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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 27 — Dec. 19, 2011
  • pp: 26269–26274
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Novel approach towards cross-relaxation energy transfer calculation applied on highly thulium doped tellurite glasses

Masaud Taher, Hrvoje Gebavi, Stefano Taccheo, Daniel Milanese, and Rolindes Balda  »View Author Affiliations


Optics Express, Vol. 19, Issue 27, pp. 26269-26274 (2011)
http://dx.doi.org/10.1364/OE.19.026269


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Abstract

In this paper we calculated, for the first time to the best of our knowledge, the cross relaxation parameter of Tm3+ ions in tellurite glasses over a wide range of concentrations: from 0.36 mol% up to 10 mol%. A new measurement approach based on emission spectra monitoring is proposed. This method is very simple and allows to measure even very highly doped samples. The obtained values of cross-relaxation parameter show a linear dependence with respect to dopant concentration over the full investigated interval, suggesting a dipole-dipole interaction process. The measured slope is 1.81x10−17 cm3 s−1 mol%−1.

© 2011 OSA

1. Introduction

2. Theoretical modeling and measurement procedures

Figure 1
Fig. 1 Simplified energy level diagram of Tm3+ ion and scheme of the cross-relaxation process involving two Tm ions.
shows for sake of clarity the energy-level diagram of the Tm3+ ion pumped at 790 nm to the 3H4 level. The 3F43H6 emission of the neighboring ion is due to the cross-relaxation process: 3H4, 3H63F4, 3F4 as indicated in Fig. 1. As the result of this process for one pump photon it is possible to achieve two ions into the 3F4 manifold [19

19. J. Wu, S. Jiang, T. Luo, J. Geng, N. Peyghambarian, and N. P. Barnes, “Efficient thulium-doped 2 µm germanate fiber laser,” IEEE Photon. Technol. Lett. 18(2), 334–336 (2006). [CrossRef]

].

Since the average distance between two neighboring Tm3+ ions plays an important role in co-operative processes, the cross-relaxation parameter should depend on the doping level and this dependency has to be understood. The doping concentration range starts from a very low for long fiber lasers to extremely high for ultra - compact single-frequency lasers. In addition, evaluation of the cross-relaxation process will improve the predictions for a laser performance [20

20. J. Wu, Z. Yao, J. Zong, and S. Jiang, “Highly efficient high-power thulium-doped germanate glass fiber laser,” Opt. Lett. 32(6), 638–640 (2007). [CrossRef] [PubMed]

,21

21. J. Wu, S. Jiang, T. Qiu, M. Morrell, A. Schulzgen, and N. Peyghambarian, “Cross-relaxation energy transfer in Tm3+ doped tellurite glass,” in Optical Components and Materials II (San Jose, CA, USA, 2005) 152–161.

]. Tm3+ has a quite complex system of energy levels [14

14. C. A. Evans, Z. Ikonić, B. Richards, P. Harrison, and A. Jha, “Theoretical modeling of a 2 μm Tm3+ doped Tellurite fiber laser: the influence of cross relaxation,” J. Lightwave Technol. 27(18), 4026–4032 (2009). [CrossRef]

] but we can consider empty 3H5 level due to non radiative fast relaxation to 3F4 without losing in model accuracy. The corresponding rate-equation system used to analyze our experimental data is:
dN0dt=W03N0+N3τ30+N1τ1CRN3N0
(1)
dN1dt=N3τ31N1τ1+2CRN3N0
(2)
dN3dt=W03N0N3τ30N3τ31CRN3N0
(3)
where N0, N1, and N3 are the populations of Tm3+ ions in the 3H6, 3F4, and 3H4 levels respectively, W03 is the pump rate (s−1) and CR the cross relaxation parameter, τxy is the lifetime of the x to y transition and τx is the lifetime of level x. Note that τ3 = (τ31−1 + τ30−1)−1. The CR parameter is a function of the Tm doping level. At steady state the time derivatives in the rate equations are equal to zero. Considering the conservation law of Tm3+ ions populations, we can also write Nt = N0 + N1 + N3. The above rate equations system can be solved using a suitable numerical program. However, to optimize doping level it is important to have available parameters as a function of the concentration. Here, we were focused on the CR parameter. The cross-relaxation rate CRN0 can be estimated by using a standard model and the relation from the measurement of the experimental lifetime of 3H4 level [12

