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Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 19 — Sep. 18, 2006
  • pp: 8535–8539
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Gain improvement by internal laser cavity in Tm3+/Yb3+-codoped tellurite fiber amplifier pumped by 980-nm laser

Jun Chang, Qingpu Wang, Gangding Peng, Xingyu Zhang, Zejin Liu, Shuanghong Ding, Zhaojun Liu, Sasa Zhang, and Gongtang Wang  »View Author Affiliations


Optics Express, Vol. 14, Issue 19, pp. 8535-8539 (2006)
http://dx.doi.org/10.1364/OE.14.008535


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Abstract

S-band Tm3+/Yb3+ codoped tellurite fiber amplifier pumped by a 980nm laser diode is proposed and modeled taking into consideration of the energy transfer process from Yb3+ to Tm3+ and the laser cavity inside a codoped fiber amplifier. S-band spectral gains for the codoped fiber amplifiers are investigated. The results show that considerable gain improvement can be achieved by constructing 1050nm laser cavity inside the amplifier.

© 2006 Optical Society of America

1. Introduction

Since Yb3+ have large absorption cross-section at 980nm, Tm3+/Yb3+ codoped silica fiber [1

1. Jun Chang, Qingpu Wang, and Gangding Peng, “Optical amplification in Yb3+-codoped thulium doped silica fiber,” Opt. Mat. 28, 1088–1094(2006). [CrossRef]

], fluoride fiber [2

2. Jun Chang, Qingpu Wang, Xingyu Zhang, Zejin Liu, Zhaojun Liu, and Gangding Peng, “S-band optical amplification by an internally generated pump in thulium ytterbium codoped fiber, ” Opt. Express 13, 3902–3912(2005). [CrossRef] [PubMed]

], and tellurite fiber[3

3. Shaoxiong Shen, Animesh Jha, Lihui Huang, and Purushottam Joshi, “980-nm diode-pumped Tm3+/Yb3+-codoped tellurite fiber for S-band amplification,” Opt. Lett. 30,1437(2005). [CrossRef] [PubMed]

] have been studied to take advantage of the low cost 980nm laser diode (LD). The sensitization of Tm3+ by Yb3+ is mainly through 2 ways: nonradiative energy transfer process [1

1. Jun Chang, Qingpu Wang, and Gangding Peng, “Optical amplification in Yb3+-codoped thulium doped silica fiber,” Opt. Mat. 28, 1088–1094(2006). [CrossRef]

, 4

4. A. Braud, S. Girard, J. L. Doualan, M. Thuau, and R. Moncorge, “Energy-transfer processes in Yb:Tm-doped KY3F10, LiYF4, and BaY2F8 single crystals for laser operation at 1.5 and 2.3 µm,” Phys. Rev. B 61, 5280 (2000). [CrossRef]

, 5

5. C. Y. Chen, R. R. Petrin, D. C. Yen, and W. A. Sibley, “Concentration-dependent energy-transfer processes in Er3+-and Tm3+-doped heavy-metal fluoride glass,” Opt. Lett.s 14, 432(1989). [CrossRef]

] and radiative energy transfer process[2

2. Jun Chang, Qingpu Wang, Xingyu Zhang, Zejin Liu, Zhaojun Liu, and Gangding Peng, “S-band optical amplification by an internally generated pump in thulium ytterbium codoped fiber, ” Opt. Express 13, 3902–3912(2005). [CrossRef] [PubMed]

,3

3. Shaoxiong Shen, Animesh Jha, Lihui Huang, and Purushottam Joshi, “980-nm diode-pumped Tm3+/Yb3+-codoped tellurite fiber for S-band amplification,” Opt. Lett. 30,1437(2005). [CrossRef] [PubMed]

]. These processes have been reported in cases of lasers at 1.5µm and 2.3µm using 975nm pump in Tm3+/Yb3+ codoped YLiF4 crystal [4

4. A. Braud, S. Girard, J. L. Doualan, M. Thuau, and R. Moncorge, “Energy-transfer processes in Yb:Tm-doped KY3F10, LiYF4, and BaY2F8 single crystals for laser operation at 1.5 and 2.3 µm,” Phys. Rev. B 61, 5280 (2000). [CrossRef]

