# Strategies for Dielectric Contrast Enhancement in 1D Planar Polymeric Photonic Crystals
## 5 Prospects for Polymer Planar Microcavities
The fluence threshold of this process decreases for an increasing quality factor (Q = \(\lambda_{\text{MC}}\)/\(\lambda_{\text{MC}}\)) of the microcavity [185], which scales linearly with LPDOS [37]. Lasing action has been demonstrated for polymer microcavities fabricated by solution [186; 102] and melt processing [187; 188; 189; 35]. Polymeric [84; 190; 191; 192; 193; 194; 195; 196] and hybrid [160] structures as well as elastomeric [187; 95] and thermal responsive [34] microcavity lasers have been extensively investigated. The lasing threshold can also be reduced by the radiative rate enhancement of spontaneous emission. Additionally, this effect is particularly promising for increasing LED efficiency [197]. The rate of spontaneous emission can be altered by modifying the dielectric environment of a medium, obtaining strong spatial confinement [198; 199; 200; 201; 202; 203; 204]. A tight confinement also leads to strong spectral redistribution, intensity enhancement [205; 168], and strong directional control [98; 106] and intensifies light-matter interactions [207; 208; 209; 14; 184; 210]. These effects are particularly effective for small modal volumes of the microcavity and for large ratios between the density of states at \(\lambda_{\text{MC}}\) and at the PBG (LPDOS\({}_{\text{MC}}\)/LPDOS\({}_{\text{SB}}\)), which ideally tends to infinity [198; 199; 200; 202; 207; 208; 211]. In a planar structure, the modal volume can be approximated to the effective length of the MC (L\({}_{\text{eff}}\)), depending on  
Figure 4: **(a)** Schematic of a planar microcavity structure. **(b)** Calculated reflectance spectra for a PS:CA (black line, \(\Delta\)n = 0.11) and a Hy:TiO\({}_{2}\)-PVA (red line, \(\Delta\)n = 0.58) microcavity of two DBRs composed of 31 alternated layers with thicknesses of d\({}_{\text{L}}\) = 120 nm and d\({}_{\text{L}}\) = 80 nm. The defect layer has a thickness of d\({}_{\text{D}}\) = 40 nm and refractive index of n\({}_{\text{MC}}\) = 1.5.  
the field penetration into the DBRs at the side of the defect layers, and then on the dielectric contrast among the DBR components. To date, emission rate enhancement (Purcell effect [201; 212; 213]) has not been observed for polymer microcavities owing to the low dielectric contrast leading to field penetration into the dielectric mirrors [14; 98; 106; 214; 215; 216; 217; 218]. Moreover, the rate enhancement effect requires emitters with a sharp spectrum. Indeed, if the emission linewidth is spectrally wider than the defect mode, emission suppression at the PBG compensates enhancement effects at the cavity mode, resulting in the lowering of the rate or the rate being unaffected [14; 197; 214; 215]. As mentioned above, the polymers described in the previous paragraph have never been investigated for lasing or radiative rate enhancement. Thus, it is worthwhile to quantify the effect of the enhanced dielectric contrast obtained with the strategies described in Section 3 on the LPDOS and on L\({}_{\text{eff}}\). The LPDOS can be easily calculated as a function of the Fresnel coefficients of the top and bottom DBRs from Green's function, as reported in [219]. Conversely, the effective length depends on \(\lambda_{\text{MC}}\), n\({}_{\text{MC}}\), n\({}_{\text{H}}\), and n\({}_{\text{L}}\), as described in [37; 180] and in the SI. The contour plot of Figure 5a reports the LPDOS as a function of \(\Delta\)n and of the wavelength normalized by the value at the cavity mode (\(\lambda\)/\(\lambda_{\text{MC}}\)). The calculation was performed for microcavities made of the same polymer pairs discussed in Figure 3. The defect layer has a thickness of d\({}_{\text{D}}\) = 40 nm and refractive index of n\({}_{\text{MC}}\) = 1.5, and it is embedded in a structure identical to that considered in Figure 4. LPDOS values are reported in false color so that small values are in green-blue shades while larger values are in red shades. Qualitatively, for all structures investigated, the LPDOS is at maximum at the cavity mode (\(\lambda\)/\(\lambda_{\text{MC}}\) = 1, red area).