Abstract

We present the experimental investigation of a single-mode double-clad Tm3+-doped silicate fiber with ion concentration of 7 wt.% (8.35 x 1020/cm3). A gain per unit length of 5.8 dB/cm at 1945 nm has been successfully achieved in a 3-cm Tm3+-doped silicate fiber amplifier, pumped with 647.6 mW at 1567 nm. To the best of our knowledge, this would be the highest gain per unit length reported for Tm3+-doped fibers. Furthermore, we experimentally demonstrate efficient cm-long fiber lasers and watt-level cladding pumped Tm3+-doped silicate fiber amplifiers.

© 2015 Optical Society of America

1. Introduction

Fiber laser sources in the 2-μm region have attracted extensive attention owing to their applications in environmental sensing, retina-safe LIDAR, medical surgery, particle accelerators, and pump sources for efficient mid-IR generation. Tm3+ is a favorable ion to produce 2-μm emission in fibers because of its high quantum efficiency, broad gain bandwidth, and strong absorption band around 800 nm, the wavelength available from commercial high-power diode lasers. Through the “two-for-one” cross-relaxation energy transfer, more than 70% slope efficiency has been reported in 790-nm pumped Tm3+-doped fiber lasers [1]. Furthermore, the broad gain bandwidth from 1.8 µm to 2.1 µm allows a large wavelength tuning range and makes Tm3+-doped fiber a suitable gain medium for femtosecond pulse generation. In recent years, the output power from continuous-wave (cw) and pulsed Tm3+-doped fiber lasers and amplifiers has been scaled to the kilowatt and megawatt level, respectively [2,3]. Further power scaling of these fiber laser sources will require higher gains per unit length to avoid detrimental nonlinear effects, while maintaining good spatial mode qualities. This goal can be met by increasing the Tm3+ concentration to reduce the required fiber lengths for sufficient pump absorption. More importantly, the high Tm3+ concentration enables the efficient two-for-one cross-relaxation processes under 790-nm pump. Unfortunately, a high doping level is not easy to achieve in commercial silica fiber hosts because excessive amounts of Tm3+ in silica fibers may cause concentration quenching and photodarkening [4].

Fabricating highly Tm3+-doped fibers has been an active subject in the field of 2-µm fiber lasers. Several glass hosts, such as germanate, tellurite, and silicate, have been intensely studied. In 2007, Wu et al. successfully demonstrated a 106-W germanate fiber laser with 5 wt.% of the Tm2O3 concentration [5]. Although this result makes the Tm3+-doped germanate fiber a promising gain medium for high-power 2-µm laser generation, these fibers tend to have low photodarkening resistance and low compatibility with passive silica fibers, leading to the difficulty of building all-fiber laser systems. An efficient 2-µm tellurite fiber laser has been presented; however, the reported Tm3+ concentration is relatively low and the fiber background loss is still high [6]. A good alternative approach reported here is using multi-component silicate glass as the fiber host. Compared with silica glass, multi-component silicate glass has a less-defined glass network, which provides much higher Tm2O3 solubility. It is believed the multi-component silicate fibers could be doped with more than 10 wt.% of Tm2O3 without concentration quenching. The high ion concentration enables the high gain per unit length, which is beneficial for the mitigation of nonlinear effects, high-repetition-rate pulse operation, and efficient two-for-one cross-relaxation processes in Tm3+-doped fiber laser sources. It should be noted that in comparison with germanate and tellurite glasses, the main glass network of the silicate fiber is SiO2, which has strong mechanical strength and better compatibility with conventional passive silica fibers.

The first cw and Q-switched Tm3+-doped silicate fiber lasers were successfully built by Geng et al. in 2009 [7, 8]. Following this research, all-fiber passively mode-locked lasers based on Tm3+ doped silicate fibers were also demonstrated [9,10]. All of these promising results were achieved in Tm3+-doped silicate fibers with concentration less than 5wt.% (6 x 1020 /cm3). As a step further, we report in this paper our latest progress in the fabrication and material studies of silicate fibers with one of the highest published concentrations of 7wt.% (8.35 x 1020/cm3) for a Tm3+-doped fiber in the world. We also describe the related numerical modeling and optical testing of the gain per unit length, extractable from the highly Tm3+-doped silicate fiber. Finally, the experimental demonstration of short Tm3+-doped silicate fiber lasers and watt-level cladding-pumped Tm3+-doped silicate fiber amplifiers is presented.

