Abstract

A novel and simple solution doping technique is used to explore the refractive index behavior of Al,P-doped SiO2 in the vicinity of the Al:P-ratio of 1:1 at low doping concentrations (0.4 up to 2.0 mol% Al2O3 and/or P2O5). It is found that even if Al:P = 1:1 is matched precisely, an index increase is observed. This is in contradiction to previous findings in the literature and the already sophisticated models need to be refined in this region. In the proposed model, an incomplete formation of AlPO4 is assumed and solves the contradiction. Furthermore, the presented model can be combined with previous literature models.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

For the fabrication of high power laser fibers a large variety of different glass systems are possible. The most common combination of co-dopants is the addition of Al and P into the matrix of fused silica besides the laser active ion (e.g. Yb3+). This is done to increase the solubility of the active ions in the glass matrix and to decrease the troublesome photodarkening rate of the final fiber. Especially at equimolar amounts of Al and P this combination is of interest due to the significantly reduced influence on the refractive index of the core region in comparison to using only one of these co-dopants. Consequently, this leads to the possibility to increase the doping concentration of laser active ions in the core without additionally increasing the NA of the core. In the literature, it is well known that the usage of Al and P in the ratio of 1:1 leads to a slight index decrease with respect to the fused silica cladding material [1–3]. However, the stated references focus on the behavior at rather high concentrations i.e. > 2 mol% of each constituent, Al and P.

For high power single-mode fiber lasers rather low doping concentrations of the active ion Yb3+ are favored in order to mitigate transversal modal instabilities [4] by a) decreasing photodarkening and b) reducing the heat load per meter in the fiber [5–7]. Since a certain concentration ratio of active ions (like Yb3+) to solutizing ions (like Al3+ and P5+) is known to effectively dissolve the active ions without clustering in the glass matrix, also the amount of solutizing ions is quite low, e.g. P2O5, Al2O3 ~1 mol% [8]. With active step index fibers having these relatively low concentrations of active ions it is possible to extract more than 4 kW in a MOPA setup while maintaining single-mode output [9,10]. The fibers in these cases had a very low NA of approx. 0.04 and the following doping concentrations: 0.06 mol% Yb2O3, 0.6 mol% Al2O3.and 0.6 mol% P2O5. In these regions the optimization of the core composition is very important in order to maintain a stable and reproducible beam quality in high power operation. From a material point of view, the concentrations of the active ion Yb and the solutizer ions Al and P need to be precisely adjusted in order to achieve such outstanding results. The reason for choosing low doping concentrations is due to fact that at Al and P concentrations starting at around 3 mol% the material crystallizes easily during hot processing of the preform. Furthermore, at high doping concentrations of Al and P, the effect of phosphorus evaporation during collapsing leads to large refractive index changes in the very center of the preform.

In this contribution we will show that one the most important parameters here, the refractive index, does not follow the expected behavior known from earlier literature findings for the used lower concentrations and in the direct vicinity of Al:P = 1:1. The behavior in this compositional region therefore needs to be elucidated further, which is of high interest especially for the design of novel fibers (regarding possible NA and doping concentration). In order to investigate the relationship between refractive index and Al and P concentration, several fiber preforms were fabricated using all-solution doping and analyzed regarding their refractive index and their dopant concentration. From the measured values a model was established, which will be shown to give an improved relationship between theory and measurement.

2. Experimental

The preforms were fabricated using MCVD in combination with a solution doping method – more specifically all-solution doping. This consists of the deposition of porous undoped SiO2 layers on the inside of a fused silica tube using a gas flow containing SiCl4 within the substrate tube and an oxygen hydrogen burner to heat the substrate tube from the outside. The deposition was conducted at temperatures below 1600 °C. The number of porous layers can be adjusted in a certain range and their porosity was adjusted altogether using a single sintering step. The temperatures were kept below 1600 °C in this case in order to assure open porosity for the soaking solution to be able to infiltrate all of the layers. Afterwards these layers are soaked with a solution containing all required elements, i.e. Al, P (, Yb). The aluminum to phosphorus ratio could easily be adjusted in this stage by simply choosing the concentration ratios within the solution. The used precursors were AlCl3∙6H2O (, YbCl3∙6H2O) and H3PO4. After drying and purification steps using a chlorine containing atmosphere the consolidation step of the porous layers at temperatures below 2000 °C followed. Afterwards, the tubes were collapsed into a rod at temperatures above 2100 °C – the preform. Within the fabricated compositional range the temperatures necessary for consolidation and collapsing did not change much from composition to composition.

In order to prevent the volatile phosphorus from evaporation the collapsing atmosphere could enriched with POCl3. The compositional range (in oxides) of the prepared preforms was as follows:

  • • 96 - 99 mol% SiO2
  • • 0.4 - 2 mol% Al2O3
  • • 0.4 - 2 mol% P2O5
  • • (0 - 0.2 mol% Yb2O3)
In the case of Yb2O3 containing preforms, the ratios of Al:Yb or P:Yb were kept constant in order to maintain a good solubility of Yb3+ ions in the glass matrix and to prevent the formation of clusters.

These preforms (diameter ≥ 10 mm, length > 700 mm) were then characterized regarding their refractive index and chemical composition. For characterization of the refractive index a commercial device was used (Photon Kinetics PK2610) and several slices along the preform and at each slice several angles were measured in order to assure the longitudinal and radial homogeneity of the refractive index. It was found that the core diameter variation along the preform (>700 mm length) was better than 1% and the refractive index fluctuations along the preform was measured to be better than Δn = ± 0.5∙10−4. The measurement error of the device is given by Δn = ± 0.1∙10−4 according to the supplier.

