Significant effects from heating occur in both single and two tone fiber amplifiers. Single tone 1064 nm amplifiers have highest efficiency when the external environment surrounding the gain fiber is cold while 1064 nm two tone amplifiers co-seeded with broadband 1040 nm have maximum efficiency when the gain fiber is hot. It is shown experimentally that changes in the temperature of the core of the gain fiber have dramatic effects on the 1064 nm / 1040 nm power distribution in the output of two tone amplifiers. This has been attributed to temperature dependence of the absorption and emission cross-sections at the wavelengths of interest.
©2011 Optical Society of America
A high power laser system with a diffraction limited beam is desirable. To achieve high power using fiber laser technology, multiple fiber amplifiers need to be coherently combined since the output power of each individual amplifier is limited by nonlinear effects. In the case of narrow linewidth amplifiers, the output power is limited by Stimulated Brillouin Scattering (SBS). To enable as simple a high power fiber laser system as possible, it is desirable to maximize the output power of the individual fiber amplifiers. A number of techniques have been suggested or implemented to mitigate SBS in narrow linewidth fiber amplifiers including large-mode area fibers , thermal gradients [2, 3], stress , and various designs of the core or cladding regions of a fiber to alter the acoustic properties [5, 6]. Another method for decreasing the nonlinear length is discussed in  where a tandem pumping, two-stage brightness enhancing technique is utilized. Two tone seeding of an amplifier with narrow and broad linewidth photons [8–12] has also been shown to be effective in mitigating SBS by suppressing the growth of the intensity profile of the narrow linewidth signal in the gain fiber resulting in a decrease in the effective length for SBS. By co-seeding a narrow linewidth 1064 nm fiber amplifier with broad linewidth 1040 nm, a power enhancement of approximately 1.6 to 1.8 for 70% efficient 1064 nm narrow linewidth two tone fiber amplifiers relative to 70% efficient narrow linewidth 1064 nm single tone fiber amplifiers was obtained . A broad linewidth co-seed was used to prevent the 1040 nm from prematurely reaching the SBS threshold. It was also previously observed that the efficiency of a 1064 nm amplifier increased when the terminal segment of the gain fiber had a pump induced temperature (with the remainder of the fiber kept at 16°C) versus the entire gain fiber being kept cold at 16°C . This seemed to indicate that modest heating of the gain fiber could significantly affect the efficiency of 1064 nm two tone fiber amplifiers as well as the spectral composition of the output. Finally, it was found that amplifiers having lengths of gain fiber shorter than 7 m were plagued with significant amounts of 1040 nm in the output . The significantly decreased 1064 nm efficiency is problematic since highest 1064 nm output powers are expected to occur at shorter lengths of gain fiber due to an increased SBS threshold. Previously, temperature effects in single tone fiber amplifiers have been observed experimentally [13–15]. Specifically, for a fixed level of pump power, changes in the output power were observed to occur as the temperature of the external environment surrounding the gain fiber was increased from room temperature. These effects were attributed to changes in the absorption and emission cross-sections brought about by changes in the temperature of the core of the gain fiber [13, 14, 16–20]. Because thermal effects are extremely significant in high power fiber amplifiers, the effect of gain fiber temperature on the efficiency of 1064 nm narrow linewidth single and two tone fiber amplifiers will be the subject of this paper.
2. Thermal effects in single and two tone fiber amplifiers
The efficiencies of narrow linewidth 1064 nm single tone and 1064 nm two tone fiber amplifiers co-seeded with broad linewidth 1040 nm have been found to be dependent on the temperature of core of the gain fiber. The effect of temperature on amplifier efficiency has been found to be much more significant in two tone amplifiers than in single tone amplifiers.