2. Tm3+ doped single-mode double-clad silicate fiber

2.1 Material properties

The Tm3+-doped silicate fiber was manufactured using the rod-in-tube technique at AdValue Photonics. This well-developed technology is commonly used for producing soft-glass fibers [11] and silica-based fibers with compound glass core compositions [12]. The main reason is that some of the chemicals required to fabricate silicate fibers cannot be volatilized. Both core and cladding glasses were carefully prepared to ensure that their chemical and thermo-mechanical characteristics are compatible, especially their softening temperature and thermal expansion coefficient. The preforms of the Tm3+-doped used in this paper were made of multi-component silicate glasses, including SiO2, A12O3, BaO, ZnO, and La2O3. Al2O3 was added to ensure high mechanical strength and good chemical durability. Transition metals such as Fe, Cu, and alkali ions were eliminated to further enhance the glass properties. A core glass rod and two cladding tubes were fabricated and assembled to form the fiber preform. Both the inside and outside surfaces of the glass tubes for the inner and outer claddings were polished to a high surface quality. The inside diameter of the inner cladding tube was matched to the diameter of the core rod, and the inside diameter of the outer cladding tube was matched to the outer diameter of the inner cladding tube. The fiber was drawn in a special furnace optimized for non-silica glasses. One important advantage of fabricating double-clad fibers by using the rod-in-tube method is that one can control the refractive indices of the fiber core and inner-cladding glasses precisely and independently.

A photograph of the cleaved fiber end is shown in Fig. 1.The fiber has a double-clad structure with a 152 μm circular outer cladding, a 125 μm circular inner cladding with a NA of 0.617, and a 10 μm circular core with a NA of 0.149 that allows for single mode operation at wavelengths above 1550 nm. A low-index rod was inserted inside the inner cladding to provide cladding mode mixing and improve spatial overlap between the pump modes and doped core. It has been reported that the added low-index rod increases the pump absorption in the doped core by 1-2 dB/cm [9]. It should be noted that the outer cladding of double-clad silicate fibers is also made of silicate glass that provide better thermal properties than polymers in commercial double-clad silica fibers.

 figure: Fig. 1

Fig. 1 Photograph of the cleaved Tm3+-doped silicate fiber.

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The upper state lifetime of 7 wt% Tm3+-doped bulk silicate glass was measured to be 0.635 ms, which is similar to the reported values in Tm3+-doped silica fibers [13]. The measured fluorescence relaxation curve showed a single exponential, thus demonstrating negligible concentration quenching in spite of such a high Tm3+ concentration. The propagation loss was measured using the cut-back method in a 150-cm-long Tm3+ doped silicate fiber doped with a 250-mW 976-nm probe laser. The wavelength of the probe laser was chosen to be outside of the Tm3+ absorption band. The propagation loss and a lunched laser power were inferred from an exponential fit to the measured residual power as a function of the fiber length. The measured propagation loss is 0.7 dB/m at 976 nm, which is slightly higher than that of Tm3+ doped silica fibers.

2.2 Spectroscopic properties

In general, the glass host composition affects the solubility of the rare-earth dopant and may affect absorption and emission cross-sections of the dopant transitions. Figure 2 shows the absorption and emission cross-section spectra of 7 wt.% Tm3+ doped silicate glass. The absorption cross-sections were obtained by measuring the white-light absorption spectrum of the bulk silicate glass sample, which has the same chemical composition and ion concentration as the Tm3+-doped silicate fiber core. The spectral shape and absolute scaling of the emission cross-section were determined by applying the McCumber method to the measured peak absorption cross-section [14]. As shown in Fig. 2, the absorption and emission peaks are located at 1640 nm and 1865 nm, respectively. The maximum absorption cross-section was measured to be 4.16 x 10−25 m2 and the calculated peak emission cross-section was 3.59 x 10−25 m2. The results indicate the spectra of Tm3+ ions in silicate glass are fairly similar to that in silica glass [13], except that Tm3+ doped silicate glass has larger emission cross-sections in the long-wavelength region. Although the McCumber method has been shown to be rather inaccurate in rare-earth doped glass fibers when precise cross-section values are required [15], it provides a convenient estimate for the related theoretical modeling in this work.

 figure: Fig. 2

Fig. 2 The absorption and emission cross-section spectra of the 7 wt.% Tm3+-doped silicate glass.

