1 Introduction

For many years, doping of glasses with cerium (Ce) has found numerous applications in the development of optical components. Incorporated in the core of optical fibers, Ce sensitizes the material to UV pulses thus enabling the inscription of fiber Bragg gratings (FBG) in passive or active fibers without previous hydrogen treatment or germanium (Ge) co-doping [1]. The strong absorption of Ce in the UV wavelength range was also utilized in protective filters [2], e.g. for the optics in high power lasers with frequency conversion, however, the photoionization of Ce³⁺ [3] may cause electron-related color centers that are to be bleached by visible light between the laser pulses to maintain the filter performance [2]. Furthermore, Ce doping has been successfully applied to improve the resistance of optical glasses to UV or higher energetic radiation [4]. Hence, it was supposed that Ce co-doping could also help to reduce the photodarkening (PD) effect in Yb fibers. PD means the pump-induced evolution of excess loss with equilibrium values depending on pump power and dopant concentrations [5, 6]. Actually, Yb/Ce/Al-doped fibers with improved PD resistivity and degradation-resistant lasing at 980 nm were demonstrated [7, 8]. Different favorable phenomena like self-bleaching and enhanced photo-bleaching of photodarkened Yb/Ce fibers were also observed [9, 10]. A disadvantage of Ce co-doping is the induced rise of refractive index; countermeasures like fluorine (F) co-doping [11] or an index pedestal around the core [12] are needed to keep the single-mode beam quality in laser applications. Thus, Ce addition should be evaluated in all its bearings and compared to other methods of PD mitigation like combined phosphorus (P) and Al co-doping [13].

The PD-reducing impact of Ce ions is attributed to their different valence states that allow trapping of holes as well as electrons. Since the PD excess loss with its long tail to the NIR range is assumed to be caused mainly by hole-related color centers [14–16], Ce³⁺ ions with their capability to trap holes are most interesting to avoid this degradation. However, the details of this process perpetually inhibiting the evolution of PD loss, the degree of Ce³⁺ involvement in this process and the nature of electron traps are still open questions.

The optical properties of Ce co-doped silica were studied in detail in [17]. A predominant part of Ce in Al co-doped silica fibers was found to be incorporated as trivalent ions also under the common oxidizing conditions of preparation (only some percent exist as Ce⁴⁺). Therefore, this composition is a good candidate to avoid the hole-related PD color centers. Yb/Ce/Al-doped fibers fabricated by the Modified Chemical Vapor Deposition (MCVD) [18] or by the REPUSIL technology [19] were already applied successfully for high-power fiber lasers; output powers up to 4 kW were reported [17].

Low PD loss is indispensable for the long-term power stability and efficiency of fiber lasers and amplifiers. Recently, the thermal load caused by the absorption of PD color centers [20] at pump and laser wavelength was identified as an additional issue. Mode instabilities, which can impair the beam quality of fiber lasers and amplifiers during high power operation, were found to be mainly caused by thermal effects [21], and PD is suspected to play a substantial role in this process, first of all in the degradation of the mode instability threshold. For fibers with strongly reduced PD loss evolution, the long-term stability of laser efficiency, fiber temperature as well as beam quality would be expected. However, a distinct heating of a Ce co-doped fiber core under pump irradiation was found from the wavelength shift of an inscribed FBG although no PD loss appeared [22].

In this work, we investigated the PD behavior of Yb/Ce/Al-doped silica fibers in dependence on the concentrations of dopants to achieve a better insight into the process of PD mitigation due to Ce co-doping. Typical features of temporal loss measurements like loss jumps and self-bleaching were understood from comparison with Ce-free samples. The involvement of Ce³⁺ ions and the reduction of their concentration only during pumping were proved and evaluated from changes in the transient UV absorption spectra (see [23] for explanation). The fast regeneration of Ce³⁺ even during pumping was concluded from our experiments and seems to be essential for the perpetual inhibition of PD. Detailed temperature investigations were performed on the pumped fibers to review the indications of [22] and to suggest an optimal Ce/Yb ratio concerning moderate refractive index change as well as low PD and thermal issues in the application of these laser fibers.

