0.2, in air. This two-phase mixture refractive index is determined with the Bruggeman effective medium theory [23; 24]. Instead, the solid curves in Figure 1b represent the real (black) and imaginary (red) part of the effective dielectric function of an ITO:TiO\({}_{2}\):air mixture. It is clear that the resonance related to the ITO plasmonic peak shows a splitting, and one resonance shifts towards higher energies in the three-material mixture evidencing the possibility to further tailor the optical response of ITO nanostructures. In Figure 2 we show the difference between a photonic crystal with layers of silica nanoparticles alternated with layers of titania nanoparticles (black curve), and a photonic crystal with layers of silica nanoparticles alternated with a layer of ITO nanoparticles (red curve). Figure 1: (**a**) Sketch of an indium tin oxide (ITO):TiO\({}_{2}\):air layer, with ITO nanoparticles (blue dots), TiO\({}_{2}\) nanoparticles (grey dots), and air (white interstitial volume); (**b**) real part (solid black curve) and imaginary part (solid red curve) of the dielectric function of a ITO:TiO\({}_{2}\):air (20:50:30 ratio) layer, calculated with the Rayleigh mixing formula, and real part (dashed black curve) and imaginary part (dashed red curve) of a ITO:air (20:80 ratio) layer, calculated with the Bruggeman approximation. Figure 2: Light transmission spectrum of a SiO\({}_{2}\) nanoparticle/TiO\({}_{2}\) nanoparticle photonic crystal (black curve) both with a filling factor of 0.7, and light transmission spectrum of a SiO\({}_{2}\) nanoparticle/ITO nanoparticle photonic crystal (red curve) both with a filling factor of 0.7. The silica/ITO photonic crystal shows a strong transmission valley at lower energy due to the plasmon resonance of ITO. Moreover, the silica/ITO photonic crystal shows a less intense photonic band gap with respect to the one of the silica/titania photonic crystal because of the smaller refractive index contrast. We can now relate to the two spectra in Figure 2 as the two extremes of a three-phase mixture of ITO nanoparticles, TiO\({}_{2}\) nanoparticles, and air in which we keep constant the volume of air and we change the ITO:TiO\({}_{2}\) ratio. We show this ratio variation in Figure 3, where the increasing content of ITO relates to an increase in the transmission valley intensity due to the plasmon resonance. Interestingly, the plasmon resonance is blue shifted with respect to the one of the ITO:air layer. In Figure 4 we show the transmission value in correspondence of the plasmon resonance and the photonic band gap of the structure as a function of the ITO content, highlighting a cross over between \(f_{ITO}=0.2\) and \(f_{ITO}=0.3\) (corresponding to the red and blue curves in Figure 3). Figure 4: Transmission minima of the plasmon resonance and of the photonic band gap as a function of the ITO nanoparticles, keeping constant the sum of \(f_{ITO}+f_{TiO_{2}}=0.7\). Figure 3: Light transmission spectra of ITO:TiO\({}_{2}\):air/SiO\({}_{2}\):air multilayer photonic crystals with different ITO:TiO\({}_{2}\) ratios, keeping constant the sum of \(f_{ITO}+f_{TiO_{2}}=0.7\).