The chemical composition of the materials was analyzed using Electron Probe Micro-Analysis (EPMA). The measurement error here is around 5%. The position of the EPMA samples was carefully chosen to coincide with a particular slice of the refractive index measurement in order to be able to compare both measurements. It was checked that both measurements showed the same core diameter etc. and samples with large deviation between both measurements were rejected from the model.

As will be shown in the following, the substrate tubes (cladding material) as well as some of the analyzed core regions of the preforms contained small amounts of chlorine, which was represented in terms of SiCl4 as its molecular representation. This chlorine additionally raises the refractive index of SiO2 and was taken into account during the presentation of the data and the fitting procedure. The molar refractivity for SiCl4, as molecular representation for chlorine, was experimentally determined and found to be ΔnSiCl4 = 20⋅10−4 mol%−1. In all cases the concentration of SiCl4 is very low compared to the investigated compounds and very little amounts of chlorine are present in the core material itself.

A fraction of the presented preforms contained Yb as codopant, which is known to increase the refractive index. The index raise per mol% of Yb2O3 in SiO2 is known in the literature (molar refractivity of Yb2O3 is 67⋅10−4 mol%−1) [11] and is independent of the codopants. The data of preforms containing Yb2O3 and/or chlorine was corrected before processing them further.

3. Results

Using all-solution doping technique several preforms were fabricated and analyzed as described previously. In Fig. 1(a) a concentration profile of a fabricated preform containing Al2O3, P2O5 (and SiCl4) is shown and several ripples in the Al and P concentration can be seen, representing the individual layers. The core material here was prepared by using a solution with a molar ratio of Al:P = 1:1. In the outer regions (|radius| > 0.5 mm) the concentrations of Al2O3 and P2O5 are exactly the same. Hence, the Al:P ratio can be predetermined while preparing the soaking solution. In the center the effect of phosphorus evaporation and diffusion during tube collapse can be seen. In the case of this preform the collapsing atmosphere was enriched with too little POCl3 and the result is a phosphorus decrease due to evaporation in the center. The depth of this effect depends on the diffusion length during the collapsing phase. By adjusting the collapsing atmosphere the evaporation of phosphorus can be suppressed nearly completely.

 

Fig. 1 (a) concentration profile of an example preform prepared by means of all-solution doping; (b) measured refractive index and calculated refractive index according to Ref. [1] and [2].

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It was expected that the resulting preform would show a depressed refractive index compared to the cladding material. However, the measured refractive index data presented in Fig. 1(b) (black curve) does not show this expected result. From the shown concentration profile the refractive index profile was calculated (red and blue curve in Fig. 1(b)) using the models proposed in Refs. [1] and [2]. Compared to the measured refractive index profile a significant deviation can be stated, especially in the outer regions of the core. The predicted refractive index is much lower than the actual measured refractive index. It has to be noted that the concentration range, which is under investigation here, lies not within the analyzed concentration range of the models in Refs. [1] and [2] and therefore it can be said that the target compositions here do not fit the models given in the literature. In the center the effect of changing the Al:P ratio due to evaporation of phosphorus can clearly be seen as an increase of the refractive index in this region.

To show that this effect is consistent, the spatially resolved measured refractive indices of various preforms prepared with different Al/P ratios are plotted vs. the measured concentration ratio in Fig. 2. The absolute doping concentrations of Al2O3 and P2O5 were below 2 mol% in all cases.

 

Fig. 2 measured refractive index as function of the Al/P (P excess) or P/Al (Al excess) for SiO2 concentrations ranging from 96 to 99 mol%; comparison to the calculated refractive indices from EPMA using models in Ref. [1] and [2].

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In Fig. 2, the abscissa has been calculated from the ratios of Al/P in case of P excess and P/Al in case of Al excess. Similar to Fig. 1 the refractive index according to the models in Refs. [1] and [2] is calculated and plotted in addition to the measured data in Fig. 2. One can see that the deviation between the models and the measurement is more pronounced in the very center of the graph, i.e. the region of nearly equal concentrations of aluminum and phosphorus. When moving to P excess (left of Al = P) or Al excess (right of Al = P) the deviation shrinks and at a certain amount of excess P or Al the deviation even disappears.

This effect cannot be explained by the given measurement errors (see experimental section), since this error would influence all data points and here only the data near Al:P = 1:1 are influenced.

Each data point represents a point in the radial index/ concentration profile like shown in Fig. 1. To ensure correct comparison of concentration and refractive index measurement each refractive index and concentration profile was checked if both data sets coincide with each other. Furthermore, only representative data points, i.e. only significant concentrations (due to elemental analysis error) and radial parts outside the very center of the profile (due to significantly higher index measurement error in the center), were chosen for the modelling. This point by point analysis was also used in Ref. [2] and it was found to be more reliable than modelling average values for refractive index and concentration.

4. Modelling related to the glass structure of Al,P:SiO2

To increase the solubility of rare earth ions in fused silica co-doping with Al and/or P is required. Both co-dopants increase the refractive index of fused silica [1,2]. It is well known that Al and P in the molar ratio of 1:1 lead to the structurally equivalent to SiO2 – AlPO4. This is shown in Fig. 3 where the principle glass structure of AlPO4-doped SiO2 is depicted. Here SiO2 forms a tetrahedral network, where every Si atom is connected to four other Si atoms via so-called bridging oxygen. AlPO4 is structurally equivalent with the difference that Al and P ions are alternatingly connected to each other – Al is connected to P and vice versa. The structure however is similar to SiO2 [12,13]. As a result the refractive index of SiO2 is not altered upon co-doping with AlPO4, moreover the refractive index is reported to decrease slightly in comparison to undoped SiO2.

 

Fig. 3 Glass structure of Al,P-doped SiO2 with 100% formation of AlPO4 units.