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3. Single-mode Tm3+-doped fiber amplifier with high gain-per-unit- length

3.1 Numerical modeling

Based on the theory derived by Giles and Desurvire for modeling fiber amplifiers [16], the gain per unit length g at frequency ν and position z can be expressed as [17]:

gv(z)=N0Γv{σevne(z)σav[1ne(z)]}
where N0 is the total rare-earth-ion and Γν is the normalized spatial overlap between the propagating mode and the rare-earth concentration profile. σav and σev are the wavelength dependent absorption and emission cross-sections of Tm3+ ions, respectively. ne is the normalized excited-state population density. Equation (1) indicates that the maximum gain per unit length gv is mainly determined by the emission and absorption cross-sections as well as the population inversion of the active ions. Considering a general case with a spatial overlap Γν of 100% and normalized excited-state population density ne of 80%, the maximum gain per unit length at 1945 nm could be as high as 6.5 dB/cm in a 7wt.% Tm3+-doped silicate fiber. Furthermore, Eq. (1) implies that measuring the signal gain per unit length of Tm3+doped fibers by using fully population inverted amplifiers provides a suitable performance evaluation of Tm3+ ions in silicate fibers.

To correctly evaluate the normalized excited-state population density and gain per unit length expected from silicate 7wt.% Tm3+-doped silicate fiber amplifiers, LIEKKI Application Designer v4.0 was employed for the numerical modeling in this research [18]. This code solves the coupled laser rate equations numerically to predict the output performance of the fiber laser sources. The abovementioned absorption and emission cross-section spectra, propagation loss, and upper state lifetime were employed in the following theoretical simulation. Figure 3 shows the theoretical prediction of normalized excited-state population density ne and population inversion along a 1567-nm core-pumped 7wt.% Tm3+-doped silicate fiber amplifier. The 10-μm fiber core was seeded by a 0.45-mW signal laser at 1945 nm. The power of 0.45 mW was much less than the saturation power, 51.3 mW, and was chosen to probe the small signal gain at 1945 nm. The employed 1567-nm laser had output power of 650-mW, which was much larger than the saturation power of the fiber core (~152mW). Such a highly saturated fiber amplifier generated relatively high population inversion along the gain fiber. As shown in Fig. 3, in the first 3-cm section, the 6.5-cm Tm3+- doped fiber amplifier had approximately uniform distribution of normalized excited-state population density ne and population inversions with average numbers of 80.1% and 60.3%, respectively. The population inversions significantly decreased after 3 cm of pump propagation and led to the decreased signal gain per unit length.

 figure: Fig. 3

Fig. 3 Theoretical predictions for the distribution of normalized excited-state population density ne and population inversion along the 6.5-cm Tm3+-doped silicate fiber amplifier, under the 1567-nm pump power of 650 mW.

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In the next step, we performed the numerical simulations to confirm the high average gain per unit length of highly saturated 7wt.% Tm3+-doped silicate fiber amplifiers. These amplifiers were seeded with 0.45 mW of laser light at 1945 nm and core-pumped at 1567 nm. Figure 4 represents the theoretical prediction of the average gain per unit length as a function of pump power for various fiber lengths. As expected, increasing the pump power results in the enhancement of the average gain per unit length to the level where the fiber absorption is fully saturated. As shown in Fig. 4, the gains per unit length get clamped under pump power of more than 500 mW. Although the highest total gain of 26 dB can be reached in the 6.5-cm amplifier, the corresponding average gain per unit length is relatively low because of the low population inversion in the final section of the gain fiber. Further shortening the fiber length leads to relatively higher and more uniform population inversion along the fiber, and thus the average gain per unit length is significantly increased. The average gain per unit length of 6.45 dB/cm at 1945 nm can be reached in the 1-W 1567 nm core-pumped 2.5-cm 7wt.% Tm3+-doped silicate amplifier.

 figure: Fig. 4

Fig. 4 Theoretical predictions of the gain per unit length of fiber amplifiers versus 1567-nm pump power for various fiber lengths.

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3.2 Experimental investigation

We developed 1567-nm core-pumped Tm3+-doped silicate fiber amplifiers to experimentally investigate the highest gain per unit length extractable from the short Tm3+ doped silicate fibers. The experimental setup is shown in Fig. 5.. The seed was a Tm3+-doped silicate fiber laser, followed by a Tm3+-doped silicate fiber amplifier. The aforementioned 7 wt% Tm3+-doped silicate fibers were employed in both the seed laser and the amplifier. Without the use of wavelength selection devices, the seed laser was naturally operated at 1945 nm. A 1/99 directional coupler and isolator were used to monitor the input signal power and to protect the seed laser, respectively. In addition, a beam splitter was used to filter out the residual pump power.

 figure: Fig. 5

Fig. 5 Experimental setup of the 1945-nm Tm3+-doped silicate fiber amplifier.