12. A. S. S. de Camargo, S. L. de Oliveira, D. F. de Sousa, L. A. O. Nunes, and D. W. Hewak, “Spectroscopic properties and energy transfer parameters of Tm3+ ions in gallium lanthanum sulfide glass,” J. Phys. Condens. Matter 14(41), 9495–9505 (2002). [CrossRef]

,22

22. G. X. Chen, Q. Y. Zhang, G. F. Yang, and Z. H. Jiang, “Mid-infrared emission characteristic and energy transfer of Ho3+-doped tellurite glass sensitized by Tm 3+.,” J. Fluoresc. 17(3), 301–307 (2007). [CrossRef] [PubMed]

]:
CR=1N0(1τ3+1τ3*)
(5)
where τ3* is the measured lifetime of the 3H4 level. However, as we will discuss later this requires an experimental set-up with time resolution of the order of 1 μs or below [16

16. H. Gebavi, D. Milanese, R. Balda, S. Chaussedent, M. Ferrari, J. Fernandez, and M. Ferraris, “Spectroscopy and optical characterization of thulium doped TZN glasses,” J. Appl. Phys. 43, 135104 (2010).

] and the sensitivity fail to provide reliable values for very highly-doped samples. To overcome this limitation we propose to investigate the steady-state emission from 3H4 and the 3F4 levels. In steady-state condition from Eq. (2) follows:

CR=12N0[1τ31+N1N3τ1]
(6)

We can now use the Fuchtbauer-Landenburg rule [23

23. C. R. Giles, C. A. Burrus, D. DiGiovanni, N. K. Dutta, and G. Raybon, “Characterization of erbium-doped fibers and application to modeling 980-nm and 1480-nm pumped amplifiers,” IEEE Photon. Technol. Lett. 3(4), 363–365 (1991). [CrossRef]

] and the relationship that provides the amount of the spontaneous emission [24

24. C. R. Giles and E. Desurvire, “Propagation of signal and noise in concatenated erbium-doped fiber optical amplifiers,” J. Lightwave Technol. 9(2), 147–154 (1991). [CrossRef]

]. The first rule relates the transition lifetime to emission spectra and emission cross section, the second one the amount of emitted spontaneous photons to the number of excited ions and their emission cross section. Therefore, the emission cross section can be written as:
σe,ij(λp,ij)=Kλp,ij4Ai,j,normn2(λp,ij)τij=HΦij(λp,ij)NiΔν
(7)
where σij, Aij,norm, τij are the emission cross section, the area of emission spectrum normalized to the maximum and the transition radiative lifetime of the transition from level i to level j; respectively. The parameters H and K are constants independent from the transition, n is the glass refractive index at the transition wavelength; Φij is the number of photons emitted at peak wavelength in the frequency interval Δν, Ni is the excited ion population, and λp,ij is the emission peak wavelength of the transition labeled as ‘ij’. By combining the two above written equations we have:

NiτijΦij(λp,ij)Δνpλp,ij4Aij,normn2(λp,ij)
(8)

Please, note we are not interested in the exact value of the ratio. If we now rewrite the Eq. (6) and use Eq. (8) for the 1800 nm (i = 1, j = 0) and 1470 nm (i = 3, j = 1) transitions, we have:
CR=β312N0τ3[Δνp,31Φ10λp,314A10,normn2(λp,10)Δνp,10Φ31λ4p,10A31,normn2(λp,31)τ1,0τ11]
(9)
where β31 is the branching ratio of the 1470 nm transition and is equal to 0.076 [20

20. J. Wu, Z. Yao, J. Zong, and S. Jiang, “Highly efficient high-power thulium-doped germanate glass fiber laser,” Opt. Lett. 32(6), 638–640 (2007). [CrossRef] [PubMed]

] and τ10 is the lifetime of 3F4 level for an isolated ion. In the paper we will use this formula to calculate the cross relaxation even for the highest doped samples were Eq. (5) fails due to experimental resolutions limits.