2.1 Investigation of 1040 and 1064 nm single tone fiber amplifiers
Investigation of the effect of the temperature of the external environment surrounding the gain fiber on the efficiency of 1040 and 1064 nm single tone amplifiers was carried out for lengths of gain fiber between one and six meters over a temperature range of 20 to 80°C. The 1040 and 1064 nm single tone fiber amplifiers were seeded at the 2.3 W level and were pumped with a maximum of 83.1 W of wavelength-stabilized 976-977 nm pump power emanating from two pump banks. Spectra, from both pump banks, as a function of output power within the range of use, are shown in Fig. 1 along with a plot of the absorption cross-sections for Yb in silica as a function of wavelength. Two distinct wavelengths, both falling within the strong absorption peak of Yb in silica centered at 977 nm, were emitted from both pump banks. The emission wavelengths of pump bank 1 occurred at 976.5 and 976.9 nm and the emission wavelengths of pump bank 2 occurred at 976.4 and 977.2 nm. The percentage of pump emission tended to shift slightly toward the longer wavelength as the output power of both pump banks increased within the range of use. Nufern generation 7 25/400 Yb-doped double-clad polarization-maintaining gain fiber was used with care being taken to spool as much fiber as possible into a diameter of 10.5 cm in the region of constant temperature. The percentage of gain fiber outside the constant temperature zone increased slightly as the length of the gain fiber became shorter with approximately 7% of the gain fiber being outside the temperature zone for a 6 m fiber and 12.4% being outside the temperature zone for a 1 m fiber. For both single tone fiber amplifiers, the unabsorbed 976 nm pump along with either the 1040 nm or 1064 nm signal was measured, see the experimental setup in Fig. 2 .
For all lengths of gain fiber, it was found that both the 1040 and 1064 nm fiber amplifiers became less efficient (lower output power) as the temperature of the external environment surrounding the gain fiber was increased with the efficiency (output power) of the 1040 nm amplifier decreasing more rapidly with environmental temperature, see Figs. 3a-c . This is consistent with what had been previously observed in references 13-15. The percentage decrease in output power between environmental temperatures of 20 and 80°C for 1064 and 1040 nm single tone amplifiers with a 6 m gain fiber is 2.66 and 5.16 percent, respectively. For both 1064 and 1040 nm amplifiers, the unabsorbed pump was found to increase as the temperature of the environment surrounding the gain fiber increased, see Figs. 3d-f. The percentage increase in unused pump between environmental temperatures of 20 and 80°C for the 1064 and 1040 nm single tone amplifiers with a 6 m gain fiber is 6.7 and 7.9 percent, respectively. Of interest is the fact that the efficiency of the 1064 nm amplifier is greater than that of the 1040 nm amplifier for amplifiers having longer lengths of gain fiber with the trend being reversed for amplifiers having shorter lengths of gain fiber. Also, the amount of unabsorbed 976 nm pump is greater for 1040 nm single tone amplifiers relative to 1064 nm single tone amplifiers for amplifiers having longer lengths of gain fiber with the trend being reversed for amplifiers having shorter lengths of gain fiber. The cross-over point for both the efficiency of the signal and amount of unabsorbed pump occurs in amplifiers with increasingly shorter lengths of gain fiber as the temperature of the external environment surrounding the gain fiber is increased. This can be most easily seen by comparing the 20 and 80°C points for the three lengths of gain fiber in either Figs. 3a-c or Figs. 3d-f. For both sets of figures, the cross-over occurred in less than 4 m of gain fiber at 80°C (1040 and 1064 nm data points have flip-flopped) whereas at 20°C, the cross-over has yet to occur (relative position of 1040 and 1064 nm data points is unchanged). It should be noted that since the numerical aperture increases with temperature, the wave guiding ability of the gain fiber is not affected.
2.2 Investigation of 1064 nm narrow linewidth two tone fiber amplifiers
The effect of the temperature of the external environment surrounding the gain fiber was further explored for two tone fiber amplifiers through a series of experiments aimed at determining the effect of the environmental temperature on the efficiency of a narrow linewidth 1064 nm fiber amplifier co-seeded with broad linewidth 1040 nm.
The amplifier utilized in the experiment was simultaneously seeded with both narrow linewidth (10 kHz) 1064 nm and broad linewidth (250 GHz) 1040 nm photons. Both seeds were amplified before being injected into the gain fiber along with 976 nm wavelength-stabilized diode pump power. Nufern generation 7 25/400 double clad polarization maintaining gain fiber was utilized again. A gain fiber length of 608 cm was spooled into a single temperature zone as shown in Fig. 4 .
