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Abstract
In this paper we present numerical and experimental results revealing that the mode instability threshold of highly Yb-doped, Ce/Al co-doped pedestal fibers is affected by the size of the index-increased pedestal structure surrounding the core. An alternative preparation technology for the realization of large mode area fibers with very large Al-doped silica pedestals is introduced. Three different pedestal fiber design iterations characterized by low photodarkening were manufactured and tested in counter-pumped amplifier setups. Up to 1.9 kW continuous-wave output power of near-diffraction-limited beam quality (M2 = 1.26) was achieved with an 18/200/420 µm fiber of very low NA = 0.042, limited only by the occurrence of mode instabilities.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The evolution of ytterbium (Yb)-doped fiber lasers as brilliant high-power light sources with nearly diffraction limited beam quality independent of the output power has been interrupted by a nonlinear thermo-optical effect called transverse modal instability (TMI) [1,2]. This effect is characterized by a threshold-like onset of beam-fluctuations between the fundamental mode (FM) and higher order modes (HOM), rapidly decreasing the output beam quality [3]. Due to its thermo-optical nature, this effect is influenced by the fiber modal content and mode excitation [4], the core/cladding diameters and gain saturation [5] as well as the thermal load introduced via the quantum defect, background absorption losses and photodarkening [6]. Additionally, the distribution of the thermal load along the active fiber is changing the TMI threshold [7]. During laser operation, even single-mode fibers experience refractive index changes induced by temperature- and population inversion changes [8,9] which can lead to the guidance of HOM. Increasing the HOM differential losses via bending [10] can raise the TMI threshold. However, the first step towards developing fibers with high TMI thresholds is always optimizing the fiber design and fabrication technology.
One established approach is to reduce the cores numerical aperture (NA) for given core/cladding diameters in order to obtain fibers with low V-parameters and thus few-mode to single-mode properties. Beyond this, doping with rather low Yb3+-concentrations can significantly decrease the thermal load due to the approximately quadratic dependence of photodarkening equilibrium losses on the Yb concentration [11]. Since longer fiber lengths are then required to obtain the same pump absorption and signal amplification, the heat load per meter due to quantum defect in the fiber is reduced as well. This combined advantage can increase the TMI threshold significantly, enabling the development of fiber amplifiers with single-mode output powers greater than 4 kW [12].
However, very low Yb-doping concentrations are not always desirable. To achieve sufficient pump absorption, the required active fiber lengths of low-Yb-fibers are often very long (> 30 m). This hampers the compact design of fiber lasers for industrial applications, and the long absorption lengths also favor undesirable nonlinear effects like Stimulated Brillouin Scattering (SBS) and Stimulated Raman Scattering (SRS). Hence, a solution is needed to maintain sufficiently high Yb concentrations along with low photodarkening. By co-doping with cerium (Ce) ions the photodarkening effect can be almost completely prevented in highly Yb-doped silica laser fibers [13,14].
In order to improve the incorporation of Yb and Ce ions into silica, aluminium (Al) is needed as a solutizer [15]. Unlike co-doping Al and phosphorus (P) at equimolar amounts [16,17], these three ions (Yb/Ce/Al) increase the refractive index. To keep the core NA low either index-decreasing co-dopants like fluorine (F) could be added [18], or the core could be surrounded by a pedestal structure of increased refractive index [19]. Such a pedestal is typically doped with germanium (Ge) in erbium (Er)/Yb-doped [20,21] and thulium (Tm)/Al-doped fibers [22,23], respectively.
Only a few experiments were carried out so far employing Yb-doped fibers (YDF) with pedestal structures [24–29]. Very recently, Liu et al. [29] reported the fabrication of a 25/50/400 µm (core/pedestal/cladding diameter) Yb-doped phosphosilicate fiber with a Ge-doped pedestal resulting in a core NA of 0.054. The 8 m fiber was tested in a high-power bidirectionally pumped amplifier system and 3.2 kW output power were obtained with a beam quality of M2 = 1.79, confirming some HOM-content. Their results show that pedestal structures can be suitable for high-power fiber lasers. However, further steps have to be taken to obtain nearly diffraction-limited beam quality for single-mode high-power applications.
In this paper we present numerical and experimental results, which reveal that the pedestal size has significant impact on the achievable TMI threshold. In section 2, the current common choice of pedestal diameter is discussed taking numerical mode overlap simulations into account. Section 3 introduces two technologies for the realization of Ce/Al co-doped, highly Yb-doped Large Mode Area (LMA) fibers with pedestal structure for very-low core NA and high-power, narrow-linewidth operation. The technological limits of the modified chemical vapor deposition (MCVD) process in combination with the solution doping technique concerning both geometry and refractive index, are overcome by the powder-sinter-process (REPUSIL [30]). Three different pedestal fiber design iterations with very low photodarkening were manufactured and tested. The experimental results presented in section 4, and discussed in section 5, demonstrate in their entirety a general scaling concept towards single-mode high-power fiber lasers. For completion, a summary is shown in section 6.
2. Mode simulation and pedestal design considerations
Current research agrees that, due to the interference of the FM with HOM/s, modal instabilities are initiated (Ref. [31] and references therein). Here, the mode content as well as the mode excitation at the beginning of the fiber affect the TMI threshold significantly. TMI has only been observed for single-mode and few-mode fibers, but never for multimode fibers, as their modal interference seems to hinder the necessary introduction of a thermal grating. Therefore, only the lowest order modes with the largest overlaps (OL) with the doped core area could be of interest for TMI. Compared to typical non-pedestal fibers, the index-raised pedestal results in distinct changes in the modal content beyond the core modes. In this section, we numerically investigate the influence of the pedestal design on the OL of the resulting modes with the doped core region, for bent and unbent scenarios.
