Radial distribution and absorption cross section of active centers in bismuth-doped phosphosilicate fibers

Aleksandr Khegai; Sergei Firstov; Konstantin Riumkin; Sergey Alyshev; Fedor Afanasiev; Alexey Lobanov; Alexey Guryanov; Mikhail Melkumov

doi:10.1364/OE.402279

1. Introduction

Bismuth-doped active fibers are a unique medium that can be used for amplification and lasing in a wide spectral region from 1.15 to 1.75 µm [1–4]. The versatility of the properties of the fibers is explained by the fact that electrons responsible for optical transitions in bismuth ion are very sensitive to the local environment and, in particular, to the host glass composition. Apart from the fact that the variability of optical properties allows to manage the absorption and gain spectra of bismuth-doped fibers by slight modification of the core glass composition (except for high-germania fibers that need about 50 mol% of GeO$_2$ [2]) it also results in the effects that are not observed in the fibers doped with rare-earth elements. For instance, in the bismuth-doped fibers several types of centers can form inside the single glass host. Not all of them, however, are laser active centers (bismuth active centers – BACs), some are responsible for a considerable unsaturable loss in the spectral region of operation. In bismuth-doped phosphosilicate fibers, there are at least three types of bismuth centers, among which are BACs associated with phosphorus (BACs-P), BACs associated with silicon (BACs-Si), and ones attributed to unsaturable losses. Additionally, some bismuth-doped fibers have sensitivity to intensive visible radiation [5]. The experiments showed a significant degradation of the BACs and, interestingly, of the centers responsible for the unsaturable losses under green (532 nm) light irradiation, the effect is the most intensive for a high-germania glass host. The other work demonstrated recovery and even formation of new BACs by thermal treatment of the fibers [6,7]. One more peculiarity of the bismuth-doped fibers is that working concentration of bismuth in the fibers is relatively small $\sim 10^{19}$ cm$^{-3}$ and even smaller part of the bismuth atoms transform into the BACs. The measurement of the BACs concentration had long been an issue since not all of bismuth ions that are introduced into the fiber preform form the BACs, hence the use of direct analysis of bismuth concentration like the Electrothermal Atomization Atomic Absorption Spectrometry (EA-AAS), and the Inductively Coupled Plasma Atomic Emission Spectroscopy (ICP-AES) and similar methods do not provide adequate results. To date, there were no any successful attempts to experimentally measure the concentration of the BACs in fiber samples. Approximate estimations of BACs content in alumino- and germanosilicate fibers doped with bismuth based on emission cross section and assumption of equality of emission and absorption ones were performed in [8,9]. Another challenge is to determine the distribution of BACs across the fiber and using both data, eventually, obtain absorption cross sections. In [10–12] the authors managed to measure a relative BACs distribution in germano-alumino silicate and pure silica preforms spectroscopically. Nevertheless, for phosphosilicate samples such experiments were yet to be performed. In this work, the attention was paid to the bismuth-doped phosphosilicate fibers and fiber preforms. We determined average concentration of BACs-P in the fibers with bismuth using an effect of pulse energy limitation and found relative BACs-P distribution across fiber preform by means of the luminescence spectroscopy. Combining these data, absolute distribution of BACs-P was established. According to the obtained radial distribution and using absorption spectrum of BACs-P, absorption cross sections were calculated. The results can be useful for the simulation of amplifiers and lasers, optimization of the fiber preforms fabrication process, and more.