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In the literature, this effect has been shown in a variety of papers [1–3]. Models describing the effect of Al/P codoping on the refractive index are built on the assumption that AlPO4 is completely formed, when Al and P are nominally able to form the compound, i.e. the following chemical reaction is complete:

Al2O3+P2O52AlPO4
One reason for the above stated deviations between measured and calculated refractive index might be that up to now all literature data and models assume a 100% formation of AlPO4 – in other words the reaction in Eq. (1) is assumed to be complete. An incomplete reaction was not taken into account up to now. The following chemical reaction takes this into account, were f is the so called fraction parameter, which is a measure of the probability of AlPO4 formation.
Al2O3+P2O52fAlPO4+(1f)(Al2O3+P2O5)
This is equivalent to:
Al2O3+P2O52AlPO4
For f = 1 the reaction is complete and gives Eq. (1), if f = 0 no formation of AlPO4 takes place at all.

Figure 4 shows a possible glass structure when AlPO4 is not formed completely in the glass, where nominally a complete formation would be possible. In red the AlPO4 groups are shown, which are structurally equivalent to the host glass SiO2. In blue and green phosphate groups and aluminum ions are shown, respectively, as they are present in solely P- or Al-doped SiO2.

 

Fig. 4 proposed glass structure when an incomplete formation of AlPO4 units (AlPO4 marked in red) takes place.

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If one includes this assumption and Eq. (2) into the literature models of Refs. [1] and [2] the calculated refractive index can be very precisely fitted to the measured refractive index data as shown in Fig. 5, here a fraction parameter f of 0.8 was used. This means that only 80% of the nominally possible AlPO4 groups are formed.

 

Fig. 5 measured refractive index (black curve), calculated refractive index using the models presented in Ref. [1] and [2] taking a fraction f = 0.8 into account.

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This figure shows that the adjustment of the fraction parameter leads to a very precise match of calculated and measured data. Hence, in order to match calculated and measured refractive indices the correct value for f has to be found.

We have tried to fit all fabricated preforms according to Fig. 5 with a constant f but found that f is not equal for every composition. By choosing different constant f parameters, only small regions of the plotted points in Fig. 2 can be matched but no overall match was found. It turns out that f depends on the actual Al:P ratio and on the absolute concentration c of the ions. To account for both dependencies, f is expressed as follows:

f=1(1fc(c))exp((x1)22fsigma2)
with:
x={cAlcP,  cAl<cPcPcAl,cAlcP
Here cAl and cP are the concentrations of Al2O3 and P2O5, respectively. The dependency of f on the Al/P (P/Al) ratio x is assumed to follow a Gaussian distribution. Here fc(c) is the concentration dependent minimum of the Gaussian curve (explanation follows below), while fsigma is the variance. A Gaussian distribution is assumed since the formation of AlPO4 groups is expected to statistically depend on the Al:P (P:Al) ratio, i.e. if a ratio of 1:1 is present, then each Al needs to “find” a P counterpart to form AlPO4. Hence, the probability of AlPO4 formation is lowest in this case and increases with P or Al excess, since in both cases the minority component has more possibilities to find a corresponding “reaction partner” and therefore the probability of AlPO4 formation is increases. In fact, the relative portion of nominally possible AlPO4 increases.

The concentration dependent value of fc(c), i.e. the minimum of the above described Gaussian curve, was assumed to follow an asymptotical function, which approaches the value of fc = 1 for high concentrations. The following exponential function was used to represent this behavior in a mathematical function.

fc(c)=1(1fmin)exp(cfτ)

In this equation fmin is the minimum f parameter at a fictive concentration of 0 mol% and fτ is a measure for the effect of concentration on the f parameter. The reason why this is used instead of a linear relationship is the fact that this model can be used in a wide concentration range since it is known from the literature that at high concentrations an refractive index decrease of Al,P-doped SiO2 with respect to undoped SiO2 indeed can be found. Hence, in terms of this model, the f parameter needs to approach unity.

The following graph shows example curve progressions of f vs the respective parameters (ratios and concentration).

In Fig. 6(a) the effect of the concentration ratios according to Eq. (3) is shown. The chosen parameter fsigma = 0.32 was used in this case (see best fit model in Table 1). The proposed dependency can be explained in the following way: The f parameter is low when the Al:P-ratio is close to 1:1, since here every Al has to find a P counterpart in order to form AlPO4 and vice versa, so the probability of AlPO4 is lowest here. In the case of Al or P excess the minority component has more possiblities to form AlPO4 units together with the mayority component and therefore the probability or f parameter shows higher values, i.e. the fraction of formed AlPO4 units increases.

 

Fig. 6 (a) Assumed dependency of parameter f on the respective ratios of Al:P or P:Al according to Eq. (3) (fsigma = 0.32); (b) Assumed dependency of the fraction parameter f on the absolute concentration according to Eq. (4) (fmin = 0.52, fτ = 2.7 mol%).

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Tables Icon

Table 1. Molar refractivities of Al2O3 (∆nAl), P2O5 (∆nP) and AlPO4 (∆nAlP) and f parameter values resulting from the least-squares fitting method for the model equations (Eq. (5-6); comparison to and extension of the previously reported values in the literature (Refs. [1] and [2])

In Fig. 6(b) the effect of the absolute concentration of Al and/or P on the minimum of the Gaussian curve in Fig. 6(a) is shown according to Eq. (4). The chosen parameters where fmin = 0.52 and fτ = 2.7 mol% (see best fit model in Table 1). The proposed dependency might be explained by the concentration dependent diffusion coefficients of Al and P [14,15] – the diffusion coefficients increase with concentration, which lead to higher mobilities of the compounts in the glass. In fact, it was found that if the concentration of the dopants increases, the f parameter is increased as well, so more AlPO4 units are formed or the probability of AlPO4 formation is higher. Since every chemical reaction follows a certain kinetic law (influenced e.g. by diffusion), an increased diffusion coefficient (or reduced viscosity of the glass) increases the reaction rate and therefore an influence of the absolute concentration on the probability of AlPO4 formation can be explained.