]. Theoretical model were established for Tm3+ doped amplifiers (TDFA) in silica fiber [6

6. P. Peterka, B. Faure, W. Blanc, M. Karasek, and B. Dussardier, “Theoretical modelling of S-band thulium-doped silica fiber amplifiers,” Optical and Quantum Electron. 36, 201–212(2004). [CrossRef]

] and fluoride fiber [7

7. Claudio Floridia, M. T. Carvalho, S. R. Lüthi, and A. S. L. Gomes, “Modeling the distributed gain of single-(1050 or 1410 nm) and dual-wavelength (800+1050 nm or 800+1410 nm) pumped thulium-doped fiber amplifiers,” Opt. Lett. 29, 1983–1985(2004). [CrossRef] [PubMed]

,8

8. Tadashi Kasamatsu, Yutaka Yano, and Takashi Ono, “1.49-µm-Band gain-shifted thulium-doped fiber amplifier for WDM transmission system,” J. Lightwave Technol. 20, 1826–1838(2002). [CrossRef]

], and also for Tm3+/Yb3+ codoped amplifiers (TYDFA) in silica fiber [1

1. Jun Chang, Qingpu Wang, and Gangding Peng, “Optical amplification in Yb3+-codoped thulium doped silica fiber,” Opt. Mat. 28, 1088–1094(2006). [CrossRef]

] and fluoride fiber [2

2. Jun Chang, Qingpu Wang, Xingyu Zhang, Zejin Liu, Zhaojun Liu, and Gangding Peng, “S-band optical amplification by an internally generated pump in thulium ytterbium codoped fiber, ” Opt. Express 13, 3902–3912(2005). [CrossRef] [PubMed]

].

Tellurite glass fibers exhibit significant advantages over the fluoride and silicate glass fibers for amplification outside the C-band. The tellurite glass has comparatively lower phonon energy (780 cm-1) than silicate glass, and it exhibits better environmental resistance than fluoride fibers, in addition, tellurite glass provides a much broader fluorescence spectra and larger rare earth oxide solubility than silicate and fluoride glasses [3

3. Shaoxiong Shen, Animesh Jha, Lihui Huang, and Purushottam Joshi, “980-nm diode-pumped Tm3+/Yb3+-codoped tellurite fiber for S-band amplification,” Opt. Lett. 30,1437(2005). [CrossRef] [PubMed]

,9

9. S. Tanabe, “Properties of Tm3+-doped tellurite glasses for 1.4-um amplifier,” Proc. SPIE 4282, 85(2001). [CrossRef]

]. Recently, Tm3+-doped tellurite fiber for S-band amplification were reported under dual-wavelength pumping (795/1064 nm and 1047/1550 nm) schemes [10

10. L. N. Ng, E. R. Taylor, and J. Nilsson, “795 nm and 1064 nm dual pump thulium-doped tellurite fibre for S-band amplification,” Electron. Lett. 38, 1246 (2002). [CrossRef]

, 11

11. E. R. Taylor, L. N. Ng, J. Nilsson, R. Caponi, A. Pagano, M. Potenza, and B. Sordo, “Thulium-Doped Tellurite Fiber Amplifier,” IEEE Photonics Technol. Lett. 16, 777(2004). [CrossRef]

], demonstrating a 35-dB internal gain and broader band amplification than in fluoride glass fiber, however, these pump scheme is complicated and the pump wavelength is difficult to get by laser diode (LD). Tm3+/Yb3+ codoped tellurite fiber was studied to take advantage of low cost 980nm LD and 6 dB gain at 1490nm was achieved in Tm3+/Yb3+ codoped tellurite fiber by single120mW 980nm pump [3

3. Shaoxiong Shen, Animesh Jha, Lihui Huang, and Purushottam Joshi, “980-nm diode-pumped Tm3+/Yb3+-codoped tellurite fiber for S-band amplification,” Opt. Lett. 30,1437(2005). [CrossRef] [PubMed]

]. Here, we proposed a scheme of Tm3+/Yb3+ codoped fiber amplifier in tellurite host with an internal laser cavity operating at 1050nm. This scheme has the advantage of producing an internally generated pump wavelength for improved pump efficiency in Tm3+ fiber amplifier. The results show that S-band gain can be improved by constructing 1050nm laser cavity inside the amplifier.