3. Experimental set-up

All samples had the same host composition 75TeO2-20ZnO-5Na2O (mol%), labeled as TZN, and were doped with Tm3+ concentrations ranging from 0.36 mol% to 10 mol% [16

16. H. Gebavi, D. Milanese, R. Balda, S. Chaussedent, M. Ferrari, J. Fernandez, and M. Ferraris, “Spectroscopy and optical characterization of thulium doped TZN glasses,” J. Appl. Phys. 43, 135104 (2010).

]. In our set-up the excited pump beam from a 785 nm laser diode was first collimated and then focused on the sample edge to reduce undesired effects of radiation trapping and re-absorption that may alter the measurement. The signal was collected orthogonally with respect to the excited beam by a low N.A. lens (N.A. = 0.25). This reduced the signal intensity but at the same time reduced the lifetime measurement errors due to reabsorption. Before the photodiode a long-pass filter with cut-off at around 1500 nm was used to measure the 3F4 level lifetime whilst a 1450 nm pass-band filter was used to measure the 3H4 lifetime. The spectra were recorded by an array of ccd covering the 900 nm – 2500 nm wavelength interval.

4. Cross-relaxation measurement

As it is described in the theoretical investigation, in order to obtain the CR parameter it is necessary to measure the lifetime of 3H4 level for all samples or, alternatively, the lifetime of 3F4 level and the emission spectra. We measured the lifetime of 3H4 and 3F4 levels and fitted the experimental lifetime values using the formula proposed by Auzel et al [25

25. F. Auzel, F. Bonfigli, S. Gagliari, and G. Baldacchini, “The interplay of self-trapping and self-quenching for resonant transitions in solids; role of a cavity,” J. Lumin. 94–95, 293–297 (2001). [CrossRef]

]:
τ=τ0(1+92π(NNq)2)
(10)
where τ is the measured lifetime at a given concentration N, τ0 is the lifetime of a single isolated ion, and Nq the quenching concentration. Figure 2a
Fig. 2 Measured lifetimes for: (a) 3F4 level, and (b) 3H4 level versus Tm3+ concentration.
and Fig. 2b show the measured values. Note that for our purpose we do not need to measure the highest-doped samples.

The quenching concentration for 3F4 and 3H4 levels obtained by the Eq. (10) were ~1.6 and 1 mol%, respectively. The lifetime τ0 for 3H4 was 0.37 ms whilst for 3F4 equal to 2.7 ms. For the samples doped with concentrations higher than 4 mol% the lifetime of 3H4 level was affected by the response time of our photodiode that is of about few microsecond. To calculate the cross-relaxation parameter for samples with higher doping concentration we measured the emission spectra. Again, samples of Tm-doped tellurite glasses were excited at the wavelength of 785 nm and the two transition bands centered at 1.47 and 1.8 µm, which corresponding to 3H43F4 and 3F43H6 respectively, were observed and are shown in Fig. 3a
Fig. 3 (a) Emission spectra, inset magnifies the of 3H43F4 transition at 1.47 μm; (b) Ratio between the emission from 3F4 and 3H4 levels.
where we normalized all curves to the peak of 3H43F4 transition at 1.47 μm. The ratio between the emission peak from 3F4 and 3H4 levels is reported in Fig. 3b. We were using the peak ratios and not the integral value since the emission shape was not changing significantly.

Using data from emission spectra and Eq. (9) we calculated the CR parameter. Since the detector bandwidth was similar at 1470 nm and at 1800 nm and the refractive index difference if less than 1% [16

16. H. Gebavi, D. Milanese, R. Balda, S. Chaussedent, M. Ferrari, J. Fernandez, and M. Ferraris, “Spectroscopy and optical characterization of thulium doped TZN glasses,” J. Appl. Phys. 43, 135104 (2010).