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Figures 6 shows the measured gain per unit length as a function of launched 1567-nm pump power in core-pumped Tm3+-doped silicate fiber amplifiers with various fiber lengths. The 3-, 4.5-, and 6.5-cm Tm3+-doped silicate fiber amplifiers were seeded with a signal power of 0.46, 0.43, and 0.47 mW, respectively. The highest average gain per unit length of 5.81 dB/cm was achieved in the 3-cm fiber amplifier. This value is close to the expected value of 5.8 dB/cm, shown in Fig. 4. The experimental results successfully verify the good optical property of the heavily Tm3+-doped silicate fiber. To the best of our knowledge, this is the highest gain per unit length reported in the literature for a Tm3+-doped fiber. The output spectrum of the fiber amplifier with its peak at 1944.7 nm is shown in the inset of Fig. 6.

 figure: Fig. 6

Fig. 6 The average gain per unit length versus launched pump power in core-pumped Tm3+-doped silicate fiber amplifiers of 3, 4.5, and 6.5 cm in length. The inset shows the amplifier output spectrum.

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4. Short Tm3+-doped silicate fiber lasers

With such a high gain per unit length, it is expected that short Tm3+-doped silicate fiber lasers can be easily achieved using relatively short gain fibers and low-Q cavities. To this end, we experimentally demonstrated the Tm3+-doped silicate fiber lasers of 8.5, 6.5, 4.5 and 3 cm in length. As shown in Fig. 7, the cavity feedback of the lasers was provided by a bulk silver mirror butt-coupled to one cleaved fiber end, which served as the high reflector (HR), and the Fresnel reflection from the other cleaved end, which acted as a 96% output coupler. The system was pumped at 1567 nm through a wavelength-division multiplexing (WDM) coupler. The broadband reflection spectrum of the HR allowed the unabsorbed pump to be reflected back into the fiber.

 figure: Fig. 7

Fig. 7 Experimental setup of Tm3+-doped silicate fiber lasers.

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Figure 8 illustrates the laser output power measured as a function of launched pump power. All of the laser thresholds were below 500 mW. With enough pump absorption, the measured laser slope efficiencies of the 8.5- and 6.5-cm lasers are 58.1% and 58.9%, respectively. Although further shortening the fiber length to 4.5 and 3 cm results in relatively lower laser slope efficiency, the successful lasing with such short gain fibers and low-Q cavities confirms the high gain per unit length of the 7 wt.% Tm3+-doped silicate fiber. The output spectra under pump power of 600 mW are shown in the inset of Fig. 8(a) and (b). The spectra were measured using an OSA with a 0.5-nm resolution. The FWHM linewidth of both lasers was narrower than 1 nm. The results indicate shorter fiber length lasers at shorter wavelengths. The result was obtained without active fiber cooling; the fiber was simply resting on the optical bench. Therefore, the center wavelength of the laser drifted slightly. The output beam was in the fundamental fiber mode (LP01) and was of excellent quality, as expected for a single-mode core.

 figure: Fig. 8

Fig. 8 Laser output versus launched pump power in core-pumped Tm3+-doped silicate fiber lasers of (a) 8.5 and 6.5 cm (b) 4.5 and 3 cm in length. The insets are the measured laser output spectra.

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5. Watt-level cladding pumped Tm3+-doped silicate fiber amplifier

To provide an experimental validation of the heavily Tm3+ doped silicate fiber under high-power operation, we developed a 793-nm cladding-pumped Tm3+-doped silicate fiber MOPA. The experimental setup is shown in Fig. 9. It was a ring-cavity 1985-nm Tm3+-doped silicate fiber laser, followed by a Tm3+-doped silicate fiber amplifier. The aforementioned 7 wt.% Tm3+-doped fibers were employed in both the fiber oscillator and amplifier. Without the use of wavelength selecting devices, the laser was naturally operated at 1985 nm with the maximum output power of 26.5 mW. The 1985-nm seed laser was then amplified by another 50-cm 7 wt.% Tm3+-doped silicate fiber.

 figure: Fig. 9

Fig. 9 Experimental setup of Tm3+-doped silicate fiber amplifier.