2. Theoretical model

The diagram of Tm3+ and Yb3+ energy levels, the relevant absorption and emission transitions, spontaneous emission, energy transfer process between Tm3+ and Yb3+ are shown in Fig. 1, the detailed construction of the internal laser cavity can be found in Ref. [2

2. Jun Chang, Qingpu Wang, Xingyu Zhang, Zejin Liu, Zhaojun Liu, and Gangding Peng, “S-band optical amplification by an internally generated pump in thulium ytterbium codoped fiber, ” Opt. Express 13, 3902–3912(2005). [CrossRef] [PubMed]

]. The rate equations and propagation equations for Tm3+ and Yb3+ can be established as follows:

dNT1dt=NT2AT21nr+NT3(WT31+AT31r)KYT2NT1NY1NT1(WT13+WT14+AT10r)
(1)
dNT2dt=NT0WT02NT2AT21nr+NT5AT52r+KYT1NT0NY1
(2)
dNT3dt=NT1WT13+NT4AT43nrNT3(WT31+WT35+AT30r)
(3)
dNT4dt=NT1WT14NT4AT43nr+KYT2NT1NY1
(4)
dNT5dt=NT3WT35NT5(AT50r+AT52r)
(5)
NT=NT0+NT1+NT2+NT3+NT4+NT5
(6)
dNY1dt=NY0WY01NY1WY10KYT1NT0NY1KYT2NT1NY1NY1Y1
(7)
NY=NY0+NY1
(8)
Fig. 1. Energy level of Tm 3+, Yb 3+ and pump scheme

Aijr and Ainr are radiative and nonradiative decays respectively, K YT1 and K YT2 are the energy transfer parameter between 3 H 6 (Tm 3+)+2 F 5/2(Yb 3+)→3 H 5 (Tm 3+)+2 F 7/2(Yb 3+) and 3 F 4 (Tm 3+)+2 F 5/2 (Yb 3+)→3 F 2,3 F 3 (Tm 3+)+2 F 7/2 (Yb 3+), N T0 , N T1 , N T2 , N T3 , N T4 , N T5 , N Y0 , N Y1 are population densities of relevant energy levels of Tm3+ and Yb3+, W ij denotes the interaction of the electromagnetic field and the ions and it can be written as [6

6. P. Peterka, B. Faure, W. Blanc, M. Karasek, and B. Dussardier, “Theoretical modelling of S-band thulium-doped silica fiber amplifiers,” Optical and Quantum Electron. 36, 201–212(2004). [CrossRef]

]:

Wij(z)=0λΓ(λ)σij(Pλ+(z,λ)+Pλ(z,λ))hcπb2dλ
(8)

Here Pλ± are the spectral power densities of the radiation propagating in the forward (+) and backward (-) directions along the fiber, σ ij is the transition cross-section between the energy levels i and j, and Γ is the so-called overlap factor defined by [6

6. P. Peterka, B. Faure, W. Blanc, M. Karasek, and B. Dussardier, “Theoretical modelling of S-band thulium-doped silica fiber amplifiers,” Optical and Quantum Electron. 36, 201–212(2004). [CrossRef]

]:

Γ(λ)=0E(r,φ,λ)2N(r)rdrN0E(r,φ,λ)2rdr
(9)

It is worth noting that N(r) denotes N Tm (r) or N Yb (r), the concentration distribution of Tm3+ or Yb3+, depending on whether Tm3+ or Yb3+ ions is involved in the process of W ij . Similarly N denotes N T or N Y , the concentration of Tm3+ or Yb3+ that N T =∫0N Tm (r)rdr and N y =0 N yb (r)rdr. Powers along the fiber can be expressed by propagation equations:

dP±(λ)dz=Γ(λ)P±(λ)ij(Niσij(λ)Njσji(λ))πΓ(λ)ij2hνijΔνNiσij(λ)
(10)