A two tone fiber amplifier seeded with five different seed ratios of P1064/P1040 ranging from 0.11 to 0.88 were studied, see Table 1 for the input powers of the 1040 and 1064 nm seeds. Seed ratios were chosen to enable a significant range of 1064 nm amplifier efficiencies, from 40 to 69.2 percent (or corresponding percentages of 1040 nm in the amplifier output ranging from 48.6 to 11.2 percent) at 20°C. This was done to enable an assessment as to how much the 1064 nm amplifier efficiency can be increased or 1040 nm output percentage decreased, by raising the temperature of the environment of the gain fiber. Levels of amplified spontaneous emission were found to be approximately 1-3 percent with no discernable temperature dependence. For the initial series of experiments, the gain fiber was held at a series of environmental temperatures ranging from 20°C to 80°C in 15°C increments. The upper limit of 80°C was chosen since the outer coating of the fiber is known to breakdown around 100°C. Care was taken to put as much gain fiber as possible into the temperature zone with 39.5 cm residing outside the hot area or 6.5% of the total length. For each fiber amplifier at each temperature studied, the pump was increased incrementally up to a level of 71 W. The following quantities in the output of the amplifier were measured: unused pump, 1040 nm and 1064 nm. Upon examination of Fig. 5 , it is apparent that the percentage of 1040 nm in the amplifier output can be reduced significantly, i.e., the percentage of 1064 nm in the amplifier output and the 1064 nm efficiency increased when the environmentaltemperature of the gain fiber was increased from 20°C to 80°C. The percentage decrease of 1040 nm in the amplifier output ranged from 43 to 58.9% for the generation 7 fiber. Therefore, for two tone 1064 nm amplifiers co-seeded with 1040 nm, the best efficiency will be obtained when the gain fiber is kept as hot as possible. Also, choice of the seed ratio, P1064/P1040, needs to be done carefully to enable, in conjunction with environmental temperature, an efficient 1064 nm amplifier having a maximum amount of 1064 nm and a minimal amount of 1040 nm in the output. It should be noted that the effective length for SBS increases when the percentage of 1040 nm in the output of the amplifier decreases and the 1064 nm amplifier efficiency increases. As an example, consider two distinct fiber amplifiers having P1064/P1040 seed ratios of 0.88 and 0.11 with corresponding percentages of 1040 nm in the output of 11.2 and 48.6, respectively. For amplifiers with seed ratios of 0.88 and 0.11, the ratio of the effective length for SBS relative to that of an equivalent single tone amplifier is 0.71 and 0.23, respectively, and the ratio of the increase in the critical pump power relative to an equivalent single tone amplifier is 1.4 and 4.3, respectively. This results from the point of maximum power transfer between the 1040 and 1064 nm occurring in a shorter length of gain fiber for amplifiers having higher P1064/P1040 seed ratios leading to greater growth of 1064 nm along the gain fiber and an increase in the effective length for SBS. Therefore, as the efficiency of the 1064 nm increases, the ultimate achievable output power in 1064 nm will decrease.
3. Analysis of data
Macroscopic features of the experimental data can be explained by a change in the absorption and emission cross-sections for the 976, 1040, and 1064 nm wavelengths with temperature. To enable accurate design of two tone fiber amplifiers for a specific gain fiber, a model needs to adequately capture the amount of heat deposited in the fiber core; the dependence of the absorption and emission cross-sections on temperature; and the dependence of other propagation losses not described by ytterbium absorption on the wavelength.