2 Experimental

The preform samples investigated in this work were prepared by MCVD with solution doping and collapsing in an O₂/Cl₂ atmosphere [18]. For characterization purposes, fiber samples with cladding diameter of 125 µm and core diameter of about 11 µm were drawn from these preforms. The core compositions characterized by electron probe microanalysis (EPMA) are summarized in Table 1 for the investigated series. The conversion of Ce content to molecular concentration of Ce₂O₃ neglects the fact that a small fraction (< 5%) is incorporated as tetravalent ions in these Al co-doped samples [17]. Few additional samples, e.g. without Yb, used for comparison purposes are specified in the text.

Table 1. Core composition of the samples investigated in this paper. The samples of series A were additionally co-doped with 0.5 mol% P₂O₅ to improve the solubility of rare earth ions and to reduce photodarkening.

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The temporal development of PD loss during core or cladding pumping with 976 nm or 915 nm, respectively, was determined for a probe wavelength of 633 nm at short fibers (1 to 2 cm) using the measurement method described in earlier publications [5, 24, 25]. In these experiments, the fibers are cooled in a water bath to keep temperature increase below 10 K [26]. The pump-induced Yb inversion was estimated in each case from the launched pump power and the core material properties of our samples by means of commercial software [27].

Absorption spectra in the UV wavelength range were measured on thin preform slices (0.1 to 0.2 mm) with a low-power white light source (combined halogen/deuterium lamp) and a suitable optical spectrum analyzer (Spectro 320D from Instrument Systems) in a set-up described in [23]; the curves measured before, during and after pumping with 902 nm were compared to derive the spectra of transient loss, which only appear when Yb ions are excited.

Fiber temperature was measured in the same set-up as PD characterization with a FLIR Systems Therma CAM P25. For this purpose, the short un-coated fibers under test were held in air (without forced cooling) during core pumping with 976 nm (launched power 450 mW).

3 Results

3.1 Typical features of excess loss measurements on Yb/Ce/Al-doped silica fibers

Figure 1(a) shows the kinetics of excess loss measured during and after cladding pumping (915 nm, 15.6 W, Yb inversion 0.69) of an Yb/Al fiber co-doped with Ce. Typical features observed for core as well as cladding pumping of Ce co-doped fibers are: an instantaneous rise of core loss at start of pumping (Fig. 1(b)), the evolution of weak PD loss and the immediate loss reduction just at the end of pumping (Fig. 1(c)) followed by a long-time decrease of pump-induced PD loss. The loss jumps at pump-on/-off and the self-bleaching behavior after switching-off the pump do not appear in fibers without Ce.

 

Fig. 1 Typical PD curve of an Yb/Ce/Al fiber with additional loss observed only during pumping (about 10 dB/m) and partial self-bleaching of PD color centers after pump switched-off, (a) complete measurement, (b) time axis stretched around start of pump and (c) around end of pump.

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In the example of Fig. 1 (fiber with 0.45 mol% Yb₂O₃ and a ratio of Ce/Yb = 0.62), the PD loss measured at 633 nm is rising to about 30 dB/m (loss jump under pump subtracted), which is, however, well below 10% of the PD equilibrium loss in a comparable Ce-free fiber under these experimental conditions. More detailed results of PD loss as a function of Ce concentration are shown in section 3.2.

To understand the reason of loss jumps at pump-on/off, further experiments were performed at fiber types with dopant ratio Ce/Yb ≈1.7, which are best suited to analyze the phenomenon because the development of PD color centers is almost completely inhibited. The remaining loss jumps clearly depend on Yb concentration, as can be seen from Fig. 2(a). It is to be mentioned that roughly 5 dB/m of residual loss are observed after pump switched-off in case of high dopant concentrations.

 

Fig. 2 (a) Excess loss in fibers with ion ratio Ce/Yb ≈1.7 measured during and after core pumping with 976 nm, 200 mW. (b) Loss jump at pump-on varying with probe wavelength, measured for core pumping with 976 nm, 200 mW and (c) varying with density of excited Yb ions, measured for cladding pumping with 915 nm (probe wavelength 633 nm).

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In Fig. 2(b), the loss jump under pump is depicted as a function of probe wavelength for a fiber without PD loss evolution. The results can be fitted by an exponential decay in a first approximation suggesting that loss further grows toward the UV range. Figure 2(c) reveals the nearly linear increase of this loss jump with rising density of Yb excitation (Yb* means the product of Yb concentration and inversion adjusted by the pump power in fiber cladding).