The spectroscopic parameters used in our analysis are carefully chosen from the literature and are summarized in Table 1, the spectral emission cross-sections at S-band of Tm3+-doped tellurite glasses are derived from Ref. [12

12. Mira Naftaly, Shaoxiong Shen, and Animesh Jha, “Tm3+-doped tellurite glass for a broadband amplifier at 1.47µm,” Applied Optics 39, 4979(2000). [CrossRef]

], the spectral absorption cross-section at S-band can be calculated by McCumber relation [13

13. D. E. McCumber, “Theory of phonon-terminated optical masers,” Phys. Rev. 134: A299–A306 (1964). [CrossRef]

]:

σ21(ν)=σ12(ν)exp(εhνkT)
(11)

Because there is no available cross-section data of Tm3+ at 1050nm in tellurite glasses, so we calculated it from the data of fluoride host by σ∝(n 2+2)2/9n [14

14. A. Mori, Y. Ohishi, and S. Sudo, “Erbium-doped tellurite glass fibre laser and amplifier,” Electron. Lett. 33, 863(1997). [CrossRef]

]. The 1050nm cross-section data of Tm3+ in fluoride are obtained from Ref.7. The nonradiative transition rates (AT43nr and AT21nr) were calculated using the empirical energy-gap law [15

15. William J. Minisccalco, “Optical and Electronic Properties of Rare Earth Ions in Glasses,” in Rare-earth-doped fiber lasers and amplifiers, Michel J.F. Digonnet, ed. (Marcel Dekker, New York, 2001)

].

Table 1. Parameters used in the numerical simulations

table-icon
View This Table

The cross-section data of Yb3+ at 980nm and 1050nm in tellurite glasses are obtained from Ref. 16. Since there is no data available for the energy transfer parameters K YT1 and K YT2 in ytterbium-thulium codoped tellurite materials, we have made use of the experimental data of the energy transfer parameters from ytterbium and thulium codoped single crystal materials in Ref. [4

4. A. Braud, S. Girard, J. L. Doualan, M. Thuau, and R. Moncorge, “Energy-transfer processes in Yb:Tm-doped KY3F10, LiYF4, and BaY2F8 single crystals for laser operation at 1.5 and 2.3 µm,” Phys. Rev. B 61, 5280 (2000). [CrossRef]

]. In Ref. [1

1. Jun Chang, Qingpu Wang, and Gangding Peng, “Optical amplification in Yb3+-codoped thulium doped silica fiber,” Opt. Mat. 28, 1088–1094(2006). [CrossRef]

], K YT1 and K YT2 were collected from Ref. [4

4. A. Braud, S. Girard, J. L. Doualan, M. Thuau, and R. Moncorge, “Energy-transfer processes in Yb:Tm-doped KY3F10, LiYF4, and BaY2F8 single crystals for laser operation at 1.5 and 2.3 µm,” Phys. Rev. B 61, 5280 (2000). [CrossRef]

] and delineated in terms of the product of the total Tm3+ and Yb3+ concentrations, NTm and NYb, here we estimate the values of K YT1 and K YT2 based on the extrapolation curves in Fig. 2 of Ref. [1

1. Jun Chang, Qingpu Wang, and Gangding Peng, “Optical amplification in Yb3+-codoped thulium doped silica fiber,” Opt. Mat. 28, 1088–1094(2006). [CrossRef]

].

3. Results and discussion

The model is numerically resolved using a point by point and iterative method. Here we first investigate the gain characteristics of the codoped tellurite fiber which has the concentration of Tm3+ 5000ppm and Yb3+ 10000ppm. The fiber has the core diameter of 3 µm and is pumped by a 980nm LD. In Fig. 2, 4 lines represent the spectral gain from 1450nm to 1520nm of 4 different cases.