], we used the followed approximated equation:

CR=12N0τ31[kR1]
(11)

Where R = (Φ1030)(τ1,01) depends on the measurements and ‘k’ contains all other constants k = (λp,31/ λp,10)4 (Δνp,31/ Δνp,10) (A10,norm/A31,norm). Since the two peak wavelengths are 1470 nm and 1800 nm and the normalized area of the A31,norm is half the normalized area A10,norm so we have k = 1.33. The final value of ‘k’ was also calculated considering frequency interval Δν. The measurement of output spectra were carried out using a similar interval in the wavelength domain, therefore the ratio between frequency intervals were scaled considering Δν = c Δλ/λ2 where c is the speed of light. Figure 4
Fig. 4 Cross-relaxation parameter versus Tm concentration.
shows as triangles the values calculated by using Eq. (11). We can note a quite clear linear increase even for highest doped samples where, however the slope is slightly reduced.

From the experimental data the fitted CR is 1.81x10−17 cm3 s-1%mol−1 is obtained. This value is below the one previously reported in TZN glass [14

14. C. A. Evans, Z. Ikonić, B. Richards, P. Harrison, and A. Jha, “Theoretical modeling of a 2 μm Tm3+ doped Tellurite fiber laser: the influence of cross relaxation,” J. Lightwave Technol. 27(18), 4026–4032 (2009). [CrossRef]

] but is consisted with the one used for silica fiber modeling [17

17. S. D. Jackson and T. A. King, “Theoretical modeling of Tm-doped silica fiber lasers,” J. Lightwave Technol. 17(5), 948–956 (1999). [CrossRef]

]. To verify our results further, we used the common method of calculating CR parameter from Eq. (5) and results are shown in Fig. 4. The linear dependence on concentration of the cross-relaxation parameter is in agreement with the behavior of the concentration quenching of the lifetimes, as predicted by Auzel in the framework of dipole-dipole interaction processes [26

26. F. Auzel, G. Baldacchini, L. Laversenne, and G. Boulon, “Radiation trapping and self-quenching analysis in Yb3+, Er3+, and Ho3+ doped Y2O3,” Opt. Mater. 24(1-2), 103–109 (2003). [CrossRef]

]. We can notice an excellent agreement between the two methods until 4 mol%, the highest-doped sample we were able to measure with a suitable accuracy. We believe that the data here reported will be useful to model and design laser in TZN glasses. This measurement method can be easily extended to other type of glasses.

5. Conclusion

We experimentally calculated the cross relaxation parameter of Tm3+ ions in tellurite glasses over a wide range of concentrations: from 0.36 mol% up to 10 mol%. A new and simple approach based on the emission spectra measurements was developed to investigate samples with very high doping levels. This approach demonstrates to be very sensitive and can be further applied to other kind of glasses. The obtained values of cross-relaxation show a linear dependence with dopant concentration. The value of the linear fit slope was 1.81x10−17 cm−3 s-1%mol−1. This value allows a proper modeling of Tm-doped tellurite glass laser using a suitable value for the cross-relaxation parameter.

Acknowledgments

We acknowledge the support by FP7 LIFT project (Leadership in Fiber Technology, Grant #228587), and the collaboration within COST Action MP0702. R. Balda acknowledges financial support from the Spanish Government under project MAT2009-14282-C02-02.

References and links

1.

D. C. Hanna, I. M. Jauncey, R. M. Percival, I. R. Perry, R. G. Smart, P. J. Suni, J. E. Townsend, and A. C. Tropper, “Continuous-wave oscillation of a monomode thulium-doped fibre laser,” Electron. Lett. 24(19), 1222–1223 (1988). [CrossRef]

2.

S. D. Jackson and A. Lauto, “Diode-pumped fiber lasers: a new clinical tool?” Lasers Surg. Med. 30(3), 184–190 (2002). [CrossRef] [PubMed]

3.

J. Y. Allain, M. Monerie, and H. Poignant, “Tunable CW lasing around 0.82, 1.48, 1.88 and 2.35 µm in thulium-doped fluorozirconate fibre,” Electron. Lett. 25(24), 1660–1662 (1989). [CrossRef]

4.

E. R. M. Taylor, L. N. Ng, J. Nilsson, R. Caponi, A. Pagano, M. Potenza, and B. Sordo, “Thulium-doped tellurite fiber amplifier,” IEEE Photon. Technol. Lett. 16(3), 777–779 (2004). [CrossRef]

5.

