We propose a novel scheme in which Yb3+ codoping and a laser cavity are introduced in Tm3+ doped fiber to achieve efficient S-band optical amplification with a 980 nm pump source. This scheme makes it possible for conventional 980 nm pump sources for Er3+ doped fiber amplifiers to be used for S-band Tm3+ doped fiber amplifiers (TDFAs). By introducing a laser cavity into an amplifier, an internally generated pump from Yb3+ at a desirable wavelength for pumping Tm3+ could be produced. We establish and analyze, for the first time to our knowledge, a new theoretical model that takes into consideration both the internal lasing operation inside the optical amplification process and the energy transfer between the Tm3+ and the Yb3+ ions in TDFAs. Various situations such as Tm3+ doping concentration and cavity reflectivity have been investigated. The results show that high optical gain and high pump efficiency can be achieved by use of 980 nm sources. With a laser cavity of 1050 nm in Tm3+ and Yb3+ codoped fiber, for example, it is possible to achieve high optical gain of greater than 20 dB, a noise figure of approximately 5 dB in the wavelength range from 1450 to 1480 nm with a 0.3 W power at 980 nm pump source.
©2005 Optical Society of America
The improvement of optical fiber fabrication technology creates an opportunity for optical communication in the S-band . The emission associated with the Tm3+ transition from 3 H 4 to 3 F 4 covers the spectral range from 1440 to 1520 nm . Hence Tm3+ doped fiber amplifiers (TDFAs) could be desirable for S-band (1460–1520 nm) optical amplification and has attracted considerable attention as a means of extending the transmission bandwidth of optical fibers beyond the range available from Er3+ doped fiber amplifiers (EDFAs) . A variety of pumping schemes and methods have been proposed for TDFAs, including single-wavelength pumping at 1047 , 1050 , or 1064 nm [6,7], and dual-wavelength pumping at 800 + 1050 nm  and 800+1410 nm . These pump sources are usually either solid-state lasers or semiconductor laser diodes that operate at some uncommon wavelengths. This could make it more difficult to acquire low-cost and high pump power sources for TDFAs than EDFAs that use readily available 980 nm pump laser diodes.
Yb3+ has been frequently used as a codopant in erbium-doped fibers because it has only two multiplets: the ground-state level of 2 F 7/2 and the excited-state level of 2 F 5/2, which are separated by ΔE~10,000 cm-1, corresponding to the highly efficient absorption in the 900–1000 nm range [8,9]. This particular energy level structure is highly desirable for efficient absorption of commercially available laser diodes that emit around 980 nm and, at the same time, avoid any undesirable excited-state absorption under intense optical pumping. Yb3+ doped fiber has been used to produce highly efficient fiber lasers; it has efficient emission from 1000 to 1100 nm , which is significant since Tm3+-doped fibers have their most important pump wavelengths in this range. As mentioned above, various pump wavelengths in the range of 1000–1100 nm have been useful for pumping TDFA (e.g., 1047 , 1050 , and 1064 nm ).
Obviously it is possible that a Yb3+-doped fiber laser could be used as the pump source for a Tm3+-doped fiber amplifier. Yb3+ has been successfully used to sensitize Er3+ [10,11]. The advantage of a Yb3+-doped fiber laser that is worth mentioning is that it uses 980 nm diode lasers as its pump [11,12]. Such diode lasers are commonly used as pump sources for EDFAs and fiber lasers. They are widely available and typically low in cost in comparison with other uncommon wavelengths.
Based on the above considerations, we propose a new scheme for S-band optical amplification that incorporates both Yb3+ codoping and an internal laser cavity into a TDFA. In this scheme we use a 980 nm diode laser to pump built-in TDFA. The laser operates at a wavelength that could achieve high efficiency in both Yb3+ emission and Tm3+ absorption. The internal laser plays an important role here that produces the necessary pump for the TDFA operation.
Here we have established and analyzed a new theoretical model that takes into consideration two unique processes that feature this scheme: the lasing operated inside an optical amplification process and the energy transfer between the Tm3+ and the Yb3+ ions. We have presented results from various design situations such as Tm3+ doping concentration and cavity reflectivity. We have also demonstrated that, by introducing an internal laser cavity at 1050 nm into Tm3+–Yb3+ codoped fiber, one can achieve a high optical gain of more than 20 dB, a noise figure (NF) of approximately 5 dB in the wavelength range from 1450 to 1480 nm with 0.3 W power at a 980 nm pump source.