With these assumptions, the following model equations were established for different regions (Al excess or P excess) in the graph of Fig. 2.

P ≥ Al (P excess):

Δn=(cPcAl)ΔnPexcess P+fcAlΔnAlPformed AlPO4+(1f)cAl0.5(ΔnP+ΔnAl)not formed AlPO4
f=1(1fc(c))exp((cAlcP1)22fsigma2)
fc(c)=1(1fmin)exp(cfτ)

Al > P (Al excess):

Δn=(cAlcP)ΔnAlexcess Al+fcPΔnAlPformed AlPO4+(1f)cP0.5(ΔnP+ΔnAl)not formed AlPO4
f=1(1fc(c))exp((cPcAl1)22fsigma2)
fc(c)=1(1fmin)exp(cfτ)
The model was fitted to the measured refractive index and concentration data using a least-squares fitting procedure. At first the literature models from Refs. [1] and [2] were extended by the proposed model. Here the molar refractivities ΔnAl, ΔnP and ΔnAlP were kept constant and only the parameters from the extended model (fsigma, fmin, fτ) were fitted. The found parameters are summarized in the first four columns of Table 1. In the “best fit model” column of the table all parameters were optimized to fit the data points of the present data using the same least-squares fitting procedure.

From Table 1 it can be stated that the proposed best fit model and the literature models lead to comparable molar refractivities for aluminum ΔnAl and phosphorus ΔnP. For the molar refractivity of AlPO4, ΔnAlP, a rather large deviation was found and the value found in the best fit model is significantly lower than reported before. The f parameter values from the fits can give the following information:

The gaussian curve describing the f parameters as function of the ratio Al/P or P/A, respectively, has a variance of fsigma = 0.32 in the case of the best fit model. The respective value for the extended models from Refs. [1] and [2] are lower compared to the best fit model, meaning that here the shape of the Gaussian curve is narrower and the overall f parameter approaches a value of one earlier than in the best fit model when moving from Al:P = 1:1 to P or Al excess. The parameter fmin is comparable for all fitted models and is around 0.5, meaning that the f value at a hypothetical concentration of 0 mol% is near 0.5 and only 50% AlPO4 groups are formed in this case. The parameter fτ has a value of 2.7 mol% in the case of the best fit model which differs from the values found for the extended models of Refs [1] and [2], were values near 1.5 mol% have been fitted. This parameter is a measure (characteristic concentration) for the concentration effect on the AlPO4 formation. The lower this characteristic concentration is, the faster the f parameter approaches f = 1, when the concentration is increased.

In Fig. 7 the comparison of the measured refractive index data and the calculated model data of the proposed models is shown. The used model is indicated in the title of each graph. From the graphs it can be seen that all proposed models fit the measured data of refractive index as function of the ratio Al/P (P excess) or P/Al (Al excess) very well and for the present concentrations no refractive index below that of undoped SiO2 can be found.

 

Fig. 7 dependency of the refractive index on the ratio of Al/P (P excess) and P/Al (Al excess); (black points) measure values; a) (green circles) best fit model; b) (blue circles) extended model of Ref. [1]; c) (red circles) extended model of Ref. [2].

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The best fit model and the extended model according to Ref. [1] show the best coincidence between measurement and model, while the deviations of the extended model of Ref. [2]. are slightly larger. Nevertheless, all models show a significantly better fit to the present data points compared to the previous, unextended literature models (previously shown in Fig. 2).

5. Discussion

The deviation between experiment and existing literature models is largely reduced by the extended model presented in this contribution. It has to be stated that the presented model here is not intended to replace to previously reported models, moreover it is meant to extend the works, which had already been done. For all analyzed models, a significant improvement of the fitting behavior by using the extended model was found.

In Fig. 8 the found relationship (best fit model) between refractive index and the respective ratios of Al/P (P excess) and P/Al (Al excess) is shown for various concentrations between 1 and 5 mol%. For low concentrations the proposed effect of incomplete formation of AlPO4 in the vicinity of Al:P = 1:1 is more pronounced than for high concentrations. The higher the concentration gets, the less the effect incomplete AlPO4 formation becomes and the more the presented model approaches the previously published models in Refs. [1] and [2], i.e. the sharp transition at Al:P = 1:1 and negative ∆n becomes more pronounced (starting at around 3 mol%). The curves for concentrations above 2 mol% are shown in non-solid lines in Fig. 8, since the model is mainly derived for concentrations below 2 mol% and therefore the non-solid lines are seen to be an outreach to higher concentrations.

 

Fig. 8 Best fit model for the dependency of the refractive index on the respective ratios for different concentrations

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With regard to high-power fiber lasers, where low NA fibers (e.g. 0.04) are targeted, it can be said that if one tries to accomplish low NA fibers with rather low doping concentrations of the components Al, P and Yb, it has to be borne in mind that a relatively low concentration of aluminum and phosphorus leads to a slightly increased refractive index, compared to undoped SiO2. This is in contradiction to the previously reported behavior. Hence, for a given target NA not only Yb adds to the refractive index but AlPO4 (through the incomplete formation) as well. From the data given in Fig. 8 and the proposed models one would think higher concentrations of Al and P should be targeted. However, a higher crystallization probability and with that high attenuations in the final fiber might limit this approach in another physical and glass chemical dimension. Furthermore, slight changes in the compositions during collapsing in the very center of the refractive index profile can lead to large deviations from the desired Δn.

