# In-Band Pumped Thulium-Doped Tellurite Glass Microsphere Laser
## 4 Experimental Results and Discussion  
An experimental microsphere was made of TeO\({}_{2}\)-ZnO-La\({}_{2}\)O\({}_{3}\)-Na\({}_{2}\)O glass doped with thulium ions with concentration \(N_{Tm}=5\cdot 10^{19}\) cm\({}^{-3}\). This glass was similar in composition  
Figure 3: (**a**) Calculated coupling coefficients \(\kappa\) as functions of the total Q-factor for different diameters of tellurite microspheres indicated in the legend. Calculated laser wavelengths (**b**) and slope efficiencies (**c**) above the threshold pump power as functions of the total Q-factor for different thulium ion concentrations \(N_{Tm}\). Threshold pump powers for different microsphere diameters \(d\) for thulium ion concentration of \(1\cdot 10^{19}\) cm\({}^{-3}\) (**d**), \(5\cdot 10^{19}\) cm\({}^{-3}\) (**e**), and \(1\cdot 10^{20}\)cm\({}^{-3}\) (**f**). Threshold values of \(\kappa P_{Thr}\) (pump powers multiplied by coupling coefficients) for different microsphere diameters \(d\) for thulium ion concentration of \(1\cdot 10^{19}\) cm\({}^{-3}\) (**g**), \(5\cdot 10^{19}\) cm\({}^{-3}\) (**h**), and \(1\cdot 10^{20}\)cm\({}^{-3}\) (**i**). The legend shown in subplots (**d,g**) is the same as for subplots (**d–i**). and method of preparation to the core of the fiber used for laser generation earlier [34]. The glass was prepared by melting the initial high-purity oxides and sodium carbonate Na\({}_{2}\)CO\({}_{3}\) in platinum crucible inside sealed a silica chamber in the atmosphere of purified oxygen. After several hours melting at 800 \({}^{\circ}\)C, the melt was poured into a mold of silica glass and annealed at a glass transition temperature. A glass sample was cut, ground, and polished (see a photo in Figure 4a). The sample did not contain noticeable point scattering defects and striae in the glass volume. A polished parallelepiped was examined in a red laser beam to determine point defects. He-Ne laser beam scanning did not reveal bubbles and scattering inclusions in the volume of the samples (see Figure 4b). A single-index fiber was produced from the prepared glass (see Figure 4c). Next, we fabricated a microsphere with diameter \(d\) = 320 \(\upmu\)m by softening the tapered end of this tellurite single-index fiber using a resistive micro-heater [36]. Coupling of the pump wave at 1.55 \(\upmu\)m to the tellurite microsphere and outcoupling of the generated laser wave at \(\sim\)1.9 \(\upmu\)m were realized with a silica fiber taper as schematically shown in Figure 1. Despite the significant refractive index difference between silica and tellurite glasses, it is possible to achieve large (critical and even overcritical) coupling in the experiment. This is evident from the fact that at small distances between the taper and the microsphere the measured fraction of absorbed power near the resonance can be more than 0.5. For an in-band pump and Q-factor measurements, we used a standard telecommunication C-band laser based on a micro-integrable tunable laser assembly (Pure Photonics, PPCL550-180-60, line width 10 kHz, tuning range 190.3-197.9 THz). The measured Q-factor at a wavelength of 1.52 \(\upmu\)m was \(\sim\)10\({}^{6}\). To measure the Q-factor, we chose the wavelength shorter than the pump wavelength to mitigate the impact of ground state absorption of thulium ions on effective Q-factor. Note that our value \(Q\) = 10\({}^{6}\) agrees well with the Q-factors of tellurite microspheres reported previously by other researches [20; 24]. The experiment was conducted in an acrylic glove box to protect the microsphere and fiber taper against dust and airflows from the conditioning system [37]. The fiber taper was made of a telecommunication fiber SMF28e [38]. Coarse adjustment of relative position of the microsphere and fiber taper was done manually using two CCD cameras recording  
Figure 4: (**a**) A photography of the polished thulium-doped tellurite glass parallelepiped with dimensions of 8 \(\times\) 8 \(\times\) 44 mm. (**b**) A photography of He-Ne laser beam in this sample.