2. Design and theoretical model
Figure 1 shows the new design of a TDFA that consists of a section of Tm3+–Yb3+ codoped fiber and a pair of reflectors. Here we believe that the reflectors reflect light only of a certain wavelength, and they are transparent at other wavelengths. Under proper conditions, the reflectors could form a desirable Fabry–Perot laser cavity and produce internal laser output in an optical amplifier. To achieve high optical gain in the S-band amplification in which we are interested, it would be desirable for the Yb3+–Tm3+ codoped fiber to be pumped at an appropriate wavelength of efficient Yb3+ absorption. Since 980 nm is one of the most efficient Yb3+ absorption wavelengths and 980 nm pump diodes are both readily available and cost effective, here we focus mainly on those cases for which 980 nm diodes are used as pump sources. In fact, as we will discuss later, diode lasers that operate at other wavelengths such as 800 nm can also be useful for this scheme.
Moreover, it would be desirable for the laser cavity to be operated at an appropriate wavelength for both efficient Yb3+ emission and efficient Tm3+ absorption. It is obvious that the laser that operates at an efficient Yb3+ emission wavelength would produce high internal laser output power. At the same time, the laser that operates at an efficient Tm3+ absorption wavelength would ensure high pump efficiency for high gain optical amplification at Tm3+ emission wavelengths in the S-band. In general we could select an internal laser cavity that operates at a desirable wavelength from 1040 to 1070 nm. Here we present analysis and results only for those cases of internal laser cavities that operate at 1050 nm.
The diagram of Tm3+ and Yb3+ energy levels, the relevant absorption and emission transitions, spontaneous emission, and energy transfer process between Tm3+ and Yb3+ are shown in Fig. 2. Energy levels of 3 F 2 and 3 F 3 of Tm3+ are close and thus they are treated as a single level (level 4). Spontaneous decay processes are described by radiative and nonradiative decays, and , respectively. KYT1 and KYT2 are the energy transfer parameters between 3 H 6 (Tm3+)+2 F 5/2(Yb3+)→ 3 H 5 (Tm3+)+2 F 7/2(Yb3+) and 3 F 4 (Tm3+)+2 F 5/2(Yb3+)→3 F 2,3 F 3 (Tm3+)+2 F 7/2(Yb3+). Based on the above considerations, the rate equations for the Tm3+ population densities of relevant energy levels NT0 , NT1 , NT2 , NT3 , NT4 , and NT5 are established as follows:
The rate equations for the Yb3+ population densities of the two energy levels NY0 and NY1 are given by
Here NT and NY are the total Tm3+ and Yb3+ concentrations in the fiber. Wij describes the interaction of the electromagnetic field and the ions and can be written as 
Here represents the spectral power densities of the radiation that propagates in the positive and negative directions of the fiber axis, σij is the transition cross section, and Γ is the so-called overlap factor defined by 
N(r) is the Tm3+ or Yb3+ concentration distribution with NTm (Yb)= N(r)rdr. Powers of pump, signal, and internal laser along the fiber length can be expressed by the following propagation equations:
We have considered the boundary conditions as follows:
Here R 1 is the reflectivity of the laser cavity in the front end, and R 2 is the reflectivity of the laser cavity in the back end.
Using a point-by-point and iteration method, we have solved the set of Eqs. (1)–(8) under the boundary conditions given by Eqs. (12)–(15). Consequently the output power, gain of optical signal, and NF at various wavelengths has been obtained. The material and design parameters used in our analysis are based on ZBLAN, a fluoride glass host, and they are summarized in Table 1. The signal transition cross-sectional spectra of Tm3+ are obtained from Fig. 2 of Ref. , and the absorption and emission cross sections of Yb3+ at 980, 1064, and 1050 nm are based on Fig. 1 of Ref. .
Figure 3 shows the optical gain distribution in laser cavities of various lengths for signals at a 1470 nm wavelength. Here seven curves represent the gain distribution for laser cavity lengths of 4, 8, 12, 16, 20, 24, and 28 m, respectively. In all these cases, the 980 nm pump power is 0.3 W at the input end (z=0). The codoped fiber has concentrations of Tm3+ at 1000 parts per million (ppm) and Yb3+ at 600 ppm, respectively. We found that the optical gain along the fiber in a shorter cavity increases faster than in a longer cavity and that the 1050 nm laser intensity generated in a shorter cavity is higher than in a longer cavity. From Fig. 3 it is clear that the short cavity length is not sufficient to produce larger gain. For cavity lengths shorter than 12 m, the optical gain is significantly increased when the cavity length is increased. However, for cavity lengths longer than ~16 m, the optical gain does not increase appreciably with the cavity length. Clearly an optimal cavity length exists similar to conventional optical amplifiers without an internal laser cavity. This optimal cavity length behavior (by use of the same codoped fiber as that used in Fig. 3) could be clearly seen in Fig. 4, where the curves that represent signal gain at various wavelengths range from 1440 to 1520 nm. The optimal cavity length for the spectral gain can be found to be approximately 13.5 m.
