# Wavelength Conversion Enhancement Achieved by Using Resonance in an Array of Nanocylinders
## 2 Upconversion Material Nanocylinder
### Spontaneous Emission Enhancement at 660 nm  
Next, in order to investigate the emission properties of the converted visible light with wavelengths of 660 nm, we calculated the spontaneous emission (SE) enhancement of dipole sources in the proposed structure, as seen in Figure 4a, which are horizontally polarized (E\({}_{\mathrm{x}}\)) or perpendicularly polarized (E\({}_{\mathrm{z}}\)). SE enhancement is calculated using the following equation: SE enhancement = (emitted power of dipole source in UC nanocylinder)/(emitted power of dipole source in bulk UC material). We put a dipole source with a wavelength of 660 nm inside a UC nanocylinder and measured the total output power of the dipole source by integrating the Poynting vectors outgoing from the nanocylinder. We scanned the position of the dipole source with a spatial resolution of 20 nm. The actual calculation region is set to a quarter of a nanocylinder due to the mirror symmetry of the nanocylinder. The E\({}_{\mathrm{x}}\) dipole source, parallel to the gold substrate, has a maximum SE rate enhancement of 2.0 at a plane with z = 100 nm above the substrate, as shown in Figure 5b. Considering an image electric dipole on a gold substrate, which is anti-parallel to the original E\({}_{\mathrm{x}}\) dipole source, the height of 100 nm corresponds to approximately a quarter wavelength of 660 nm in the UC material, such that the image dipole can constructively interfere with the original dipole [29]. The horizontal mapping of the enhancement is similar to the mode profile of the ED mode (left of Figure 1c), which indicates that the emission of the E\({}_{\mathrm{x}}\) dipole source is enhanced via the Purcell effect of the ED mode in a nanocylinder [30]. The E\({}_{\mathrm{y}}\) dipole source has the same spatial distribution as the SE enhancement of the E\({}_{\mathrm{x}}\) dipole, except for a rotation by 90\({}^{\circ}\). Figure 4: **(a)** Schematic of the proposed UC nanocylinder array structure with a gold substrate. Here, the UC cylinders have a height of 300 nm and a diameter of 500 nm. The period in the array is 520 nm; **(b)** Reference structure consisting of a UC film with a thickness of 130 nm and a gold substrate. The thickness is determined to have the same UC volume as the proposed nanocylinder array; **(c)** The absorptances of the proposed structure (black) and reference structure (blue) as functions of wavelength. The absorptance of a cylinder array is 67.1% at 980 nm; **(d)** The electric field intensity profile with a vector field plot of the UC cylinder array. On the other hand, the E\({}_{\rm z}\) dipole source emits light strongly at the surface of the gold substrate, which is shown in Figure 5c. Here, the maximum enhancement position 20 nm above the substrate is limited by the spatial resolution of the scanning (20 nm). If a smaller resolution is applied for the enhancement of the E\({}_{\rm z}\) dipole, the maximum enhancement is at nearest position to the gold substrate. The SE rate of the E\({}_{\rm z}\) dipole source is enhanced 4.0 times its normal maximum for the plasmonic mode. Finally, we summarize the SE rate enhancements at a visible wavelength of 660 nm, the absorption enhancement at an NIR wavelength of 980 nm for the proposed nanocylinder array structure, and the reference structure in Table 1. The absorption of the nanocylinder structure is 7.3 times larger than that of the reference structure due to the fact it has coupled with the SPPs and the MDs in each nanocylinder. For the emission of 660 nm, the properties of the SE rate enhancements are very different depending on the direction of the dipole sources. In the case of parallel dipole sources (E\({}_{\parallel}\)) such as E\({}_{\rm x}\) or E\({}_{\rm y}\) dipole sources, the SE rate averaged over the nanocylinder is 0.62 times that of the SE rate in bulk UC material because the SE rate is suppressed near a half wavelength in the UC material [29], which is smaller than that of the reference structure.