The analysis of this phenomenon as a function of wavelength, Yb concentration and inversion indicates that the loss jumps at pump-on/off can be understood as the long tail of the transient absorption spectra of NIR-pumped Yb fibers as described in [23]. The spectral behavior of this transient loss was found to strongly depend on the core composition [23]. It is obviously higher in Ce co-doped samples (compare section 3.3) and thus also measurable in the visible range (Fig. 2(b)). In contrast, no measurable value is observed in Ce-free Yb fibers at our probe wavelength of 633 nm.

In the following section, the contribution of these loss jumps at pump-on/off in Ce co-doped fibers measurable at the probe wavelength of 633 nm is neglected and the real PD equilibrium loss just after pump-off is discussed in more detail.

The phenomenon of partial self-bleaching of PD loss after pump power switching-off is discussed in connection with other results in section 4.

3.2 Photodarkening loss at 633 nm as a function of Ce concentration

Figure 3(a) shows the PD curves measured on the fibers of series A. Equal density of excited Yb ions (Yb*) was achieved by appropriate choice of pump power to respect the slightly different Yb concentrations. The fibers with Ce co-doping show much weaker PD loss evolution. The PD parameters were determined from the curves in Fig. 3(a) by a fitting procedure with the stretched exponential function as described in [28]. It was found that the time of PD evolution is less influenced by Ce co-doping; the PD rate constants and stretching parameters are very similar for these fibers. The results for PD loss in equilibrium are depicted in Fig. 3(b) as a function of Ce concentration. To demonstrate the influence of higher Yb concentration, the results for series B supplemented by two fibers of series C are included in this graph. From the semi-logarithmic plot, one can deduce a nearly exponential decrease of PD loss down to 10% of the initial values; this reduction is achieved with Ce concentrations according to a dopant ratio Ce/Yb ≈0.5 in both fiber series A and B.

 

Fig. 3 (a) PD kinetics of the Yb fibers of series A measured at 633 nm during (and after) cladding pumping with 915 nm, (b) loss in PD equilibrium (without transient loss) versus Ce concentration for the series A and B (including fibers #C4 and #C5). The density of excited Yb ions was adjusted to Yb* = 1.1 10²⁶ m⁻³ in all these measurements.

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The solid lines in Fig. 3(b) were calculated in analogy to the model of Stroud [29, 30] that describes the color center formation in Ce-containing glasses by X-ray or gamma irradiation (each with same rates and doses in a series of samples). The induced absorption change α is attributed to centers of trapped holes α_h and trapped electrons α_e which contribute to the measured absorption at defined wavelengths as described by Eq. (1) in case of negligible Ce⁴⁺ concentration. Here, Ce³⁺ means the concentration of trivalent Ce ions in units of m⁻³. The volume V contains the defect that releases a pair of charge carriers under irradiation, possible traps and one Ce³⁺ ion able to capture the hole thus inhibiting the formation of a color center absorbing at the analyzed wavelengths.

For ion ratios of Ce/Yb > 1 (Ce concentrations higher than 2⋅10²⁶ m⁻³ in Fig. 3(b)), the PD loss saturates to values of some dB/m possibly caused by trapped electrons (as assumed in [29, 30]) or other pump-induced defects.

Further measurements on fibers with higher Al concentrations than in the samples of series A and B have shown that PD loss can additionally be reduced by increased Al content similar to results already known from earlier investigations on Ce-free fibers [6].

3.3 UV absorption spectra during NIR pumping of samples without and with Ce co-doping

In [23], a transient absorption under NIR pumping was reported for Yb-doped fibers and preform samples. Figure 4 shows the absorption spectra of an Yb/Al-doped preform before (thin black line) and during pumping (thick black line). Obviously, the UV absorption edge connected with the dopants in the silica core is partly shifted by the energy of Yb³⁺ excitation (1.25 eV) for those complexes of the glass matrix containing an excited Yb³⁺ ion (termed as PD complexes). The observed loss arising immediately with start of pumping but completely vanishing at pump-off reflects the absorption of these glass complexes (in an excited state) and was interpreted as the first step of the PD process [23]. In this interstage, displacements of charge carriers and temperature increase may already occur (see section 3.4 and discussion). Each PD complex has the potential to generate a PD color center during further pumping; however, relaxation to the de-excited state has a much higher probability. This conclusion is drawn from the large time constants (minutes to hours or longer) of PD loss evolution in comparison to the lifetime of Yb³⁺ excitation.

 

Fig. 4 Typical absorption spectra in the UV range measured on Yb/Al- and Yb/Ce/Al-doped preform slices before (or after) and during pumping.

