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Abstract
We present a thulium-doped silica fiber, featuring a depressed cladding, for applications at wavelengths below 1800 nm. The depressed cladding is used as a distributed filter suppressing amplified spontaneous emission at longer wavelengths, which helps promote emission at shorter wavelengths. We describe the fiber design process that was carried out by using a combination of numerical methods. The fiber was prepared in-house by a combination of the standard modified chemical vapor deposition method and nanoparticle doping. We demonstrate the effectiveness and tunability of ASE filtering, which is influenced by fiber bend radius and its variation.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The spectral range 1625-1800 nm is of interest for applications in medicine, where a suitable absorption line of lipids at around 1720 nm exists in a region of low absorption and scattering of water [1–5], and material processing, where strong absorption of plastic materials allows for efficient polymer welding [6]. Interesting opportunities have also recently arisen for extending the bandwidth of optical telecommunications beyond the conventional L-band (1565-1625 nm) [7], mainly thanks to the advancement of hollow-core fiber technology [8,9], which allows for low-loss transmission at wavelengths, where traditional silica fibers experience higher losses due to material absorption and bend-induced losses. However, utilizing this band has so far proven difficult due to the lack of suitable laser sources. Some fiber sources based on nonlinear effects such as stimulated Raman scattering [3] and parametric chirped-pulse amplification [10] were developed, and fiber lasers based on Bi-doped fibers [11], Tm-doped fibers co-doped with Ho [12], Tb [13], and Ge [14] were also presented. It nonetheless seems that none of these solutions have seen wider adoption so far.
Thulium-doped fiber lasers and amplifiers are candidates for cost effective and scalable sources, thanks in part to the broad emission band of Tm3+ ions in silica glass matrix, which spans from 1600 to 2100 nm [15,16]. Accessing the part of the fluorescent spectrum below 1800 nm is, however, challenging due to strong quasi-three-level behavior, which results in significant reabsorption. The reabsorption can be mitigated by intense pumping, which generates high population inversion and as such, decreases the number of Tm3+ ions in ground state, which cause reabsorption. One of the issues with this approach is that the gain coefficient at wavelengths above 1800 nm is high even for low levels of inversion, which leads to strong generation of amplified spontaneous emission (ASE). The ASE in turn depletes the upper laser level population, limiting the maximum achievable inversion, or worse, initiates parasitic lasing at undesired wavelengths. Using short lengths of fiber and an ASE filter is one way to overcome these issues [17–19].
Another way is to prevent the amplification of spontaneous emission by extracting it from the core region of the fiber. This can be achieved in a practical manner by introducing an inner cladding with a lower refractive index (RI) than that of the outer cladding. The resulting RI profile of the fiber has a characteristic “W” shape with a depress in the cladding around the core. This waveguide feature allows us to engineer a fundamental mode (LP01) cutoff, beyond which the fiber becomes highly lossy. The whole fiber then acts as a distributed ASE filter, which can be tuned by varying the fiber bend radius [20]. Theoretical analysis of “W” profile fibers has been extensively covered in literature from many points of view including the development of simplified formulas [21], examination of coupling between the LP01 mode and discrete cladding modes [22], development of efficient matrix methods [23], rigorous numerical modeling [24] and simulation using the beam propagation method [25]. Meanwhile, the use of “W” profile fibers as dispersion shifted and dispersion compensating fibers has established itself in optical communication networks. Even more relevantly, a thorough examination of “W” profile fibers for S-band erbium-doped fiber amplifiers has been carried out by Vincetti et al. [26] and usage in S-band erbium-doped fiber lasers (EDFL) has likewise been documented [27]. In addition, a theoretical analysis of a fluoride, “W” profile, depressed-cladding thulium-doped fiber (dc-TDF) for wavelengths beyond 1650 nm has been carried out by Kakkar et al. [20], no such fiber has, however, to the best our knowledge been prepared and published yet. As stated by Kakkar et al., the advantage of using a dc-TDF compared to optical filters stems from the fact that gain suppression in the active fiber leads to redistribution of power among signal wavelengths. When using an optical filter, the power is instead wasted on generating ASE, which is subsequently filtered out leading to reduced gain and efficiency. This is true for gain flattening as well and as such dc-TDFs are potentially much more efficient when used in optical amplifiers. Some caveats not yet covered in literature in relation to dc-TDFs include the fact that the losses of “W” profile fibers are not monotonous with increasing wavelength, but rather contain quasi-periodic peaks [22]. The lack of experimental coverage of more sophisticated fiber bending techniques, which help eliminate these effects, is readily apparent. In this article, we aim to design, prepare and characterize a silica dc-TDF for efficient applications below 1800 nm. We also briefly examine techniques aimed at smoothing of the loss characteristics of the prepared fiber.