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Figure 10 shows the measured signal output power as a function of launched 793-nm pump power. A maximum output power of 1.48 W was reached with the corresponding 1985-nm signal gain of 17.5 dB. The amplifier efficiency is 63.2% under the high-power operation. With no sign of the output power roll-over or instabilities, the maximum signal gain is limited by the absorbed pump power. The output spectrum of the fiber amplifier measured at 1.4 W is shown in the inset of Fig. 10. It indicates that the ASE power level is more than 25 dB below the 1985.6-nm signal level.

 figure: Fig. 10

Fig. 10 Measured 1985-nm signal output power generated by the 50-cm-long Tm3+ doped silicate fiber amplifier as a function of launched pump power.

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5. Conclusions

In conclusion, we investigated the essential material properties and gain per unit length of the 7 wt.% Tm2O3 doped silicate fiber as well as its potential for application in short fiber lasers and fiber amplifiers. To the best of our knowledge, 7 wt.% is the record high Tm3+ ion concentration in fibers. The material studies include the measurement of absorption cross-sections, upper-state lifetime, and fiber background loss. These results allow us to precisely evaluate the potential gain per unit length of the 7 wt.% Tm3+-doped silicate fiber. Our simulation results indicate that a signal gain-per-unit-length of 6.45 dB/cm can be reached in a core-pumped 1945-nm 2.5-cm 7 wt.% Tm3+-doped silicate fiber amplifier with 1567-nm pump power of 1 W. As a step in this direction, we present the experimental evidence that a small signal gain of 5.81 dB/cm can be achieved by employing 3 cm of this high concentration silicate fiber into a 1567-nm core-pumped amplifier. In addition, experimental demonstrations of efficient Tm3+-doped silicate fiber lasers with short gain fibers and a low-Q cavity as well as a watt-level cladding-pumped 1985-nm fiber amplifier with a slope efficiency of 63.2% are reported. All of the results indicate that this heavily Tm3+-doped silicate fiber could have a significant advantage for generating high-repetition-rate 2-μm mode-locked fiber lasers and amplifying ultra-short 2-μm laser pulses because of the use of short gain fibers.

Acknowledgments

This research is based upon work supported by the Ministry of Science and Technology (MOST) of Taiwan under the award number NSC-101-2218-E-027-003-MY3.

References and links

1. W. A. Clarkson, L. Pearson, Z. Zhang, J. W. Kim, D. Shen, A. J. Boyland, J. K. Sahu, and M. Ibsen, “High power thulium-doped fiber lasers,”in The Optical Fiber Communication Conference and Exposition (OFC 2009) Technical Digest, Los Angeles (US) (Optical Society of America, March, 2009), paper OWT1.

2. M. N. Zervas and C. A. Codemard, “High power fiber lasers: a review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0904123 (2014). [CrossRef]  

3. C. Gaida, F. Stutzki, M. Gebhardt, F. Jansen, C. Jauregui, J. Limpert, and A. Tünnermann, “200 MW peak power from a Tm-doped fiber CPA system,” in Advanced Solid State Lasers (ASSL 2014) Technical Digest, Shanghai (China) (Optical Society of America, 2014), paper ATu5A.2. [CrossRef]  

4. M. M. Broer, D. M. Krol, and D. J. Digiovanni, “Highly nonlinear near-resonant photodarkening in a thulium-doped aluminosilicate glass fiber,” Opt. Lett. 18(10), 799–801 (1993). [CrossRef]   [PubMed]  

5. 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]  

6. B. Richards, Y. Tsang, D. Binks, J. Lousteau, and A. Jha, “Efficient ~2 μm Tm3+-doped tellurite fiber laser,” Opt. Lett. 33(4), 402–404 (2008). [CrossRef]   [PubMed]  

7. J. Geng, Q. Wang, T. Luo, S. Jiang, and F. Amzajerdian, “Single-frequency narrow-linewidth Tm-doped fiber laser using silicate glass fiber,” Opt. Lett. 34(22), 3493–3495 (2009). [CrossRef]   [PubMed]  

8. J. Geng, Q. Wang, J. Smith, T. Luo, F. Amzajerdian, and S. Jiang, “All-fiber Q-switched single-frequency Tm-doped laser near 2 µm,” Opt. Lett. 34(23), 3713–3715 (2009). [CrossRef]   [PubMed]  

9. Q. Wang, J. Geng, T. Luo, and S. Jiang, “Mode-locked 2 µm laser with highly thulium-doped silicate fiber,” Opt. Lett. 34(23), 3616–3618 (2009). [CrossRef]   [PubMed]  

10. J. Geng, Q. Wang, Y. W. Lee, and S. Jiang, “Development of eye-safe fiber lasers near 2 μm,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0904011 (2014).