3.1. Spectroscopy of ytterbium in silica
Ytterbium in silica is a simple, two level system having four Stark levels in the lower 2F7/2 manifold and three Stark levels in upper 2F5/2 manifold. An energy level diagram specific to Nufern 5/125 fiber is shown in Fig. 6 . Because the splitting of the levels depends on the glass composition, concentration of dopants and co-dopants, and the degree of structural disorder of the glass network [19, 20, 22–25], the energy level diagram for Yb in silica may vary with each individual fiber. The absorption and emission cross-sections for Yb in silica are related to the temperature and the energy of the levels by the following relationships:16]. As the temperature of the core of the gain fiber is increased, the population of levels a and e are expected to decrease and the populations of levels b-d and f-g are expected to increase. Numerous researchers have measured the absorption and emission cross-sections of ytterbium in silica and some have measured the dependence of the cross-sections on temperature [13, 14, 16–21]. Upon comparing measurements of the absorption and emission cross-sections at a fixed temperature among the various sources, quite a bit of variability is seen at the wavelengths of interest. With respect to the dependence of the absorption and emission cross-sections on temperature, researchers in references  and  measured a decrease in the absorption and emission cross-sections at 976 nm and an increase in the absorption cross-sections at 1040 and 1064 nm as temperature increased [13, 16]. Researchers in the two references differ on the direction of change in the emission cross-sections at 1040 and 1064 nm when temperature is increased with  reporting that the cross-sections increase and  showing that they decrease. In addition, significant variability is also seen in the two references with respect to the size of the change in the cross-sections for a fixed change in temperature, with  reporting a smaller change in the cross-sections than  for a fixed change in temperature. Finally, besides changes in the populations of the energy levels as temperature is increased, broadening of the homogenous linewidth with temperature may also lead to changes in cross-sections.
3.2. Temperature dependent modeling
Insights into the experimental data can be obtained through development of a rudimentary model for both single and two tone fiber amplifiers using information on the absorption and emission cross-sections in the literature. Within the gain fiber, changes in the intensity with distance for the three wavelengths of interest are described by the rate equations shown below21] were utilized as the baseline at 20°C since absolute values were given. Weighted values for the absorption and emission cross-sections for the pump based on the relative proportion of pump emission into the two wavelengths in the 976-977 nm region, see Fig. 1, were utilized at 20°C. Since the shift of pump power into the longer wavelength is relatively small over the range of currents (5 to 18 A) applied to the diodes, absorption and emission cross-sections for banks 1 and 2 were based on an applied current of 15 A. In addition, since pump banks 1 and 2 were incremented at the same rate, i.e., the current applied to pump banks 1 and 2 was equal for every data point, an average value of the absorption and emission cross-sections for pump banks 1 and 2 was utilized in the model. The wavelengths of the pump and sources were measured by an optical spectrum analyzer and the following values were utilized in the model: 976.58 (a weighted average of the two emission peaks), 1039.9, and 1064.25 nm. Parameter values associated with the model are shown in Table 2 .
Finally, the relationships derived in  were utilized to relate changes in the cross-sections to changes in the temperature as follows:
It was assumed throughout the course of this work that the cross-sectional delta's had a linear dependence on temperature over the range of interest with the model developed in , based on Eqs. (1) and 2, providing some basis for this. Finally, the relationships for the variation of the absorption and emission cross-sections with temperature in both  and  were investigated during the course of the data analysis and were found to provide fits to the experimental data within ± 3%.
3.3. Analysis of single tone data
Single tone 1040 and 1064 nm fiber amplifiers were modeled using the temperature dependent absorption and emission cross-sections in  as the 20°C baseline and the relationships given in section 3.2 or  to increment the cross-sections with temperature. The amount of pump power delivered to the fiber was determined by comparing the measured output power at 20°C to the model. In Fig. 7 , from the model for both the 1040 and 1064 nm single tone fiber amplifiers, as the temperature of the fiber core increased and the cross-sections incremented, the efficiency (output power) was found to decrease and the unabsorbed pump was found to increase. Also, in Fig. 7 (Figure 9 for the two tone case) are the 20 to 80°C temperature increments corresponding to references 13 and 16. It must be noted that because the temperature of the core of the fiber is not known, i.e., the temperature of the external environment may be less than that of the core of the gain fiber due to quantum defect and other sources of heating, no specific temperatures are indicated on the horizontal axes in either Figs. 7 or 9. For the single tone case, it was found that the ratio of the output powers 1064 nm/976 nm and 1040 nm/976 nm depended linearly on the temperature of the fiber core and therefore linearly on the values of the 1064 nm, (or 1040 nm) and 976 nm absorption (or emission) cross-sections. Trends associated with the 1040 and 1064 nm single tone fiber amplifiers can be attributed to a simultaneous decrease in both the absorption and emission cross-sections at 976 nm as well as an increase in the absorption cross-section for the signal. In addition, the more rapid decrease in the efficiency (or output power) of the 1040 nm amplifier with temperature relative to the 1064 nm amplifier can be explained by the fact that the 1040 nm absorption cross-section increases faster with temperature relative to the 1064 nm absorption cross-section.