The 2 lines, with square and triangle respectively, represent the spectral gain of the amplifiers under the same pump conditions and with the same fiber length. Both the amplifiers have a fiber length of 24cm and are pumped by a 980nm laser at 120mW; the only difference between them is that the line with triangle has an internal 1050nm laser cavity, while the other line with square hasn’t. It is clear that about 2dB gain improvement is obtained by the internal 1050nm laser cavity. The gain of the amplifier without the internal 1050nm laser cavity is shifted to longer wavelength. The reason is that, without the internal laser cavity, the 1050nm emission generated by the Amplified Spontaneous Emission (ASE) in the codoped fiber is not strong enough to achieve high population inversion. The low inversion leads to the gain shift to longer wavelengths [17

17. Tadashi Kasamatsu, Yutaka Yano, and Hitoshi Sekita, “1.50-µm-band gain-shifted thulium-doped fiber amplifier with 1.05µ and 1.56µm dual-wavelength pumping,” Opt. Lett. , 24, 1684–1686(1999). [CrossRef]

,18

18. Tadashi Kasamatsu, Yutaka Yano, and Takashi Ono, “Laser-Diode-Pumped Highly Efficient Gain-Shifted Thulium-Doped Fiber Amplifier Operating in the 1480–1510-nm Band,” IEEE Photonics Technol. Lett. 13, 433–435(2001) [CrossRef]

].

Fig.2 . pectral gain of the codoped fiber

The line with diamond represents the spectral gain of the amplifier with a fiber length of 50cm and under the 300mW pump of a 980nm laser. The line with circle represents the spectral gain of the amplifier with the same length and pumping parameters, except it has an internal 1050nm laser cavity. It is shown that a maximum of about 5dB gain improvement can be obtained with the internal 1050nm laser cavity.

4. Conclusion

In summary, a scheme that the S-band Tm3+/Yb3+ codoped tellurite fiber amplifier pumped by single 980nm laser is proposed. By introducing an internal laser cavity at 1050nm into the Tm3+/Yb3+ codoped fiber amplifier, improved gain can be obtained when pumped by a single wavelength at 980nm. Clearly the built-in laser generated in the internal cavity provides effective optical pumping at 1050nm and leads to the improvement in the amplification gain. As an example, we have shown that the gain improvement as high as 5dB can be achieved by the 1050nm internal laser cavity under 300mW 980nm laser pump.

Acknowledgments

The authors acknowledge the financial support from China Scholarship Council, Natural Science Foundation of China, Natural Science Foundation of Shandong Province of China (grant no.Y2003G01 and Y2002G06), and Research Fund for the Doctoral Program of Higher Education of China.

References and links

1.

Jun Chang, Qingpu Wang, and Gangding Peng, “Optical amplification in Yb3+-codoped thulium doped silica fiber,” Opt. Mat. 28, 1088–1094(2006). [CrossRef]

2.

Jun Chang, Qingpu Wang, Xingyu Zhang, Zejin Liu, Zhaojun Liu, and Gangding Peng, “S-band optical amplification by an internally generated pump in thulium ytterbium codoped fiber, ” Opt. Express 13, 3902–3912(2005). [CrossRef] [PubMed]

3.

Shaoxiong Shen, Animesh Jha, Lihui Huang, and Purushottam Joshi, “980-nm diode-pumped Tm3+/Yb3+-codoped tellurite fiber for S-band amplification,” Opt. Lett. 30,1437(2005). [CrossRef] [PubMed]

4.

A. Braud, S. Girard, J. L. Doualan, M. Thuau, and R. Moncorge, “Energy-transfer processes in Yb:Tm-doped KY3F10, LiYF4, and BaY2F8 single crystals for laser operation at 1.5 and 2.3 µm,” Phys. Rev. B 61, 5280 (2000). [CrossRef]

5.

C. Y. Chen, R. R. Petrin, D. C. Yen, and W. A. Sibley, “Concentration-dependent energy-transfer processes in Er3+-and Tm3+-doped heavy-metal fluoride glass,” Opt. Lett.s 14, 432(1989). [CrossRef]

6.

P. Peterka, B. Faure, W. Blanc, M. Karasek, and B. Dussardier, “Theoretical modelling of S-band thulium-doped silica fiber amplifiers,” Optical and Quantum Electron. 36, 201–212(2004). [CrossRef]

7.