11. Y. W. Lee, M. J. F. Digonnet, S. Sinha, K. E. Urbanek, R. L. Byer, and S. Jiang, “High-power Yb3+-doped phosphate fiber amplifier,” IEEE J. Sel. Top. Quantum Electron. 15(1), 93–102 (2009). [CrossRef]  

12. E. Snitzer and R. Tumminelli, “SiO2-clad fibers with selectively volatilized soft-glass cores,” Opt. Lett. 14(14), 757–759 (1989). [CrossRef]   [PubMed]  

13. S. D. Agger and J. H. Povlsen, “Emission and absorption cross section of thulium doped silica fibers,” Opt. Express 14(1), 50–57 (2006). [CrossRef]   [PubMed]  

14. D. E. McCumber, “Theory of phonon terminated optical masers,” Phys. Rev. Lett. 134(2A), A299–A306 (1964).

15. M. J. F. Digonnet, E. Murphy-Chutorian, and D. G. Falquier, “Fundamental limitations of the McCumber relation applied to Er-doped silica and other amorphous-host lasers,” IEEE J. Quantum Electron. 38(12), 1629–1637 (2002). [CrossRef]  

16. C. R. Giles and E. Desurvire, “Modeling Erbium-doped fiber amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991). [CrossRef]  

17. J. L. Wagener, D. G. Falquier, M. J. F. Digonnet, and H. J. Shaw, “A Mueller matrix formalism for modeling polarization effects in Erbium-doped fiber,” J. Lightwave Technol. 16(2), 200–206 (1998). [CrossRef]  

18. LIEKKI™ Application Designer, v4.0, Available online: http://www.nlight.net/download/lad

References

  • View by:

  1. W. A. Clarkson, L. Pearson, Z. Zhang, J. W. Kim, D. Shen, A. J. Boyland, J. K. Sahu, and M. Ibsen, “High power thulium-doped fiber lasers,”in The Optical Fiber Communication Conference and Exposition (OFC 2009) Technical Digest, Los Angeles (US) (Optical Society of America, March, 2009), paper OWT1.
  2. M. N. Zervas and C. A. Codemard, “High power fiber lasers: a review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0904123 (2014).
    [Crossref]
  3. C. Gaida, F. Stutzki, M. Gebhardt, F. Jansen, C. Jauregui, J. Limpert, and A. Tünnermann, “200 MW peak power from a Tm-doped fiber CPA system,” in Advanced Solid State Lasers (ASSL 2014) Technical Digest, Shanghai (China) (Optical Society of America, 2014), paper ATu5A.2.
    [Crossref]
  4. M. M. Broer, D. M. Krol, and D. J. Digiovanni, “Highly nonlinear near-resonant photodarkening in a thulium-doped aluminosilicate glass fiber,” Opt. Lett. 18(10), 799–801 (1993).
    [Crossref] [PubMed]
  5. 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]
  6. B. Richards, Y. Tsang, D. Binks, J. Lousteau, and A. Jha, “Efficient ~2 μm Tm3+-doped tellurite fiber laser,” Opt. Lett. 33(4), 402–404 (2008).
    [Crossref] [PubMed]
  7. J. Geng, Q. Wang, T. Luo, S. Jiang, and F. Amzajerdian, “Single-frequency narrow-linewidth Tm-doped fiber laser using silicate glass fiber,” Opt. Lett. 34(22), 3493–3495 (2009).
    [Crossref] [PubMed]
  8. J. Geng, Q. Wang, J. Smith, T. Luo, F. Amzajerdian, and S. Jiang, “All-fiber Q-switched single-frequency Tm-doped laser near 2 µm,” Opt. Lett. 34(23), 3713–3715 (2009).
    [Crossref] [PubMed]
  9. Q. Wang, J. Geng, T. Luo, and S. Jiang, “Mode-locked 2 µm laser with highly thulium-doped silicate fiber,” Opt. Lett. 34(23), 3616–3618 (2009).
    [Crossref] [PubMed]
  10. J. Geng, Q. Wang, Y. W. Lee, and S. Jiang, “Development of eye-safe fiber lasers near 2 μm,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0904011 (2014).
  11. Y. W. Lee, M. J. F. Digonnet, S. Sinha, K. E. Urbanek, R. L. Byer, and S. Jiang, “High-power Yb3+-doped phosphate fiber amplifier,” IEEE J. Sel. Top. Quantum Electron. 15(1), 93–102 (2009).
    [Crossref]
  12. E. Snitzer and R. Tumminelli, “SiO2-clad fibers with selectively volatilized soft-glass cores,” Opt. Lett. 14(14), 757–759 (1989).
    [Crossref] [PubMed]
  13. S. D. Agger and J. H. Povlsen, “Emission and absorption cross section of thulium doped silica fibers,” Opt. Express 14(1), 50–57 (2006).
    [Crossref] [PubMed]
  14. D. E. McCumber, “Theory of phonon terminated optical masers,” Phys. Rev. Lett. 134(2A), A299–A306 (1964).
  15. M. J. F. Digonnet, E. Murphy-Chutorian, and D. G. Falquier, “Fundamental limitations of the McCumber relation applied to Er-doped silica and other amorphous-host lasers,” IEEE J. Quantum Electron. 38(12), 1629–1637 (2002).
    [Crossref]
  16. C. R. Giles and E. Desurvire, “Modeling Erbium-doped fiber amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
    [Crossref]
  17. J. L. Wagener, D. G. Falquier, M. J. F. Digonnet, and H. J. Shaw, “A Mueller matrix formalism for modeling polarization effects in Erbium-doped fiber,” J. Lightwave Technol. 16(2), 200–206 (1998).
    [Crossref]
  18. LIEKKI™ Application Designer, v4.0, Available online: http://www.nlight.net/download/lad