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It is to be mentioned that no changes in the UV absorption spectra of Yb-free Ce/Al samples were observed at all under irradiation with the pump wavelengths (samples with Ce concentrations up to 0.53 mol% were investigated). These findings are consistent with the negligible absorption of Ce ions in the NIR region.

For samples with Yb as well as Ce co-doping, the UV absorption spectrum (thin orange line in Fig. 4) can be understood as an additive superposition of the Ce- and Yb/Al-related absorption features, and the peak centered at 300 nm is characteristic for Ce³⁺ ions in Al-doped silica [17]. During pumping, the absorption is enlarged (thick orange line) due to the transient loss in Yb-related complexes but, at second glance, a lower increase of absorption around 300 nm is noticed. This fact becomes clearer if one compares the derived transient loss spectra (difference of absorption spectra during and before pumping [23]), which are depicted in Fig. 5(a) for the preform samples of series B. Compared to the Ce-free sample, the transient losses are generally higher with Ce co-doping, and the depression around 300 nm becomes stronger with increasing Ce concentration. The inset of Fig. 5(a) suggests a distinct correlation between the depression Δα (difference of minimal transient loss at 300 nm and estimated maximum assumed in case without depression) and the Ce concentration.

 

Fig. 5 Transient loss spectra during pumping with 902 nm (a) measured on preform slices of series B with fixed Yb concentration (Yb inversion 0.22), inset: depression of transient loss at 300 nm vs. Ce concentration, (b) measured on preform sample #B4 for different pump powers, inset: depression of transient loss at 300 nm vs. Yb inversion (maximal 0.28).

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A similar depression of transient loss at 300 nm was found for varying the pump power and with it the Yb inversion in the sample #B4 (Fig. 5(b)). A nearly linear change of Δα versus Yb inversion can be recognized for the applied pump powers. All these results are discussed in section 4 as a reduction of Ce³⁺ content in consequence of the interaction with excited Yb³⁺ ions and the inhibition of PD.

It should be emphasized once more that all transient absorption features vanish immediately with pump power switching-off. No change in the UV absorption spectra remains, neither in case of Ce co-doping.

3.4 Fiber temperature during pumping

The heat sources during pumping are mainly located in the fiber core. With a thermal camera, only the fiber surface temperature can be determined, however, the difference to core temperature is expected to be lower than 3 K in our conventional fibers [31].

In Yb-free fibers with Ce concentrations of up to 0.53 mol%, no change of fiber temperature during core irradiation with 976 nm (450 mW) was observed. This is consistent with the negligible absorption of these fibers in the NIR wavelength region.

In Yb-doped fibers, thermal load is expected to be caused by the pump absorption process of Yb ions (quantum defect between the energies of pump and emitted photons), the core background loss, the PD process itself (loss of pump energy in generation and annihilation of color centers) and the absorption tail of PD-induced color centers at pump wavelength. The first three heat sources may arise just at activation of pump power whereas heating by color center absorption develops with progress of PD loss.

In the first centimeter of the fibers investigated in our set-up, maximal 20 mW of pump power are absorbed up to saturation of Yb inversion [27] independent of further boosting of pump power. Assuming a quantum defect of about 10%, this means a thermal load of maximal 2 mW/cm (or 0.2 W/m) in the short fibers. Thus, very low heating by the quantum defect is expected in our experiments. The temperature measurement on a PD-free (P co-doped) Yb fiber with inscribed FBG confirm this assumption; a temperature increase of only 2 K was found from the shift of the FBG reflection wavelength [22].

Other sources of thermal load P_abs/L can be estimated from Eq. (2), derived from Lambert-Beer’s law, with the launched power P₀, the absorption coefficient α (in dB/m) and the fiber length L = 0.01 m.

Figure 6(a) shows the temporal development of temperature change for the fibers of series B. Heating by the PD process itself cannot be quantified exactly but appears already in the immediate rise of temperature at start of pumping, additionally to quantum defect heating. The temperature kinetics during further pumping resembles the form of PD loss evolution measured simultaneously (not shown here). In these experiments, the fibers were hold in air (not cooled by water as usually in PD measurements) but the influence on the PD parameters is weak in this temperature range [25].