2. Fiber design
2.1 Engineering the LP01 mode cutoff
In an optical fiber, a mode cutoff of a particular guided mode occurs at the wavelength where the value of the effective RI of the mode, neff, reaches the value of the RI of the cladding (see Fig. 1(a)). This principle is usually observed at the cutoff wavelength of standard single-mode fibers, where the fiber begins to guide only the LP01 mode. Similarly, “W” profile fibers have an LP01 mode cutoff wavelength beyond which no propagating modes are supported because the value of the effective RI of the LP01 mode can decrease below that of the outer cladding. To determine this wavelength, we used a proprietary mode solver capable of quickly finding modes and their associated effective refractive indices in an arbitrary, radially symmetrical waveguide structure by numerically solving the Helmholtz equation in cylindrical coordinates [28]. The “W” fiber geometry has four degrees of freedom in our case, those being: $\Delta$ndep - the “depth” of the depress, $\Delta$ncore - the “height” of the core, wdep - the width of the depressed region, and rcore - the half-width of the core. The exact boundaries are displayed in Fig. 1(b), where wdep is determined from the positions of the outer half-depth of the depress and half-width of the core.
The RI of the outer cladding is determined by the type of tube, typically fused silica, used for preform preparation and also serves as the reference point for $\Delta$n values. We reduced the dimensionality of this problem by first setting $\Delta$ndep to 4.8×10-3, which is close to the limits of our modified chemical vapor deposition technology. We also reused a core design from a standard TDF, which performed well in amplifier applications [29]. This selection reduces the number of degrees of freedom to one, wdep, and guarantees that the designed fiber stays within technological constraints. A model of the RI profile was made using a linear combination of two super-Gaussian approximations, one for the depress and core each. A step-index model can be used as well but offers little advantage when used in conjunction with the numerical methods we employed. The LP01 mode cutoff wavelength was arbitrarily set to a range from 1800 nm to 1900 nm, from which a range of suitable wdep was generated. The first attempt was unsuccessful as the starting combination of rcore = 3.02 µm and $\Delta$ncore = 10.02×10-3 resulted in LP01 mode cutoff far beyond the desired range. The second attempt with $\Delta$ncore lowered by 2×10-3 to 8.02×10-3 succeeded and a suitable RI profile with LP01 mode cutoff at 1853 nm was found. Several variations of this model with either varied wdep or reduced $\Delta$ndep were generated (see Fig. 2) to study the influence of these parameters on bend losses. It bears mention that the RI of the core is directly influenced by the concentration of aluminum and thulium oxides in the core region. High concentrations of aluminum oxide are linked with increased fluorescent lifetimes and quantum efficiency in TDFs [30]. Notice in Fig. 2 that to keep the LP01 mode cutoff at around 1850 nm with reduced $\Delta$ndep we must also reduce $\Delta$ncore, which undesirably restricts the aluminum oxide concentration. A way to avoid decreasing $\Delta$ncore is to reduce rcore, which is effective because there is a large overlap with the LP01 mode. This approach carries a penalty in form of increased coupling losses as the mode field mismatch between the LP01 modes of the dc-TDF and SMF-28 fiber, which most fiber components use, will increase. The width of the depress, wdep, has only small influence on the LP01 mode cutoff wavelength, mainly because the overlap of the LP01 mode with the outer cladding is relatively small.
Fig. 2. Generated variations with reduced $\Delta$ndep (blue) and varied wdep (red); original (black).
2.2 Studying bend induced losses
Finding the LP01 mode cutoff wavelength is insufficient for the design of dc-TDF mostly because the propagation losses can substantially vary with fiber bend radius. We used a freely available finite difference beam propagation method (FD-BPM) package for the Matlab environment [31,32] to investigate propagation losses and splice losses in the designed dc-TDF. The package includes a solver capable of quickly finding modes in an arbitrary 2-D structure with a complex RI. We modified this solver to calculate complex effective indices of improper, lossy modes, whose real refractive indices are close to those of proper, propagating modes. The imaginary part of the complex RI is then used to estimate losses. This method is relatively fast in estimating propagation losses in bent waveguides and we used it to study the differences between RI profile models with LP01 mode cutoffs close to 1850 nm from Fig. 2. The results of those simulations are displayed in Fig. 3 and the parameters are summarized in Table 1. Note that the size of the main area was intentionally kept small enough such that the loss curves are without inflection points, which allowed us to easily identify the key differences. Since the LP01 mode of a bent fiber is symmetric about the axis parallel to the bend direction, the X-axis in our case, we set the symmetry of the simulation area along the X-axis, which halved its size and sped up the calculation. The full simulation area included an absorbing padding that is defined by the pad factor, which is the ratio of the widths of the full simulation area to the widths of the main simulation area, and absorption coefficient $\alpha$ [31,32].