In literature, an appropriate pedestal diameter is typically selected such that the core modes are no longer influenced by a change in pedestal size [19]. Then the pedestal is not behaving like an extended core feature, but rather like a cladding. The realized pedestal to core diameter ratios are typically ranging from 1.5:1 to 4:1 [23–27,29]. Yet, these pedestal sizes might not be the optimal choice. As described by Simakov et al. [23] in the context of Tm-doped fibers, pedestal structures guide coupling losses from splices and could capture a significant fraction of spontaneous emission from the core. They argue, that the pedestal light could be amplified and interact with the core. In order to estimate the detrimental interaction strength between the pedestal- and the core radiation, the relative area overlap of core and pedestal was considered. Increasing pedestal diameter yields effective overlaps with the core area proportional to 1/dped2 (Ref. [23], Fig. 3). However, this purely geometric consideration neglects the modal composition of the fiber determined by its refractive index structure. As previously argued, only pedestal-confined modes having a significant OL with the doped area could be parasitically amplified.
Table 1. Mode simulation parameter
To investigate how an increased pedestal diameter affects the mode OL with the doped area, we performed mode simulations based on a ‘poor man’s approach’ [32] for a straight 18/x/310 µm step-index fiber (SIF), varying the pedestal diameter x. In Table 1, the simulation and fiber parameter for this first “Simulation 1” are listed. The core dimension and pedestal NA were chosen to match our drawn pedestal fibers and computation times were significantly reduced by keeping the cladding diameter at 310 µm, instead of 420 µm. In a second set of simulations (“Simulation 2”), the coiling diameter of fibers was varied to investigate bending-induced effects while keeping the pedestal at exemplary diameters of 50 µm and 200 µm. The same pedestal diameters were chosen for “Simulation 3”, where the pedestal NA was varied to test whether the doping OLs change for different core/pedestal doping concentrations. All calculated modes are orthogonal eigenmodes of the entire fibers refractive index structure. Nevertheless, for better differentiation and visualization we will refer in this paper to core-confined modes with the largest OLs with the doped area as “core modes”, and to the modes confined in the pedestal/cladding as “pedestal/cladding modes”.
2.1 Simulation results for straight fiber
Resulting from simulation 1, in Fig. 1 the mode OL with the uniformly doped core area is shown over the pedestal diameter. Despite having coupled central core, pedestal core and cladding core modes, with the parameters used here, the coupling is low enough to label the core modes LP01 (blue) and LP11 (red) separately from the pedestal- and cladding-confined modes (grey). The mode profile insets in Fig. 1 correspond to the labeled OLs (crossing of dashed lines). For 50 µm pedestal diameter the LP01 (OL = 93.1%), LP11 (78.9%) and first pedestal-confined mode shaped like a LP21 (43.2%) are depicted. Increasing the pedestal diameter above 50 µm, arcuate rising and falling pedestal mode OLs can be found. These pedestal modes have the shape of LP21-modes in the direct vicinity of core, as shown for 200 µm pedestal diameter (OL = 17.3%, pedestal indicated by dashed white line, with zoom to core area), but expand into the pedestal in the shape of LP2m-modes with increasing m for larger pedestals. They occur because the fiber is close to the cutoff of the LP21 core modes, which would be guided for a V-parameter of Vcore > 3.832 (compare Table 1).
Fig. 1. Mode OL with the doped area (%) over the pedestal diameter for 150 calculated modes of an unbent 18/x/310 µm pedestal SIF. Mode profiles (incl. whitely dashed core and pedestal area boundaries) and OLs for 50 µm and 200 µm pedestal diameter are shown. All simulation parameters are summarized in Table 1.
According to the initial discussion, a 50 µm pedestal diameter would seem like an appropriate choice, since the mode OL of the core modes is not changing for larger pedestal diameters anymore. However, the OL of the pedestal modes is up to > 40%, as marked by the black dotted line in Fig. 1. This is significantly higher, than the purely geometrically estimated area overlap with the core as done in [23], which would be 182/502 ∼ 13%. Consequently, the influence of the pedestal modes on the laser performance could be higher than expected. Amplified pedestal modes can degrade the beam quality, reduce the core-light slope efficiency and might induce TMI earlier, since they effectively behave like core HOM. Hence, a larger pedestal diameter should be chosen to reduce the pedestal mode OL with the doped fiber core area significantly. For the 200 µm pedestal diameter, the doping OL of the pedestal modes is reduced by a factor of ∼ 2.5 to OL < 18%. Restricting ourselves to not consider index reduced cladding or trench designs here, the ultimate limit would be enlarging the pedestal to the cladding size. A maximum cladding mode OL of 12.1% was obtained for a fully index-raised cladding of an 18/400 µm SIF with NA = 0.066.
While this first simulation was done for a straight SIF and revealed that small pedestal diameters result in detrimental large OLs of pedestal modes, in reality the fiber is typically coiled to a specific diameter. This deforms the refractive index profile and affects the guiding properties as well as the modal composition [33]. To compare the mode OL with the doped area of a bent small pedestal SIF (dped = 50 µm) with large pedestal SIF (dped = 200 µm) additional mode simulation were performed.
2.2 Simulation results for bent fiber
The simulation parameters of this “Simulation 2” are shown in Table 1 and the resulting mode OLs are illustrated in Fig. 2 for the 18/50/310 µm SIF (left) and 18/200/310 µm SIF (right) for coil diameters from dcoil = 0.08 m to 0.48 m. Since the long-term mechanical stability of our drawn pedestal fibers was not ensured for coil diameter smaller than 0.1 m, the blue shaded area represents an experimental constraint.
Fig. 2. Simulated OLs with doped core area (%) over the coil diameter for an 18/50/310 µm SIF (left) and 18/200/310 µm SIF (right). Mode profiles are shown for the pedestal mode of largest OL at dcoil = 0.48 m. All simulation parameters are summarized in Table 1.
While the two LP11 modes were degenerate for the unbent fiber, the notation of “even” and “odd” modes is required for bent fibers and refers to the mode’s intensity lobes being aligned in direction of the bending (“even”) or perpendicular to it (“odd”). The depicted mode profile insets of the pedestal modes of largest OL at dcoil = 0.48 m once again illustrate their LP21-like shape as well as the significant reduction of the OL from 40.8% (18/50/310 µm) to 14.7% (18/200/310 µm) found for the straight fibers. Decreasing the coil diameter is not continuously reducing the largest pedestal mode’s OL. Instead, different pedestal modes exhibit rising and falling doping OLs, competing for maximum OL. Nonetheless, the 50 µm pedestal modes’ OLs (Fig. 2 left, grey) remained > 33% for any coil diameter (min. at dcoil ∼ 0.17 m), while those for the 200 µm pedestal (Fig. 2 right, grey) never exceeded 22% (max. at dcoil ∼ 0.11 m). Hence, this advantage of the larger pedestal diameter persisted over all coil diameters.
