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Abstract
In this work, we conduct experimental investigations of transverse mode instabilities (TMI) in a large mode area ultra-low numerical aperture polarization maintaining fiber amplifier. This fiber is few mode in the slow-axis (conventional operation mode), but single mode in the fast-axis. We test the stability of the output beam by changing the input polarization angle and systematically investigate the transverse mode instability threshold in the two principal polarization axes. The lowest TMI threshold at 300 W was found when the input polarization angle was aligned parallel to the slow-axis. Detuning the input polarization angle from the slow-axis led to increased TMI thresholds. For input polarization angle of 90° (parallel to the fast-axis), the output signal was stable up to 475 W and further scaling was limited by the available pump power. However, for fast-axis operation a lower polarization ratio compared to slow-axis operation was observed as well as an unexpected static energy transfer from the fast-axis into the slow-axis above 400 W.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fiber laser systems allow for diffraction-limited output beams, which is mainly due to the unique feature of fiber lasers having a waveguide structure in the gain medium. Moreover, they allow for a good thermal management in comparison to other laser architectures due to their high surface to volume ratio [1,2], enabling high average output powers. Thus, Yb-doped fiber lasers have reached powers well into the kW class with an excellent beam quality [3,4]. The absorption peak of Yb at a wavelength of 976 nm enables the use of cost-effective, high-power pump diodes. Furthermore, they allow for an efficient emission at 1 $\mathrm{\mu}$m with low quantum defect and therefore low thermal loads [2]. Yet power scaling of fiber lasers is currently hindered by nonlinear and thermal limitations [5]. The most dramatic limiting effect is transverse mode instabilities (TMI). It manifests as a threshold-like onset of fluctuation of the output beam once a certain power has been reached. TMI is caused by a thermally induced index grating that enables modal energy transfer between different transverse modes [6]. Typically, this happens between the fundamental mode (FM) and the first high order mode (HOM). Since the first observation of TMI [7], scientist have made a strong effort to understand the physical insights behind it. The research has been mainly focused on step index fibers (SIF) [4,8], large pitch fibers (LPF) [9,10] and distributed mode filtering fibers [11]. Hereby, only a few experimental investigations of TMI in PM fibers have been published and systematic measurements are missing. Tao et al. presented a monolithic PM high power system, showing a degradation of polarization extinction ratio PER when the TMI threshold was reached [12]. Jauregui et al. published a numerical study on the effect of changing the polarization angle of the excited fiber modes [13]. Furthermore, in [14], the TMI threshold was experimentally investigated in dependence of the input linear polarization angle, which it was changed by rotating the fiber splice at the input port. However, the interpretation of the results is difficult, since important details such as the guiding conditions and mode content of the fiber are missing. For the first time, we present a direct comparison of the dependence of TMI on the numerical apertures of a fiber by taking advantage of the PM structure. The fiber has well defined guiding properties and mode content in each polarization main axes that were simulated and verified with experiments. It is shown that detuning the linear polarization input angle from the slow-axis in a PM fiber leads to an important enhancement of the TMI threshold. Furthermore, we demonstrate that coupling the seed laser with a polarization at 90$^{\circ }$ leads to an enhancement of at least 50% of the TMI threshold. However, in this case a reduced polarization ratio was observed for power levels below the TMI threshold. Furthermore, the output polarization unexpectedly changed and significant HOM content was observed in a stable beam above 400 W.
