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Abstract
A diode-pumped actively Q-switched polarization-maintaining Tm3+-doped fiber laser is reported generating pulse energies of 630 μJ, minimum pulse widths of 42 ns, and a maximum peak power of 13.9 kW with linear polarized output and diffraction-limited beam quality at a wavelength of 2044 nm. The unpolarized fiber laser even reaches pulse energies of 800 μJ, pulse widths of 41 ns, and peak powers of 18.6 kW.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
High power laser sources emitting at wavelengths around ${2}\;\mu \textrm {m}$ offer numerous applications in the fields of medicine, material processing, and pumping of optical parametric oscillators (OPOs) based on nonlinear crystals like orientation-patterned GaAs (OP-GaAs) or ZnGeP$_2$ (ZGP) for frequency conversion into the mid-IR. The efficient operation of OPOs requires pulsed and polarized pump laser sources that provide high average output power, high pulse energies, excellent beam quality, and narrow linewidth. Owing to their special geometry, fiber lasers are ideally suited to meet these requirements, since they offer excellent thermal management and diffraction-limited beam quality up to high power levels. Furthermore, the mechanical flexibility of fibers and their easy system integration allows the creation of compact and robust laser systems. It has already been demonstrated that pumping of OPOs using Q-switched single-oscillator fiber lasers doped with rare-earth ions like Tm$^{3+}$ or Ho$^{3+}$ is ideal for power scaling [1,2]. To also generate high mid-IR pulse energies from OPOs and obtain a highly efficient nonlinear conversion, the optimization of Q-switched single-oscillator fiber lasers towards high pulse energies at emission wavelength above ${2}\;\mu \textrm {m}$ is a major subject of current research.
In the following, an actively Q-switched Tm$^{3+}$-doped fiber laser is developed and characterized to investigate the pulse energy limits of this technology. First, the theory of Q-switched fiber lasers is reviewed followed by the description of the experimental setup, which is optimized for providing high pulse energies. Subsequently, the measurement results are reported and it is pointed out how the pulse energy limit is accurately determined. Finally, the results are summarized in the conclusion and an outlook for future experiments is given.
2. Theory of Q-switched fiber lasers
By repetitive Q-switching of a laser, a series of pulses is generated by periodic variation of the resonator losses. In oscillation theory, the quality factor (Q-factor) describes the damping of an oscillating system (oscillator). Here, a high Q-factor stands for a weakly damped system. A linear fiber laser resonator is damped by the reflectivities of its output coupler $R_{OC}$, its high reflector $R_{HR}$, and by other losses $\Lambda$ due to scattering, reflection, or absorption at optical interfaces in the passive resonator or within the active fiber. To allow oscillation of the laser, the single-pass gain along the fiber must reach the threshold:
For this, the corresponding threshold population inversion
In active Q-switching, a loss modulator periodically switches between a high and a low Q-factor in the laser cavity. In the period with the low Q-factor, the additional losses prevent oscillation in the laser resonator and thus result in charging of the inversion. At the end of the charging period, the inversion reaches the level $\langle {\Delta N}\rangle _{i} > \langle {\Delta N}\rangle _{th}$. Switching to the high Q-factor leads to a fast discharge of the accumulated inversion and the formation of a high and narrow pulse with a Gaussian shape in the output signal. Thereby the inversion drops to the level $\langle {\Delta N}\rangle _{f} < \langle {\Delta N}\rangle _{th}$. Using the definition
Since the inversion level corresponds to the energy stored in the active fiber, the extracted pulse energy is proportional to the inversion drop:
Thus, the pulse energy can be increased by supplying more pump energy during the inversion charging period. This is done either by increasing the pump power $P_p$ or by extending the charging period, which means a lower pulse repetition rate $\nu _{rep}$. Scaling of the pulse energy is accompanied by an increase in pulse peak power and a shortening of the pulse width in terms of the full width at half maximum (FWHM).