Furthermore, the fabrication method itself does not influence the refractive index dependency much. This was found in additional preliminary tests using chelate doping. During chelate doping all dopants are fed into the reaction zone through the gaseous phase [16]. Here a similar effect of the ratio between Al and P was found (not shown). Up to now it is not clear if there is a big difference to the here presented fabrication method “all-solution doping” or not. However, for solely aluminum doped SiO2 a certain deviation between solution doping and gas phase doping was found by Lindner et al. [17], namely an altered (lower) molar refractivity of Al2O3 was found for chelate doped materials. To clarify the behavior for Al and P doped materials prepared by means of chelate doping further experiments are required.

The influence of stress was left out in the discussion so far. It is known that stress can lead to an increased refractive index. The preforms themselves were not analyzed regarding their residual stresses but the fibers drawn from the preforms where tested regarding their stresses. It is expected that the stresses do not decrease during fiber drawing due to the high cooling rates. Hence, the stresses obtained from the fibers are expected to be higher than the stresses in the preforms. The measured stresses in the fibers where lower than 5 MPa. According to Ref. [18] this would lead to a refractive index change in SiO2 of around 0.3∙10−4, which is much lower than the shown effects. Hence, a significant contribution of stress on the shown data can be ruled out.

6. Summary

In this paper a newly developed and easily adjustable fabrication method – the all-solution doping method – was used to fabricate (Yb,) Al, P-doped SiO2 preforms and to precisely adjust the composition of the material regarding the Al:P ratio. The doping concentrations were in the range of 0.4 … 2.0 mol% of Al2O3 and/or P2O5. The produced preforms were analyzed regarding their concentration and their refractive index. With this data a dependency of the ratio of Al/P (P excess) and P/Al (Al excess) on the refractive index was found to be inconsistent with the existing models from the literature, where only data for rather high doping concentrations could be found. In this paper a model is derived assuming an incomplete formation of AlPO4 groups, which are responsible for the refractive index anomaly in the system – denoted as fraction f. By accounting for the found concentration ratio dependency and the absolute concentration dependency, a more precise functional dependency of the refractive index and the concentrations (absolute and relative) could be established for the analyzed low-concentration compositional region. The literature models were extended by the proposed model from this contribution as well, which led to a more satisfactory match between model and measured data.

Funding

Bundesministerium für Bildung und Forschung (BMBF) (13N13652); State of Thuringia supported by EU Programs EFRE and ESF (13030-715, 2015FGR0107, 2015FOR0017, B715-11011).

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13. M. Rokita, M. Handke, and W. Mozgawa, “Spectroscopic studies of the amorphous SiO2–AlPO4 materials,” J. Mol. Struct. 511–512, 277–280 (1999). [CrossRef]  

14. J. Kirchhof, S. Unger, and J. Dellith, “Diffusion of phosphorus doped silica for active optical fibers,” J. Non-Cryst. Solids 345–346, 234–238 (2004). [CrossRef]  

15. S. Unger, J. Dellith, A. Scheffel, and J. Kirchhof, “Diffusion in Yb2O3-Al2O3-SiO2 glass,” Phys. Chem. Glasses B 52, 41–46 (2011).

16. R. P. Tumminelli, B. C. McCollum, and E. Snitzer, “Fabrication of high-concentration rare-earth doped optical fibers using chelates,” J. Lightwave Technol. 8(11), 1680–1683 (1990). [CrossRef]  

17. F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014). [CrossRef]  

18. A. D. Yablon, M. F. Yan, D. J. DiGiovanni, M. E. Lines, S. L. Jones, D. N. Ridgway, G. A. Sandels, I. A. White, P. Wisk, F. V. DiMarcello, E. M. Monberg, and J. Jasapara, “Frozen-In Viscoelasticity for Novel Beam Expanders and High-Power Connectors,” J. Lightwave Technol. 22(1), 16–23 (2004). [CrossRef]  