 

Fig. 6 Change of fiber temperature during core pumping with 976 nm (450 mW) measured on the fibers of series B: (a) versus time of pumping, (b) versus temporally increasing PD loss α(633 nm), thin solid lines are linear fits to the experimental results, black dashed line was calculated by [31] from PD color center absorption α(976nm) with a conversion factor α(633nm)/α(976nm) = 16.

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In Fig. 6(b), the immediate rise of temperature at start of pumping (still without PD) can also be recognized. Afterwards, a linear relationship between temperature change and evolving PD loss is found similar to the results of [20]. The black dashed line was calculated from PD loss at 633 nm using Eq. (2) and the results of [31]; a good accordance with the measured values of the Ce-free fiber is achieved for an assumed PD loss conversion factor of 16 between probe and pump wavelength.

These results clearly reverify that PD loss is remarkably reduced in Ce co-doped Yb/Al silica fibers but, surprisingly, the fiber temperature change is not diminishing to the same extent. Nevertheless, the linear correlation between temperature change and PD loss is conserved if the degradation is already strongly mitigated (e.g. by 0.13 and 0.22 mol% Ce₂O₃) resulting in steeper slopes of the blue and green lines.

In Fig. 7, the temperature investigations on all fiber series are summarized. The maximum change of temperature during pumping is depicted as a function of Ce concentration. This temperature is reached in fibers without PD promptly after start of pumping, whereas fibers with PD need some time to evolve to the equilibrium state. Measured values are designated by full symbols. The temperature changes are generally higher in fibers with larger Yb concentration (compare series A, B and D) and also for lowered Al content (compare series C and B). To illustrate the effect expected only from the thermal load caused by PD color centers, temperature changes were estimated by [31] from loss values in PD equilibrium (measured at 633 nm and converted to pump wavelength by the factor α(633nm)/α(976nm) = 16) and depicted in Fig. 7 with open symbols. With increasing Ce content, the fiber temperature should decrease remarkably in parallel to PD mitigation, however, only a marginal reduction of temperature is found in the experiments. Really fatal is the increase of temperature in fibers which hardly develop PD loss due to their Ce content of at least 0.38 mol%. Extreme temperature changes of more than 200 K were observed in the fibers with high concentrations of both, Yb and Ce ions.

 

Fig. 7 Maximum change of fiber temperature during pumping with 976 nm (450 mW) versus Ce concentration for the fibers of series A, B, C and D (different concentrations of Yb and co-dopants, see Table 1). Full symbols: measurements, open symbols: values estimated by [31] from PD loss at pump wavelength.

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4 Discussions

In our fibers with concentration ratios of Ce/Yb > 1 (Ce concentration > 2 10²⁶ m⁻³ in Fig. 3(b)), the PD loss measured at 633 nm is reduced to about 1% in comparison to Ce-free fibers. For a ratio of Ce/Yb < 1, a low density of color centers is still developing with PD rates similar to those of Ce-free fibers (Fig. 3(a)). This allows for the assumption that the actual PD process takes place on fewer PD complexes and that the distance between Yb and Ce ions may decide about occurrence or inhibition of color center formation.

As proved in earlier publications, the PD color centers evaluated in the visible range and responsible for laser degradation in NIR are mainly caused by trapped holes [14–16]. In our Al co-doped samples, Ce ions are embedded almost all as Ce³⁺ with the typical absorption maximum near 300 nm [17]. Each Ce³⁺ ion has the potential to trap a hole released by a precursor defect in the vicinity of an excited Yb³⁺ ion thereby inhibiting the generation of a hole-related color center. This results in a Ce⁴⁺ or rather a Ce³⁺⁺ ion on a Ce³⁺ site [29]. For both, the absorption maximum is shifted towards 200 nm [35] what cannot be quantitatively evaluated from our measurements. However, the reduction of Ce³⁺ concentration during pumping is confirmed by the characteristic decrease in the transient loss spectra around 300 nm. For constant Yb concentration and inversion, this decrease is clearly stronger with higher Ce concentration (Fig. 5(a)), i.e. more Ce³⁺ ions are involved and more color centers can be inhibited (Fig. 3(a)). For constant Ce concentration, the decrease is also stronger with higher Yb inversion (Fig. 5(b)), because more holes are released and more Ce³⁺ ions are in use to capture them. Moreover, the time-averaged reduction of Ce³⁺ concentration during pumping can be quantified from the estimated absorption decrease (maximal 3500 dB/m = 800 m⁻¹ in Fig. 5) and the absorption cross section of Ce³⁺ at 300 nm of 2.1 10⁻²² m² (derived from the results in [17]). This way, a Ce³⁺ reduction of maximal 3.8 10²⁴ m⁻³ was determined for the samples of series B corresponding to 4% of Ce content and 7% compared to the Yb excitation density of Yb* = 5.2 10²⁵ m⁻³ (sample #B4 with Yb inversion 0.28). The low fraction of Ce³⁺ ions involved in the interaction process at the same time is surprising because PD loss is efficiently mitigated also in fiber #B4 with ratio Ce/Yb = 0.52. (Even for the higher Yb excitation in the fiber measurement, Fig. 3(b), not more than 10% reduction of Ce³⁺ concentration is expected.)