Fig. 3. (a) Comparison between profiles with varied wdep. (b) Comparison between profiles with reduced $\Delta$ndep. FMC: LP01 mode cutoff.
Table 1. Simulation parameter summary
Narrowing of the depressed region leads to increased losses and steeper roll-off, because the overlap of the LP01 mode with the outer cladding increases. Decreasing the overall $\Delta$n, also leads to increased losses but the roll-off is less effected. For our purposes keeping the highest $\Delta$n in combination with a relatively narrow depressed region should yield the best results, meaning low losses at operating wavelengths and high losses beyond the LP01 mode cutoff. We used FD-BPM with an extended fiber cross-section to study the losses of the fiber with the most suitable profile model. This method is computationally expensive but offers more insight into the processes taking place during the propagation of light through dc-TDF under different conditions than simpler methods. The simulation setup consisted of a couple of connected sections of fiber, one of SMF-28 fiber, the other of the dc-TDF model under investigation. The bend radius of the SMF-28 and dc-TDF fiber was the same to simulate input coupling losses corresponding to a scenario, where both sections of fiber including the splice are wound around a mandrel. The propagating beam was initialized for simplicity as the LP01 mode of a straight SMF-28 fiber and propagated for 1 cm to stabilize. The coupling loss was estimated from the ratio of total beam power at the end of the bent SMF-28 fiber and remaining beam power after 1 mm of propagation through the bent dc-TDF. The propagation losses were then determined from the ratio of total beam power after 1 mm and after 20 cm of propagation through the bent dc-TDF, similarly to the approach used by Vendeltorp-Pommer et al. [25]. The 20 cm length is a compromise between computational time and accuracy as losses are not always constant along the whole length of the simulated fiber. Other simulation parameters are summarized in Table 1. The same settings regarding symmetry and absorbing padding as before were used. We also observed loss oscillation as a function of wavelength for fixed bend radii, which is caused by varying coupling efficiency between the LP01 mode and various cladding modes as examined by Francois et al. [22]. This effect is difficult to simulate quantitatively as it requires modeling the whole fiber cross-section including the edge of the polymer coating and so it will later be investigated experimentally instead. The predicted splice loss between SMF-28 and the designed dc-TDF is 0.5-0.6 dB without optimization. We combined the calculated loss curves with gain coefficient curves to show expected gain spectra in relation to the relative population of upper metastable laser level, Nrel, and compare them to standard TDF of similar core composition (see Fig. 4).
Fig. 4. Gain coefficient dependent on relative upper metastable level population with 10 % step. (a) standard TDF, (b) comparison with proposed dc-TDF, 2 cm bend radius; Cross-section shapes taken from [30], and the absolute values are calibrated according to [33].
3. Fiber preparation
The fiber preform was prepared using a substrate glass tube (Heraeus F300) inside of which layers of fluorine-doped silica were deposited first. Then, a single porous layer of pure silica was deposited and doped using a suspension of alumina nanoparticles in a TmCl3 solution, where ethanol (99.9 %) was used as solvent. The last step forms one of the approaches developed as part of our nanoparticle doping technology [34,35]. The technology does not allow for precise control over rcore, which remains constant, and as such we used the ratio of wdep to rcore to determine the number of fluorine doped layers. The $\Delta$ndep parameter is controlled by the concentration of fluorine during deposition and the $\Delta$ncore parameter is controlled by the concentration of alumina nanoparticles and Tm3+ in the suspension. We note that the nanoparticles dissolve during the fiber drawing process [35,36], but works examining fibers where the nanoparticles persist have also been published [37,38]. The preform, more accurately called frit at this point, was then dried, sintered and collapsed, and the RI profile was measured using a preform analyzer (Photon Kinetics A2600).
