# Wavelength Conversion Enhancement Achieved by Using Resonance in an Array of Nanocylinders
## 2 Upconversion Material Nanocylinder
### Spontaneous Emission Enhancement at 660 nm
However, since the useful converted visible light is only the emitted light into free space, which escapes from the UC layer and propagates upward, an output efficiency, n\({}_{\rm z}\), defined as the ratio between the upward-directional emitted power and the total emitter power, should also be considered alongside the SE rate enhancements. The output efficiency is same as the extraction efficiency in light-emitting diodes. The upward emission of the 660 nm wavelength light is \(\times\)0.66 the total emitted power from the parallel dipole source in the nanocylinder structure due to constructive interference of the dipole source and the image dipole source on a gold substrate [29]; in contrast, the upward emission in the reference structure is only \(\times\)0.11 of the total emitter power. Therefore, combined with the SE rate enhancements and the output efficiency, the effective upward emission of the parallel dipole source in the nanocylinder is 3.8 times larger than the reference structure. Here, the effective upward emission enhancement can be estimated by the ratio of the upward emission in the nanocylinder and the reference, in which the upward emitted power is obtained by the SE rate enhancement multiplied by the output efficiency, n\({}_{\rm z}\). On the other hand, in the case of a perpendicular dipole source (E\({}_{\rm z}\)), the SE rate enhancements of the nanocylinder and the reference are similar, \(\times\)1.1 and \(\times\)1.5, respectively, because of the SPP coupling. However, the output efficiency of the nanocylinder (0.53) is distinct from that of the reference (0.01). In the reference that  
Figure 5: **(a)** A schematic diagram of one quarter of a UC nanocylinder to calculate the spontaneous emission (SE) enhancement mapping. The cylinder has a height of 300 nm and a diameter of 500 nm. The period in the array is 520 nm. SE enhancement distributions of **(b)** E\({}_{\rm x}\) and **(c)** E\({}_{\rm z}\) dipole sources; a magnified top view represents the horizontal SE enhancement mapping obtained at a plane with z = 100 nm in the case of the E\({}_{\rm x}\) dipole source and a plane with z = 20 nm in the case of the E\({}_{\rm z}\) dipole source, respectively. A plane with z = 0 nm represents the interface between the nanocylinder and gold substrate. consists of a UC film on a gold substrate, the E\({}_{\mathrm{z}}\) dipole source couples with a horizontally propagating SPP wave and the upward emission is strongly suppressed. In contrast, in the nanocylinder array, light from the E\({}_{\mathrm{z}}\) dipole source is also able to couple to the SPPs, but the coupled SPPs can scatter at the edge of the finite nanocylinder, resulting in a high output efficiency of 0.53. Therefore, the effective upward emission of the perpendicular source in the nanocylinder is 41 times larger than that of the reference due to its strong upward directionality. If two parallel polarized dipole sources, E\({}_{\mathrm{x}}\) and E\({}_{\mathrm{y}}\), and one perpendicularly polarized dipole source, E\({}_{\mathrm{z}}\), are equally considered, the total effective upward emission of 660 nm light in the nanocylinder array is 21 times larger than the reference structure. As a result of the emission enhancement (\(\times\)21) and the absorption enhancement (\(\times\)7.3), the total effective enhancement of the UC process is \(\times\)155 the reference structure due to SPP coupling, coupling between the MD mode, and effective vertical directionality.