# Strategies for Dielectric Contrast Enhancement in 1D Planar Polymeric Photonic Crystals
## 4 Role of the Dielectric Contrast in DBRs  
Because of the different architectures of the structures mentioned in the previous paragraph, they are hardly comparable in terms of their performances. Thus, we will try to quantify the effect of the dielectric contrast by modeling the optical response for a single architecture (see the SI for details). Figure 3a shows the calculated reflectance spectra for DBRs composed of 15.5 periods. For all the modeled structures, the low refractive index medium has a thickness of d\({}_{\text{L}}\) = 120 nm, while the high refractive index medium has a thickness of d\({}_{\text{H}}\) = 80 nm. Optical functions available from the literature, and reported in Figures S1 and S2 of the SI, were used for both commercial and engineered polymers. Panels b, c and d of Figure 3 compare the figures of merit of this analysis: the reflectance intensity of the first-order PBG (b), its full width at half maximum (FWHM, panel c) and its spectral position (\(\lambda_{\text{max}}\), panel d). In more detail, from bottom to top, Figure 3a shows the calculated spectra for increasing \(\Delta\)n values for PS:CA (black line and dots) [168], PAA:PVK (red line and dots) [91; 98], CA:PVK (green line and dots) [106], CA:HBP (blue line and dots) [134], PAA:IVP (cyan line and dots) [138], Hy:PVK (magenta line and dots) [110], CA:TiO\({}_{2}\)-PVA (yellow line and dots) [170], and Hy:TiO\({}_{2}\)-PVA (orange line and dots). In general, all reflectance spectra are characterized by an intense peak in the spectral range between 500 and 700 nm. This peak is assigned to the first-order PBG of the structure. The backgrounds display instead a Fabry-Perot pattern due to the entire structure. The intensity and spectral width of the PBG increase with the dielectric contrast, from the bottom spectrum to the top one. It is indeed well-known that the PBG intensity increases linearly with the dielectric contrast and exponentially with the number of periods composing the structure until unitary reflectance [37]. Figure 3b reports the reflectance intensity at \(\lambda_{\text{max}}\) for the DBRs versus the dielectric contrast. For the analyzed structure, unitary reflectance is obtained with a dielectric contrast of \(\Delta\)n \(\geq\) 0.3; that is, for the polymer couples PAA:IVP, Hy:PVK, CA:TiO\({}_{2}\)-PVA and Hy:TiO\({}_{2}\)-PVA. On the other hand, the exponential dependence of the reflectance intensity on the number of periods allows unitary reflectance also to be reached with a lower dielectric contrast, employing a larger number of layers [37]. Regarding the width of the PBG, Figure 3c shows that it increases linearly with \(\Delta\)n [37]. Indeed, for the lower value corresponding to PS:CA, it approached 44 nm, while it reached 150 nm for the Hy:TiO\({}_{2}\)-PVA structure. This value is competitive with those obtained for inorganic multilayers fabricated by vacuum technologies [171; 172] and with those of mesoporous metal oxide particles fabricated by spin-coating deposition [173; 174; 175; 176]. Concerning the spectral position of the PBG, Figure 3a shows that there is no simple correlation to the dielectric contrast. Indeed, the spectra show that \(\lambda_{\text{max}}\) tends to red shift for \(\Delta\)n values between 0.11 (PS:CA bottom spectrum) and 0.3 (PAA:IVP, orange spectrum). Then, for Hy:PVK DBR (magenta spectrum), \(\lambda_{\text{max}}\) shifts to the blue part of the spectrum with respect to the PAA:IVP structure (cyan line). In fact, \(\lambda_{\text{max}}\) depends on the effective refractive index of the DBRs, and then on the refractive index value of both media composing the DBRs averaged regarding the thickness of the layers (see the SI for details). Indeed, \(\lambda_{\text{max}}\) moves to the short-wavelength side of the spectrum when a low-index perfluorinated polymer is inserted in the DBR structure as a low refractive index component. This increases \(\Delta\)n on one side and decreases n\({}_{\text{eff}}\) on the other.