Exceptions were anti-crossings of the coupled core and cladding waveguide modes. They occur between pedestal- and LP11 modes, when the two modes’ effective indices are about to cross under perturbation, but the transverse mode profiles evolve to be nearly identical [34]. Within the chosen fiber dimensions and coil diameter step size of Δdcoil = 2 mm these anti-crossings were only observed for the 18/200/310 µm SIF and not for the smaller pedestal version. One reason for this is the increased bending-susceptibility of large pedestal diameter SIFs. In Fig. 3 the conformal mapped refractive index profiles (cRIP) of SIFs with 50 µm (left) and 200 µm pedestal diameter (right) are shown at a coil diameter of 0.114 m, along with the corresponding effective indices of the core modes (dashed lines, black) and pedestal/cladding modes (dashed lines, grey). As illustrated, the outermost refractive index of the pedestal structure is higher for the 200 µm version (Fig. 3, right). Consequently, the pedestal modes effective indices are raised above the core modes effective indices and anti-crossings occur, which is not the case for the small pedestal version. Additionally, the larger the pedestal diameter, the more modes are guided and the closer the modes’ effective indices are spaced (see Fig. 3), increasing the possibility of mode coupling.
Fig. 3. Conformal mapped refractive index profile (cRIP) over the fiber radius for the two SIFs from “Simulation 2” (see Table 1) at a coil diameter of 0.114 m. The effective refractive indices (neff) of all 250 modes are shown as dashed lines (black = core modes, grey = pedestal/cladding modes). The intensity (red) of the LP11e is shown schematically.
Another important difference between the core modes in small and large pedestal fibers can be observed in Fig. 2. While the fundamental mode OLs of both designs were indistinguishable, the OLs of the core-confined LP11e/o-modes were different. To quantify this difference, we determined the coil diameter, at which the LP11e/o OL was reduced by 5% (factor 0.95) compared to the straight fiber’s mode OL, i.e. at OL = ($0.789\: \cdot \:.95$) = 0.749 ∼ 74.9%. However, due to the anti-crossings it is difficult to define these values for the large pedestal design. Hence, we considered an envelope of the LP11e/o OLs, which was obtained by applying a moving average filter of 50 points to the red (LP11o) and green points (LP11e) in Fig. 2 (right). The resulting coil diameters were d74.9%, LP11e = 0.108 m / 0.162 m and d74.9%, LP11o = 0.080 m / 0.120 m, for 50 µm / 200 µm pedestal diameter, respectively. Two conclusions can be drawn from this: Firstly, obviously, the even LP11e modes, which have their intensity lobes aligned in direction of the bending, are stronger affected by the bending [33,35]. Therefore, they start leaking into the pedestal already at a larger coil diameter than the odd LP11o modes. Secondly, the 18/50/310 µm SIF’s LP11o/e modes are better confined in the core for tight coil diameters (here < 0.2 m) compared to the 18/200/310 µm SIF. This is caused by the confining index step from pedestal to cladding (NAped = 0.1) being (spatially) much closer to the core, as illustrated in Fig. 3. In conclusion, for a small coil diameter the core’s HOM-OL is (slightly) reducing for increasing pedestal diameter, i.e. at dcoil = 0.1 m the LP11o OL with the doped area reduced from 76.5% to 72.6% for 50 µm and 200 µm, respectively. Together with the reduction of pedestal mode OL this might be beneficial to obtain effective single-mode operation in few-mode fibers. So far, the pedestal NA of 0.1 has been a fixed parameter. To test the validity of the previous results for different doping compositions with the same core NA, mode simulations with varying pedestal NA were performed.
2.3 Simulation results for varying pedestal NA
Mode simulation for unbent 18/50/310 µm and 18/200/310 µm SIF of NAcore = 0.066 and varying pedestal NA from 0.05 to 0.2 were performed and the results are shown in Fig. 4 left and right, respectively. The doping OL of the core’s and highest pedestal modes changed negligibly, apart from anticrossings between pedestal and cladding modes. For the 18/50/310 µm SIF, the confinement of the pedestal modes increased slightly with increasing pedestal NA. The highest OL of a pedestal mode (shape: LP21, inset in Fig. 4 left) increased from NAped = 0.05 / 0.096 to NAped = 0.2 by less than 5 / 2%, while the core modes’ OL increased negligibly by less than 0.4 / 0.3%, respectively. For the large pedestal version in Fig. 4 (right) the doping OL of the core modes is increasing by less than 0.3% from NAped = 0.05 to 0.2, while the highest OL of the pedestal modes is slightly decreasing from 17.8% (shape: LP24, inset in Fig. 4 right) to 16.7% (shape: LP23), respectively.
Fig. 4. Simulated OLs with the doped core area (%) for varying pedestal NA but fixed core NA of 0.066 for an unbent 18/50/310 µm SIF (left) and 18/200/310 µm SIF (right). The simulation parameters are summarized in Table 1.
Two main conclusions result from these mode simulations. First, the disadvantage of small pedestal structures in terms of increased pedestal mode OL are the same for increased pedestal NAs. Consequently, even for higher core and pedestal doping concentrations than the ones chosen in this paper, larger pedestal structures should be preferred. They are expected to result in larger TMI thresholds than their smaller pendants for the given doping composition. Additionally, for constant doping concentrations of core and pedestal, but varying pedestal NA, i.e. by reducing the refractive index of the silica cladding by doping with boron or fluorine, the TMI threshold should not be affected, as the mode content is not changing.
To validate the hypothesis that the aforementioned numerical results are related to the TMI threshold experimentally, the performance of a 50 µm pedestal fiber and 200 µm pedestal fiber have to be compared. The next section will discuss the fabrication process of the small pedestal fiber 1 and which limitations were to overcome to successfully fabricate the large pedestal fibers 2 & 3, before section 4 discusses the TMI laser results.