2. Methods

2.1 Average BACs concentration

As it was stated above, direct methods do not allow to determine BACs concentration. Therefore, in this work, to evaluate average BACs concentration ($\overline {C}$), we used the method described in [13]. The idea of the concentration measurements is based on two properties characteristic to bismuth-doped fibers. It is that the BACs amount in the fibers under investigation is very small while the unsaturable losses, on the contrary, are high enough. It leads to the fact that when we use such a medium for amplification of energetic ns-pulses the pulse energy limitation occurs at a level of just tens µJ. The energy limit is well observed in Q-switched lasers as shown in [13]. The mechanism of this limitation does not stem from nonlinear effects like four-wave mixing, mode instabilities, stimulated Raman or Brillouin scattering. In the case of bismuth-doped active fibers, the maximum energy of the single pulse that can be achieved is limited by the extractable energy characteristic of a certain fiber sample. In other words, if we amplify pulses in a long laser medium (long enough to achieve the limit) and assume that the pump power provides the maximum inversion population along the entire fiber length, then the pulse energy saturates when the energy, which can be extracted from the medium is sufficient only to compensate unsaturable losses. The change in the pulse energy ($E_{\textrm{p}}(x)$) can be expressed as

(1)$${\frac{dE_\textrm{p}(x)}{dx}=\varepsilon _{\textrm{ex}}} - E_\textrm{p}(x) \cdot {\alpha _\textrm{u}},$$

where $\varepsilon _{\textrm{ex}}$ is extractable energy per unit length and $\alpha _{\textrm{u}}$ is unsaturable losses at the wavelength of signal. It is easy to show that when the pulse amplification stops (reaching maximum pulse energy) the derivation should be equal to zero that means [13]

(2)$${\varepsilon _{\textrm{ex}}} = E_\textrm{p}^{\max } \cdot {\alpha _\textrm{u}}$$

where $E_{\textrm{p}}^{\max }$ is maximum pulse energy. At the same time $\varepsilon _{\textrm{ex}}$ can be represented as a difference $\varepsilon _{\textrm{ex}}=\varepsilon _{\textrm{st}}-\varepsilon _{\textrm{bl}}$, where $\varepsilon _{\textrm{st}}$ is the energy stored per unit length of the active fiber in the case of maximum population of BACs at the first excited state in medium being pumped at the wavelength of $\lambda _{\textrm{p}}=1230$ nm and $\varepsilon _{\textrm{bl}}$ is the stored energy corresponding to a zero gain in the medium at the wavelength of the signal $\lambda _{\textrm{s}}=1330$ nm when neglecting the losses by $\alpha _{\textrm{u}}$ (or, equivalently, to a maximum population of the first excited state when pumped at $\lambda _{\textrm{s}}$. Additionally, for these conditions, one can consider that $\varepsilon _{\textrm{st}}=N_2^{\lambda _{\textrm{p}}}\cdot \overline {C} \cdot A_c\cdot h\nu$ and $\varepsilon _{\textrm{bl}}=N_2^{\lambda _s}\cdot \overline {C} \cdot A_c\cdot h\nu$, where $\overline {C}$ is an average across the fiber core BACs-P concentration, $N_2^{\lambda _{\textrm{p}}}$ and $N_2^{\lambda _{\textrm{s}}}$ are maximal achievable for pumping at $\lambda _{\textrm{p}}$ and $\lambda _{\textrm{s}}$ relative population of the first excited state, $A_c=\pi d_c^2/4$ is the core area and $h\nu$ is the photon energy at $\lambda _{\textrm{s}}$. Combining the expressions and using (2) we can obtain the relation for $\overline {C}$ in the bismuth-doped fiber

(3)$$\overline C = \frac{{{\varepsilon _{\textrm{ex}}}}}{{\left( {N_2^{_{{\lambda _\textrm{p}}}} - N_2^{{\lambda _\textrm{s}}}} \right){A_c}h\nu }} = \frac{{4E_\textrm{p}^{\max } \cdot {\alpha _\textrm{u}}}}{{\left( {N_2^{_{{\lambda _\textrm{p}}}} - N_2^{{\lambda _\textrm{s}}}} \right)\pi d_\textrm{c}^2h\nu }}.$$

Thus, the measurement of maximum pulse energy that could be achieved in the bismuth-doped fiber, unsaturable loss, and core diameter allows determining the average BACs concentration. To evaluate the approximate values of $N_2^{\lambda _{\textrm{p}}}$ and $N_2^{\lambda _{\textrm{s}}}$, one needs to know the shape of emission and absorption cross sections and the ratio of their maxima. The exact spectrum of the emission cross section could be easily calculated via the equation derived from McCumber relations [14,15]

