A 2.3 W single transverse mode thulium-doped fluoride fiber laser based on fiber Bragg gratings is presented. The laser has a conversion efficiency of 65% to be compared to the quantum limit of 72%. The performances of the laser are compared for two pump wavelengths of 1040 and 1064 nm and are analyzed based on a rate equation analysis.
©2008 Optical Society of America
High power lasers emitting at 1480 nm are the ideal pump sources for erbium-doped fiber amplifiers (EDFA) and Raman fiber amplifiers (RFA) found in long distance optical fiber-based telecommunications networks. In fact, EDFAs pumped at this wavelength feature lower ASE levels compared to 980 nm-pumped amplifiers. Also, RFAs could eventually replace EDFAs to create less complex systems since the same fiber can be used for transmission and amplification purposes. They also feature a much wider gain bandwidth and reduced ASE levels due to a gain distribution that can span the whole network . There has been a renewal of interest in RFAs in the middle of the 1990s when high power laser diodes at around 1480 nm became commercially available . However, these laser diodes (LD) typically operate at low efficiencies so that the maximum power achievable is strongly limited by overheating problems. In fact, the maximum output power at 1480 nm is currently limited to 400 mW in commercial products and to 1 W-1.2 W in laboratories [3, 4]. Raman fiber lasers (RFL) pumped at 1064 nm can also deliver high power at around 1480 nm by using cascaded (i.e. nested pairs of) fiber Bragg gratings (FBG). Since six Raman shifts are required with Ge-doped silica fibers, the overall conversion efficiency is limited by splice losses. Whereas only two Raman shifts are needed with P-doped silica fibers, they exhibit larger background losses than Ge-doped fibers . However, RFLs are currently the most powerful pump sources at 1480 nm with output powers in excess of 10 W. Rare-earth-doped fiber lasers are another alternative, especially thulium-doped fluoride fibers which are known to have an emission band around 1480 nm and were initially used in thulium-doped fiber amplifiers (TDFA) to cover the S-band. Now, Tm3+-doped fiber lasers operating at this wavelength are much more efficient with fluoride fibers [6,7] due to the self-terminating nature of the laser transition. In fact, fluoride glasses like ZBLAN possess lower phonon energy than silica so that rare earth ions have longer lifetimes. This allows the use of an upconversion pumping scheme that promotes the ions to the upper level of the transition while at the same time depleting very efficiently the lower level .
Previously reported Tm3+-doped fiber lasers were built with bulk optical elements [6–10] that increase the intracavity losses. Thus, despite their huge potential, the development of fluoride fiber lasers has been hindered by the inability to write strong FBGs in these fibers. Recently, we demonstrated the efficient writing of strong and permanent FBGs  in a ZBLAN fiber. We used these FBGs to build the first monolithic fluoride fiber laser . In this paper, we report what we believe is the highest output power and efficiency in a single transverse mode fluoride fiber laser at 1480 nm, corresponding to a ten-fold power increase with respect to previous reports .
2. Experimental results
2.1 Experimental setup
Figure 1 shows the experimental setup . Two ytterbium-doped fiber lasers at 1040 and 1064 nm were used as pump sources. The 2000 ppm thulium-doped ZBLAN fiber was provided by Le Verre Fluoré. It has a core diameter of 2.9 µm, a numerical aperture of 0.235 and a LP11 cutoff wavelength of 870 nm so that the fiber supports only one mode at both the pump and signal wavelengths. Using an aspheric lens, the pump beam is launched through the fiber end where a 10.5 dB FBG has been written according to the method described in . The output coupler consisted of either the 4% fiber end Fresnel reflection or a low reflectivity FBG. Also note that the input FBG was thermally annealed prior to the experiments so that its Bragg wavelength and reflectivity would not drift. This allowed us to operate the fiber laser over a period of eight months without any noticeable change in its performance. However, the input FBG was cooled during laser operation in order to prevent it from possible overheating due to pump power absorption along its length.
A prism was used to separate the signal at 1480 nm and the residual pump at the output. The reflected beam on the face of the prism is used to monitor the laser output spectrum with an optical spectrum analyzer (OSA).
2.2 Pumping scheme
The upconversion pumping scheme is illustrated in Fig. 2. The pump absorption cross-section spectra of the 3H6→3H5, 3F4→3F2 and 3H4→1G4 transitions overlap each other significantly  so that it is possible to sequentially populate levels 3F4, 3H4 and 1G4 with the same wavelength in the range 1030–1200 nm. Ions in the ground state (3H6) are excited to the 3H5 level and rapidly decay to the 3F4 metastable energy level through multiphonon relaxation. These ions are excited by photons of the same pump laser to the 3F2 level, from which they quickly relax to the 3H4 level.