3. Fabrication of pedestal fibers
3.1 Yb/Ce/Al-doped fiber with Ge-doped pedestal via MCVD/ solution doping
First an Yb/Ce/Al doped fiber with a Ge-doped silica pedestal via MCVD process was prepared in combination with solution doping technique according to the following method: GeO2 doped silica layers with low amounts of P2O5 were deposited on the inner surface of a F300 quartz glass tube (outer and inner diameters of 28 mm and 26 mm, respectively) by the common MCVD process. This was followed by the deposition of a porous silica layer, impregnation with an aqueous solution of YbCl3, CeCl3 and AlCl3, drying and purification under chlorine/oxygen (Cl2/O2) atmosphere. During subsequent high temperature treatments, the silica was consolidated to a fused glassy layer and the salts were converted to Yb, Ce and Al oxides and incorporated into the silica matrix. Then the coated tube was collapsed to a solid rod (preform) [36].
This primary preform was characterized with respect to the radial concentration profiles of the dopants of core and pedestal via wavelength dispersive electron probe microanalysis (WD-EPMA) on thin polished preform slices. Additionally, the radial refractive index profile was characterized non-destructively by a beam deflection method [37]. The measured profiles are shown in Fig. 5. The core was doped with 0.21 mol% Yb2O3, 0.09 mol% Ce2O3 and 2.4 mol% Al2O3. To obtain the effective core NA of 0.063, the pedestal was doped with 4.3 mol% GeO2 and 0.6 mol% P2O5, resulting in a pedestal NA of 0.127. The preform was jacketed with a further F300 tube, cut to an octagonal cross section and drawn into fiber 1, which was coated with a low index acrylate polymer to give a cladding NA of 0.46. The outer, pedestal and core diameters of fiber 1 are 300, 52 and 16 µm, respectively. The background loss of fiber 1 was determined using the conventional cut-back method in combination with the pinhole-fiber-method [38], to be sure to measure only within the core region where the laser light is guided in double-clad fibers. At 1200 nm a background loss of 15 dB/km was measured. The pump absorption on the other hand gives information about how strong the whole fiber structure absorbs the pump light. The measurement is a conventional cut-back method, where the whole fiber structure is included. The pump absorption of fiber 1 is 0.66 dB/m at 915 nm. The pump-induced photodarkening loss was measured with a core-pumping setup [39] at 633 nm and ∼50% Yb inversion over 24 hours by a pump power of 200 mW at 976 nm. Fitting of the measured photodarkening curve with a stretched exponential function [40] yields an equilibrium loss αeq of about 9 dB/m at 633 nm. The photodarkening losses at 1060 nm were measured to be smaller by a factor of ∼37. This indicates an excellent suppression of photodarkening by Ce co-doping.
Fig. 5. Radial dopant concentration profiles of core and pedestal (left), radial refractive index profile (right) of the preform.
3.2 Yb/Ce/Al doped fibers with Al-doped pedestal via powder-sinter-technique
Sidharthan et al. [28] demonstrated the fabrication of a highly Yb-doped P/Al core (19 µm) surrounded by a wide index increased Ge-doped silica pedestal (136 µm). In this case the doping concentration of ∼ 1.2 mol% GeO2 resulted in a low pedestal NA of 0.07. However, the preparation of our Yb/Ce/Al-doped LMA fibers requires significantly higher pedestal NAs (NA > 0.12) and thus higher GeO2 concentrations (> 4 mol%) due to the higher core refractive indices. The realization of much larger thicknesses of such highly Ge-doped silica pedestal is very difficult via the MCVD technique. Ge- and P-doped silica layers induce significant stress in the preform due to the thermal expansion mismatch compared to the undoped silica cladding, which can lead to fragility of the preform. This stress is enhanced for larger pedestal thicknesses and doping concentrations. Using Al-doped silica pedestal significantly reduce the thermal expansion discrepancy versus the silica cladding, by around one order of magnitude compared to P-doped and more than half compared to Ge-doped silica pedestal layers, respectively [25]. But the preparation of a much wider Al-doped silica pedestal is effectively not possible via MCVD/ solution doping technique. Only narrow pedestals of good optical quality can be realized. To overcome this limit a technology based on the powder-sinter-technique (REPUSIL) [30] was developed for the preparation of fibers 2 and 3.
First, starting rod materials for the pedestal (Al-doped) and core (Yb/Ce/Al-doped) were produced via REPUSIL technique (diameter of about 14 mm, length of about 100 mm) and characterized concerning the radial dopant concentration and refractive index distribution. In Fig. 6 the radial concentration profiles of the pedestal and core material are shown. The core material is doped with 0.18 mol% Yb2O3, 0.11 mol% Ce2O3 and 1.14 mol% Al2O3, the pedestal material of the first rod with 1.7 mol% Al2O3, and that for the second rod slightly increased with 1.9 mol% Al2O3. From these materials, rods with 1 mm diameter were drawn at the drawing tower.
Fig. 6. Radial dopant concentration profiles of the pedestal material of the first rod (left) and core rod material (right), respectively.
Subsequently, the fabrication of fibers 2 and 3 took place under the following steps: Firstly, two packages consisting of a Yb/Ce/Al-doped core rod in the center surrounded by corresponding Al-doped pedestal rods were prepared using the stacking technique (see Fig. 7, left). Secondly, the packages were treated with chlorine/helium atmosphere to eliminate contaminations (OH, 3d elements) in a F300 tube. Then the package and tube were fused on the MCVD lathe. Finally, the fused packages were drawn together with a further F300 tube (octagonal cross section) by the rod-in-tube technique into the fibers 2 and 3. Figure 7 (right) shows the cross section of the final fiber with outer, pedestal and core diameters of 420 µm, 200 µm (both flat-flat) and 18 µm, respectively.