Because the single-pass gain $G_i \propto \langle {\Delta N}\rangle _{i}$ reaches high values when scaling the pulse energy, the maximum achievable pulse energy in a fiber laser is usually limited by the occurrence of parasitic lasing. In this case, the accumulated inversion is sufficient to amplify even small feedback in the laser cavity despite the reduced Q-factor. This causes a parasitic oscillation before switching to the high Q-factor, which prevents further inversion build-up. The initial inversion $\langle {\Delta N}\rangle _{i}$ is therefore limited to $\langle {\Delta N}\rangle _{paras}$, which sets a limit for the maximum achievable pulse energy according to Eq. (5). Thus, the pulse energy limit in a Q-switched fiber laser depends on the difference between the high and the low Q-factor or, more precisely, the difference between the threshold inversion $\langle {\Delta N}\rangle _{th}$ according to Eq. (2) and the threshold $\langle {\Delta N}\rangle _{paras}$ for parasitic lasing. Thus, a low-loss resonator design with minimized parasitic feedback due to backscattering from optical components is required to enable high pulse energies. However, owing to fiber intrinsic scattering centers, some degree of parasitic feedback remains unavoidable.
The pulse energy limit is a characteristic of a fiber laser and can be specified by the parameter
which corresponds to the maximum achievable pulse energy of the fiber laser, independent of its operating point [4,5]. This means that actively Q-switched fiber lasers can be scaled in average output power $P_{avg}$ by increasing the pulse repetition rate $\nu _{rep}$ while maintaining the pulse energy. In particular, this property makes them attractive pump sources for optical parametric oscillators for nonlinear frequency conversion into the mid-IR.3. Experimental setup
To generate high pulse energies from an actively Q-switched fiber laser, an experimental setup is used which only consists of essential components. This facilitates the optimization of the laser to reduce parasitic feedback, which would limit the maximum achievable pulse energy. The setup is shown in Fig. 1. The investigated 3.7 m long Tm$^{3+}$-doped fiber is placed in a water bath for cooling. This is a commercially available polarization-maintaining large mode area fiber with a core diameter of ${20}\;\mu \textrm {m}$, a core NA of 0.08, and a cladding diameter of ${300}\;\mu \textrm {m}$. One fiber end is cleaved perpendicular to an angle of ${0}^{\circ }$ and acts as the output coupler (OC). The opposite fiber end is cleaved to an angle of ${8}^{\circ }$ to prevent parasitic feedback between the end faces. A volume Bragg grating (VBG) with a diffraction efficiency $>$99% and a bandwidth $<$1 nm centered at a wavelength of 2044 nm acts as the high reflector (HR). An operating wavelength of 2044 nm is advantageous for use as a pump source for OPOs, since nonlinear crystals such as ZGP exhibit improved transparency for wavelengths above ${2}\;\mu \textrm {m}$. In addition, the high Q-factor at the operating wavelength and the low feedback of ASE provide excellent conditions for pulse energy scaling by Q-switching. The active double-clad fiber is pumped at both ends by laser diodes, which can each supply up to 30W of optical pump power. The diodes emit at a wavelength of $\sim$790 nm, which allows efficient pumping using the cross-relaxation process in Tm$^{3+}$-doped silica [6]. Pump and laser radiation are spatially separated by dichroic mirrors. To actively Q-switch the fiber laser, an acousto-optical modulator (AOM) is placed inside the cavity. Some applications, e.g. pumping of birefringent nonlinear crystals like ZGP, require a linearly polarized output signal. Thus, a polarizer is inserted into the fiber laser cavity between the AOM and the VBG to provide a linear polarized laser output. An additional polarizer on the output side filters unpolarized radiation from the output signal. The laser is examined both polarized and non-polarized, i.e. with and without polarizers.
4. Experimental results and discussion
By plotting the output power versus the supplied pump power, the power characteristic of the fiber laser is measured. The left graph in Fig. 2 shows the power characteristic of the unpolarized laser in CW operation. Fitting the measured data yields a slope efficiency of $\eta _s= {43.1}\%$ up to an output power of 20.7W. The threshold pump power to enable laser oscillation is 5.3W.
Fig. 2. Output power characteristics. Left: Output power versus pump power of the unpolarized laser in CW operation. Right: Output power versus pump power of the polarized laser in CW and Q-switched pulse operation. The inset shows the output power at a constant pump power of 43W versus the pulse repetition rate.