2. Experimental setup, fiber design and method
2.1 Setup
The experimental setup is presented in Fig. 1. The seed laser consisted of a continuous wave (CW) external cavity diode laser (ECDL) with the wavelength centered at 1030 nm. Its linewidth was broadened to 120 pm, to avoid parasitic Brillouin scattering. The seed was amplified up to 3 W in a first stage using an Yb-doped commercial single-mode 10/125 $\mathrm{\mu}$m fiber. It passed through an isolator (30 dB polarization extinction ratio) situated at the output of the pre-amplifier to protect the seed laser from backreflections and guarantee a linear polarized input for the main amplifier. A half-waveplate behind the isolator was used to rotate the linear polarization input angle. The laser beam was coupled into the signal core of the PM fiber amplifier by means of two mirrors and a lens. The mirrors did not change the linear polarization state of the input beam. The fiber was aligned with its stress rods parallel to the horizontal axis and this orientation was maintained over the whole length. No twist or rotation of the fiber was present. The whole fiber was water-cooled. The pump power was provided by an 800 W diode (Dilas Compact Evolution) with a center wavelength at 976 nm. Its power was coupled to the pump core of the fiber with 94% coupling efficiency. At the output, the signal beam was separated from the pump using a dichroic mirror. The reflection of the signal from a fused silica wedge was used for characterization of beam quality (ISO standard with Cinogy M2), optical spectrum (OSA Yokogawa), TMI threshold and polarization ratio. The transmitted power was measured with a powermeter. TMI was characterized by analyzing the temporal characteristic of the signal measured with a photodiode, as described in [15]. The PM properties of the fiber were characterised by the ratio between the polarization in the slow and fast axis ($P_{\mathrm {slow}}/P_{\mathrm {fast}}$), when the polarization was aligned with respect the slow-axis, and vice versa ($P_{\mathrm {fast}}/P_{\mathrm {slow}}$), with alignement with respect the fast-axis. Both powers were measured using a polarization beam splitter, (see Fig. 1(b)). This measurement allows for 30 dB contrast between polarization when the measurement is performed with the transmitted beam. In order to measure the powers in transmission, the half-waveplate WP2 was rotated.
Fig. 1. Schematic representation of the experimental setup (a) and polarization characterization (b). ISO: isolator; WP1: half-waveplate used to rotate the incoming polarization; M: mirror; DM: dichroic mirror; PM: powermeter; W: wedge L: lens; WP2: half-waveplate used to rotate the polarization output for polarization measurement; BS: beam splitter; and BD: beam dump.
2.2 Fiber design
The fiber amplifier consisted of an in-house Yb-doped LMA PM fiber, with a core diameter of 35 $\mathrm{\mu}$m and a pump cladding diameter of 220 $\mathrm{\mu}$m (NA=0.22), to provide for high absorption using a short fiber length of 1.2 m. The PM fiber was used straight to suppress propagation losses of the modes induced by fiber coiling. The PM properties of the fiber were realized by using a panda-type structure, with two circular stress rods next to the fiber core. The resulting birefringence in the signal core leads to a splitting of the effective refractive index for each polarization [16]. The refractive index of the slow-axis (parallel to the stress rods) is slightly increased, whereas for the fast-axis (perpendicular to the stress rods) is reduced. Consequently, the optical modes vary for each polarization axis. To illustrate this effect, the fiber modes were calculated using FEM (Comsol). Firstly, mechanical stresses were obtained to model the refractive indexes for each polarization axis, following a similar approach as in [17]. Secondly, the optical transverse modes were calculated. The refractive index could not be directly measured with the required accuracy ($10^{-4}$). However, it was reconstructed by measuring the effective area of the FM and the geometry of the fiber core. The effective area of the slow-axis FM was measured to be 950 $\mathrm{\mu}$m$^2$. With this mode area and a measured core radius of ($17.5\pm$1.0 $\mathrm{\mu}$m) the numerical aperture of the fiber (without addition of stress-corrections) was calculated to be NA ~0.028 resulting in a V-parameter of 2.8, assuming an ideal step index profile. This fiber design supports the propagation of three transverse modes in the slow-axis, whilst only one mode in the fast-axis. They are described here as linearly-polarized modes: LP$_{01}^{\mathrm {slow}}$ (FM slow-axis); LP$_{01}^{\mathrm {fast}}$ (FM fast-axis); LP$_{11}^{\mathrm {slow,e}}$ (first HOM slow-axis even) , LP$_{11}^{\mathrm {slow,o}}$ (first HOM slow-axis odd, perpendicular orientation to the previous one), Fig. 2. The horizontal lines in Fig. 2 correspond to the effective refractive indexes of each transverse modes. For a polarization aligned parallel to the fast-axis, the fiber is single-mode, whereas it becomes few-mode in the slow-axis.