The refractive index distribution of both fibers was measured by a tool called Interfiber Analysis (IFA) in each case in three angular directions. Figure 8 shows the averaged profiles compared to adapted oil, inserted are the cross sections of the 2D profiles. Core NAs of 0.065 (fiber 2) and 0.042 (fiber 3) were measured. The pump absorptions at 915 nm were in the range of 0.5 dB/m to 0.4 dB/m, and the background loss at 1200 nm of 30 dB/km to 20 dB/km, respectively. The photodarkening losses of fiber 2 and 3 were not measured. Nevertheless, due to the slightly larger Ce/Yb-doping ratio of 0.6 compared to 0.43 of fiber 1, the photodarkening equilibrium loss at 633 nm was estimated to be αeq ∼ 5 dB/m [14].
4. Experimental results
Before testing the fabricated fibers in high-power amplifiers, suitable coil diameters were experimentally determined in bend loss measurements. These measurements were compared to the analytic bend loss formula from Marcuse [41] edited by Schermer [42] and are shown in the Appendix. The results are used in the following discussion regarding the laser tests from a counter-pumped amplifier characterizing the performances of fiber 1, 2 and 3.
4.1 Laser performance of fiber 1: 16/52/300 µm, NAcore = 0.063
Fiber 1 was tested in a free-space counter-pumped amplifier configuration, seeded by a 7.5 W pre-amplifier at a wavelength of 1066 nm. Anti-reflective coated fused silica endcaps in water-cooled connectors were spliced to the fiber ends to avoid back reflections and to ensure stable coupling conditions. The active fiber was coiled and cooled in a water basin. Wavelength-stabilized fiber-coupled diode lasers (fiber: 200/220 µm, NA = 0.22) operating at 976 nm were utilized as optical pumps and coupled into the 300 µm, NA = 0.46 fiber cladding via a 1:1 imaging system. The signal output beam was separated from the pump light by a dichroic mirror and its power (Pout) measured on a thermal power sensor. Low-power reflexes of an optical wedge were used to detect the spectral and temporal evolution with an Optical Spectrum Analyzer (OSA) and a photodiode (PD) in the near field image of the beam, respectively. As introduced in [3], the standard deviation (STD) of the normalized PD trace increases rapidly, when TMI occur.
An 8.5 m fiber length was chosen in order to obtain a pump absorption of > 15 dB at 976 nm, in this case 16.8 dB (∼ 98%). The fiber was coiled to 42 cm diameter and scaled up to a TMI-free signal power level of 510 W with a laser efficiency (signal output power to launched pump power) of 86%, as shown in Fig. 9 (top left, blue circles). At 510 W signal power, the beam quality was M2 = 1.31, indicating a low guided content of LP11 mode up to this power-level, most likely due to a slightly imperfect FM-mode excitation at the fiber input. The STD of the normalized PD time trace is shown in Fig. 9 (top right). It is rapidly increasing between the two measured values of 510 W and 545 W signal power, indicating the occurrence of TMI. Figure 9 depicts 20 ms of the PD time traces at power levels around the TMI threshold (bottom left) and the corresponding RF-frequency spectra (bottom right). In the transition region (red curve, at 545 W), oscillations at characteristic frequencies of 2.9, 5.8 and 8.7 kHz can be identified, which confirmed the thermal origin of this effect [3]. The latter two graphs are shown as examples to prove that the observed effect is indeed TMI. For all other coil diameters and fibers similar temporal evolutions were measured (see below). However, for simplicity, the corresponding graphs are not included into this article.
Fig. 9. Amplifier efficiency (top left) and STD of the normalized PD time trace (top right), indicating the onset of TMI, for the two bending diameters 42 cm and 21 cm of fiber 1 (16/52/300 µm, NA = 0.063). The temporal (bottom left) and corresponding RF-spectral characteristics (bottom right) of the TMI onset for 42 cm bending diameter are shown.
The smaller diameter of 21 cm, with reduced HOM content, resulted in a minor increase of the TMI threshold to 580 W signal power. Note, the sharp increase in bending losses of the LP11o mode to 16.9 dB/m (compare Appendix Fig. 14, left) is not reflected in the small increase of the TMI threshold, which it should be according to [43], and will be discussed in section 5.1. Meanwhile, the amplifier efficiency shown in Fig. 9 (top left, red diamonds) was 85.3% and hence not influenced compared to the 42 cm diameter experiment.
4.2 Laser performance of fiber 2: 18/200/420 µm, NAcore = 0.065
Fiber 2 was tested in a monolithic counter-pumped amplifier configuration, which is described in detail in [44]. Here, the central wavelength was 1060 nm and the seed power 3.5 W. One absorption length of 10 m active fiber was coiled into the water basin and spliced to a matching passive counter-sided (6 + 1)x1-pump-coupler fiber pigtail. Please note that the following beam quality measurements are influenced by the passive output fiber, which was a GDF-20/400 (NA = 0.065) with higher mode content than the active fiber itself.
Once the TMI threshold is reached in the tightly coiled monolithic amplifier, significant HOM content couples into the pedestal/cladding. As a result, the core’s output power decreases. However, this signal light previously propagating in the active fiber’s pedestal and cladding can be measured in one unused counter-sided pump-coupler fiber (Pcounter-sig), as done in [44]. Assuming a homogeneous splitting into all six coupler ports, the signal power at the end of the active fiber (Pfib) is given by: Pfib = Pout + 6· Pcounter-sig. This power Pfib, referred to as “signal power”, can be used to plot slope efficiencies and the STD of the PD-traces without the decrease of values that would otherwise occur for plotting over Pout. Thereby, the TMI threshold power can be determined with greater accuracy and the results can be compared directly with the free-space amplifier setup.
At a coil diameter of 30 cm, fiber 2 was scaled up TMI-free to 560 W signal power with an amplifier efficiency of 78.7%, as shown in Fig. 10 (left). While the beam quality was M2 = 1.33 at 550 W signal power, it degraded rapidly to M2 = 1.55 at 575 W, followed by M2 = 1.89 at 585 W. This decrease in beam quality matched the increase in STD shown in Fig. 10 (right), confirming the onset of TMI. As the 30 cm coil diameter corresponded to the fibers few-mode regime, it was reduced to 15 cm and 10 cm for the second and third test. The TMI thresholds were then found at 600 W and 790 W signal power, respectively. This trend is well explained by the increasing LP11o bend losses (compare Appendix Fig. 14 center), which grew from < 0.4 dB/m at 30 cm to ∼ 2.5 dB/m at 15 cm and ∼18 dB/m at 10 cm coil diameter.