M. Yamane and Y. Asahara, Glasses for Photonics (Cambridge University Press, 2004).

6.

A. Jha, S. Shen, and M. Naftaly, “Structural origin of spectral broadening of 1.5- µm emission in Er3+ -doped tellurite glasses,” Phys. Rev. B 62(10), 6215–6227 (2000). [CrossRef]

7.

T. Yamamoto, Y. Miyajima, and T. Komukai, “1.9 μm Tm-doped silica fibre laser pumped at 1.57 μm,” Electron. Lett. 30(3), 220–221 (1994). [CrossRef]

8.

J. Wu, S. Jiang, T. Luo, J. Geng, N. Peyghambarian, and N. P. Barnes, “Efficient thulium-doped 2-μm germanate fiber laser,” IEEE Photon. Technol. Lett. 18(2), 334–336 (2006). [CrossRef]

9.

Q. Huang, Q. Wang, J. Chang, X. Zhang, Z. Liu, and G. Yu, “Optical parameters and upconversion fluorescence in Tm3+/Yb3+ co-doped tellurite glass,” Laser Phys. 20(4), 865–870 (2010). [CrossRef]

10.

B. Richards, Y. Tsang, D. Binks, J. Lousteau, and A. Jha, “Efficient 2 μm doped tellurite fiber laser,” Opt. Lett. 33(4), 402–404 (2008). [CrossRef] [PubMed]

11.

P. F. Moulton, G. A. Rines, E. V. Slobodtchikov, K. F. Wall, G. Frith, B. Samson, and A. L. G. Carter, “Tm-Doped Fiber Lasers: Fundamentals and Power Scaling,” IEEE J. Sel. Top. Quantum Electron. 15(1), 85–92 (2009). [CrossRef]

12.

A. S. S. de Camargo, S. L. de Oliveira, D. F. de Sousa, L. A. O. Nunes, and D. W. Hewak, “Spectroscopic properties and energy transfer parameters of Tm3+ ions in gallium lanthanum sulfide glass,” J. Phys. Condens. Matter 14(41), 9495–9505 (2002). [CrossRef]

13.

R. R. Petrin, M. G. Jani, R. C. Powell, and M. Kokta, “Spectral dynamics of laser pumped Y3Al5O12: Tm: Ho lasers,” Opt. Mater. 1(2), 111–124 (1992). [CrossRef]

14.

C. A. Evans, Z. Ikonić, B. Richards, P. Harrison, and A. Jha, “Theoretical modeling of a 2 μm Tm3+ doped Tellurite fiber laser: the influence of cross relaxation,” J. Lightwave Technol. 27(18), 4026–4032 (2009). [CrossRef]

15.

D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, and G. Monnom, “Energy transfer up-conversion in Tm3+-doped silica fiber,” J. Non-Cryst. Solids 352(2), 136–141 (2006). [CrossRef]

16.

H. Gebavi, D. Milanese, R. Balda, S. Chaussedent, M. Ferrari, J. Fernandez, and M. Ferraris, “Spectroscopy and optical characterization of thulium doped TZN glasses,” J. Appl. Phys. 43, 135104 (2010).

17.

S. D. Jackson and T. A. King, “Theoretical modeling of Tm-doped silica fiber lasers,” J. Lightwave Technol. 17(5), 948–956 (1999). [CrossRef]

18.

H. Gebavi, D. Milanese, G. Liao, Q. Chen, M. Ferraris, M. Ivanda, O. Gamulin, and S. Taccheo, “Spectroscopic investigation and optical characterization of novel highly thulium doped tellurite glasses,” J. Non-Cryst. Solids 355(9), 548–555 (2009). [CrossRef]

19.

J. Wu, S. Jiang, T. Luo, J. Geng, N. Peyghambarian, and N. P. Barnes, “Efficient thulium-doped 2 µm germanate fiber laser,” IEEE Photon. Technol. Lett. 18(2), 334–336 (2006). [CrossRef]

20.

J. Wu, Z. Yao, J. Zong, and S. Jiang, “Highly efficient high-power thulium-doped germanate glass fiber laser,” Opt. Lett. 32(6), 638–640 (2007). [CrossRef] [PubMed]

21.