Laser oscillation occurs between the 3H4 and 3F4 levels. Due to the upconversion process, the pump laser populates the upper level of the transition (3H4) while also depleting the lower level (3F4). The otherwise self-terminated 3H4→3F4 transition is then allowed to continuously oscillate even though the 3F4 level has a longer lifetime than the 3H4 level (8.95ms and 1.54 ms, respectively).
Figure 3 shows the laser output power with respect to the launched pump power at both pump wavelengths that is 1040 and 1064 nm. The fiber length was 5.45 m and the output coupler was simply the cleaved fiber end. Although it corresponds to a higher threshold, 1040 nm pumping yields both larger slope efficiency and higher maximum output power. Also, the laser has a peculiar behavior at threshold characterized by a sharp inflection when pumped at 1040 nm. This behavior is attributed to a weak reabsorption of the signal at 1480 nm through the 3H6→3F4 transition (GSA1480) as we demonstrate in the next section. In fact, when the fiber is pumped at 1064 nm, the laser exhibits a more typical behavior with a gradual saturation of the output power as the pump power is increased. However, we observed a sharp reduction in slope efficiency at higher pump powers that we attribute to the onset of lasing around 815 nm. Indeed, we observed that at 1064 nm pump powers higher than 900 mW, the 4% reflections due to the Fresnel reflections at each fiber end provide enough feedback for the 3H4→3H6 transition to also oscillate. The two transitions (3H4→3F4 and 3H4→3H6) then compete for the available gain in the fiber. We should note that this problem can be fixed simply by polishing the input fiber end at an angle.
3.1. Spectroscopic properties
In order to explain the behavior of the laser, particularly when it is pumped at 1040 nm, we have developed a numerical model that takes into account all the transitions at the pump and signal wavelengths. We also introduced energy transfer processes between ions that can affect the population distribution of the energy states. The complete energy level diagram is shown in Fig. 4.
Cross-section values of the various transitions at 1480 nm are summarized in table 1. The GSA1480 cross-section of the 3H6→3F4 transition is very weak and is not known precisely at the signal wavelength because this transition is centered at 1680nm and extends well into the signal region [10, 14–15]. Its value is given as a fit to the experiments. Spontaneous emission rates and energy transfer coefficients used in our model have been taken from  and are listed in tables 2 and 3 respectively. Coefficient X1102 has been taken from .
3.2. Rate equations
As shown on Fig. 4, the 3F2 and 3F3 levels are very close and rapidly relax to the 3H4 level, so that these three levels can be treated as a single level. The same assumption is made for levels (3F4, 3H5) and (1I6, 2P0, 2P1, 2P2). Normalized population densities of the energy levels 3H6, (3F4, 3H5), (3H4, 3F3, 3F2), 1G4, 1D2, and (1I6, 2P0, 2P1, 2P2) are labeled n0, n1, n2, n3, n4 and n5 respectively, such that n0+n1+n2+n3+n4+n5=1. According to the energy level diagram presented on Fig. 4, we built the system of rate Eqs. (1a)–(1e) which is numerically solved to compute population densities.
are the stimulated emission and absorption rates for the signals at 1480 nm and the pump respectively, Aij and σij are respectively the spontaneous emission rates and the cross-sections for transition |i>→|j>, Xjklj are the energy transfer coefficients. Although the energy transfer coefficients do not play a major role in the overall behaviour of the laser, they must be taken into account especially near threshold for the model to be as accurate and reliable as possible. C is the Tm3+ ions concentration in the fiber core, and the ions distribution profile in the core is supposed to be uniform so that the evolution of the optical powers along the fiber are governed by (Eqs. (3a)–(3b)
where αi and ψi are the background losses of the fiber and the normalized intensity profile of the LP01 mode at the wavelengths λi. The net round-trip gain at a wavelength of 1480nm is then given by:
3.3. Results and discussion
The solid curves appearing in Fig. 3, along with the experimental results, were obtained from our numerical simulation. These results confirm the accuracy of the numerical model. The observed discrepancy is actually within the range of accuracy of the experimental results which is of the order of 5%. More importantly, our numerical results exhibit the peculiar behaviour characterized by the sharp inflection observed at threshold for the 1040 nm pump.