Fig. 10. Amplifier efficiency (left) and STD of normalized PD time trace over signal power (right) for pedestal fiber 2 (18/200/420 µm, NA = 0.065) at three different coil diameters of 30, 15 and 10 cm.
One might consider bending the fiber further in order to increase the TMI threshold until the FM core losses would increase. However, the limitation was the long-term mechanical stability of the pedestal fiber, which was not ensured for coil diameters smaller than 10 cm.
4.3 Laser performance of fiber 3:18/200/420 µm, NAcore = 0.042
One absorption length of 13.3 m was tested in the same monolithic amplifier as fiber 2, with 4 W seed power at 1070 nm and a -3dB-bandwidth of 204 pm ( = 53.4 GHz). The first experiment at 60 cm bending diameter was scaled up to a TMI-free power-level of 1640 W signal power with an amplifier efficiency of 82.9%, as shown in Fig. 11 (left, blue dots). At the next measured power step of 1750 W signal power TMI occurred, as shown in Fig. 11 (right, blue dots). As the coil diameter was reduced to 30 cm, the TMI threshold was increasing to 1910 W signal power (see Fig. 11, right, red diamonds). The beam quality (M2) was measured to be as low as M2 = 1.26 at 1892 W signal power.
Fig. 11. Amplifier efficiency (top left) and STD of normalized PD time trace (top right) for pedestal fiber 3 (18/200/420 µm, NA = 0.042) at two coil diameters of 60 and 30 cm.
Please note that at 1892 W signal power, the -3/-10 dB bandwidth was 180/416 pm containing 65/96% of the total spectral power. Up to the highest signal power, neither SBS nor SRS were observed. This shows an advantage of highly Yb-doped fibers: For high Yb concentrations, short fiber lengths can be chosen, which results in low nonlinearities.
4.4 Summary of experimental results for fibers 1, 2 and 3
In this subsection the fiber design parameters and experimental results are summarized in Table 2 to provide an overview over all parameters, which have an influence on modal instabilities. The parameters of this table are the basis for the following discussion. In the next section the impact of the small pedestal design on the TMI threshold is discussed based on the experimental results, followed by a general discussion.
Table 2. Summary of fiber design and experimental parameters of fiber 1, 2 and 3
5. Discussion
5.1 Pedestal diameter influences TMI threshold
In section 2 it was shown, that larger pedestal diameter result in decreased pedestal mode OLs with the doped area (see Fig. 1) and simultaneously smaller LP11 OLs at tight coil diameter (see Fig. 2). Both effects combined should reduce the TMI threshold for small pedestal design. In order to verify this, the results of the small pedestal fiber 1 and the large pedestal fiber 2 must be compared. However, at first sight no clear differences can be seen: the TMI thresholds listed in Table 2 are similar for the coil diameter dcoil = 0.15–0.42 m, i.e. between PTMI = 530–600 W. Yet, since both fibers have slight differences, a precise evaluation of the varying parameters is required. At first it is shown that by a detailed discussion of the key parameters influencing TMI [31] - average gain, thermal load and mode composition - the influence of the pedestal size cannot be properly identified for the fabricated fiber designs. However, a connection is then established between the bending loss measurement and the TMI threshold, which indicates the undesired effect of the small pedestal.
Firstly, the different fiber absorption lengths are discussed. Typically, a larger pump absorption and thus a shorter fiber length (LFiber1 = 8.5 m vs. LFiber2 = 10 m) increases the gain. Reduced gain saturation results in a stronger LP11 gain and a lower TMI threshold [5]. By choosing different seed powers we achieved the same average gain per meter at the TMI thresholds of ∼580 W (2.22 dB/m for fiber 1 and 2.21 dB/m for fiber 2).
With the gain being comparable, a difference in heat load could change the expected TMI threshold. The total heat load consists of heat induced by photodarkening, the quantum defect and background absorption [6]. The photodarkening losses at 1.06 µm were calculated from those measured at 633 nm to be αeq = (9 dB/m : 37) · (n : 0.5) = 18:37 dB/m · n and αeq = 10:37 dB/m · n for fiber 1 and 2, respectively, and depend on the (local) population inversion n(z) at the position z of the active fiber. The total background losses (αtotal) at the wavelength λ consist of heat introducing absorption losses (αabs) and non-heat introducing scattering losses (αscat), i.e. αtotalλ = αabsλ + αscatλ. We assumed that the background losses measured at 1200 nm were dominated by scattering losses and would remain constant to the shorter seed and pump wavelengths, i.e. αtotal1.2µm = αscat = 15 / 30 dB/km for fiber 1 and 2, respectively. They were higher for fiber 2 due to inhomogeneities in the REPUSIL material. The total background losses at λseed/ λpump were estimated from the attenuation spectra (not shown) by fitting a Gaussian distribution of the spectral regions surrounding the Yb3+ absorption peaks. Subtracting the (constant) scattering losses from the total background losses yielded absorption losses of αabs976nm = αtotal976nm – αscat = 39.1 / 43.7 dB/km and αabs1066/1060nm = 15.0 / 25.5 dB/km for fiber 1 and 2, respectively. Those background absorption losses can be attributed to the wide absorption tails of Yb2+ ions, which can occur during the preform and fiber fabrication [45]. We implemented the parameters shown in Table 2 together with the discussed photodarkening- and background absorption losses in rate-equation simulations. Average heat loads of 10.2 / 9.0 W/m and output signal powers of 614 / 602 W were obtained at 700 W pump power for fiber 1 and 2, respectively. In conclusion, fiber 1 had a higher average heat load than fiber 2 due to the shorter absorption length. Thus, from a heat load perspective, fiber 2 should theoretically have a slightly higher TMI threshold than fiber 1.