J. Wu, S. Jiang, T. Qiu, M. Morrell, A. Schulzgen, and N. Peyghambarian, “Cross-relaxation energy transfer in Tm3+ doped tellurite glass,” in Optical Components and Materials II (San Jose, CA, USA, 2005) 152–161.

22.

G. X. Chen, Q. Y. Zhang, G. F. Yang, and Z. H. Jiang, “Mid-infrared emission characteristic and energy transfer of Ho3+-doped tellurite glass sensitized by Tm 3+.,” J. Fluoresc. 17(3), 301–307 (2007). [CrossRef] [PubMed]

23.

C. R. Giles, C. A. Burrus, D. DiGiovanni, N. K. Dutta, and G. Raybon, “Characterization of erbium-doped fibers and application to modeling 980-nm and 1480-nm pumped amplifiers,” IEEE Photon. Technol. Lett. 3(4), 363–365 (1991). [CrossRef]

24.

C. R. Giles and E. Desurvire, “Propagation of signal and noise in concatenated erbium-doped fiber optical amplifiers,” J. Lightwave Technol. 9(2), 147–154 (1991). [CrossRef]

25.

F. Auzel, F. Bonfigli, S. Gagliari, and G. Baldacchini, “The interplay of self-trapping and self-quenching for resonant transitions in solids; role of a cavity,” J. Lumin. 94–95, 293–297 (2001). [CrossRef]

26.

F. Auzel, G. Baldacchini, L. Laversenne, and G. Boulon, “Radiation trapping and self-quenching analysis in Yb3+, Er3+, and Ho3+ doped Y2O3,” Opt. Mater. 24(1-2), 103–109 (2003). [CrossRef]

OCIS Codes
(160.2750) Materials : Glass and other amorphous materials
(160.5690) Materials : Rare-earth-doped materials

ToC Category:
Materials

History
Original Manuscript: October 20, 2011
Revised Manuscript: November 22, 2011
Manuscript Accepted: November 22, 2011
Published: December 8, 2011

Citation
Masaud Taher, Hrvoje Gebavi, Stefano Taccheo, Daniel Milanese, and Rolindes Balda, "Novel approach towards cross-relaxation energy transfer calculation applied on highly thulium doped tellurite glasses," Opt. Express 19, 26269-26274 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-27-26269