2014 (2)

M. N. Zervas and C. A. Codemard, “High power fiber lasers: a review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0904123 (2014).
[Crossref]

J. Geng, Q. Wang, Y. W. Lee, and S. Jiang, “Development of eye-safe fiber lasers near 2 μm,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0904011 (2014).

2009 (4)

2008 (1)

2007 (1)

2006 (1)

2002 (1)

M. J. F. Digonnet, E. Murphy-Chutorian, and D. G. Falquier, “Fundamental limitations of the McCumber relation applied to Er-doped silica and other amorphous-host lasers,” IEEE J. Quantum Electron. 38(12), 1629–1637 (2002).
[Crossref]

1998 (1)

1993 (1)

1991 (1)

C. R. Giles and E. Desurvire, “Modeling Erbium-doped fiber amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
[Crossref]

1989 (1)

1964 (1)

D. E. McCumber, “Theory of phonon terminated optical masers,” Phys. Rev. Lett. 134(2A), A299–A306 (1964).

Agger, S. D.

Amzajerdian, F.

Binks, D.

Broer, M. M.

Byer, R. L.

Y. W. Lee, M. J. F. Digonnet, S. Sinha, K. E. Urbanek, R. L. Byer, and S. Jiang, “High-power Yb3+-doped phosphate fiber amplifier,” IEEE J. Sel. Top. Quantum Electron. 15(1), 93–102 (2009).
[Crossref]

Codemard, C. A.

M. N. Zervas and C. A. Codemard, “High power fiber lasers: a review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0904123 (2014).
[Crossref]

Desurvire, E.

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Digonnet, M. J. F.

Y. W. Lee, M. J. F. Digonnet, S. Sinha, K. E. Urbanek, R. L. Byer, and S. Jiang, “High-power Yb3+-doped phosphate fiber amplifier,” IEEE J. Sel. Top. Quantum Electron. 15(1), 93–102 (2009).
[Crossref]

M. J. F. Digonnet, E. Murphy-Chutorian, and D. G. Falquier, “Fundamental limitations of the McCumber relation applied to Er-doped silica and other amorphous-host lasers,” IEEE J. Quantum Electron. 38(12), 1629–1637 (2002).
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J. L. Wagener, D. G. Falquier, M. J. F. Digonnet, and H. J. Shaw, “A Mueller matrix formalism for modeling polarization effects in Erbium-doped fiber,” J. Lightwave Technol. 16(2), 200–206 (1998).
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Falquier, D. G.

M. J. F. Digonnet, E. Murphy-Chutorian, and D. G. Falquier, “Fundamental limitations of the McCumber relation applied to Er-doped silica and other amorphous-host lasers,” IEEE J. Quantum Electron. 38(12), 1629–1637 (2002).
[Crossref]

J. L. Wagener, D. G. Falquier, M. J. F. Digonnet, and H. J. Shaw, “A Mueller matrix formalism for modeling polarization effects in Erbium-doped fiber,” J. Lightwave Technol. 16(2), 200–206 (1998).
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Geng, J.

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C. R. Giles and E. Desurvire, “Modeling Erbium-doped fiber amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991).
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Jha, A.

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M. J. F. Digonnet, E. Murphy-Chutorian, and D. G. Falquier, “Fundamental limitations of the McCumber relation applied to Er-doped silica and other amorphous-host lasers,” IEEE J. Quantum Electron. 38(12), 1629–1637 (2002).
[Crossref]

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Richards, B.