Inserting the polarizers results in a slight reduction of the measured slope efficiency. The power characteristics of the polarized laser are depicted in Fig. 2 on the right. In CW operation, the slope efficiency is 41.4%. The threshold is still at a pump power of 5.3W. The figure also shows the measured average output power characteristics in Q-switched operation for pulse repetition rates of 20kHz and 30kHz. In the inset, the output power for a constant pump power of 43W is plotted versus the pulse repetition rate. Increasing the pump power at a constant repetition rate as well as decreasing the repetition rate at a constant pump power result in a reduction in efficiency compared to CW operation. The reduced pump absorption at higher population inversions causes the charging process to require more and more energy. Scaling of pulse energy is therefore associated with a loss of efficiency. Moreover, the output power curve at $\nu _{rep}= {20}$ kHz shows a kink in its slope when exceeding a pump power of about 46.7W. While the slope efficiency is about 26.4% just before the kink, it drops to only 4.2% after it. Similar behavior has already been observed in [7] and has been identified as a sign for reaching the pulse energy limit. According to Eq. (6), the pulse energy limit of the polarized laser can thus be estimated to be around $k_s \approx \;{650}\;\mu \textrm {J}$. In the following paragraphs, the pulse energy limits of both the polarized and the unpolarized laser are investigated in more detail.
Figure 3 shows the measured pulse durations of the unpolarized laser for constant pump powers of $P_p= {43}$W and $P_p = {54}$W versus the pulse repetition rate. The pulse duration in terms of the FWHM is determined from a Gaussian fit to the temporal pulse shape measured by a photodetector. One data point in Fig. 3 corresponds to the mean value of the pulse widths of several observed pulses at the same operating point. By decreasing the repetition rate, an almost linear shortening of the pulse width can be observed, which agrees with the theory of Q-switching [3]. For the pump power of 43W, a decrease in pulse duration is measured down to a repetition rate of 16 kHz. The corresponding pulse shape is shown in the left inset and has a pulse width of $t_p= {42}$ ns. In the measurement series with 54W of pump power, the duration of the shortest pulse (right inset) is $t_p= {41}$ ns at a repetition rate of 21 kHz. In both cases, further reduction of the repetition rate no longer causes a decrease in pulse width which indicates reaching the pulse energy limit.
Fig. 3. Pulse duration versus repetition rate of the unpolarized laser at constant pump powers of 43W and 54W. The insets show the pulse shapes of the shortest measured pulses.
The pulse energy is determined from the ratio of measured average output power and pulse repetition rate $E_s=\frac {P_{avg}}{\nu _{rep}}$, which is valid in the absence of significant ASE or parasitic lasing. Figure 4 shows the pulse energy at the constant pump powers of $P_p = {43}$W and $P_p = {54}$W versus the repetition rate of the unpolarized laser. The corresponding pulse peak power is derived by the relation $P_{peak}=0.94 \frac {E_s}{t_p}$ assuming Gaussian shaped pulses. At the repetition rates where the shortest pulse durations were previously measured, the pulse energy limit is determined. For $P_p = {43}$W, this results in a maximum pulse energy of $k_s = {800}\;\mu \textrm {J}$ and a corresponding peak power of $P_{peak} = {18.1}$ kW at the repetition rate $\nu _{rep} = {16}$ kHz. The measurement at $P_p = {54}$W yields a pulse energy limit of $k_s = {806}\;\mu \textrm {J}$ and a peak power of $P_{peak} = {18.6}$ kW at $\nu _{rep} = {21}$ kHz. As predicted by theory, the pulse energy limit is in both cases nearly the same regardless the power level.
Fig. 4. Pulse energy versus repetition rate of the unpolarized laser at constant pump powers of 43W and 54W. The inset shows the corresponding peak power versus the repetition rate at both pump powers.