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References

  1. D. C. Hanna, I. M. Jauncey, R. M. Percival, I. R. Perry, R. G. Smart, P. J. Suni, J. E. Townsend, and A. C. Tropper, “Continuous-wave oscillation of a monomode thulium-doped fibre laser,” Electron. Lett.24(19), 1222–1223 (1988). [CrossRef]
  2. S. D. Jackson and A. Lauto, “Diode-pumped fiber lasers: a new clinical tool?” Lasers Surg. Med.30(3), 184–190 (2002). [CrossRef] [PubMed]
  3. J. Y. Allain, M. Monerie, and H. Poignant, “Tunable CW lasing around 0.82, 1.48, 1.88 and 2.35 µm in thulium-doped fluorozirconate fibre,” Electron. Lett.25(24), 1660–1662 (1989). [CrossRef]
  4. E. R. M. Taylor, L. N. Ng, J. Nilsson, R. Caponi, A. Pagano, M. Potenza, and B. Sordo, “Thulium-doped tellurite fiber amplifier,” IEEE Photon. Technol. Lett.16(3), 777–779 (2004). [CrossRef]
  5. M. Yamane and Y. Asahara, Glasses for Photonics (Cambridge University Press, 2004).
  6. A. Jha, S. Shen, and M. Naftaly, “Structural origin of spectral broadening of 1.5- µm emission in Er3+ -doped tellurite glasses,” Phys. Rev. B62(10), 6215–6227 (2000). [CrossRef]
  7. T. Yamamoto, Y. Miyajima, and T. Komukai, “1.9 μm Tm-doped silica fibre laser pumped at 1.57 μm,” Electron. Lett.30(3), 220–221 (1994). [CrossRef]
  8. J. Wu, S. Jiang, T. Luo, J. Geng, N. Peyghambarian, and N. P. Barnes, “Efficient thulium-doped 2-μm germanate fiber laser,” IEEE Photon. Technol. Lett.18(2), 334–336 (2006). [CrossRef]
  9. Q. Huang, Q. Wang, J. Chang, X. Zhang, Z. Liu, and G. Yu, “Optical parameters and upconversion fluorescence in Tm3+/Yb3+ co-doped tellurite glass,” Laser Phys.20(4), 865–870 (2010). [CrossRef]
  10. B. Richards, Y. Tsang, D. Binks, J. Lousteau, and A. Jha, “Efficient 2 μm doped tellurite fiber laser,” Opt. Lett.33(4), 402–404 (2008). [CrossRef] [PubMed]
  11. P. F. Moulton, G. A. Rines, E. V. Slobodtchikov, K. F. Wall, G. Frith, B. Samson, and A. L. G. Carter, “Tm-Doped Fiber Lasers: Fundamentals and Power Scaling,” IEEE J. Sel. Top. Quantum Electron.15(1), 85–92 (2009). [CrossRef]
  12. A. S. S. de Camargo, S. L. de Oliveira, D. F. de Sousa, L. A. O. Nunes, and D. W. Hewak, “Spectroscopic properties and energy transfer parameters of Tm3+ ions in gallium lanthanum sulfide glass,” J. Phys. Condens. Matter14(41), 9495–9505 (2002). [CrossRef]
  13. R. R. Petrin, M. G. Jani, R. C. Powell, and M. Kokta, “Spectral dynamics of laser pumped Y3Al5O12: Tm: Ho lasers,” Opt. Mater.1(2), 111–124 (1992). [CrossRef]
  14. C. A. Evans, Z. Ikonić, B. Richards, P. Harrison, and A. Jha, “Theoretical modeling of a 2 μm Tm3+ doped Tellurite fiber laser: the influence of cross relaxation,” J. Lightwave Technol.27(18), 4026–4032 (2009). [CrossRef]
  15. D. A. Simpson, G. W. Baxter, S. F. Collins, W. E. K. Gibbs, W. Blanc, B. Dussardier, and G. Monnom, “Energy transfer up-conversion in Tm3+-doped silica fiber,” J. Non-Cryst. Solids352(2), 136–141 (2006). [CrossRef]
  16. H. Gebavi, D. Milanese, R. Balda, S. Chaussedent, M. Ferrari, J. Fernandez, and M. Ferraris, “Spectroscopy and optical characterization of thulium doped TZN glasses,” J. Appl. Phys.43, 135104 (2010).
  17. S. D. Jackson and T. A. King, “Theoretical modeling of Tm-doped silica fiber lasers,” J. Lightwave Technol.17(5), 948–956 (1999). [CrossRef]
  18. H. Gebavi, D. Milanese, G. Liao, Q. Chen, M. Ferraris, M. Ivanda, O. Gamulin, and S. Taccheo, “Spectroscopic investigation and optical characterization of novel highly thulium doped tellurite glasses,” J. Non-Cryst. Solids355(9), 548–555 (2009). [CrossRef]
  19. J. Wu, S. Jiang, T. Luo, J. Geng, N. Peyghambarian, and N. P. Barnes, “Efficient thulium-doped 2 µm germanate fiber laser,” IEEE Photon. Technol. Lett.18(2), 334–336 (2006). [CrossRef]
  20. J. Wu, Z. Yao, J. Zong, and S. Jiang, “Highly efficient high-power thulium-doped germanate glass fiber laser,” Opt. Lett.32(6), 638–640 (2007). [CrossRef] [PubMed]
  21. J. Wu, S. Jiang, T. Qiu, M. Morrell, A. Schulzgen, and N. Peyghambarian, “Cross-relaxation energy transfer in Tm3+ doped tellurite glass,” in Optical Components and Materials II (San Jose, CA, USA, 2005) 152–161.
  22. G. X. Chen, Q. Y. Zhang, G. F. Yang, and Z. H. Jiang, “Mid-infrared emission characteristic and energy transfer of Ho3+-doped tellurite glass sensitized by Tm 3+.,” J. Fluoresc.17(3), 301–307 (2007). [CrossRef] [PubMed]
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