We have found that this peculiar behaviour of the laser originated from the reabsorption of the signal through the 3H6→3F4 transition (GSA1480). Komukai et al.  already mentioned that this signal reabsorption was responsible for the increase in the noise figure of a thulium-doped fluoride fiber amplifier and that even though the value of the cross-section is rather weak, it should be incorporated in the numerical model. This is of course especially true with relatively long fiber lengths such as in our experiments (5.45 m). Note however that the laser characteristic curve is essentially linear when plotted as a function of the absorbed pump power (see Fig. 5(a)), which shows that the high threshold is resulting from the weak pump absorption. In fact, up to the laser threshold, the pump is largely unabsorbed due to a low GSA cross section at 1040 nm. Furthermore, since the GSA1480 rate is about four times higher than the pump GSA rate near threshold, every photon at 1480 nm that is absorbed from the ground state allows the absorption of a pump photon through the 3F4→3F2 pump ESA transition. This very efficient process creates an avalanche of signal photons that rapidly depletes the high available pump energy. Since it still takes two absorbed pump photons to produce every signal photon, we see no inflection point when the output power is plotted as a function of the absorbed pump power. Thus, the inflection in the laser curve at threshold is only due to the dynamical interplay between the levels.
Accordingly, Fig. 5(b) shows the effect of varying the amplitude of the GSA1480 cross-section on the laser behaviour. The figure clearly demonstrates that when we do not account for the GSA1480 in the model, the laser exhibits a rather typical behaviour. The effect of the GSA1480 is particularly significant right after threshold when there is still a significant amount of thulium ions in the ground state that could absorb photons at 1480 nm to be promoted to the 3F4 energy level. From this level, the absorption of a pump photon through the ESA transition leads to a net population inversion gain of two so that the avalanche process can build up. At high pump power, this effect tends to disappear because fewer ions remain in the ground state causing the reabsorption of the signal at 1480 nm to become negligible.
Accordingly, results previously presented on Fig. 3 have been re-plotted as a function of the absorbed pump power on Fig. 6. Whereas the laser curves at both pumping wavelengths were very different, they appear to be very similar regarding to the absorbed pump power, exhibiting a conversion efficiency of 65% to be compared to the quantum limit of 72%. Since the pump GSA is very weak, the conversion efficiency depends on pumping rate of the ESA transition. The value of the ESA pump cross-section at both pumping wavelengths is nearly at its maximum (@1050 nm ) so that our pumping scheme approaches a 3-level pumping scheme. Indeed, the probability that each thulium ion in the 3F4 energy level to be excited to the upper laser level is thus very high, leading to a conversion efficiency approaching the quantum limit.
4.1 Pump wavelength optimization
Based on the previous observations, we have used our numerical model to calculate the optimal pump wavelength. Figures 7(a) and 7(b) show the output power of the laser with respect to the launched and absorbed pump power for a fiber length of 5.45 m and reflectivities of 90% and 4% for entrance and output coupler respectively.
Laser characteristics are very different depending on the choice of the pump wavelength (Fig. 7(a)), especially the behavior at threshold that was attributed to the GSA1480. A wavelength of 1050 nm seems to be a good compromise between high output power and low threshold. Indeed, threshold for the launched pump power increases when the pumping wavelength is lower than 1050 nm, and overall efficiency strongly decreases for higher pumping wavelengths. This result is confirmed by Fig. 7(b) where the laser output power has been plotted as a function of the absorbed pump power. The laser exhibits the best conversion efficiency when pumped at 1050 nm which corresponds to the maximum value of the cross-section of the 3F4→3F2 transition as we already mentioned [13, 15]. For higher pumping wavelengths, the efficiency is reduced due to strong ESA from the 3H4 energy level that depletes the upper laser level, and a cross-section value of the 3F4→3F2 transition lower than at 1050 nm. On the other hand, for lower pumping wavelengths than 1050 nm, the efficiency is reduced because of the weak GSA and a lower cross-section value of the ESA from the 3F4 energy level. If the pumping wavelength is too far from the optimal wavelength, the pumping scheme could not be considered as a 3-level pumping scheme and the efficiency is reduced.
Finally, the net gain given by Eq. (4) has been plotted at different pump powers as a function of the pumping wavelength (Fig. 8). The parameters are all kept the same as those used in the previous numerical results. The maximum gain at each pump power is identified by an open circle. The peak gain shifts to lower pumping wavelengths as the pump power is increased reflecting the experimental observations. The threshold for oscillation is first reached at higher pump wavelengths, but at high power the maximum gain moves to shorter wavelengths. These results are also in agreement with the simulations reported by Lee et al.  for thulium-doped amplifiers where it was demonstrated that a pump wavelength of 1070 nm was optimal for amplification at low pump powers whereas 1045 nm was more appropriate when the pump power was increased. Accordingly, our results show that a pump wavelength of 1053 nm provides the highest net gain with a relatively low threshold and is found to be the optimal wavelength for pumping the laser under our experimental conditions.