To investigate the pulse energy limits of the polarized laser, the measurements of pulse duration (Fig. 5), pulse energy, and pulse peak power (Fig. 6 and inset) are performed in the same way. As can be seen in Fig. 5, the pulse durations versus the repetition rate for the polarized laser deviate more from the linear behavior compared to the unpolarized laser. Since the individual pulses are more irregular in their pulse width, it is difficult to precisely determine the operating point of the lowest pulse duration. Therefore, another criterion is used to determine the pulse energy limit: a parasitic lasing signal is measured below a repetition rate of 19.5 kHz for $P_p = {43}$W and 26 kHz for $P_p = {54}$W, respectively. Figure 7 shows the spectrum of this parasitic signal with a logarithmic scale on the y-axis. The parasitic oscillation appears at the maximum of the broad amplified spontaneous emission (ASE) spectrum at a wavelength of $\lambda _{paras} = {1946}$ nm. Thus, the parasitic lasing does not receive feedback via the VBG, since it lies outside of its reflection bandwidth of $\Delta \lambda _{VBG}<{1}$ nm centered at 2044 nm. The inset in Fig. 7 shows a screenshot from the oscilloscope on which the temporal signal is recorded. The rectangular curve displayed in orange illustrates the signal for driving the AOM. If the square wave signal is high, the resonator is blocked, whereas a low signal opens the resonator. Thus, in the optical laser signal shown in purple, a parasitic pulse appears even before the resonator opens. Before the parasitic oscillation occurs, a maximum pulse energy of $k_s = {621}\;\mu \textrm {J}$, a pulse duration of $t_p = {44}$ ns, and a peak power of $P_{peak} = {13.1}$ kW can be measured at a pump power of $P_p = {43}$W. At $P_p = {54}$W, a maximum pulse energy of $k_s = {627}\;\mu \textrm {J}$, a pulse width of 42 ns and a peak power of 13.9 kW is obtained. Note that this criterion for determining the pulse energy limit is also applicable to the unpolarized laser, where it leads to the same results ($k_s \approx \;{800}\;\mu \textrm {J}$) as given above.
Fig. 5. Pulse duration versus repetition rate of the polarized laser at constant pump powers of 43W and 54W. The insets show the pulse shapes at the respective pulse energy limits.
Fig. 6. Pulse energy versus repetition rate of the polarized laser at constant pump powers of 43W and 54W. The inset shows the corresponding peak power versus the repetition rate at both pump powers.
Fig. 7. Measured spectrum of the parasitic lasing after exceeding the pulse energy limit. The inset shows a screenshot of the measured temporal signal displayed on the oscilloscope after exceeding the pulse energy limit.
When scaling the pulse energy, the high peak intensities occurring within the fiber affect the spectral properties of the Q-switched fiber laser. Figure 8 shows the spectra of the polarized laser with logarithmic intensity scale for a constant pump power of 43W at different repetition rates. The optical spectrum analyzer (Yokogawa) was set to a resolution of 0.05 nm for this measurements. The inset shows the spectrum at 20 kHz with a linear intensity scale. While the FWHM of the emission spectrum at 20 kHz repetition rate is still narrow ($\textrm {FWHM} = {0.8}$ nm), a significant broadening with reducing the repetition rate is observed for lower intensity levels. This behavior is typical for a Q-switched fiber laser and has already been studied in [8], where it was attributed to the effect of self-phase modulation (SPM). The left graph in Fig. 9 illustrates the intensity dependence of this spectral broadening by plotting the linewidth at different intensity levels from the maximum versus the pulse peak power. The line width at −20 dB and −10 dB from the maximum behaves almost proportional to the peak power, which confirms the influence of a nonlinear effect. Since this effect depends on the peak intensity within the fiber, the broadening of the spectrum goes into saturation after the pulse energy limit is reached. This behavior is illustrated in the right graph in Fig. 9, where the line width at different intensity levels is plotted versus the repetition rate. In the measured data at the intensity levels of −10 dB and −20 dB, the increase in spectral broadening saturates below a repetition rate of 19 kHz. This nearly agrees with the pulse energy limit at 19.5 kHz for a pump power of 43W determined above.
Fig. 8. Measured spectra of the polarized laser at a constant pump power of 43W and different repetition rates with a logarithmic intensity scale. The inset shows the spectrum at 20 kHz repetition rate with a linear intensity scale.