Fig. 2. Numerical simulation of transverse modes. Refractive indexes and intensity profiles of the corresponding transverse modes in the slow-axis (a) and fast-axis (b) of the transversal cut of the fiber perpendicular to stress rods. The horizontal lines correspond to the eigenvalues ($n_{\mathrm {eff}}$) of the supported transverse modes. Inset, fiber geometry and polarization direction of the corresponding refractive index.
2.3 Method
In a first experiment, the TMI threshold was characterized with the polarization input angle parallel to the slow-axis. The pump power was increased stepwise while the temporal stability of the output signal was recorded. In a second experiment, the signal was set to the TMI threshold power found for the slow-axis and the polarization input angle was rotated stepwise. The temporal stability of the output beam was characterised at each angle. Finally the amplifier was characterised with the polarization input angle aligned at 90$^{\circ }$ (parallel to the fast-axis).
3. Experimental results
3.1 Amplifier performance in the slow-axis
In this experiment, the output power of the fiber amplifier was measured with the polarization input angle aligned parallel to the slow-axis. The results are presented in Fig. 3. The linear slope in Fig. 3(a) is plotted with respect to the absorbed power. The slope efficiency of the fiber amplifier was measured to be ~93%. The output beam quality was measured to be nearly diffraction limited (M2<1.1) below the TMI threshold (inset of Fig. 3(b)). The polarization ratio was measured to be 15 dB in average, which corresponds to 97% of the power in the slow-axis. Figure 3(b) shows the optical spectrum with high spectral purity (70 dB suppression), measured at 270 W output power. The TMI threshold measurements are presented in Fig. 4(a). The standard deviation was statistically calculated from the beam fluctuations measured in 50 ms time intervals and it was normalized to the average value of the traces. The standard deviation of the beam photodiode traces was measured to be low up to 300 W output power. A sudden increase was detected above 300 W indicating the TMI threshold. In Fig. 4(b) a comparison of the photodiode traces below (275 W) and at the TMI threshold (300 W) is presented. It can be concluded that the fiber is TMI-limited at 300 W, when the polarization input angle is aligned parallel to the slow-axis.
Fig. 3. Fiber amplifier performance with the polarization input angle aligned parallel to the slow-axis. Slope (a); spectrum, output beam and beam quality (b) at 270 W output power.
Fig. 4. Standard (std) deviation of normalized photodiode traces of the output beam (TMI indicator) (a) and 50 ms photodiode traces at 275 W and 300 W (b).
3.2 TMI dependence on polarization angle at 300 W
In a second experiment, the influence of polarization input angle on the TMI threshold was investigated. For a polarization input angle parallel to the fiber slow-axis, the TMI threshold was measured to be 300 W. The pump power was kept constant to maintain this output power, and the polarization input angle was systematically changed by rotating the half-waveplate (WP1, Fig. 1). At each angle, a measurement of the beam temporal stability was performed. The results are presented in Fig. 5. Figure 5(a) shows the measured normalized standard (std) deviation of the output beam photodiode traces, in dependence on the polarization input angle. The output power was independent of the input polarization angle. By detuning the polarization input angle from the slow-axis, the temporal fluctuations of the output signal rapidly decreased, indicating a stable regime below the TMI threshold. The fiber output temporal traces showed strong fluctuations at angles smaller than 20$^{\circ }$ relative to the slow-axis and they became highly stable at angles larger than 20$^{\circ }$, with no signs of TMI. The output stayed stable up to a polarization input angle of 160$^{\circ }$. This was expected since an angle of 180$^{\circ }$ corresponds to the slow-axis again. In Fig. 5(b) the selected photodiode traces at both polarization main axes are presented at 300 W output power. The high stability of the output at 90$^{\circ }$ is shown in comparison to the strong fluctuations at 0$^{\circ }$. These measurements demonstrate, that TMI is mitigated by detuning the polarization input angle from to the slow-axis.