The parameters obtained from preform analysis were then used to model the drawn fiber, assuming only scaling in the radial coordinate (see Fig. 5 and Table 2) neglecting changes induced by dopant diffusion during fiber drawing. The $\Delta$ncore of the prepared preform was found to be too high, we therefore modified wdep and rcore to maintain the desired loss profile. We used a 10/25 mm (inner/outer) diameter glass tube to overclad the preform and drawn the fiber with standard 125 µm cladding diameter. The fiber was immediately coated with high-index polymer (DeSolite 3471-3-14). The choice of polymer coating plays a small role in the final transmission characteristics of the fiber due to the existence of cladding modes and their coupling to the LP01 mode [22]. The predicted splice losses between the drawn fiber and SMF-28 fiber are 0.7-0.8 dB but can be theoretically lowered to 0.3-0.4 dB by using an intermediate section of Nufern 1310M-HP fiber without additional splice optimization.
Table 2. RI profile parameters at different stages of fiber design and preparation. The drawn fiber was measured from both ends.
4. Fiber characterization
We first verified the RI profiles of both ends of the whole drawn fiber (ca. 400 m) using an interferometric fiber analyzer (Interfiber Analysis IFA-100) to uncover possible inhomogeneities. Slight differences between RI profiles of the rescaled preform and the fiber ends are apparent. The measured RI profiles of both fiber ends together with that of the preform are displayed in Fig. 5 and the values of parameters are summarized in Table 2 together with the parameters from previous stages. The RI profile of the preform has been scaled and adjusted for the measurement wavelength. The doping concentration was verified by measuring absorption spectra on 11 cm long sections of straight fiber taken from both ends of the drawn fiber. Comparing the measured values to known Tm3+ absorption cross-section at 1640 nm we approximate the Tm3+ doping concentration to around 2400 ppm. The difference in the absorption spectra, displayed in Fig. 6, can be explained by the difference in core overlap factor, which is 0.67 and 0.6 at 1640 nm at the start and at the end of the fiber respectively. We also verified the concentration using electron microprobe analysis (EMPA), which confirms that the Tm3+ concentrations of both fiber ends are approximately the same. We also determined that the concentration of Al2O3 is 5 mol. % in the core area using the same method. We also attempted to measure the concentration and distribution of fluorine but the EMPA measurements are difficult to interpret due to the complicated nature in which the fluorine incorporates itself into the silica matrix. We nevertheless found that some fluorine penetration into the core area probably occurred, which might influence the fluorescent properties of the fiber [35].
Fig. 6. Absorption spectra of both fiber ends. Note the influence of excess fiber losses on the absorption spectra. Digital filtering was applied in post-processing.
The background losses of the fiber are relatively low at around 41 dB/km at 981 nm as measured by the cutback technique using an optical spectrum analyzer (Ando AQ6317B) and a tungsten light bulb as a broadband light source.
Fluorescence decay curves were measured using a 792 nm laser diode (Lumics LU793M250) as a source and an InGaAs PIN photodiode (Hamamatsu G12183-10K) detector on approximately 2 mm long samples with sideways emission detection. The fluorescence lifetime was determined according to procedure described in [36]; the decay curves were measured in a wide range of excitation powers, the decay times were obtained from 1/e value on the normalized curves and the fluorescence lifetime was obtained by extrapolation to zero power. The fluorescence lifetime was nearly identical for both fiber ends, the measured curves for dc-TDF end are depicted in Fig. 7(a). The curves exhibit typical behavior with deviations from single-exponentiality and faster decay with increasing power due to energy transfer (ET) processes [30]. Slight deviation from single exponentiality can be observed even at lowest used power, where the influence of ET should be suppressed. This phenomenon can be likely ascribed to the partial penetration of fluorine into the core, which leads to minor variations of Tm3+ environment throughout the core. The 3F4→3H6 fluorescence lifetime determined from this measurement was around 600 µs, as depicted in Fig. 7(b), which is in a good agreement with values typically found in MCVD fibers with similar compositions [39].
Fig. 7. Fluorescence lifetime characterization of dc-TDF end, (a) measured decay curves, (b) decay time-power dependency and extrapolation to zero power according to Eq. (1) from [36].
LP01 mode losses were measured using an approximately 11 cm section of fiber, which was subjected to various bending conditions. We used a tungsten light bulb as a source and a Fourier transform optical spectrum analyzer (FTIR, Thorlabs OSA203C) to first capture the transmission characteristics of a straight section of fiber and then used those characteristics as a reference to determine the bend induced losses measured the same way. We wound the fiber around a mandrel at several fixed bend radii to match the conditions of the simulation setup. It is important to note here that both ends of the drawn fiber behave differently despite only minor differences in their respective RI profiles. One of the ends of the fiber displays loss characteristics close to those predicted by the simulation using the rescaled preform model as shown in Fig. 8(a). As previously mentioned, the loss characteristic exhibits quasi-periodic variation, while the fiber bend radius is kept constant. This behavior can be mitigated by varying the bend radius of the fiber. Some well-established techniques used in construction of cladding-pumped fiber lasers can be used as a reference; for example, deforming the fiber in a kidney shape. We also used a 3D printed fiber bending device, in which a section of coiled fiber can be placed and subsequently bent in direction perpendicular to the coiling direction by adjusting the position of the upper and lower part of the bending device. Using this device, it is possible to achieve a tunable and monotonous loss characteristic as shown in Fig. 8(b), which simplifies the construction of fiber lasers and amplifiers.