Now we review the mode composition: For that the mode simulation from section 2.2 were repeated for the fibers’ measured refractive index profiles and are shown in Fig. 12. Compared to fiber 2 (V = 3.45), fiber 1 had a smaller core diameter and a lower core NA, resulting in the V-parameter of V = 2.95. This is reflected in the lower LP11 OLs shown in Fig. 12, which were OL(LP11o) = 70.3% and 61.7% at 0.48 m coil diameter for fiber 2 and fiber 1, respectively. As expected for fibers closer to the single-mode regime, the LP11 doping OLs of fiber 1 are reducing at larger coil diameter than for fiber 2. A lower LP11 doping OL results in reduced LP11 gain. Consequently, from a core-mode perspective, a higher TMI threshold for fiber 1 would be expected. This is in agreement to literature, since decreasing the V-parameter has been shown to increase the TMI threshold [46].
Fig. 12. Mode simulation over the coil diameter for fiber 1 (left) and fiber 2 (right) with their real refractive index profiles from Fig. 5 (right) and Fig. 8 (left), assuming a circular pedestal. The core, pedestal-, cladding diameters and wavelengths are summarized in Table 2. The cladding diameter of fiber 2 was reduced to 310 µm to save simulation time. For both fibers 350 modes were calculated for dcoil > 0.08 m. For 0.02 m < dcoil < 0.08 m 450 / 550 modes were calculated for fiber 1 / 2, while the core modes were identified by sorting all calculated modes according to their effective indices / OLs, respectively.
Up to this point, there are two competing arguments: From a core modes perspective, the TMI threshold of fiber 1 should be higher compared to fiber 2, due to the lower V-parameter. However, the average heat load of fiber 1 was slightly higher compared to fiber 2 due to the different absorption lengths. Thus, it is hard to differentiate, whether the slightly higher heat load or the increased pedestal mode OL reduced the TMI threshold of fiber 1 to the same level as measured for fiber 2. Yet, the detrimental impact of the large pedestal mode OL is revealed by evaluating the fibers’ core mode bend losses (Appendix in Fig. 14).
Numerical simulations [43] have shown that the TMI threshold increases with increasing bend loss of the HOM, as it is the case for fiber 2 (Fig. 14, center, green line). The LP11o bend losses of fiber 2 grew from smaller than 0.4 dB/m at 30 cm to ∼18 dB/m at 10 cm coil diameter, which is reflected in the TMI threshold increase from 570 W to 790 W, respectively. However, the TMI threshold of fiber 1 is not increasing to a similarly significant extent, i.e. from 530 W to 580 W, even though the LP11o core loss grew from 0.25 dB/m to 16.9 dB/m (Fig. 14, left, green line). This behavior cannot be explained by the parameters discussed above. Yet, if the core’s LP11o mode is no longer well guided, but the fiber does not behave like an effectively single-mode fiber, this can likely be due to the pedestal modes. Due to the bending, the core’s HOMs are coupled to pedestal modes, which experience gain due to high doping OLs. Thus, the interaction between amplified pedestal modes and the core’s FM seemed to have caused TMI just like the core’s HOM does.
As discussed in section 2 for idealized SIF and shown in Fig. 12 for the simulations of the real fibers refractive indices, the difference in pedestal mode OL is significant (factor ∼ 3) and persists over all coil diameters, confirming the small pedestal fiber to be susceptible to much more modes. This behavior can be observed in Fig. 12 (left) for dcoil < 0.2 m, where the core’s LP11 mode OLs decreases strongly, but the OLs of other pedestal modes increase simultaneously. It is reasonable to conclude, that under these circumstances even tighter coil diameter than the tested dcoil = 0.21 m cannot result in significantly increased TMI thresholds, which limits the scaling potential of small pedestal fiber design.
5.2 General discussion
The disadvantages of small pedestal design discussed within this paper are only relevant, if light is present and guided in the pedestal. Since coupling losses from splices, significant fraction of spontaneous emission and bend induced propagation losses of core modes are captured by the pedestal, this cannot be avoided easily, as illustrated in [23]. It can, furthermore, not be eliminated by using standard cladding light strippers, as the pedestal is surrounded by the glass cladding. From the experimental results and the previous discussion, it became clear, that the experimental operation of a small pedestal few-mode fiber differs significantly from fibers with larger pedestal diameter. Due to the strong interaction of the gain with the pedestal modes, the 52 µm pedestal fiber 1 can even under tight bending not be operated in an effectively single-mode regime, and the TMI threshold remained lower than it would be expected in comparison to 200 µm pedestal fiber 2.
The ultimate limit of our considerations would be increasing the pedestal diameter to cladding size. For this, the reduction of pedestal mode doping OL as well as the LP11 OL reduce for small coil diameter, as simulated in section 2, would be maximal. Thus, the highest TMI threshold should be obtained. The MCVD process is not suitable to produce large pedestal diameter in combination with high doping concentration. Regarding the fabrication of pedestal fibers, we introduced an alternative technology based on REPUSIL and stack-and-draw to develop large Al-doped pedestal structures. This enabled us to build stable, hexagonal-shaped and Al-doped pedestal structures with 200 µm diameter. Yet, it should be mentioned that the stacking process is very time-consuming and requires a high standard of cleanliness. Even though other existing methods such as the outside vapor deposition (OVD) technique [47] might allow the fabrication of wide index-raised pedestals/claddings as well, the powder-sinter-process with stack and draw technique provides the ultimate flexibility to create (even microstructured) pedestals and cores in different shapes and sizes. We did not find the ultimate limitation of our fabrication technology with respect to the production of large Al-doped pedestal structures. The maximum pedestal diameter that can be fabricated is expected to be limited by the stress induced due to the dopant-dependent thermal expansion mismatch in the preform [25] or by the mechanical stability of the resulting fiber. Application related requirements, such as the size of the stress-rods in a polarization-maintaining fiber, could also be constraints. How precisely the core NA can be adjusted was demonstrated by the fabrication of fiber 3 (NAcore = 0.042). To achieve the low core NA in other fibers, the Yb concentration should not exceed 0.3 mol%, with an optimal Ce/Yb ratio between 0.5 and 0.7 and an Al concentration of about 3 mol%. With this core composition, additional temperature increases are avoided [14]. Hence, pedestals are suitable for many kinds of fibers with highly index-raised cores and allow to tune the core NA precisely.