Fig. 9. Spectral broadening characteristics. Left: Measured linewidth at different levels from the maximum versus pulse peak power. Right: Measured linewidth versus pulse repetition rate. The repetition rate from which the increase of the linewidth goes into saturation indicates reaching the pulse energy limit.
To determine the beam propagation factor $M^{2}$, the beam is focused using a lens. Figure 10 shows the measured beam diameters in two orthogonal transverse directions x and y at different distances from the lens. The insets show intensity profiles of the beam at the widest and the smallest measured beam diameter. The measurement was performed in Q-switched operation of the polarized laser at a pulse repetition rate of 20 kHz and a pump power of 43W. The average output power at this operation point is 12.31W. Fitting the theoretical curve to the measured data yields $M^{2}$-factors of 1.05 in x-direction as well as in y-direction, which means a diffraction-limited beam quality.
Fig. 10. Focussed beam diameters of the polarized laser versus distance. Fits to the data yield the $M^{2}$-factors in transverse x and y-direction.
For the evaluation of the experimental setup, the parasitic feedback limiting the pulse energy can be estimated from the obtained measurement data. Because the parasitic lasing does not appear at the VBG wavelength of 2044 nm, it receives feedback from a weak parasitic reflector in front of the grating and is therefore coupled out at both sides of the laser cavity. According to [7], this explains the kink in the power curve as shown in the right graph of Fig. 2. By comparing the slope efficiencies in this graph before and after the pulse energy limit is exceeded, the reflectivity of the parasitic reflector can be roughly estimated. Assuming nearly identical inversion in the operating points around the kink, the ratio of the slope efficiencies can be approximated by:
Solving this equation to $R_{paras}$ and assuming a Fresnel reflectivity of about $R_{OC}\approx \;{4}\%$ at the glass-air transition of the OC, yields a parasitic reflectivity in the order of −78 dB. Since the slope after the kink is almost horizontal, it is affected by large relative measurement uncertainty. This measurement error has an exponential influence on the result of the parasitic reflectivity and therefore does not allow a precise determination by this method. Nevertheless, this estimation points out that the parasitic feedback is very small and sources of backscattering have been largely eliminated by the resonator design. Because a small amount of parasitic feedback cannot be completely avoided, the low Q-factor has reached a fundamental limit given by the spectroscopic properties of the active fiber. Further improvement of the pulse energy limit can therefore only be achieved by optimizing the high Q-factor. This can be seen from the different results for the pulse energy limits of the polarized and the unpolarized laser. Inserting the polarizers introduces additional losses into the laser cavity, thus reduces its Q-factor and therefore also the maximum achievable pulse energy.
5. Conclusion
In conclusion, an actively Q-switched polarization-maintaining Tm$^{3+}$-doped fiber laser optimized for providing high pulse energies was developed and characterized. From the polarized laser, pulse energies of about ${630}\;\mu \textrm {J}$, with pulse widths of 42 ns and peak powers of 13.9 kW were extracted. The laser also features diffraction-limited beam quality ($M^{2}<1.05$) and a narrow linewidth (FWHM$\approx \;{0.8}$ nm) centered at 2044 nm. By removing the polarizers from the laser resonator, it was even possible to generate pulse energies of ${800}\;\mu \textrm {J}$, with pulse widths of 41 ns, and peak powers of 18.6 kW. In future experiments, the developed fiber laser will be used as a pump source for an OPO based on OP-GaAs. Since OP-GaAs OPOs provide nonlinear frequency conversion using quasi-phase-matching, they can also be pumped with unpolarized ${2}\;\mu \textrm {m}$ lasers, although it was shown in [9] that a polarized pump source leads to higher conversion efficiencies. However, due to the significantly higher achievable pulse energy of the unpolarized laser compared to the polarized one, it is unclear which configuration will show the better results. Therefore, both options will be investigated.
Funding
Bundesamt für Ausrüstung, Informationstechnik und Nutzung der Bundeswehr; Bundesministerium der Verteidigung.
Acknowledgments
The authors acknowledge the support of the mechanical workshop of the IOSB and Artur Schander, who fabricated special opto-mechanical components for the experimental setup.
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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