(4)$${\sigma _\textrm{e}}\left( \lambda \right) = \frac{{{\lambda ^5}}}{{8\pi c{n^2}\tau }}\frac{{I(\lambda )}}{{\int_0^\infty {\lambda I(\lambda )d\lambda } }},$$

where $c$ is the speed of light in vacuum, $\tau =720$ µs is the measured BACs-P lifetime in the first excited state for pumping at $\lambda _{\textrm{p}}=1230$ nm, $I(\lambda )$ is the power spectral density of spontaneous emission per unit wavelength and $n$ is the refractive index of the core. The use of the measured lifetime instead of radiative one is not fully correct but it was justified since the luminescence decay curve of the BACs-P is exponential that point out there is no energy transfer to any other centers. In addition, in [16] it was shown that quantum yield of BACs-Si is equal to 100% for low concentrated bismuth-doped germanosilicate fibers, which means that the luminescent lifetime is equal to radiative lifetime. Since the nature of BACs-Si and BACs-P is similar it is quite reasonable to suggest that for samples with low concentration of BAC-P situation with radiative and luminescent lifetime is the same. The spectrum of the spontaneous emission of bismuth-doped phosphosilicate fiber when pumped at 1230 nm is in Fig. 1(inset). Worth noting that the shape of the spontaneous emission almost unchanged for all the samples studied. Since BACs-Si also contributed to the spontaneous emission curve right side, in (4) instead of experimental data we used the spectrum fitted with Gaussian that excluded the luminescence of BACs-Si. The resulting dependence of $\sigma _{\textrm{e}}(\lambda )$ is presented in Fig. 1(a).

Fig. 1. The emission and absorption cross section spectra (a). Spontaneous emission in phosphosilicate fiber doped with bismuth when pumped at 1230 nm fitted with Gaussian (inset). Spectrum of phosphosilicate fiber with bismuth decomposed into component bands (b).

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Determination of the absolute values of the absorption cross sections is a more complex task. To evaluate the absorption cross section spectrum, one can use two approaches. The first one involves using the following relation

(5)$${\sigma _\textrm{a}}(\lambda ) = \frac{{{\alpha _{\textrm{BAC - P}}}(\lambda )}}{{{C_{\textrm{eff}}}(\lambda )}},$$

where $C_{\textrm{eff}}$ is the effective concentration and $\alpha _{\textrm{BAC-P}}(\lambda )$ is the absorption spectrum of the BACs-P. Since the absorption spectrum of a phosphosilicate fiber doped with bismuth is not equal to $\alpha _{\textrm{BAC-P}}(\lambda )$, but it is a sum of absorption bands of OH$^{-}$, $\alpha _{\textrm{BAC-P}}(\lambda )$, $\alpha _{\textrm{BAC-Si}}(\lambda )$, and unsaturable losses, to obtain $\alpha _{\textrm{BAC-P}}(\lambda )$ we should subtract the other bands from the absorption spectrum of bismuth-doped fiber. All the bands except BAC-P absorption could be measured directly and independently: BAC-Si absorption in a pure silica fibers; OH$^{-}$ band in phosphosilicate fibers without bismuth; unsaturable losses in samples under study using the large signal absorption technique. Thus the procedure of $\alpha _{\textrm{BAC-P}}(\lambda )$ determination is straightforward. An example of such a decomposition for a typical absorption spectrum of a bismuth-doped phosphosilicate fiber is depicted in Fig. 1(b). It should be noted that an accurate measurement of the unsaturable losses in the range of 1.0 - 1.1 µm was impeded by a noticeable excited state absorption. Therefore, in our calculations of absorption cross sections, we limited the spectra to the region 1.15 - 1.5 µm. The determination of $C_{\textrm{eff}}$ is, generally speaking, more challenging. To overcome the problem, we used another approach. The method includes determination the relative shape of the $\sigma _{\textrm{a}}(\lambda )$ and the ratio between the emission (measurable with (4)) and the absorption cross sections maxima ($\sigma _{\textrm{e}}^{\textrm{max}}/\sigma _{\textrm{a}}^{\textrm{max}}$). Finding the shape of the $\sigma _{\textrm{a}}(\lambda )$ does not require knowledge of $C_{\textrm{eff}}$ when using (5), only the overlap integral ($\Gamma (\lambda )$), which could be found through an optical method described in the next section.