The ability of the model described above to predict the experimental results was evaluated next. Each experimental data point was fit by determining the set of cross-sections (linked together by Eqs. (6-11) corresponding to the correct 1064 nm and 976 nm (or 1040 nm and 976 nm) output powers, see Fig. 7. Trends predicted by the model for the 1064 nm amplifier agree fairly well with the experiment i.e., the slope of output power versus effective temperature of the core derived from the model agrees fairly well with the data. Model predictions for the 1040 nm amplifier, on the other hand, weren't as good for the lower environmental temperatures but seem to agree (have the same slope) for higher temperatures. This can be explained by either: 1. power loss from another process at the lower temperatures, 2. a nonlinear dependence of the 1040 nm cross-sections on core temperature, 3. incorrect baseline cross-sections, 4. a greater rate of change of the 1040 nm cross-sectional deltas with core temperature than is indicated in , 5. incorrect constants representing other propagation losses, and/or 6. experimental error. For the 1064 nm fiber amplifier, the 1064 nm absorption cross-sectional delta required to span the environmental temperature range from 20 to 80°C was found to be 2.07 × 10−27 m2. For the 1040 nm fiber amplifier, the 1040 nm absorption cross-sectional delta required to span the same range was found to be 8.3 × 10−27 m2. For both the 1040 and the 1064 nm single tone amplifiers, the range of cross-sections required to span the temperature range of 20 to 80°C (green in Fig. 8 ) was a little bit larger than indicated in  (red in Fig. 7) but quite a bit smaller than that indicated in  (blue in Fig. 7). Finally, it was found that the cross-sections corresponding to an environmental temperature of 20°C for the 1040 nm amplifier data were at a lower effective temperature than those for the 1064 nm amplifier. This is most likely due to either experimental error or an incorrect baseline starting point for the cross-sections.
The temperature dependence of the absorption and emission cross-sections can also explain the trends shown in Fig. 3. The trend at shorter lengths of gain fiber where the 1040 nm single tone fiber amplifier is more efficient than the 1064 nm single tone amplifier is due to a greater gain per unit length, , for the 1040 relative to the 1064 nm amplifier. The cross-over in efficiencies of the 1040 and 1064 nm amplifiers occurs because the absorption cross-section at 1040 nm is greater than that at 1064 nm. Also, because the absorption cross-section for the 1040 nm increases at a faster rate with temperature than the 1064 nm absorption cross-section, the cross-over point for the efficiencies occurs at a shorter length of gain fiber as the temperature increases.
Using the model described above and cross-sections fit to the data for environmental temperatures of 20, 55, and 80°C, profiles of the signal and pump as a function of fiber length can be derived. Upon examination of Fig. 8, it is apparent that the model predicts the cross-over point for both the signal and the unused pump to move to a shorter length of gain fiber as the temperature of the external environment and the fiber core increases. This prediction is in agreement with the trend displayed in Fig. 3a-f.
3.4. Analysis of two tone data
Five two tone fiber amplifiers having 1064 nm/1040 nm seed power ratios between 0.11 and 0.88 were measured and modeled. For each amplifier considered, the model was run by incrementing the cross-sections and thereby the effective core temperature. From the model, as the temperature of the fiber core increased, the absorption cross-section of 1040 nm increased more rapidly with temperature than did the absorption cross-section of 1064 nm, roughly by a factor of four. As a result, power transfer between the 1040 and 1064 nm occurred in a shorter length of gain fiber at higher temperatures resulting in less 1040 nm and more 1064 nm in the fiber output. Therefore, the efficiency of 1064 nm two tone amplifiers increased and the percentage of residual 1040 nm decreased as the environmental and core temperature increased.
