# Wavelength Conversion Enhancement Achieved by Using Resonance in an Array of Nanocylinders
## 3 Conclusions  
In this paper, we proposed a dielectric nanostructure made of UC material that converts NIR light into visible light. The resonances in the structure enable the enlargment of the light-matter interactions in both absorption and emission to improve the efficiency of the UC process. The absorption at 980 nm is enhanced by an electric hotspot induced by the MD resonances and surface plasmons at the interface between the nanocylinders and a gold substrate. The absorption is 7.3 times larger than the reference UC film structure. In addition, we obtain the enhanced upward emission of 660 nm wavelength light by directional scattering of the emission light due to constructive interference and scattering of the nanocylinders. The upward emission rates are 21 times larger than those of the reference structure. In total, the efficiency of the wavelength conversion combined with the absorption and emission rates is improved by a factor of 155. The converted light can be used effectively because the direction of the emitted light is upward. As a result, the efficiency of devices that use UC materials (such as solar cells and sensors) can be significantly improved. A KNbO\({}_{3}\) thin film can be deposited on the silicon substrate using the polymeric precursor method (Pechini method) [31]. Gold thicker than several hundred nanometers is deposited on the KNbO\({}_{3}\) film. Then, the sample is flipped and bonded to the other substrate. The original silicon substrate is removed by wet etching and the KNbO\({}_{3}\) film on gold layer is obtained. The next process to form an array of nanocylinders can be performed by using conventional electron-beam lithography or nanostamp techniques. Because the exciting electric field distribution in the absorption at 980 nm is spatially localized due to the resonance effects, as shown in Figure 4, the spontaneous emission enhancement can be affected by the spatial distribution of the absorption like in the case of lasing in nanocavity [32]. However, in order to consider the distribution adequately, there are several complicated factors to be considered such as the three-dimensional (3D) dynamics of carriers and photons in the multilevel system of a UC nanoclinder, carrier diffusion velocities, energy transfer rates in the UC process, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Cylinder (\(h\) 300, \(d\) 500)** & \multicolumn{2}{c}{**Reference**} & \multicolumn{2}{c}{_Cylinder \(z\) - Emission_} & \multicolumn{2}{c}{_Cylinder Absorption_} \\ \cline{2-7}  & **SE Enhancement** & \(\eta_{\mathrm{z}}\) & **SE Enhancement** & \(\eta_{\mathrm{z}}\) & \(\eta_{\mathrm{z}}\) & \(\eta_{\mathrm{z}}\) \\ \hline E\({}_{\mathrm{z}}\) & 0.62 & 0.66 & 1.0 & 0.11 & 3.8 & 7.3 \\ E\({}_{\mathrm{z}}\) & 1.1 & 0.53 & 1.5 & 0.01 & 41 & 7.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The volume average spontaneous emission (SE) enhancements of parallel (E\({}_{\mathrm{z}}\)) and perpendicular (E\({}_{\mathrm{z}}\)) dipole sources at a wavelength of 660 nm and the absorption enhancement at a wavelength of 980 nm. The UC material absorbs near-infrared (NIR) light with a wavelength of 980 nm and emits visible light with a wavelength of 660 nm. SE enhancements in an array of nanocylinders on a gold substrate and those in the reference structure are compared. SE enhancements in Table 1, the averaged SE enhancements, are calculated by integrating the values over the whole nanocylinder volume. The output efficiency \(\eta_{\mathrm{z}}\) is defined as the ratio between the upward-directional emitted power and the total emitter power. and the 3D distribution of photon densities, which should be analyzed in a further study. Our analysis of the SE enhancements assumes that the 980 nm absorption generates the corresponding carriers in a nanocylinder uniformly, which can provide a reasonable value of the SE enhancements as long as the diffusion velocities are large enough compared to the size of a nanocylinder, 500 nm.