Supposing that the overlap integrals at $\lambda _{\textrm{p}}$ and $\lambda _{\textrm{s}}$ are similar (differed by $\sim 5\%$ according to the data presented below in section 3 ), the $\sigma _{\textrm{e}}^{\textrm{max}}/\sigma _{\textrm{a}}^{\textrm{max}}$ could be found according to the value of $g/\alpha$

(6)$${g}/{\alpha }\;=\frac{\sigma _{e}^{n}({{\lambda }_{\textrm{s}}})-\tfrac{\sigma _{a}^{n}({{\lambda }_{\textrm{s}}})}{\sigma _{a}^{n}({{\lambda }_{\textrm{p}}})}\cdot \sigma _{e}^{n}({{\lambda }_{\textrm{p}}})}{\sigma _{e}^{n}({{\lambda }_{\textrm{p}}})+\tfrac{\sigma _{a}^{\max }}{\sigma _{e}^{\max }}\cdot \sigma _{a}^{n}({{\lambda }_{\textrm{p}}})},$$

where $g$ is the BACs-P gain coefficient at $\lambda _{\textrm{s}}$ (when pumped at $\lambda _{\textrm{p}}$ and considering that the measured gain is reduced by unsaturable losses and increased by gain due to BAC-Si) and $\alpha$ is the absorption of BACs-P at $\lambda _{\textrm{p}}$, “n” index point out the cross sections normalized to unity at peak value. The $g/\alpha$ coefficient is convenient to use, since it can be measured experimentally. For the bismuth-doped phosphosilicate fibers studied, the $g/\alpha$ coefficient in the case $\lambda _{\textrm{p}}=1230$ nm and $\lambda _{\textrm{s}}=1330$ nm was at a level of $0.5\pm 0.05$. Based on the shape of the emission and the absorption cross section spectra, one can plot the dependencies of the $g/\alpha$ ratio, $N_2^{\lambda _{\textrm{p}}}$ and $N_2^{\lambda _{\textrm{s}}}$ on $\sigma _{\textrm{e}}^{\textrm{max}}/\sigma _{\textrm{a}}^{\textrm{max}}$, as it is shown in Fig. 2. Taking into account that the experimental value of $g/\alpha$ is $\sim 0.5$, we can determine the $\sigma _{\textrm{e}}^{\textrm{max}}/\sigma _{\textrm{a}}^{\textrm{max}}$ ratio and estimate the difference $N_2^{\lambda _{\textrm{p}}}-N_2^{\lambda _{\textrm{s}}}$ satisfying the measured value of $g/\alpha$, which are $\sim 0.83$ and $0.31$ respectively. Then, having the shape of $\sigma _{\textrm{a}}(\lambda )$, values of $\sigma _{\textrm{e}}^{\textrm{max}}/\sigma _{\textrm{a}}^{\textrm{max}}$ and $\sigma _{\textrm{e}}^{\textrm{max}}$, the $\sigma _{\textrm{a}}(\lambda )$ takes the form depicted in Fig. 1(a). Interestingly, the difference $N_2^{\lambda _{\textrm{p}}}-N_2^{\lambda _{\textrm{s}}}$ in Fig. 2 has a rather weak change in quantities for the considered (reasonable) range of $\sigma _{\textrm{e}}^{\textrm{max}}/\sigma _{\textrm{a}}^{\textrm{max}}$ ratio. It means that regardless the accuracy of our $\sigma _{\textrm{e}}^{\textrm{max}}/\sigma _{\textrm{a}}^{\textrm{max}}$ evaluation, the calculation of the average BACs-P concertation using (3) will provide fairly reliable values. It is important that in the method presented, we ignored the effect of inhomogeneous broadening of BACs-P on the properties of cross sections and methods applied.