Fig. 5. Standard deviation of normalized photodiode traces of the output beam (TMI indicator) in dependence on polarization input angle (a) with beam profiles at selected angles. Photodiode traces at 0$^{\circ }$ and 90$^{\circ }$, respectively, in an interval of 50 ms (b). The output power was maintained constant during the measurement at 300 W.
3.3 Further power scaling in the fast-axis
In order to analyze TMI in detail, the power was increased with the polarization input angle aligned at 90$^{\circ }$. The slope and output stability were characterized at both polarization input angles. The results are presented in Fig. 6, and the previous measurement at 0$^{\circ }$ is included for comparison.
Fig. 6. Power scaling of the fiber amplifier. Slope at 0$^{\circ }$ and 90$^{\circ }$ (a), standard deviation of normalized photodiode traces (TMI indicator) (b).
The same linear slope was obtained when the polarization input angle aligned parallel to the fast-axis. Also, the spectrum did not change when operating the fiber amplifier in the fast-axis. However, the power was increased to 475 W without the onset of TMI. The output temporal stability is presented in Fig. 6(b). At 90$^{\circ }$ a slight fluctuation of the output beam was observed, however the TMI threshold could not be determined properly. Higher output powers could not be analyzed, since the full power of the pump diode was reached. A measurement of the ratio between polarization powers corresponding to fast-axis operation is presented in Fig. 7. Here it can be seen that the ratio is lower than 10 dB in average, significantly lower than in the slow-axis (>15 dB). Furthermore, higher order mode content in the slow-axis (in this case the rejection port) was always visible after a polarizer, which was aligned to the principal axis (see Fig. 7(b)). This was not observed in slow-axis operation and is thus not an alignment artefact, but indicates a static conversion of energy between the fast and slow-axis. Starting at 350 W output power, the energy in the slow-axis port increased, which can be seen in the decrease of ratio between polarization powers, becoming even negative at powers larger than 400 W, corresponding to a change of the dominant polarization. The mode content of the output beam profile is presented in dependence of the output power, Fig. 8. For input angle parallel to the fast-axis, the fast-axis of the fiber showed a mode content of the LP$_{01}$ close to unity, which did not change with increasing power. This demonstrates that the fiber was single-mode in the fast-axis. At a singular power of ~435 W, a deformation of the LP$_{01}^{\mathrm {fast}}$ was observed, the reasons being still unknown. In contrast, the slow-axis showed a fluctuating HOM content. At powers higher than 400 W an increasing mode content of the LP$_{11}^{\mathrm {slow}}$ was observed. Moreover, at the highest power of ~485 W, the mode content of the LP$_{11}^{\mathrm {slow}}$ was close to unity. Here dominates the slow-axis and therefore the total intensity of the beam (slow-axis and fast-axis) will be distorted. This static conversion was unexpected and the reason might lay on the small difference of $n_{\mathrm {eff}}$ between the LP$_{01}^{\mathrm {fast}}$ and the LP$_{11}^{\mathrm {slow}}$ that becomes smaller with increasing power, since modes with higher overlap experience a higher increase of $n_{\mathrm {eff}}$, approaching therefore the index of the LP$_{01}^{\mathrm {fast}}$ the one of the LP$_{11}^{\mathrm {slow}}$. This could lead to coupling under the presence of small birefringence fluctuations. This effect was also observed in other in-house fibers with comparable geometry and refractive indexes. However, this requires further investigation and will be the subject of a future work.