References

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  1. M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
    [Crossref]
  2. S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
    [Crossref]
  3. D. J. Digiovanni, J. B. MacChesney, and T. Y. Kometani, “Structure and properties of silica containing aluminum and phosphorus near the AlPO4 join,” J. Non-Cryst. Solids 113(1), 58–64 (1989).
    [Crossref]
  4. T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express 19(14), 13218–13224 (2011).
    [Crossref] [PubMed]
  5. C. Jauregui, H.-J. Otto, F. Stutzki, J. Limpert, and A. Tünnermann, “Simplified modelling the mode instability threshold of high power fiber amplifiers in the presence of photodarkening,” Opt. Express 23(16), 20203–20218 (2015).
    [Crossref] [PubMed]
  6. C. Jauregui, H.-J. Otto, C. Stihler, J. Limpert, and A. Tünnermann, “The impact of core co-dopants on the mode instability threshold of high-power fiber laser systems,” Proc. SPIE 100830, 100830N (2017).
  7. C. Jauregui, H.-J. Otto, S. Breitkopf, J. Limpert, and A. Tünnermann, “Optimizing high-power Yb-doped fiber amplifier systems in the presence of transverse mode instabilities,” Opt. Express 24(8), 7879–7892 (2016).
    [Crossref] [PubMed]
  8. F. Beier, C. Hupel, J. Nold, S. Kuhn, S. Hein, J. Ihring, B. Sattler, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Narrow linewidth, single mode 3 kW average power from a directly diode pumped ytterbium-doped low NA fiber amplifier,” Opt. Express 24(6), 6011–6020 (2016).
    [Crossref] [PubMed]
  9. F. Beier, C. Hupel, S. Kuhn, S. Hein, J. Nold, F. Proske, B. Sattler, A. Liem, C. Jauregui, J. Limpert, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Single mode 4.3 kW output power from a diode-pumped Yb-doped fiber amplifier,” Opt. Express 25(13), 14892–14899 (2017).
    [Crossref] [PubMed]
  10. F. Beier, F. Moeller, J. Nold, B. Sattler, S. Kuhn, C. Hupel, S. Hein, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “TMI Investigations of Very Low NA Yb-doped Fibers and Scaling to Extreme Stable 4.4 kW Single-mode Output,” in Advanced Solid State Lasers (Optical Society of America, 2017), ATu3A.2.
    [Crossref]
  11. J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
    [Crossref]
  12. S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
    [Crossref]
  13. M. Rokita, M. Handke, and W. Mozgawa, “Spectroscopic studies of the amorphous SiO2–AlPO4 materials,” J. Mol. Struct. 511–512, 277–280 (1999).
    [Crossref]
  14. J. Kirchhof, S. Unger, and J. Dellith, “Diffusion of phosphorus doped silica for active optical fibers,” J. Non-Cryst. Solids 345–346, 234–238 (2004).
    [Crossref]
  15. S. Unger, J. Dellith, A. Scheffel, and J. Kirchhof, “Diffusion in Yb2O3-Al2O3-SiO2 glass,” Phys. Chem. Glasses B 52, 41–46 (2011).
  16. R. P. Tumminelli, B. C. McCollum, and E. Snitzer, “Fabrication of high-concentration rare-earth doped optical fibers using chelates,” J. Lightwave Technol. 8(11), 1680–1683 (1990).
    [Crossref]
  17. F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
    [Crossref]
  18. A. D. Yablon, M. F. Yan, D. J. DiGiovanni, M. E. Lines, S. L. Jones, D. N. Ridgway, G. A. Sandels, I. A. White, P. Wisk, F. V. DiMarcello, E. M. Monberg, and J. Jasapara, “Frozen-In Viscoelasticity for Novel Beam Expanders and High-Power Connectors,” J. Lightwave Technol. 22(1), 16–23 (2004).
    [Crossref]

2017 (2)

C. Jauregui, H.-J. Otto, C. Stihler, J. Limpert, and A. Tünnermann, “The impact of core co-dopants on the mode instability threshold of high-power fiber laser systems,” Proc. SPIE 100830, 100830N (2017).

F. Beier, C. Hupel, S. Kuhn, S. Hein, J. Nold, F. Proske, B. Sattler, A. Liem, C. Jauregui, J. Limpert, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Single mode 4.3 kW output power from a diode-pumped Yb-doped fiber amplifier,” Opt. Express 25(13), 14892–14899 (2017).
[Crossref] [PubMed]

2016 (2)

2015 (1)

2014 (1)

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

2011 (2)

2009 (1)

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

2007 (1)

S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
[Crossref]

2005 (1)

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

2004 (2)

1999 (1)

M. Rokita, M. Handke, and W. Mozgawa, “Spectroscopic studies of the amorphous SiO2–AlPO4 materials,” J. Mol. Struct. 511–512, 277–280 (1999).
[Crossref]

1990 (1)

R. P. Tumminelli, B. C. McCollum, and E. Snitzer, “Fabrication of high-concentration rare-earth doped optical fibers using chelates,” J. Lightwave Technol. 8(11), 1680–1683 (1990).
[Crossref]

1989 (1)

D. J. Digiovanni, J. B. MacChesney, and T. Y. Kometani, “Structure and properties of silica containing aluminum and phosphorus near the AlPO4 join,” J. Non-Cryst. Solids 113(1), 58–64 (1989).
[Crossref]

1988 (1)

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

Aichele, C.

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

Beier, F.

Breitkopf, S.

Bubnov, M. M.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

Dellith, J.

S. Unger, J. Dellith, A. Scheffel, and J. Kirchhof, “Diffusion in Yb2O3-Al2O3-SiO2 glass,” Phys. Chem. Glasses B 52, 41–46 (2011).

S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
[Crossref]

J. Kirchhof, S. Unger, and J. Dellith, “Diffusion of phosphorus doped silica for active optical fibers,” J. Non-Cryst. Solids 345–346, 234–238 (2004).
[Crossref]

DiGiovanni, D. J.

DiMarcello, F. V.

Douglas, D. C.

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

Duncan, T. M.

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

Eberhardt, R.

Eidam, T.

Gur’yanov, A. N.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

Haarlammert, N.

Handke, M.

M. Rokita, M. Handke, and W. Mozgawa, “Spectroscopic studies of the amorphous SiO2–AlPO4 materials,” J. Mol. Struct. 511–512, 277–280 (1999).
[Crossref]

Hein, S.

Hupel, C.

Ihring, J.

Jansen, F.

Jasapara, J.

Jauregui, C.

Jetschke, S.

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

Jones, S. L.

Kirchhof, J.

S. Unger, J. Dellith, A. Scheffel, and J. Kirchhof, “Diffusion in Yb2O3-Al2O3-SiO2 glass,” Phys. Chem. Glasses B 52, 41–46 (2011).

S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
[Crossref]

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

J. Kirchhof, S. Unger, and J. Dellith, “Diffusion of phosphorus doped silica for active optical fibers,” J. Non-Cryst. Solids 345–346, 234–238 (2004).
[Crossref]

Knappe, B.

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

Kometani, T. Y.

D. J. Digiovanni, J. B. MacChesney, and T. Y. Kometani, “Structure and properties of silica containing aluminum and phosphorus near the AlPO4 join,” J. Non-Cryst. Solids 113(1), 58–64 (1989).
[Crossref]

Kosinski, S. G.

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

Krol, D. M.

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

Kuhn, S.

Leich, M.