These results facilitate the hypothesis that each Ce³⁺ ion can interact with different PD complexes to capture a released hole and that the recombination of Ce³⁺⁺ to Ce³⁺ takes place very fast. (Otherwise, all Ce³⁺ ions would be involved and converted to Ce³⁺⁺ at some point of time followed by common PD loss evolution.) This conclusion is consistent with the exponential decay of PD loss for low ratios of Ce/Yb (Fig. 3(b)) and the immediate recovery of the UV absorption spectra after pump switched-off. The operating radius of the Ce³⁺ ion was estimated from Fig. 3(b) by the model of Stroud [30] to be about 2 nm. In the clusters of rare-earth-doped silica [36, 37], many potential PD complexes (containing one Yb³⁺ ion each) with minimum distance of about 0.5 nm [38] may be located in the corresponding glass volume. The degree of Yb³⁺ clustering was found to be nearly unaffected by the presence of Ce ions in aluminosilicate fiber glass preforms [39].

Summarizing the results of our investigations, the following conception of PD inhibition by Ce³⁺ was developed and is depicted schematically in Fig. 8: an Yb³⁺ ion excited by NIR pumping may transmit its energy to a precursor defect which releases a pair of charge carriers.

 

Fig. 8 Conception of PD inhibition in Yb/Al fibers by Ce³⁺ co-doping: the course of processes is to be read from left to right (* means the excitation of the Yb³⁺ ion by NIR-pumping, PD-CC⁺ terms a hole-related PD color center).

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With further application of energy (by pump photons, excited Yb ions and/or phonons), the hole has a certain (low) probability to be shifted and trapped in another defect nearby resulting in a common PD color center, which can also be bleached optically by the pump radiation itself (equilibrium process [5], denoted by the dashed double arrow). The actual mechanism is still an open question; several models have been proposed (e.g. [14, 40, 41]) but cannot be evaluated within the framework of this paper. With a Ce³⁺ ion in adequate vicinity, however, the hole is rather attracted to this ion resulting in supposed conversion to Ce³⁺⁺ with UV-shifted absorption and a decrease of Ce³⁺ absorption at 300 nm. The electron is probably not trapped by Yb³⁺ because the typical structure of Yb²⁺ absorption was not observed in the transient absorption spectra during pumping. Moreover, no Ce³⁺ fluorescence (around 360 nm in this fiber type [17]) was measurable during or after NIR pumping. This probably means that Ce³⁺ is not ionized as known to be caused by UV or higher energy irradiation [2–4] but the electron remains localized in next vicinity. This would favor the fast recombination with Ce³⁺⁺ and enable the restored Ce³⁺ ion to inhibit the color center generation again and again for all neighbored PD complexes.

Possibly arising color centers have a good chance to be bleached during pumping or later because a self-bleaching phenomenon (Fig. 1(a)) is observed in all our Ce co-doped fibers after pump power switched-off. The attraction of Ce³⁺ for holes seems to be strong enough to even extract them from PD color centers (light-blue dashed arrow in Fig. 8). Without Ce co-doping, the PD color centers are known to be very stable at room temperature [24]. The longtime behavior of the self-bleaching process in the presence of Ce³⁺ could be understood by different distances of PD color centers to Ce³⁺ ions.

In our experiments, the absorption of PD color centers at the pump wavelength was found to be the dominating heat source in Ce-free fibers (Figs. 6(b) and 7). However, the PD process itself significantly contributes to the thermal load. This fact becomes visible already at start of pumping by the sharp increase of temperature (Fig. 6) higher than expected from only quantum defect heating in our experiments.