Fig. 7. Results for fast-axis operation: (a) Ratio between the power in the fast-axis and slow-axis in dB vs output power. (b) Exemplary output beam profile after the polarizer aligned to show fast-axis (left) and slow axis (right).
Fig. 8. Mode content of the output beam profile for fast-axis operation. Upper graph: mode content corresponding to fast-axis of the fiber (main port). Lower graph: mode content corresponding to slow-axis of the fiber (rejection port). The beam profiles at selected powers are presented.
4. Discussion
Despite the fact that above 400 W in fast-axis operation, the main power is in LP$_{11}^{\mathrm {slow}}$, it is still stable and does not show TMI. It is known that TMI originates from the interference of the FM LP$_{01}$ and a HOM (usually the LP$_{11}$). The resulting mode inferference pattern (MIP) induces a refractive index grating (RIG) that allows for dynamic energy transfer between the different modes, provided that there is a phase shift between the MIP and RIG [6,18]. Thus, one requirement for TMI is the presence of at least two interfering transverse modes. In the PM fiber under investigation, a splitting of the refractive indexes in the slow and fast-axis occurs as illustrated in Fig. 2. The refractive index in the slow-axis is higher than in the fast-axis, guides the FM and the first HOM, whilst the fast-axis guides just the FM. This difference in guiding explains the different TMI thresholds for input polarization parallel to the slow-axis and fast-axis and the stabilization of the output when changing the polarization input angle at 300 W. The slow-axis is, thus, effectively few-mode and fulfill the requirement for TMI to happen. On the other hand, along the fast-axis the fiber is efficiently single-mode and results in a higher TMI threshold. During laser operation, due to quantum defect a thermal gradient is formed that is transferred to the refractive index through the thermo-optical effect [2] and results in an increase of NA. Consequently, few-mode operation of the fast-axis and thus TMI is also expected at higher powers [19]. However, this threshold could not be reached in our experiments. The significant difference in TMI-threshold for the slow and fast-axis found in our experiments is not general for PM-fibers but is a consequence of the difference of few-mode and single-mode guiding in the slow-axis and fast-axis of this particular fiber, respectively. A higher refractive index of the fiber core would lead to effective few-mode guiding in both axes. In this case, a significant reduction of the TMI-threshold in the fast-axis similar to that in the slow-axis is expected, which was theoretically analyzed in [13]. It is evident that for fast-axis operation, the static power conversion between the fast-axis and the slow-axis decreases the actual impact of the increase in the TMI threshold. However, a more detailed investigation is needed to evaluate the static conversion been observed, and to determine if it is a general effect in low NA PM fibers.
5. Conclusion
In this work, we have experimentally studied the dependence of TMI on the polarization input angle in an ultra-low NA PM fiber. The fiber under investigation was effectively few-mode in the slow-axis, whilst single-mode in the fast-axis. This results in different TMI thresholds in the two main polarization axes of the fiber. We found a minimum TMI threshold of 300 W, with operation of the fiber in the slow-axis. Detuning the light with respect the slow-axis lead to suppression of TMI and further enhancement of the output power. With the polarization input angle aligned with respect the fast-axis, the power could be increased to up to 475 W. The fiber did not show TMI in the fast-axis. However, an increasing static energy transfer between the LP$_{01}^{\mathrm {fast}}$ and LP$_{11}^{\mathrm {slow}}$ was observed, when operating the fiber in the fast-axis above 400 W. This is currently under further investigation and will be the subject of a future work. These results can be exploited to design PM fibers and enhance the TMI thresholds by taking advantage of the different guiding strength of each polarization axis.
Funding
Free State of Thuringia and the European Social Fund (2017FGI0014, 2018FGR0099); Bundesministerium für Bildung und Forschung (16KIS1474K, 13N15978); Deutsche Forschungsgemeinschaft (416342637).
Acknowledgments
C.J. acknowledges financial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 416342637.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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