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Y. W. Lee, M. J. F. Digonnet, S. Sinha, K. E. Urbanek, R. L. Byer, and S. Jiang, “High-power Yb3+-doped phosphate fiber amplifier,” IEEE J. Sel. Top. Quantum Electron. 15(1), 93–102 (2009).
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Y. W. Lee, M. J. F. Digonnet, S. Sinha, K. E. Urbanek, R. L. Byer, and S. Jiang, “High-power Yb3+-doped phosphate fiber amplifier,” IEEE J. Sel. Top. Quantum Electron. 15(1), 93–102 (2009).
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Wang, Q.

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IEEE J. Quantum Electron. (1)

M. J. F. Digonnet, E. Murphy-Chutorian, and D. G. Falquier, “Fundamental limitations of the McCumber relation applied to Er-doped silica and other amorphous-host lasers,” IEEE J. Quantum Electron. 38(12), 1629–1637 (2002).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (3)

M. N. Zervas and C. A. Codemard, “High power fiber lasers: a review,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0904123 (2014).
[Crossref]

J. Geng, Q. Wang, Y. W. Lee, and S. Jiang, “Development of eye-safe fiber lasers near 2 μm,” IEEE J. Sel. Top. Quantum Electron. 20(5), 0904011 (2014).

Y. W. Lee, M. J. F. Digonnet, S. Sinha, K. E. Urbanek, R. L. Byer, and S. Jiang, “High-power Yb3+-doped phosphate fiber amplifier,” IEEE J. Sel. Top. Quantum Electron. 15(1), 93–102 (2009).
[Crossref]

J. Lightwave Technol. (2)

Opt. Express (1)

Opt. Lett. (7)

Phys. Rev. Lett. (1)

D. E. McCumber, “Theory of phonon terminated optical masers,” Phys. Rev. Lett. 134(2A), A299–A306 (1964).

Other (3)

W. A. Clarkson, L. Pearson, Z. Zhang, J. W. Kim, D. Shen, A. J. Boyland, J. K. Sahu, and M. Ibsen, “High power thulium-doped fiber lasers,”in The Optical Fiber Communication Conference and Exposition (OFC 2009) Technical Digest, Los Angeles (US) (Optical Society of America, March, 2009), paper OWT1.

LIEKKI™ Application Designer, v4.0, Available online: http://www.nlight.net/download/lad

C. Gaida, F. Stutzki, M. Gebhardt, F. Jansen, C. Jauregui, J. Limpert, and A. Tünnermann, “200 MW peak power from a Tm-doped fiber CPA system,” in Advanced Solid State Lasers (ASSL 2014) Technical Digest, Shanghai (China) (Optical Society of America, 2014), paper ATu5A.2.
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 Photograph of the cleaved Tm3+-doped silicate fiber.
Fig. 2
Fig. 2 The absorption and emission cross-section spectra of the 7 wt.% Tm3+-doped silicate glass.
Fig. 3
Fig. 3 Theoretical predictions for the distribution of normalized excited-state population density ne and population inversion along the 6.5-cm Tm3+-doped silicate fiber amplifier, under the 1567-nm pump power of 650 mW.
Fig. 4
Fig. 4 Theoretical predictions of the gain per unit length of fiber amplifiers versus 1567-nm pump power for various fiber lengths.
Fig. 5
Fig. 5 Experimental setup of the 1945-nm Tm3+-doped silicate fiber amplifier.
Fig. 6
Fig. 6 The average gain per unit length versus launched pump power in core-pumped Tm3+-doped silicate fiber amplifiers of 3, 4.5, and 6.5 cm in length. The inset shows the amplifier output spectrum.
Fig. 7
Fig. 7 Experimental setup of Tm3+-doped silicate fiber lasers.
Fig. 8
Fig. 8 Laser output versus launched pump power in core-pumped Tm3+-doped silicate fiber lasers of (a) 8.5 and 6.5 cm (b) 4.5 and 3 cm in length. The insets are the measured laser output spectra.
Fig. 9
Fig. 9 Experimental setup of Tm3+-doped silicate fiber amplifier.
Fig. 10
Fig. 10 Measured 1985-nm signal output power generated by the 50-cm-long Tm3+ doped silicate fiber amplifier as a function of launched pump power.

Equations (1)

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g v ( z )= N 0 Γ v { σ ev n e ( z ) σ av [ 1 n e (z) ] }

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