Claudio Floridia, M. T. Carvalho, S. R. Lüthi, and A. S. L. Gomes, “Modeling the distributed gain of single-(1050 or 1410 nm) and dual-wavelength (800+1050 nm or 800+1410 nm) pumped thulium-doped fiber amplifiers,” Opt. Lett. 29, 1983–1985(2004). [CrossRef] [PubMed]

8.

Tadashi Kasamatsu, Yutaka Yano, and Takashi Ono, “1.49-µm-Band gain-shifted thulium-doped fiber amplifier for WDM transmission system,” J. Lightwave Technol. 20, 1826–1838(2002). [CrossRef]

9.

S. Tanabe, “Properties of Tm3+-doped tellurite glasses for 1.4-um amplifier,” Proc. SPIE 4282, 85(2001). [CrossRef]

10.

L. N. Ng, E. R. Taylor, and J. Nilsson, “795 nm and 1064 nm dual pump thulium-doped tellurite fibre for S-band amplification,” Electron. Lett. 38, 1246 (2002). [CrossRef]

11.

E. R. Taylor, L. N. Ng, J. Nilsson, R. Caponi, A. Pagano, M. Potenza, and B. Sordo, “Thulium-Doped Tellurite Fiber Amplifier,” IEEE Photonics Technol. Lett. 16, 777(2004). [CrossRef]

12.

Mira Naftaly, Shaoxiong Shen, and Animesh Jha, “Tm3+-doped tellurite glass for a broadband amplifier at 1.47µm,” Applied Optics 39, 4979(2000). [CrossRef]

13.

D. E. McCumber, “Theory of phonon-terminated optical masers,” Phys. Rev. 134: A299–A306 (1964). [CrossRef]

14.

A. Mori, Y. Ohishi, and S. Sudo, “Erbium-doped tellurite glass fibre laser and amplifier,” Electron. Lett. 33, 863(1997). [CrossRef]

15.

William J. Minisccalco, “Optical and Electronic Properties of Rare Earth Ions in Glasses,” in Rare-earth-doped fiber lasers and amplifiers, Michel J.F. Digonnet, ed. (Marcel Dekker, New York, 2001)

16.

Chun Jiang, Fuxi Gan, and Junzhou Zhang, “Yb: tellurite laser glass with high emission cross-section,” Mat. Lett. 41, 209–214 (1999). [CrossRef]

17.

Tadashi Kasamatsu, Yutaka Yano, and Hitoshi Sekita, “1.50-µm-band gain-shifted thulium-doped fiber amplifier with 1.05µ and 1.56µm dual-wavelength pumping,” Opt. Lett. , 24, 1684–1686(1999). [CrossRef]

18.

Tadashi Kasamatsu, Yutaka Yano, and Takashi Ono, “Laser-Diode-Pumped Highly Efficient Gain-Shifted Thulium-Doped Fiber Amplifier Operating in the 1480–1510-nm Band,” IEEE Photonics Technol. Lett. 13, 433–435(2001) [CrossRef]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.2330) Fiber optics and optical communications : Fiber optics communications

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: June 13, 2006
Revised Manuscript: August 9, 2006
Manuscript Accepted: August 19, 2006
Published: September 18, 2006

Citation
Jun Chang, Qingpu Wang, Gangding Peng, Xingyu Zhang, Zejin Liu, Shuanghong Ding, Zhaojun Liu, Sasa Zhang, and Gongtang Wang, "Gain improvement by internal laser cavity in Tm3+Yb3+-co-doped tellurite fiber amplifier pumped by 980-nm laser," Opt. Express 14, 8535-8539 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-19-8535


