1. Introduction

The requirement of carrying higher bit-rate through one commercial silica fiber which has a broad low-loss band (1460-1650 nm < 0.25 dB/Km) has drawn attention of research to thulium oxide doped material whose ³H₄→³F₄ transition at 1.5μm covers the S-band (1460nm-1530nm) of optical communication (see Fig. 1). However, such transition is a self-terminating transition that is hard to achieve population inversion because its lower level lifetime is significantly longer than its upper level lifetime. Several special techniques have been developed to depopulate the lower level of the transition at 1.5μm. Trivalent rare-earth ions, such as Ho³⁺, Tb³⁺, and Nd³⁺, are codoped with Tm³⁺ to reduce the population of the long-lived ³F₄ state [1–3] through resonant energy transfer process. Some studies, in order to achieve population inversion, used dual-wavelength pump method to depopulate the ³F₄ state by exciting thulium ions at ³F₄ state to a higher energy level by excited state absorption [4]. In this paper we demonstrate a 1.5-μm laser from the self-terminating transition of Tm³⁺ in a microsphere resonator, and study the condition of CW lasing in such a laser system.

 

Fig. 1. Absorption coefficient of the 0.5 wt% Tm₂O₃ doped tellurite glass. Inset illustrates the energy diagram of the electronic state of Tm³⁺.

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2. Experiment

Among oxide glasses, tellurite glass is an attractive host for thulium ions due to its low phonon energy that helps Tm³⁺ to stay at the upper level of the ³H₄→³F₄ transition by decreasing the multi-phonon decay rate from ³H₄ to ³H₅. Tm-doped tellurite glass samples with different concentrations are fabricated and characterized in order to choose the optimum concentration for the 1.5 μm microsphere laser. Figure 1 shows the absorption coefficient of the 0.5 wt% Tm₂O₃ doped tellurite glass and the corresponding energy level diagram of the electronic states of Tm³⁺. Spontaneous emission rates of different transitions are calculated by Judd-Oflet theory. Lifetimes of both ³F₄ and ³H₄ states are measured for glasses with different concentrations. We find that when concentration is larger than 0.5wt%, the lifetime of ³H₄ state drop from 180 μs to 120 μs or less. This is mainly because of the cross relaxation that occurs at high thulium doping concentrations and dramatically depopulates the energy level of ³H₄, the upper lasing level of 1.5 μm transition. The emission spectrum also shows that when the doping concentration is higher than 0.5 wt%, the intensity ratio between 1.9 μm transition and 1.5 μm transition increases nonlinearly [5]. Hence, thulium doping concentration of 0.5 wt% was chosen in the experiment in order to eliminate the cross-relaxation energy transfer that decrease the emission intensity of 1.5-μm-band transition and to achieve efficient pump absorption.

In microsphere light can propagate around the edge with very low loss due to total internal reflection. The propagation mode, called whispering-gallery mode, applies to all wavelengths generally, which means microsphere can be used as a laser resonator working at most wavelengths within the gain band. In our research microsphere is used as a laser cavity for both 1.9 μm and 1.5 μm lasers. Microspheres are fabricated by the spin method [6]. The diameter of the microsphere ranges from the tens of to the hundreds of micron. A fiber taper made of Corning SMF-28 fiber by the typical heat-and-stretch method was used to couple the pump light into and signal laser out of the microsphere. A Ti-sapphire laser at 793 nm is employed to directly excite the ³H₄ state of Tm³⁺.

3. Lasing condition on self-terminating transition

The condition for CW lasing on a self-terminating transition (level 3 -> level 1) was described by [7],

where in the case of thulium, level 1, 2, and 3 represent ³F₄, ³H₅, and ³H₄ states. A₁ is the sum of spontaneous emission rate and nonradiative decay rate of the state ³F₄, lower level of laser transition, and $A_{31}^{*}$ 1 is the total decay rate from state ³H₄ to state ³F₄. The criterion derived under the condition that no stimulated emission and absorption were considered in the steady state rate equations. It states that in order to get population inversion, the requirement for CW lasing, the total decay rate of the lower level of laser transition should be greater than the total relaxation rate from the upper level to the lower level. In the case of Tm³⁺, the calculated spontaneous emission rates are A₁₀=540 s^-1, A₃₂=98 s^-1, A₃₁=260.5 s^-1, A₃₀=2863 s^-1, where the subscript number i represents the corresponding energy level shown in Fig. 1. All ions reaching the ³H₅ state will decay to the ³F₄ state immediately through multiphonon relaxation, because ³H₅ and ³F₄ states are so close in energy that only 2 or 3 phonons needs to be generated to accomplish the multi-phonon decay. Therefore, to simplify the analysis, a 3-level model in which the population of ³H₅ is zero is adopted. The total decay rate from ³H₄ state to ³F₄ state ($A_{31}^{*}$) can be written as,

where A_ijnr and A_ij are the nonradiative and radiative decay rate from level i to level j respectively.