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

Liem, A.

Likhachev, M. E.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

Limpert, J.

Lindner, F.

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

Lines, M. E.

Lipatov, D. S.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

MacChesney, J. B.

D. J. Digiovanni, J. B. MacChesney, and T. Y. Kometani, “Structure and properties of silica containing aluminum and phosphorus near the AlPO4 join,” J. Non-Cryst. Solids 113(1), 58–64 (1989).
[Crossref]

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

McCollum, B. C.

R. P. Tumminelli, B. C. McCollum, and E. Snitzer, “Fabrication of high-concentration rare-earth doped optical fibers using chelates,” J. Lightwave Technol. 8(11), 1680–1683 (1990).
[Crossref]

Monberg, E. M.

Mozgawa, W.

M. Rokita, M. Handke, and W. Mozgawa, “Spectroscopic studies of the amorphous SiO2–AlPO4 materials,” J. Mol. Struct. 511–512, 277–280 (1999).
[Crossref]

Nold, J.

Otto, H.-J.

Proske, F.

Ridgway, D. N.

Rokita, M.

M. Rokita, M. Handke, and W. Mozgawa, “Spectroscopic studies of the amorphous SiO2–AlPO4 materials,” J. Mol. Struct. 511–512, 277–280 (1999).
[Crossref]

Sandels, G. A.

Sattler, B.

Scheffel, A.

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

S. Unger, J. Dellith, A. Scheffel, and J. Kirchhof, “Diffusion in Yb2O3-Al2O3-SiO2 glass,” Phys. Chem. Glasses B 52, 41–46 (2011).

Schmidt, O.

Schreiber, T.

Schwuchow, A.

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
[Crossref]

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

Simpson, J. R.

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

Snitzer, E.

R. P. Tumminelli, B. C. McCollum, and E. Snitzer, “Fabrication of high-concentration rare-earth doped optical fibers using chelates,” J. Lightwave Technol. 8(11), 1680–1683 (1990).
[Crossref]

Stihler, C.

C. Jauregui, H.-J. Otto, C. Stihler, J. Limpert, and A. Tünnermann, “The impact of core co-dopants on the mode instability threshold of high-power fiber laser systems,” Proc. SPIE 100830, 100830N (2017).

Stutzki, F.

Tumminelli, R. P.

R. P. Tumminelli, B. C. McCollum, and E. Snitzer, “Fabrication of high-concentration rare-earth doped optical fibers using chelates,” J. Lightwave Technol. 8(11), 1680–1683 (1990).
[Crossref]

Tünnermann, A.

C. Jauregui, H.-J. Otto, C. Stihler, J. Limpert, and A. Tünnermann, “The impact of core co-dopants on the mode instability threshold of high-power fiber laser systems,” Proc. SPIE 100830, 100830N (2017).

F. Beier, C. Hupel, S. Kuhn, S. Hein, J. Nold, F. Proske, B. Sattler, A. Liem, C. Jauregui, J. Limpert, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Single mode 4.3 kW output power from a diode-pumped Yb-doped fiber amplifier,” Opt. Express 25(13), 14892–14899 (2017).
[Crossref] [PubMed]

F. Beier, C. Hupel, J. Nold, S. Kuhn, S. Hein, J. Ihring, B. Sattler, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Narrow linewidth, single mode 3 kW average power from a directly diode pumped ytterbium-doped low NA fiber amplifier,” Opt. Express 24(6), 6011–6020 (2016).
[Crossref] [PubMed]

C. Jauregui, H.-J. Otto, S. Breitkopf, J. Limpert, and A. Tünnermann, “Optimizing high-power Yb-doped fiber amplifier systems in the presence of transverse mode instabilities,” Opt. Express 24(8), 7879–7892 (2016).
[Crossref] [PubMed]

C. Jauregui, H.-J. Otto, F. Stutzki, J. Limpert, and A. Tünnermann, “Simplified modelling the mode instability threshold of high power fiber amplifiers in the presence of photodarkening,” Opt. Express 23(16), 20203–20218 (2015).
[Crossref] [PubMed]

T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H.-J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tünnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fiber amplifiers,” Opt. Express 19(14), 13218–13224 (2011).
[Crossref] [PubMed]

Unger, S.

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

S. Unger, J. Dellith, A. Scheffel, and J. Kirchhof, “Diffusion in Yb2O3-Al2O3-SiO2 glass,” Phys. Chem. Glasses B 52, 41–46 (2011).

S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
[Crossref]

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

J. Kirchhof, S. Unger, and J. Dellith, “Diffusion of phosphorus doped silica for active optical fibers,” J. Non-Cryst. Solids 345–346, 234–238 (2004).
[Crossref]

Vechkanov, V. N.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

White, I. A.

Wirth, C.

Wisk, P.

Yablon, A. D.

Yan, M. F.

Yashkov, M. V.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

Zotov, K. V.