Fig. 2. The dependence of the $g/\alpha$ ratio, $N_2^{\lambda _{\textrm{p}}}$, $N_2^{\lambda _{\textrm{s}}}$, and $N_2^{\lambda _{\textrm{p}}}-N_2^{\lambda _{\textrm{s}}}$ versus $\sigma _{\textrm{e}}^{\textrm{max}}/\sigma _{\textrm{a}}^{\textrm{max}}$.

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Presented method allows one to determine average BACs-P concertation measuring maximum achievable pulse energy.

2.2 Determination of BACs-P distribution across the core

To determine relative radial distribution of the BACs in the fiber core we used luminescence measurement-based approach [17]. Similar measurements for bismuth-doped fibers manufactured by different technique and for another glass core composition were conducted in [10–12]. This measurement is based on two assumptions. The first one is that the radial distribution of BACs luminescence $I(r)$ is proportional to the radial distribution of BACs concentration $C(r)$, i.e. $I(r)\sim C(r)$ and the second one implies that the distribution of BACs in the fiber preform is identical to the one in the fiber apart from larger linear scale or at least that the fiber drawing process does not change the relative distribution of BACs across the core.

The schematic of the experiment is in Fig. 3. Collimated laser radiation at 798 nm was incident to the side surface of the sample that was a 300 µm-thick polished cylindrical slab of fiber preform cut at 90 degrees to the axis. The core diameter in the fiber preform was $\sim 1-1.5$ mm . The laser beam diameter near the core of the preform was $\sim 2$ mm that was enough for uniform illumination of the entire sample thickness. Luminescence of the sample was collected by a 50-µm-core (NA=0.22) fiber that was moved across the sample surface using ThorLabs NanoMax 300 stage (not shown in the figure). Before the signal was fed to an Ocean Optics NIRQuest spectrometer, it was passed through a fiber U-bench with a 1000-nm long pass filter to absorb scattered pump light collected by the fiber. The measurement of the luminescence intensity at a wavelength characteristic to certain BACs along the fiber preform core diameter allows finding the desired active centers distribution. Further, to match relative BACs distribution with absolute value of $\overline {C}$ one can use the following relation

(7)$$\overline{C}\cdot \frac{\pi d_\textrm{c}^{2}}{4}=2\pi \int_{0}^{\infty }{C(r)rdr},$$

where $C(r)$ is an absolute distribution of BACs. It should be mentioned that given measured $C(r)$ and mode field ($E(r,\lambda )$, according to refractive index profile measured by Photon Kinetic 2600) we can also estimate the overlap integral that is also equal to effective concentration $C_{\textrm{eff}}(\lambda )$ of BACs divided by the maximum value of $C(r)$ using expression

(8)$$\Gamma(\lambda) =\frac{{{C}_\textrm{eff}}(\lambda )}{{{C}_{\max }}}=\frac{\int_{0}^{\infty }{{{E}^{2}}(r,\lambda )\frac{C(r)}{{{C}_{\max }}}rdr}}{\int_{0}^{\infty }{{{E}^{2}}(r,\lambda )rdr}}.$$

Fig. 3. Schematic of luminescence radial distribution measurement in bismuth-doped fiber preform.

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Collecting the data on the absolute distributions and absorption spectra of BACs-P in the phosphosilicate fibers doped with bismuth, we can find $C_{\textrm{eff}}(\lambda )$ and accordingly the absolute values of the absorption cross section by means of the relation (5) without use of the ratio $\sigma _{\textrm{e}}^{\textrm{max}}/\sigma _{\textrm{a}}^{\textrm{max}}$.