Ce co-doping in Yb/Al fibers was shown to be very helpful to avoid PD and should also reduce the resultant thermal load. Unfortunately, the measurements of section 3.4 have shown that the fiber temperature did not decrease as expected in parallel to the vanishing of PD loss but is rather constant in the fibers of series A and B under same pump conditions. One explanation could be that the process of PD inhibition by Ce³⁺ ions consumes pump energy, too, resulting in an instantaneous rise of temperature (Fig. 6). Moreover, the actual formation of a PD color center is a rather seldom event, whereas the hole trapping by Ce³⁺ and radiation-less recombination can take place frequently. This consideration could also explain the extreme heating of fibers with high Ce content and inhibited PD. Another reason could be found in the transient absorption itself which is enhanced by co-doping with Ce (Fig. 5(a)). From its exponential wavelength dependence around 633 nm (Fig. 2(a)), a relevant absorption at the pump wavelength can be speculated, especially for the fibers with highest Yb and Ce concentrations that have shown extreme temperature increase. Furthermore, it cannot be ruled out that new defect types with enhanced absorption at the pump wavelength are generated during the described interaction process. The residual loss at 633 nm after pumping of “PD-free” fibers (Figs. 1(b) and 3(b)) supports this assumption.

5 Summary

Our investigations confirm the mitigation of photodarkening in Yb/Al fibers by co-doping with Ce and give a deeper insight into this process. The assumption of hole capturing by Ce³⁺ ions instead of the formation of harmful PD color centers was confirmed by the reduction of Ce³⁺ concentration during pumping, visible in the spectra of transient absorption in the UV wavelength range. The fast recombination of temporary existing Ce³⁺⁺ to the original Ce³⁺ state was concluded from the exponential decrease of PD loss with Ce concentration, the low degree of Ce³⁺ ions involved in the process at the same time and the immediate recovery of UV spectra after switching-off the pump power. This fast recovery of Ce³⁺ ions is imperative to maintain the PD-reducing capability of Ce co-doped Yb/Al fibers even during prolonged laser operation.

The absorption of PD color centers at the pump wavelength was identified as the dominating heat source in the Yb/Al laser fibers under test. It causes a temporally increasing temperature change in the fiber; the linear correlation with measured PD loss was confirmed. Besides, the PD process itself causes a significant contribution to the thermal load.

By Ce co-doping, PD loss in Yb/Al fibers can be mitigated to a large extent, however, the expected reduction of thermal load is not attainable with this core composition. The observed fiber temperature changes cannot be explained by the original absorption of the Ce ions themselves at the pump wavelength but must be attributed to the interaction with excited Yb ions. This assumption is also supported by the extreme temperature changes of more than 200 K found in fibers with high Yb and Ce concentrations (Yb₂O₃, Ce₂O₃ > 0.4 mol%).

6 Conclusions

A careful optimization of Ce content is recommended if this co-dopant is used to mitigate photodarkening in Yb/Al fibers. On the one hand, Ce concentration should be kept as low as possible to minimize the additional rise of refractive index. On the other hand, PD reduction succeeds the better the more Ce is in the fiber core, however, thermal issues arise from the interaction with excited Yb ions. A Ce/Yb ratio between 0.5 and 0.7 is suggested to be optimal for fibers with Yb concentrations of up to 0.4 mol%. Fibers with higher Yb and Ce concentrations seem to be less important for practical use in laser applications due to their strong thermal load.

In high-power applications, PD color centers are, in addition to quantum defect, a serious reason for the heating-up of Yb fibers that can compromise the efficiency of output power, the beam quality and the stability of fiber coating. Ce co-doping seems to bring less advantage to reduce the thermal load despite the potential of complete inhibition of PD. If any such contribution to thermal load should be avoided, e.g. to enhance the threshold of mode instabilities in high-power fiber lasers and amplifiers [21], other solutions to reduce the PD effect should be taken into account.

In further experiments, the real temperature and PD evolution in high-power applications of optimized Yb/Ce/Al fibers should be investigated in a suitable set-up and be compared to Ce-free fiber lasers or amplifiers. Especially, it should be verified, if the recombination process of Ce³⁺⁺ to Ce³⁺ is fast enough for the more frequent Yb³⁺ excitation and hole release in case of strong pump rates; otherwise, the PD loss could reappear with enhancing the pump power.

Funding

German Federal Ministry of Education and Research (BMBF), contract 13N12712 (ReMiLas)

German Federal Ministry of Education and Research (BMBF), contract 13N13683 (SurLas)