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

Inorg. Mater. (1)

M. M. Bubnov, V. N. Vechkanov, A. N. Gur’yanov, K. V. Zotov, D. S. Lipatov, M. E. Likhachev, and M. V. Yashkov, “Fabrication and optical properties of fibers with an Al2O3-P2O5-SiO2 glass core,” Inorg. Mater. 45(4), 444–449 (2009).
[Crossref]

J. Lightwave Technol. (2)

J. Mol. Struct. (1)

M. Rokita, M. Handke, and W. Mozgawa, “Spectroscopic studies of the amorphous SiO2–AlPO4 materials,” J. Mol. Struct. 511–512, 277–280 (1999).
[Crossref]

J. Non-Cryst. Solids (3)

J. Kirchhof, S. Unger, and J. Dellith, “Diffusion of phosphorus doped silica for active optical fibers,” J. Non-Cryst. Solids 345–346, 234–238 (2004).
[Crossref]

S. G. Kosinski, D. M. Krol, T. M. Duncan, D. C. Douglas, J. B. MacChesney, and J. R. Simpson, “Raman and NMR spectroscopy of SiO2 glasses CO-doped with Al2O3 and P2O5,” J. Non-Cryst. Solids 105(1-2), 45–52 (1988).
[Crossref]

D. J. Digiovanni, J. B. MacChesney, and T. Y. Kometani, “Structure and properties of silica containing aluminum and phosphorus near the AlPO4 join,” J. Non-Cryst. Solids 113(1), 58–64 (1989).
[Crossref]

Opt. Express (5)

Phys. Chem. Glasses B (1)

S. Unger, J. Dellith, A. Scheffel, and J. Kirchhof, “Diffusion in Yb2O3-Al2O3-SiO2 glass,” Phys. Chem. Glasses B 52, 41–46 (2011).

Proc. SPIE (4)

F. Lindner, C. Aichele, A. Schwuchow, M. Leich, A. Scheffel, and S. Unger, “Optical properties of Yb-doped fibers prepared by gas phase doping,” Proc. SPIE 8982, 89820R (2014).
[Crossref]

J. Kirchhof, S. Unger, A. Schwuchow, S. Jetschke, and B. Knappe, “Dopant interactions in high-power laser fibers,” Proc. SPIE 5723, 261 (2005).
[Crossref]

S. Unger, A. Schwuchow, J. Dellith, and J. Kirchhof, “Codoped materials for high power fiber lasers: diffusion behaviour and optical properties,” Proc. SPIE 6469, 646913 (2007).
[Crossref]

C. Jauregui, H.-J. Otto, C. Stihler, J. Limpert, and A. Tünnermann, “The impact of core co-dopants on the mode instability threshold of high-power fiber laser systems,” Proc. SPIE 100830, 100830N (2017).

Other (1)

F. Beier, F. Moeller, J. Nold, B. Sattler, S. Kuhn, C. Hupel, S. Hein, N. Haarlammert, T. Schreiber, R. Eberhardt, and A. Tünnermann, “TMI Investigations of Very Low NA Yb-doped Fibers and Scaling to Extreme Stable 4.4 kW Single-mode Output,” in Advanced Solid State Lasers (Optical Society of America, 2017), ATu3A.2.
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 (a) concentration profile of an example preform prepared by means of all-solution doping; (b) measured refractive index and calculated refractive index according to Ref. [1] and [2].
Fig. 2
Fig. 2 measured refractive index as function of the Al/P (P excess) or P/Al (Al excess) for SiO2 concentrations ranging from 96 to 99 mol%; comparison to the calculated refractive indices from EPMA using models in Ref. [1] and [2].
Fig. 3
Fig. 3 Glass structure of Al,P-doped SiO2 with 100% formation of AlPO4 units.
Fig. 4
Fig. 4 proposed glass structure when an incomplete formation of AlPO4 units (AlPO4 marked in red) takes place.
Fig. 5
Fig. 5 measured refractive index (black curve), calculated refractive index using the models presented in Ref. [1] and [2] taking a fraction f = 0.8 into account.
Fig. 6
Fig. 6 (a) Assumed dependency of parameter f on the respective ratios of Al:P or P:Al according to Eq. (3) (fsigma = 0.32); (b) Assumed dependency of the fraction parameter f on the absolute concentration according to Eq. (4) (fmin = 0.52, fτ = 2.7 mol%).
Fig. 7
Fig. 7 dependency of the refractive index on the ratio of Al/P (P excess) and P/Al (Al excess); (black points) measure values; a) (green circles) best fit model; b) (blue circles) extended model of Ref. [1]; c) (red circles) extended model of Ref. [2].
Fig. 8
Fig. 8 Best fit model for the dependency of the refractive index on the respective ratios for different concentrations

Tables (1)

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Table 1 Molar refractivities of Al2O3 (∆nAl), P2O5 (∆nP) and AlPO4 (∆nAlP) and f parameter values resulting from the least-squares fitting method for the model equations (Eq. (5-6); comparison to and extension of the previously reported values in the literature (Refs. [1] and [2])

Equations (12)

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A l 2 O 3 + P 2 O 5 2 A l P O 4
A l 2 O 3 + P 2 O 5 2 f A l P O 4 + ( 1 f ) ( A l 2 O 3 + P 2 O 5 )
A l 2 O 3 + P 2 O 5 2 A l P O 4
f = 1 ( 1 f c ( c ) ) exp ( ( x 1 ) 2 2 f s i g m a 2 )
x = { c A l c P ,     c A l < c P c P c A l , c A l c P
f c ( c ) = 1 ( 1 f m i n ) exp ( c f τ )
Δ n = ( c P c A l ) Δ n P e x c e s s   P + f c Al Δ n A l P f o r m e d   A l P O 4 + ( 1 f ) c A l 0.5 ( Δ n P + Δ n A l ) n o t   f o r m e d   A l P O 4
f = 1 ( 1 f c ( c ) ) exp ( ( c A l c P 1 ) 2 2 f s i g m a 2 )
f c ( c ) = 1 ( 1 f m i n ) exp ( c f τ )
Δ n = ( c A l c P ) Δ n A l e x c e s s   A l + f c P Δ n A l P f o r m e d   A l P O 4 + ( 1 f ) c P 0.5 ( Δ n P + Δ n A l ) n o t   f o r m e d   A l P O 4
f = 1 ( 1 f c ( c ) ) exp ( ( c P c A l 1 ) 2 2 f s i g m a 2 )
f c ( c ) = 1 ( 1 f m i n ) exp ( c f τ )

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