3. Results and discussions

In this work, we investigated four bismuth-doped phosphosilicate fibers (#1–#4) fabricated by conventional MCVD process. Fibers #1-#3 differed by unsaturable losses and active absorption but had similar waveguide structure parameters (see Table 1). Fibers #2 and #4 on the contrary had sufficiently close spectroscopic characteristics and differed by the core diameter. The fiber cores in samples #1-3 consist of pure SiO$_2$ doped with P$_2$O$_5$ with peak concentration up to 6 mol. %. The cladding for these samples was made of pure SiO$_2$. In sample #4 along with $\sim$4.5 mol. % of P$_2$O$_5$ the core composition included fluorine in concentration up to 1 at.%. The cladding of sample #4 was made of pure SiO$_2$ doped with $\sim$3.5 at. % of fluorine which helps to increase the refractive index difference and reduces the fiber core diameter. The maximal bismuth concentration for all samples was below 0.1 wt. %. The cutoff wavelength for all the samples was around 1.0 µm. Some general spectroscopic properties of similar phosphosilicate fibers can be found in [18].

Table 1. Properties of bismuth-doped phosphosilicate fibers.

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3.1 Average BACs-P concecntration

Using the pulse amplification method described above, we measured maximum achievable energy and average concentration of the BACs-P in the samples under study. The length of the test fiber taken was based on the value of the absorption at 1.23 µm. The lower the absorption the longer the fiber. The details of the measurement technique and some results are presented in [17] and summarized in Table 1. It is noteworthy that the $\overline {C}$ estimated for fibers #1-#3 are in consistence with values of absorption at 1.23 µm which can be considered as relative concentration of BACs-P. The same conclusion can be made regarding $\overline {C}$ of #2 and #4 despite their $E_{\textrm{p}}^{\max }$ were different due to differences in the core areas.

3.2 BACs-P radial distribution

To determine radial distribution of the BACs-P, we measured a series of luminescence spectra in the range from 1000 to 1600 nm for the preforms slabs of fibers #1-#4. An example of colormap of luminescence spectra at different distances from preform center (radial coordinate) for fiber #1 is shown in Fig. 4. Slight difference in luminescence peaks magnitude is due to little non-parallelism between the scanning fiber and the sample surface. Since the pump at 798 nm excited not only BACs-P but also BACs-Si that were present in a noticeable amount in our bismuth-doped samples, in the calculations, we used the luminescence intensity at a wavelength characteristic for BACs-P (1280 nm), the wavelength is far enough from the luminescence peak of BACs-Si (1430 nm) and simultaneously is nearby the one of BACs-P (1320 nm) that means the intensity of the signal at this wavelength is adequate for reliable measurements. Results of measurements of the absolute values of BACs-P concentrations recovered using (7) together with the refractive index difference profiles and the mode field distributions at 1330 nm for fibers #1-#4 are in Fig. 5.

Fig. 4. Colormap of luminescence in preform of fiber #1.

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Fig. 5. Radial BACs distribution (solid), fundamental mode fields at 1330 nm (dotted), and refractive index difference profiles (dashed) for bismuth-doped phosphosilicate fibers: #1 – a; #2 – b; #3 – c; #4 – d.

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The edge of BACs distribution and the fiber core match well for all the samples. However, there is a small nonzero part of the BACs distribution that is beyond the border of the fiber core. This may be due to minor diffusion of the bismuth and phosphorus inside the cladding or resolution limit of the measurements. According to the dependencies, one can see that the BACs distributions have characteristic peak near the boundary of the core with the cladding and dip in the central part. Based on data obtained it is possible to estimate overlap integrals at the operating wavelength, which are listed in Table 1. It is worth noting that for all the samples the overlap integrals are around 0.6, regardless of the BACs and mode field distributions. Obviously, to increase the overlap some measures in the MCVD process decreasing the BACs depleted part in the fiber core are necessary.