4.2 Optimization of the laser cavity
The pumping wavelength of 1053 nm has been found to be the optimal pumping wavelength for the 5.45 meter-fiber we used in our experiments. However, since the pump is rapidly absorbed, the fiber does not need to be that long. The optimal fiber length at various pump wavelengths and the corresponding laser output power for a launched pump power of 1.5W is plotted on Fig. 9. The coupler reflectivities have been kept unchanged at 90% and 4% at entrance and output respectively.
The laser output power reaches a maximum at a pumping wavelength of 1053 nm corresponding to a fiber length of 4.3 m (Fig. 9). Note that 5.45 m is the optimal fiber length for a pumping wavelength of 1040 nm but is too long for a pumping wavelength of 1064 nm. The fiber length can be even more shortened by adjusting the reflectivity of the output coupler. The evolution of the laser output power as a function of the fiber length for different values of the output coupler reflectivity has been plotted on Fig. 10. The output power has been computed for a launched pump power of 1.5 W and a pump wavelength of 1053 nm.
The results indicate that the maximum output power is obtained for a 3 meter-long fiber and an output coupler reflectivity of about 10%. The optimal fiber length decreases as the output coupler reflectivity increases but the maximum output power is also reduced.
5. Watt-level emission
5.1 Pumping at 1040 nm
Based on the results of our numerical simulations, we have optimized the laser parameters for our two pump wavelengths in order to reach watt-level output power at 1480 nm. We first investigated the 1040 nm pumping case and increased the pump power to its maximum available value. Figure 11 shows the laser output power as a function of the launched pump power along with the spectrum of the signal (cf. inset). A maximum output power in excess of 1 W has been reached for a launched pump power of 2.2 W and a fiber length of 5.45 m.
The laser threshold was measured at 500 mW of launched pump power. We also note that there is no saturation of the output power up to the maximum available pump power of 2.2 W. The slope efficiency was 53%, and the laser output spectrum had a full width at half maximum (FWHM) of about 140 pm.
5.2 Pumping at 1064 nm
As shown through our numerical simulations (cf. Fig. 9), a higher laser power is obtained for a shorter fiber segment when pumping at 1064 nm, especially if the output coupler reflectivity is larger than the 4% Fresnel reflection (cf. Fig. 10).
Figure 12 shows the laser output power as a function of the launched pump power for a pump wavelength of 1064 nm, a fiber length of 2.8 m and an output coupler of about 15% of reflectivity. The output coupler is a chirped grating we wrote at the other fiber end with the same setup as previously reported. The slope efficiency was 50% and a maximum laser output power of 2.25 W has been reached for a launched pump power of 6.5 W. This represents, to the best of our knowledge, the highest output power ever reported for a singlemode Tm3+-doped fiber laser operating at 1480 nm. The threshold is reached for a launched pump power of 280 mW, slightly higher than in the case of Fig. 3 because the fiber if shorter. Note that at high pump power, the experiment slightly diverges from the computed result due to misalignment of the fiber heated up by the focused pump laser beam. We believe that the output power could be further scaled up by the use of a double-clad fiber configuration pumped with high power laser diodes, which are becoming readily available at this wavelength .
A watt-level thulium-doped ZBLAN fiber laser based on FBGs in a singlemode fluoride fiber has been experimentally demonstrated. An exhaustive numerical analysis was developed to interpret our experimental results, particularly the peculiar behavior of the laser characterized by a sharp inflection at threshold that we observed for a pump wavelength of 1040nm. According to our modeling, this peculiar behavior is due to the reabsorption of the signal at 1480 nm. We also used our model to optimize the laser cavity in terms of pump wavelength, output coupler reflectivity and fiber length. It was found that optimum conditions would correspond to a pump wavelength of 1053nm with an output coupler of 10% and a fiber length of 3m. Under conditions approaching the optimum ones for our two pump wavelengths, we have obtained over 1W of power at 1480 nm when pumping at 1040 nm and 2.25 W when pumping at 1064 nm. In both cases the output power was limited by the maximum pump power available. So, it is expected that with a double-clad fiber design, the output power could be increased further to several watts so that Tm3+-doped fluoride fiber lasers could favorably compete with other commercial lasers at this wavelength, especially for pumping Raman fiber amplifiers.
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