Fig. 8. (a) Bend loss comparison between measured and simulated values. (b) Bend losses induced by bending device, the inset includes a drawing of the bending device from two view angles. Digital filtering was applied in post-processing.
We also measured emission spectra of the 3F4→3H6 transition under in-band pumping conditions (in-house made EDFL @ 1560 nm) using a FTIR (Thorlabs OSA203C) and filter WDMs as pump filters. The pump power was kept as low as possible and a short sample was used to avoid the generation of ASE. The samples were approximately 4 mm long and the emission was detected in the backwards direction. The normalized emission spectra are slightly blue shifted compared to a standard TDF as shown in Fig. 9(a). Furthermore, we measured forward ASE of an approximately 94 cm long section from the end of the fiber using the same instrumentation with additional fused couplers to attenuate the signal. A shorter length of standard TDF (64 cm, 1600 ppm Tm3+, overlap factor $\approx$ 1) with equivalent gain coefficient was used for comparison. Under the same pumping conditions, the dc-TDF exhibits blue shifted forward ASE spectra as shown in Fig. 9(b). Further experimental evaluation of the performance of this fiber in fiber lasers or amplifiers is beyond the scope of this article and will be presented in a another report [40].
Finally, we used a numerical model to compare the expected gain and ASE spectra for the standard TDF (1600 ppm Tm3+, overlap factor $\approx$ 1, 660 µs fluorescent lifetime) and the dc-TDF. The numerical model considers only the 3F4→3H6 transition, similarly to [41], although with a different level marking scheme. The relevant thulium cross-sections were taken from [33], assuming room temperature of 23 °C. The results obtained for 1.5 m long standard TDF and dc-TDF fibers are presented in Fig. 10. The spectral dependence of losses was the same, as shown in Fig. 8(a). We used the simulated loss profiles instead of the measured ones due to their simplicity and similarity to the measured ones. The input signal level was set at -20 dBm and the co-propagating pump was set to 3 W at 1565 nm, which is the expected performance of an erbium doped fiber pump laser. As shown in Fig. 10(a), the gain is shifted to shorter wavelengths compared to the standard TDF. The amount of wavelength shift is influenced by the bend radius. We also include the ASE noise spectra generated while amplifying a signal at 1760 nm, which are shown in Fig. 10(b).
Fig. 10. Results of numerical modeling: (a) Gain spectra for a standard TDF and dc-TDF of equivalent doping concentrations, both 1.5 m long. (b) ASE spectra for with signal at 1760 nm (amplified signal is excluded).
5. Conclusion
We presented the design and preparation of a dc-TDF for wavelengths below 1800 nm. The fiber was designed with the help of a combination of numerical methods, which were used to predict the LP01 mode cutoff and bend induced losses of the dc-TDF. We used the MCVD method together with the nanoparticle doping technique to prepare the fiber. We presented the characterization of bend induced losses of the drawn fiber and investigated techniques to ensure a monotonous loss characteristic by varying the bend radius. The depressed cladding behaves as a distributed ASE filter with attenuation of >100 dB/m measured for wavelengths above 1800 nm, which is well above the maximum gain coefficient achievable in this fiber. The ASE filtering leads to blue shifted emission characteristics and allows the construction of efficient lasers and amplifiers at wavelengths around 1700 nm. Numerical modeling was used to calculate the gain spectrum of the dc-TDF fiber and compare it to that of a standard TDF. This comparison shows a blue shift of the gain spectrum, which depends on the amount of bend induced losses in the fiber.
Funding
The work was co-funded by European Union and the state budget of the Czech Republic under the project (LasApp CZ.02.01.01/00/22_008/0004573); CESNET Development Fund (672/2021).
Acknowledgments
The authors thank the Faculty of Electrical Engineering, Czech Technical University in Prague (Matej Komanec) for the instrumental assistance during the measuring of the spectral properties.
Disclosures
The authors declare no known conflict of interest.
Data availability
Data underlying the results presented in this paper are available in Ref. [42].
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