For Tm³⁺ doped in the material with low phonon energy, the inequality (1) is satisfied. For example, 1.5 μm cascade laser of thulium ions has been demonstrated in fluoride glass [8–9]. In that case, the threshold of 1.5 μm is lower than that of the 1.9 μm laser, because the upper lasing level (³H₄) of the 1.5μm laser transition was directly excited by the pump laser, while the upper lasing level (³F₄) of the 1.9 μm laser transition was populated by the ions relaxed from ³H₄. According to the above spontaneous emission rates of different transitions, only 11% of the population excited to ³H₄ state, upper level of 1.5-μm transition, reaches the ³F₄ state, the upper level of the 1.9 μm transition. Due to the low pump efficiency, the 1.9 μm transition started to lase after 1.5 μm transition did.

In our experiment, the phonon energy of the tellurite glass was measured as 929cm^-1 which is higher than that of the fluoride glass. The nonradiative decay rate A_32nr is 2302 s^-1 calculated by A_32nr=1/τ_meas-(A₃₁+A₃₂+A₃₀). Therefore, the inequality (1) is not satisfied. However, we found the population inversion of the upper transition can be reached by making the lower transition laser first, which will depopulate the lower level of the upper transition. Under such situation, the steady state rate equations then can be written as,

where N _i is the population density of ions in level i, W ₁₀ and W ₀₁ are the stimulated emission rate and the stimulated absorption rate respectively. W ₀₃ is the pumping rate. Stimulated emission of 1.5 μm transition is not considered here, as we just need to find the condition for population inversion of the upper transition. Rate equations are solved for the population inversion ratio N ₃/N ₁. To simplify the result, only terms with the highest order of W ₀₃, W ₀₁ or W ₁₀ is considered in both denominator and numerator, because usually the pumping rate, stimulated emission rate and stimulated absorption rate are much larger than the spontaneous emission rate. Therefore, the moderated condition for population inversion is,

Inequality (2) states that if the pumping rate W ₀₃ and stimulated emission rate W ₁₀ are large enough, the population inversion of the upper transition will be built up. Furthermore, if the lower laser transition is a 4-level system, in which W ₁₀ ≫ W ₀₁, the criterion can be simplified as W ₁₀> A ^{31 *}. It’s quite similar to the inequality (1), except that A ₁₀ is replaced by W ₁₀.

4. Results and discussion

The laser performances of both 1.5μm and 1.9μm laser are shown in Fig. 2. The threshold of 1.9 μm laser is lower than that of the 1.5μm laser, which is the opposite of the phenomenon observed in fluoride glass. When the lower transition starts to lase, its intensity is not strong enough to make the stimulated emission rate satisfy the inequality (2) of the cascade laser. With the increase of pump and signal laser, the inequality (2) is then satisfied and the upper transition starts to lase. Careful inspection of Fig. 2 also shows that as soon as 1.5 μm transition start to laser, the slope of the l.9 μm laser is increased because of the high pumping efficiency resulting from the high stimulated emission rate of upper laser transition. In the experiment we also found that the intensity ratio between the upper transition laser and lower transition laser increased, when the lower transition laser operated at shorter wavelength at which the lower transition had larger emission cross-section.

 

Fig. 2. The slopes of both the 1.9 (black square) and 1.5 (red circle) μm lasers versus the pump power.

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Figure 3 shows the laser spectrum of microsphere. The emission spectrum of the glass sample with the same doping concentration is also illustrated in the inset of Fig. 2. The laser wavelengths are around 1.9 μm and 1.5 μm. Both are red shift from the emission peak of the respective transition bands. For 1.9 μm laser which is a 3-level system, the red shift of the laser wavelength results from the mode mismatch between pump and signal laser. The radial distribution of the whispering-gallery modes of pump and signal laser did not overlap well [10]. Part of the 1.9 μm laser WG mode area is not covered by the pump laser. Therefore, the reabsorption from those unpumped thulium ions make the lower transition laser operate at long wavelength. For 1.5μm laser, the red shift is caused by the reabsorption from the thulium ions at the lower laser level (³F₄). When the 1.9 μm laser is working in steady state, there are certain thulium ions at the upper level (³F₄) which is also the lower level of the 1.5 μm transition. The absorption from those ions at ³F₄ states will push the upper transition laser toward long wavelength.

 

Fig. 3. The microsphere laser spectrum of the 1.9 and 1.5 μm. The emission spectrum of the 0.5 wt% thulium doped tellurite glass sample.

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5. Conclusion

In summary, we demonstrate CW 1.5-μm-band laser from thulium doped tellurite glass microsphere. The condition for the CW laser in a self-terminating system has been studied. The 1.9 μm laser is achieved first in order to depopulate the lower level (³F₄) of the 1.5 μm laser transition that is a self-terminating transition. The improvement in slope efficiency of 1.9 μm laser is observed, after 1.5 μm transition starts to lase.