Spectral gains under different pump powers are shown in Fig. 5. Here the curves represent the gain from various pump powers in the range from 0.1 to 0.6 W, by use of the same codoped fiber as that used in Fig. 3. As indicated in Fig. 4, the cavity length is optimized for the highest gain for a particular pump power. It is noticeable that the spectral gain increases with the pump power and that the increase rate slows down when the pump power increases. For an intermediate level of 0.3 W pump power at 980 nm and a cavity length of 13.5 m, more than 20 dB gain can be achieved in the range from 1450 to 1480 nm by use of the fiber doped with 1000 ppm of Tm3+ and 600 ppm of Yb3+.
The changes in spectral gain and NF with Tm3+ concentration are shown in Fig. 6. The four curves from bottom to top denote the optical gain obtained when we varied the Tm3+ concentration of 1000, 1500, 2000, and 2500 ppm. In all the cases here Yb3+ concentration was set at 600 ppm, with 0.3 W power at 980 nm pump, and the optimal cavity lengths used in these cases were 13.5, 10.6, 7.8, and 5.6 m, respectively, It is obvious that the optimal cavity length decreases with an increase in Tm3+ concentration, the spectral gain increases with an increase in Tm3+ concentration, and the increase rate slows down at higher Tm3+ concentrations. The NF drops slightly with an increase in Tm3+ concentration, which might be because high Tm3+ concentration would have better absorption of an internal laser and produce larger gain than low Tm3+ concentration. Above a 25 dB gain, a NF of approximately 5 dB can be obtained in the range between 1450 and 1480 nm by use of a codoped fiber with 2500 ppm of Tm3+ and 600 ppm of Yb3+ with a 5.6 m, 1050 nm laser cavity and 0.3 W pump power at 980 nm.
The effects of the reflectivity of the reflectors on the spectral gain are shown in Fig. 7. Here the curves denote signal gains for wavelengths that vary between 1420 and 1520 nm. In these cases the pump power is 0.3 W at 980 nm, and the signal input power of each channel is 10-5 W, The codoped fiber has concentrations of Tm3+ at 1000 ppm and Yb3+ at 600 ppm. The optical gain increases with the reflectivity, although the increase reduces slightly at higher reflectivity, which might be because the cavity with higher reflectivity would generate higher internal laser intensity.
Here we discuss briefly some of the practical aspects related to the proposed scheme. Until now we have only mentioned the introduction of a laser cavity inside an Yb3+ codoped TDFA. The doping or codoping of different rare earth ions into various optical fiber hosts has been studied intensively and various advanced technologies have been developed. Nevertheless, the codoping of Tm3+–Yb3+ in fluoride or tellurite fibers has not been reported or demonstrated. This would be an interesting topic for future research.
Obviously an internal laser cavity in a TDFA can be constructed by use of different methods. For example, one could pigtail a pair of readily available silica fiber Bragg gratings to the TDFA. Of course it would be desirable to write a pair of fiber gratings directly into a doped fluoride or tellurite fiber amplifier. Thus any additional splicing or connection loss could be avoided. However, to the knowledge of the authors, the writing of fiber Bragg gratings in fluoride or tellurite fibers has not been reported or demonstrated. This could also be an interesting topic for future research.
So far we have presented results for cases only with an internal laser cavity that operates at 1050 nm and is pumped by 980 nm diodes. In fact, as we mentioned above, the laser cavity can be designed to operate at other wavelengths such as 1047 and 1064 nm and could be pumped at other wavelengths such as 800 nm, as far as they are satisfied with certain constraints related to the specific spectral absorption and emission characteristics of a Tm3+–Yb3+ codoped fiber.
Currently one major issue in TDFA development is to achieve the highest pump efficiency. A number of dual-wavelength pumping schemes have been proposed and demonstrated for their improved efficiencies [5,7,15]. One of the most efficient TDFA schemes has been the dual-wavelength pumping such as the combination of 800 and 1050 nm reported in Refs.  and . It is worth noting that both Tm3+ and Yb3+ ions have strong ground-state absorption at 800 nm. A laser that operates at 800 nm wavelength could highly efficiently pump Tm3+ ions into an S-band amplification process as well as pump Yb3+ ions for the internal cavity that generates laser output at another wavelength, e.g., 1050, 1047, or 1064 nm. This could be another significant benefit for use of the Tm3+–Yb3+ codoped fiber proposed here. This internally generated laser output at 1050, 1047, or 1064 nm would provide efficient pumping for the S-band optical amplification shown in this paper. Hence, by use of a single pump source at 800 nm instead of at 980 nm in the internal cavity of the Tm3+–Yb3+ codoping fiber scheme proposed here, it is possible to achieve the same excellent performance as that reported in various dual-wavelength pumping schemes for which two separate pump sources must be used. Obviously a variety of similar cases to this combination of 800 nm pump plus 1050 nm internal cavity in a Tm3+–Yb3+ codoped fiber would be worth studying in the future.