The experimental data was fit by determining the value of the effective core temperature or cross-sections that provided the proper ratios of 1064, 1040, and 976 nm. The values of the cross-sections were determined by using Eqs. (6-11) from  in conjunction with the 20°C starting point in . The relationships derived from  were also investigated with differences of ± 3% being seen. Upon examination of Fig. 9, it is apparent the experimental data agreed fairly well with the model. A significant amount of heating was found to occur in the fiber core, i.e., the set of effective cross-sections required to fit the data were associated with a higher effective temperature with a greater amount of heating seen in amplifiers having smaller 1064 nm / 1040 nm seed ratios due to increased heat dissipation. This is illustrated by the red arrow in Fig. 10 which shows the increase in effective core temperature as the 1064 nm / 1040 nm seed ratio decreases. The level of heating observed in two tone amplifiers was not observed in single tone amplifiers. It is also apparent that the cross-sectional deltas for the two tone amplifier with the largest 1064 nm / 1040 nm seed ratio and the least amount of heating in the core are more in line with the findings in  versus  as was the case for single tone amplifiers, i.e., the change in the 1064 nm cross-section required to span the 20 to 80°C environmental temperature range was 1.45 × 10−27 m2.
It is also instructive to examine the power profiles of the 1040 and 1064 nm along the gain fiber as the environmental temperature of the gain fiber is changed. Shown in Fig. 10 are the intensity profiles for a two tone fiber amplifier seeded with 156 mW of 1064 nm and 1.4 W of 1040 nm for the 20 and 80°C temperatures. Upon examination of Fig. 10, it is apparent that since the absorption cross-section of 1040 nm increases more rapidly with temperature than does the absorption cross-section of 1064 nm, power transfer between the 1040 and 1064 nm occurs in a shorter length of gain fiber at higher temperatures resulting in less 1040 nm and more 1064 nm in the fiber output. As a result, the efficiency of 1064 nm two tone amplifiers is seen to increase as the environmental and core temperature increases. The effective length for the 1064 nm also increases with temperature leading to a decrease in the SBS threshold.
Significant thermal effects have been seen in both single and two tone fiber amplifiers with those observed in two tone amplifiers being more dramatic. As the environmental temperature of the gain fiber is increased, the efficiency of 1064 nm single tone amplifiers is seen to decrease and the efficiency of 1064 nm two tone amplifiers is seen to increase. This can be explained by changes in the absorption and the emission cross-sections with temperature for the 976, 1040, and 1064 nm wavelengths. Heating of the fiber core appears to be much more significant in two tone fiber amplifiers than in single tone fiber amplifiers. It appears from an examination of Fig. 9 that the core of the gain fiber may reach temperatures approaching 160°C when external heating of the gain fiber of a two tone amplifier is combined with heating of the fiber core by various sources. The origin of this effect is not understood at this time and will be investigated further in future experiments.
Although increasing the temperature of the gain fiber can be used as a design tool to increase two tone amplifier efficiency, shifts of the intermediate pump wavelength, i.e., the 1040 nm, will have a similar effect. Even though an intermediate pump wavelength of 1040 nm has been found to work well over a range of operating conditions, it is likely that other wavelengths would be better in some specific cases.
Finally, although a model utilizing fiber non-specific cross-sectional information can be used to predict trends associated with a particular gain fiber, to reduce the discrepancies and enable predictions with greater accuracy, knowledge of cross-sectional data specific to the particular gain fiber being studied is necessary. In order to develop a model that is precise enough to enable engineering of two tone fiber amplifiers, an accurate accounting of all dissipated heat must be accomplished. In addition, absorption and emission cross-sections, measured across the expected temperature range of the core for the specific fiber, must be incorporated into the model. Also, other propagation losses of the fiber not described by ytterbium absorption need to be accurately known.
Thermal effects can have a significant impact on both the output power of single and two tone fiber amplifiers and the composition of the output of two tone fiber amplifiers. Accurate design of such amplifiers requires a model that accurately accounts for heat deposition in addition to utilizing parameters (cross-sections and constants representing other propagation losses) specific to the particular gain fiber and temperature. Also, temperature of the gain fiber and/or wavelength of the intermediate pump wavelength can be utilized to optimize a two tone fiber amplifier system through shifting of both the absorption/emission cross-sections. Finally, while our experimental work shows the effect of temperature for a system with specific intermediate pump and signal wavelengths, it falls short of a full optimization for a two tone amplifier.
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