# Wavelength Conversion Enhancement Achieved by Using Resonance in an Array of Nanocylinders
## 2 Upconversion Material Nanocylinder  
### Electric and Magnetic Dipole Resonances in a UC Nanocylinder  
First, we investigate the Mie resonances of a UC nanocylinder by calculating the scattering cross section using a three-dimensional (3D) finite-difference time-domain (FDTD) method. As shown in Figure 1a, incident light with linear polarization along the x-axis (E\({}_{\mathrm{x}}\)-polarization) propagates along the z-axis and is scattered by a nanocylinder with height \(h\) and a diameter \(d\), in which the cylinder is made of the UC material. The UC material was assumed to absorb near-infrared light with a wavelength of 980 nm and emit visible light with a wavelength of 660 nm. Because Er\({}^{3+}\) doped KNbO\({}_{3}\) has a higher upconversion efficiency at 530-550 nm (green) than at 660 nm (red), we focus on the red UC enhancement so that simultaneous efficient conversion of most of visible colors, green and red, from the NIR light can be realized. In addition, the mechanism to enhance the upconversion to red light by the resonances in an array of nanocylinder can be applied from the UC to green light in same way. For the nanocylinder with \(h\) = 400 nm and \(d\) = 400 nm, the normalized scattering cross section (Q\({}_{\mathrm{scat}}\)), defined by the ratio between a scattering cross section and a geometrical cross section, is calculated in Figure 1b. First and second resonances are observed as peaks in the graph of Q\({}_{\mathrm{scat}}\) at wavelengths of 710 nm and 960 nm, which correspond to ED and MD, respectively. The electric field intensity profiles and vector plots for the two resonances in Figure 1c,d show that the resonances are ED and MD, respectively. In particular, in the side view, the electric field of the ED near the middle of the cylinder is mainly oriented along the x-axis, which is similar to the E\({}_{\mathrm{x}}\) dipole. In contrast, the electric field of the MD exhibits a current loop in the nanocylinder as the usual magnetic dipole.  
Figure 1: **(a)** A nanocylinder with height \(h\) and diameter \(d\) created using an upconversion material (UC). Incident light with a linearly polarized electric field along the x-axis propagating along the z-axis; **(b)** normalized scattering cross section (Q\({}_{\mathrm{scat}}\)) of a UC nanocylinder with \(h\) = 400 nm and \(d\) = 400 nm. Resonant wavelengths of the electric dipole (ED) and magnetic dipole (MD) are 710 nm and 960 nm, respectively. Top and side views of the electric field intensity profiles and vector field distributions for **(c)** ED (710 nm) and **(d)** MD (960 nm). The top views are obtained from directly above the center of the nanocylinder.  
Here, we set the optical properties of the UC material and FDTD conditions as follows. In the simulation, we used Er\({}^{3+}\)-doped KNbO\({}_{3}\) (with the refractive index plotted in the graph of Figure 1) as the UC material. This UC material absorbs 980 nm wavelength light and sequentially emits 660 nm [25; 26; 27]. The spatial grid of FDTD is 10 nm and the boundary conditions are perfectly matched layers in the single nanocylinder structure and a periodic boundary condition in the array structure. In addition, the gold is fitted as Drude critical points in the model [28].