We have investigated the spectral gain and NF property of a TDFA with the laser cavity that operates at 1064 nm. The results from a 1064 nm laser cavity are compared with those given above from a 1050 nm cavity, as shown in Fig. 8. Both cases have the same parameters: Tm3+ concentration at 1000 ppm, Yb3+ concentration at 600 ppm, pump power of 0.3 W at 980 nm, and a 10-5 W signal input power for each channel. It is obvious that the spectral behavior for both cases is similar. In the 1050 nm case the optical gain is slightly higher, the NF is slightly lower, and its optimized laser cavity length is longer. One of the reasons could be that the emission cross section of Yb3+ at 1050 nm is larger than that at 1064 nm, although the absorption cross section of Tm3+ W 02 and W 14 is larger at 1064 nm than that at 1050 nm. This result agrees with the pumping wavelength dependence of TDFA .
Similar to a fiber laser, there is a threshold pump power for this kind of amplifier, and this threshold is decided by Tm3+ and Yb3+ concentration, reflection rate, reflection wavelength, and cavity length.
Compared with the TDFA pumped by an Yb3+ doped fiber laser, this design is convenient and has higher gain and a lower NF under the same 980 nm pump power as shown in Fig. 9. The curves indicated by triangles represent the gain and NF of a codoped amplifier with an internal laser cavity (codoped); the curves indicated by diamonds represent gain and NF of the TDFA pumped by Yb3+ doped fiber laser (separated), the output wavelength of an Yb3+ doped fiber laser is 1050 nm, and it has the same 980 nm pump power (0.3 W) as the codoped amplifier. Both the codoped and the separated amplifiers have the same nine-channel signal input with an each channel input power of 10-5 W. It is shown that the gain of a codoped amplifier is approximately 7 dB higher, and the NF is approximately 1 dB lower at 1470 nm than those of a separated amplifier. These improvements might result because in a codoped amplifier the Tm3+ is pumped by the internally generated 1050 nm forward and backward laser in the cavity. Consequently a codoped amplifier is more efficient than a separated amplifier that is pumped by the 1050 nm output of a Yb3+ doped fiber laser.
In the theoretical modeling of this scheme, we have considered the energy transfer process 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+). There is no experimental data available for the energy transfer parameters of KYT1 and KYT2 in thulium-ytterbium codoped ZBLAN materials. Here we made use of the experimental data reported in Ref. 8, where the energy transfer parameters K 1 and K 2 in ytterbium and thulium codoped single crystal materials have been given. We delineated the energy transfer parameters in terms of the product of the total Tm3+ and Yb3+ concentrations, NTm and NYb , and finally we estimated KYT1 and KYT2 by an extrapolation approach. However, in the cases we studied and presented here, the concentrations of Yb3+ and Tm3+ are low, the transfer parameters are quite small, and their effect on the performance of optical amplification is insignificant. Based on the results from our cases, we conclude that the primary contribution to S-band optical amplification results from the internally generated pump at 1050 nm.
A novel scheme of TDFA has been proposed for S-band optical amplification in a Tm3+ doped fiber. This scheme uses a combination of Yb3+ codoping, an internal laser cavity, and pumping at 980 nm wavelength. The key consideration of proposing this scheme is the fact that the main Yb3+ emission overlaps well with the main Tm3+ absorption in the spectral range between 1000 and 1100 nm. Hence by introducing Yb3+ ions and a laser cavity inside a TDFA, an internally generated laser output at the Yb3+ emission wavelength would provide pumping for Tm3+ at its desirable absorption wavelength. This makes it possible for conventional low-cost pump sources for EDFAs to be used for S-band amplification.
We established a theoretical model for the proposed scheme that takes into consideration two novel features: an internally generated pump for Tm3+ by Yb3+ and energy transfer between the Tm3+ and the Yb3+ ions. The model has been analyzed for various design parameters and conditions. Based on the results obtained, it is possible to achieve high optical gain by use of conventional low-cost 980 nm pump diodes. For an internal laser cavity operating at 1050 nm wavelength in Tm3+ (1000 ppm) and Yb3+ (600 ppm) codoped ZBLAN fiber, it is possible to achieve high optical gain of more than 20 dB, a noise figure of approximately 5 dB in the wavelength range from 1450 to 1480 nm, and 0.3W pump power at 980 nm wavelength. With a high Tm3+ concentration at 2500 ppm under similar conditions, it is also possible to achieve a higher gain of more than 25 dB.
The authors acknowledge support from the China Scholarship Council, Natural Science Foundation of Shandong Province of China grants Y2003G01 and Y2002G06, and Research Fund for the Doctoral Program of Higher Education of China grant 2002022048.
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