3.3 BACs-P absorption cross section

Comparing all the data presented above and using relation (5), we calculated the absorption cross section spectra of the BACs-P in the optical fibers #1-#4 presented in Fig. 6. The calculated values of the cross sections in all 4 fiber samples have similar shapes, and their absolute values differ by less than 0.6 pm$^2$. Important to note that the decomposition of the fibers absorption spectra aimed to obtain $\alpha _{\textrm{BAC - P}}$ was made for every sample individually. Since, in general, the optical properties of BACs-P for all the optical fibers presented are similar (in terms of the lifetime of the first excited state, luminescence and absorption bands shapes), the absolute values of the cross sections for the samples under investigation should be close. As one can see, for fibers #2, #3 and #4, this condition is well satisfied, however, the cross-sections for fiber #1 have greater values. This difference can be caused by inaccuracy in the determination of the $E_{\textrm{p}}^{\max }$ for the fiber #1 having lowest active absorption. In other words, it is due to the fact that an accurate measurement of the stated maximum energy most likely required the active fiber length longer than the one used in the experiment (190 m). But it should be noted that a further increase in the length of the active fiber led to an increased influence of nonlinear effects, such as stimulated Raman scattering and four-wave mixing, which also impeded the accurate measurement of the $E_{\textrm{p}}^{\max }$ and, as a consequence, the BACs-P concentration. Therefore, for fiber #1, the concentration of BACs-P is most likely underestimated, and the cross sections, due to the inverse dependence on concentration, are overestimated by $\sim 25\%$. A comparison of the peak values of the absorption cross-section in Fig. 2(a) and independently obtained data presented in Fig. 6 for samples #2-#4 shows that the absorption cross section spectra obtained with different methods are quite close to each other and differed by $\sim 0.3$ pm$^2$. The discrepancy between these two values as well as between maximal value of $\sigma _{\textrm{a}}(\lambda )$ and $\sigma _{\textrm{e}}(\lambda )$ can be caused by strong inhomogeneous broadening of BACs-P.

Fig. 6. Absorption cross section spectra of BACs-P in fibers #1-#4.

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4. Conclusions

In summary, we measured absolute distributions of BACs-P in a series of phosphosilicate fibers with different BACs-P content and fiber core geometry. The results show that the distributions, in general, are follow the shape of the refractive index difference profiles. According to the obtained data, overlap integrals and BACs-P absorption cross section spectra were calculated. The values and the shape of the spectra for most fibers studied are quite similar that is in consistence with the optical features of BACs-P in the samples. The peak values of the BACs-P absorption cross section were evaluated with two independent methods: using the measured $g/\alpha$ ratio and $C_{\textrm{eff}}$. The obtained absorption cross-section have close peak values of $\sim 1.95$ pm$^2$ and $\sim 2.3$ pm$^2$, respectively. Thus the absorption cross section peaked at $\sim 1240$ nm can be estimated as $2.1\pm 0.2$ pm$^2$. The peak emission cross section derived from the McCumber theory is 1.6 pm$^2$. We believe that the results obtained will be useful for the simulation of bismuth-doped phosphosilicate fiber-based lasers and amplifiers and will contribute to the further progress in the investigation of the nature of the bismuth active centers.

Funding

Russian Science Foundation (19-19-00715).

Disclosures

The authors declare no conflicts of interest.

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fiber	sample length, m	abs. @1.23 µm, dB/m	unsat. loss @1.33 µm, dB/m	$d_{c}$ , µm	$E_{p}^{max}$ , µJ	$\bar{C},$ $10^{16}$ cm $^{- 3}$	$Γ$ @1.23 µm	$Γ$ @1.33 µm
#1	190	0.3	0.014	7	13.8	2.9	0.62	0.59
#2	120	0.48	0.025	6.5	13.8	6.0	0.67	0.63
#3	80	0.84	0.071	7	9.6	8.9	0.67	0.63
#4	100	0.52	0.032	5	7.2	5.9	0.68	0.64

Radial distribution and absorption cross section of active centers in bismuth-doped phosphosilicate fibers

Abstract

1. Introduction

2. Methods

2.1 Average BACs concentration

2.2 Determination of BACs-P distribution across the core

3. Results and discussions

3.1 Average BACs-P concecntration

3.2 BACs-P radial distribution

3.3 BACs-P absorption cross section

4. Conclusions

Funding

Disclosures

References

Cited By

Figures (6)

Tables (1)

Equations (8)

Optics Express