# Temperature Sensing with Nd\({}^{3+}\) Doped YAS Laser Microresonators
## 4 Results and Discussion
### Upconversion  
Photon upconversion (UC) is the process whereby the absorption of two or more photons produces the emission of a photon with a shorter wavelength than the wavelength of the excitation photons. To observe the upconversion emission, the microspheres were excited with a continuous wave 808 nm laser. This emission is shown in Figure 7. The first three bands correspond to transitions from the \({}^{4}\)G\({}_{7/2}\) level to the \({}^{4}\)I\({}_{9/2}\), \({}^{4}\)I\({}_{11/2}\), and \({}^{4}\)I\({}_{13/2}\) levels, respectively. The \({}^{4}\)G\({}_{7/2}\)\(\rightarrow\)\({}^{4}\)I\({}_{13/2}\) emission band is overlapped with the \({}^{4}\)F\({}_{9/2}\)\(\rightarrow\)\({}^{4}\)I\({}_{9/2}\) emission band. The last emission band corresponds to the \({}^{4}\)F\({}_{7/2}\)\(\rightarrow\)\({}^{4}\)I\({}_{9/2}\) and is cut due to the presence of a 750 nm short-pass filter. Figure 6: (**a**) Emission spectra of a YAS:Nd\({}^{3+}\) microsphere at pump powers below the laser threshold (black line) and above the threshold (red line); (**b**) intensity of the 1072 laser emission at different pump powers. The intensities of the last two bands increase at higher rates than the shorter wavelength bands. This shows that these levels are not being populated by the same mechanisms as the other bands. Attending to the increase of intensity with the pumping power, it is observed that these bands are being populated by thermal redistribution mechanisms following a Boltzmann distribution as shown in the latter section. The laser heating of the sample is also expected to reduce the upconversion efficiency due to the increase in non-radiative relaxation mechanisms. A plot of the intensity of the upconversion emission for the \({}^{4}\)G\({}_{7/2}\)\(\rightarrow\)\({}^{4}\)I\({}_{11/2}\) band as a function of the intensity of the excitation source in a logarithmic scale is shown in the inset of Figure 7. A straight line with a slope of 1.6 has been obtained from the fit. This result indicates that two infrared photons of 808 nm wavelength are required to produce the upconversion emission. Upconversion emission can be obtained mainly via two distinct mechanisms: energy transfer upconversion (ETU) and excited state absorption (ESA) [23]. If it is by the ETU process, the population of the upper level increases, even if there is no external radiation, as the atoms from the intermediate level are promoted, and slowly decreases once the maximum is reached. On the other hand, if the upconversion is obtained by ESA, the intensity of the emission quickly decays when there is no external radiation. The upconversion mechanism that produces the emissions from \({}^{4}\)G\({}_{7/2}\) is illustrated in Figure 1. The ESA process involves the subsequent absorption of two photons of a single Nd\({}^{3+}\) ion such that the following promotion occurs: \({}^{4}\)I\({}_{9/2}\)\(\rightarrow\)\({}^{4}\)F\({}_{3/2}\)\(\rightarrow\)\({}^{2}\)D\({}_{5/2}\). This is followed by a non-radiative multiphonon relaxation to the \({}^{4}\)G\({}_{7/2}\) level. Meanwhile, the ETU process involves the absorption of photons by different Nd\({}^{3+}\) ions giving rise to an ion in the \({}^{4}\)G\({}_{7/2}\) through the non-radiative energy transfer between these ions. One of the possible ETU mechanisms is illustrated in Figure 1, while other examples can be found in Reference [24]. In order to understand the upconversion mechanism occurring in the sample, the temporal evolution of the 530 nm band under the excitation of an 808 nm pulsed laser was measured, as shown in Figure 8. It shows an instantaneous increase with a rise time of 20 ns, a similar value to the response time of the acquisition setup described in Section 3.3, and a decay with a fast and a slow component. The fast component is due to the natural decay rate of the \({}^{4}\)G\({}_{7/2}\) level, and the slow component is due to the decay rate of the \({}^{4}\)F\({}_{3/2}\) level, which is twice that of the \({}^{4}\)G\({}_{7/2}\) level [25].