The three fiber iterations represent a generally applicable fiber design strategy to increase the TMI threshold. Both, by enlarging the pedestal size (fiber 1 to fiber 2) and decreasing the V-parameter (fiber 2 to fiber 3), the fibers’ mode composition was optimized towards lower HOM OL with the doped area. This way, the TMI threshold was raised from 580 W (fiber 1) to 1.9 kW (fiber 3). Apart from increasing the pedestal diameter, this threshold could be further increased, if the total heat load would be reduced. Hence, the attenuation could be further optimized. To avoid crystallization and thus an increase in attenuation or the induce of stresses during the preparation of the Al-doped pedestal rod and the further thermal treatment, the Al concentration should not be higher than 4 mol%.
6. Summary and conclusion
In this paper we presented numerical and experimental results, which revealed that the current common choice of small pedestal design should be reconsidered, since it reduces the achievable TMI threshold. Numerical mode overlap simulations showed, that an increase of the pedestal diameter results in decreased pedestal mode overlap with the doped core area and simultaneously smaller LP11 doping overlaps under tight bending. Since large pedestal diameter cannot be realized via MCVD/solution doping technique anymore, we developed a technology based on the powder-sinter-process (REPUSIL [30]) and stack-and-draw. For the first time to the best of our knowledge, Yb/Ce-doped aluminosilicate fibers with hexagonally shaped, Al-doped silica pedestal structures of 200 µm diameter and core NA as low as 0.042 were fabricated with this new technique. By increasing the pedestal diameter from 52 to 200 µm and subsequently reducing the core NA from 0.065 to 0.042, the TMI thresholds of three manufactured fiber iterations increased from output powers of 580 W to 790 W and 1910 W, respectively. The production of the last fiber iteration, an 18/200/420 µm large pedestal fiber of very low NA = 0.042, showed how precisely the NA can be adjusted. In addition, the excellent performance demonstrated the high-power suitability of the doping composition Yb/Ce/Al, which exhibits ultra-low photodarkening. Neither SBS nor SRS were observed in the 13.3 m fiber, which was scaled TMI-free up to ∼1.9 kW output power at a wavelength of 1070 nm with a narrow -3dB spectral width of 180 pm. This is to the best of our knowledge the highest average output power of near-diffraction-limited beam quality (M2 = 1.26) obtained by an Yb-doped pedestal fiber so far. The necessity for larger pedestals in order to increase the TMI threshold could be of interest for all pedestal fiber application including Tm-, Er/Yb- and Yb-doped fibers.
Appendix: Bend loss measurements
Before testing the fabricated fibers in a high-power laser setup, suitable coil diameters were experimentally determined. Bend loss measurements were performed for various coil diameters and compared to the analytic bend loss formula from Schermer (Ref. [42], Eq. (20)).
In Fig. 13 (left), the experimental setup and laser parameters are shown. The laser beam is coupled into the test fiber’s core and the fiber’s core/cladding ratio is measured with a CCD camera for different coil diameters. Assuming that light coupled out of the fiber’s core is guided within the pedestal or cladding (of larger NA), the core losses can be determined.
Fig. 13. Left: Schematic bend loss measurement setup. Right: Power fraction in the core over the coil diameter for a bend loss measurement of fiber 2 including mode profile insets at 10 cm (LP01) and 33 cm (LP11-content). The fiber coupling was optimized for LP11-mode excitation. SM and MM refer to the single-mode and multimode regime, respectively.
For some few-mode fibers it is possible to excite significant amount of the LP11 mode at the fiber input. Then, the LP11 loss can be differentiated from the LP01 loss, as shown in Fig. 13 (right) for fiber 2. For coil diameter greater 20 cm, the fiber guided the LP11-mode, as illustrated by the mode profile inset in Fig. 13 (right). Between coil diameter of 10.5 cm and 5 cm only the FM was guided until dcoil < 5 cm, where the FM leaked into the pedestal.
In Fig. 14, the experimental results of the bend loss measurements for fiber 1 to 3 are shown, fitted with exponential functions (black dashed lines) and compared to the analytical bend loss formula from Schermer (Ref. [42], Eq. (20). For this analytical equation, we used the propagation constants βz(dcoil) obtained from mode simulation with the real refractive index profiles (depicted in Fig. 5 and Fig. 8) for varying coil diameter (like in section 2.2). All other parameters are summarized in section 4.4 in Table 2.
Fig. 14. Experimental results of bend loss measurements (blue dots) for fiber 1 to fiber 3 (left to right). The results are fitted by exponential functions (black dashed lines) and compared to the analytic bend loss formula by Schermer (Ref. [42], Eq. (20) for the LP01 (red lines) and LP11o (green lines, for few-mode fibers 1 + 2).
For fiber 1 (16/52/300 µm, NA = 0.063), the experimental fiber coupling was optimized for maximum FM excitation. Hence, the bend loss of the LP01 mode was measured and the experimental data shown in Fig. 14 (left) agree well with the analytical approximation. The analytic LP11o bend loss is < 0.4 dB/m for dcoil > 40 cm and around 20 dB/m for ∼ 20 cm. These are two suitable coil diameters for the high-power experiment, since they correspond to the few-mode and effectively single-mode regime, respectively.
The central graph in Fig. 14 corresponds to the large pedestal fiber 2 (18/200/420 µm, NA = 0.065) and is derived from the same data set previously shown in Fig. 13 (right). Due to the LP11 mode excitation at the fiber input, the bend losses for both the LP11o and LP01 were obtained, as indicated by the exponential curve fits. Here, the LP11o fit agrees very well with the analytical formula, while the analytic LP01 loss is smaller by nearly two orders of magnitude. However, the reason for this is not fully understood and under investigation. Appropriate experimental coil diameters were 30 cm, 15 cm and 10 cm for the few-mode, intermediate and single-mode regime, respectively.
For the single-mode fiber 3 with NA = 0.042, coil diameters smaller than dcoil ∼ 26 cm increase the core’s FM losses significantly. This is in good agreement with the analytical formula, as shown in Fig. 14 (right). A large and a small coil diameter of 60 cm and 30 cm, were chosen for the high-power experiment.
Funding
Bundesministerium für Bildung und Forschung (13N13654).
Disclosures
The authors declare no conflicts of interest.
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