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References

  1. Jun Chang, Qingpu Wang, Gangding Peng, "Optical amplification in Yb3+-co-doped thulium doped silica fiber," Opt. Mat. 28, 1088-1094 (2006). [CrossRef]
  2. Jun Chang, Qingpu Wang, Xingyu Zhang, Zejin Liu, Zhaojun Liu, Gangding Peng, "S-band optical amplification by an internally generated pump in thulium ytterbium co-doped fiber, " Opt. Express 13, 3902-3912 (2005). [CrossRef] [PubMed]
  3. Shaoxiong Shen, Animesh Jha, Lihui Huang, Purushottam Joshi, "980-nm diode-pumped Tm3+/Yb3+-co-doped tellurite fiber for S-band amplification," Opt. Lett. 30,1437 (2005). [CrossRef] [PubMed]
  4. A. Braud, S. Girard, J. L. Doualan, M. Thuau, R. Moncorge, "Energy-transfer processes in Yb:Tm-doped KY3F10, LiYF4, and BaY2F8 single crystals for laser operation at 1.5 and 2.3 μm," Phys. Rev. B 61, 5280 (2000). [CrossRef]
  5. <jrn> C. Y. Chen, R. R. Petrin, D. C. Yen, W. A. Sibley, "Concentration-dependent energy-transfer processes in Er3+- and Tm3+-doped heavy-metal fluoride glass," Opt. Letts 14, 432 (1989).</jrn> [CrossRef]
  6. P. Peterka, B. Faure, W. Blanc, M. Karasek, B. Dussardier, "Theoretical modeling of S-band thulium-doped silica fiber amplifiers," Optical and Quantum Electron. 36, 201-212 (2004). [CrossRef]
  7. C. Floridia, M. T. Carvalho, S. R. Lüthi, and A. S. L. Gomes, "Modeling the distributed gain of single- (1050 or 1410 nm) and dual-wavelength (800 + 1050 nm or 800 + 1410 nm) pumped thulium-doped fiber amplifiers," Opt. Lett. 29, 1983-1985 (2004). [CrossRef] [PubMed]
  8. Tadashi Kasamatsu, Yutaka Yano, Takashi Ono, "1.49-μm-Band gain-shifted thulium-doped fiber amplifier for WDM transmission system," J. Lightwave Technol. 20, 1826-1838 (2002). [CrossRef]
  9. S. Tanabe, "Properties of Tm3+-doped tellurite glasses for 1.4-um amplifier," Proc. SPIE 4282, 85 (2001). [CrossRef]
  10. L. N. Ng, E. R. Taylor, and J. Nilsson, "795 nm and 1064 nm dual pump thulium-doped tellurite fibre for S-band amplification," Electron. Lett. 38, 1246 (2002). [CrossRef]
  11. E. R. Taylor, L. N. Ng, J. Nilsson, R. Caponi, A. Pagano, M. Potenza, and B. Sordo, "Thulium-Doped Tellurite Fiber Amplifier," IEEE Photonics Technol. Lett. 16, 777 (2004). [CrossRef]
  12. Mira Naftaly, Shaoxiong Shen, Animesh Jha, "Tm3+-doped tellurite glass for a broadband amplifier at 1.47μm," Appl. Opt. 39, 4979 (2000). [CrossRef]
  13. D. E. McCumber, "Theory of phonon-terminated optical masers," Phys. Rev. 134, A299-A306 (1964). [CrossRef]
  14. A. Mori, Y. Ohishi and S. Sudo, "Erbium-doped tellurite glass fibre laser and amplifier," Electron. Lett. 33, 863 (1997). [CrossRef]
  15. W. J. Minisccalco, "Optical and Electronic Properties of Rare Earth Ions in Glasses," in Rare-earth-doped fiber lasers and amplifiers, M. J. F. Digonnet, ed. (Marcel Dekker, New York, 2001)
  16. Chun Jiang, Fuxi Gan, Junzhou Zhang, "Yb: tellurite laser glass with high emission cross-section," Mat. Lett. 41, 209-214 (1999). [CrossRef]
  17. Tadashi Kasamatsu, Yutaka Yano, Hitoshi Sekita, "1.50-μm-band gain-shifted thulium-doped fiber amplifier with 1.05μand 1.56μm dual-wavelength pumping," Opt. Lett.  24, 1684-1686 (1999). [CrossRef]
  18. Tadashi Kasamatsu, Yutaka Yano, and Takashi Ono, "Laser-Diode-Pumped Highly Efficient Gain-Shifted Thulium-Doped Fiber Amplifier Operating in the 1480-1510-nm Band," IEEE Photonics Technol. Lett. 13, 433-435 (2001) [CrossRef]

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