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Abstract
We report on changes of beam quality with rising pump pulse energy and repetition rate in a high-power mid-infrared ZnGeP2 (ZGP) OPO in a non-planar cavity. The ZGP OPO generates 25 W in 3 – 5 μm pumped by a 10 kHz Q-switched Ho:LLF MOPA system at 2 μm. The beam quality factor increases from nearly diffraction-limited at OPO threshold to a M2 = 1.8 at maximum pump power. The degradation can be attributed to thermal lensing and gain guiding effects in the nonlinear crystal. To discriminate between those effects, we monitored the beam quality as a function of the repetition rate at the highest pump pulse energy using a Pockels cell as a pulse picker. Therefore, the heat load inducing thermal lensing increases linearly, whereas gain guiding remains nearly unaffected. M2 shows a minimum of 1.2 at 1 kHz, starting from 1.3 at 100 Hz and rising to 1.8 at 10 kHz. Those findings have been reproduced by numerical simulations. Further investigations show the transient evolution of beam quality, revealing the thermal lens build-up process to the steady-state.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical conversion in parametric oscillators (OPO) and amplifiers (OPA) is a versatile and common method for tunable coherent sources [1]. Nonlinear conversion is of particular interest for the middle infrared (mid-IR) part of the spectrum, where the availability of other solid-state coherent sources is limited to quantum cascade lasers [2,3] and lasers based on chalcogenides doped with transition metals [4]. Zinc germanium phosphide (ZGP) crystals have favorable properties [5,6] among nonlinear materials suitable for conversion to mid-IR with pumping near 2 $\mu$m, where a wide choice of high power pump lasers with excellent beam quality is available. The ZGP is particularly appropriate for high-power and high-energy applications due to its thermal and mechanical properties. Recently, significant progress in growth techniques allowed reduction of residual pump absorption at 2 $\mu$m down to 0.02 cm$^{-1}$ and an increase of a laser-induced damage threshold for ns-pulses to $4-5~\textrm {J/cm}^2$ [6–13]. A demand for such laser sources stems from areas like remote sensing, free space communication or countermeasures in defense. Many of these applications require high-average power sources with good beam quality, hence power up-scaling has been investigated over many years and remains challenging [14–18].
To date, among high-power mid-IR ZGP OPO demonstrations, many suffer from limited stability and beam quality. The highest average power demonstrated in single-stage ZGP OPO reached 110 W [19], but beam quality at 100 W was poor, that is $M^2\approx 9$, and the operation at maximum output power lasted only for a few seconds before crystal damage, at the level of 30 W, authors reported $M^2\approx 4$. The most recent stable high-repetition-rate source is two-stage OPO-OPA tandem pumped by a 10 kHz Ho:YAG [20]. In this case, the first stage ZGP OPO yielded 28.4 W ($M^2 = 2.1$), while the OPA stage had $M^2\approx 3$ at an output power of 102 W. All aforementioned experiments utilized 4-mirrors planar ring resonators. In a similar cavity arrangement but with two separate ZGP crystals placed in series 41 W with $M^2 = 4.4$ was reported [21]. Other demonstrations of stable single-stage ZGP OPO include 27 W ($M^2 = 4$) with two ZGPs in a linear cavity [22] and 22 W with $M^2 = 1.4$ in 3-mirror V-shaped planar ring resonator [23].
There are two dominant effects causing deterioration of the beam quality in high-power ZGP OPOs. These are thermal lensing [24] and gain guiding [25,26]. The latter arises from a spatial intensity distribution of pump pulse energy, and thus gain distribution. It only depends on pulse energy, but not on the average power of the pump. On one hand, this can be minimized by increasing the pump spot size in the crystal, but on the other hand, the greater the pump spot size, the higher is the threshold and more difficult to maintain good beam quality [15]. Unlike the gain guiding, the thermal lens effect depends on heat absorbed by the crystal, so it is proportional to the pump repetition frequency. One way to counter the thermal lens is direct compensation with intracavity negative lens [18] or a Galilean telescope [27]. This approach was also proven to be effective in the demonstration of the OPO-OPA 102 W system [20]. The compensation with elements of fixed dioptric strengths is limited to systems of well-characterized and known thermal lens, but very often its dynamic nature is not studied carefully.
Another well-established technique to improve beam quality in OPOs is a ring resonator with a non-planar configuration of mirrors. Such resonators and their effect on beam quality improvement were first investigated by Smith et.al. [28]. A specific non-planar design with 90° image-rotation is known as a Rotated Image Singly-Resonant Twisted RectAngle (RISTRA) cavity [29]. The RISTRA as an OPO resonator was proven to be effective and advantageous compared to planar resonators in many later demonstrations of high-power and high-energy OPOs with improved beam quality [30,31]. In this study, we take advantage of this particular cavity design and its properties to focus on different factors affecting beam quality.
Within the technical limits of the experimental setup, a given OPO output power can be realized by a high pump pulse repetition rate and a low pump pulse energy or vice versa. The question is which combination yields the better beam quality.
Here, we demonstrate experimental verification of beam quality improvement using single-stage ZGP OPO in the RISTRA cavity pumped by a high-repetition rate Ho:LLF MOPA system. We experimentally investigate changes of the beam quality with pulse energy and repetition rate of the pump. The beam quality factor $M^2$ as a function of the repetition rate at constant pulse energy shows an unexpected minimum, which we support by numerical simulations. For the first time, we demonstrate time-resolved experimental studies of a steady-state thermal lens build-up process.
2. Experimental setup
2.1 Highly-efficient resonantly pumped Q-switched Ho:LLF MOPA system
A Ho:LuLiF$_4$ (Ho:LLF) MOPA system [32] serves as a pump laser, its schematic diagram is shown in Fig. 1. The unpolarized pump light of a 120 W Tm fiber laser (IPG TLR-120-WC-Y14) passes through a first telescope (L1: f = 75 mm; L2: f = −40 mm) and then is split into two orthogonally polarized pump beams passing each a second telescope (L3: f = −75 mm; L4: f = 100 mm; L5: f = −200mm). The size of the pump image in the crystals can be simply adjusted by moving lenses L3 and L4 of the second telescope [33].
Fig. 1. Setup of the end-pumped Ho:LLF MOPA system; TFP: thin-film polarizer, $\lambda /2$: half-wave plate, HR: high reflector. The graphs below: Laser power with labels indicating pulse duration (a) and spectral output (b) of the Ho:LLF MOPA system.
The 0.5 at. % doped a-cut Ho:LLF crystals have diameters of 6 mm. The c-axis of the 60 mm long oscillator and the two amplifier crystals (40 and 60 mm long) are oriented parallel to the polarization of the pump beams to take advantage of the high absorption on $\pi$-polarization of Ho:LLF at 1940 nm. The folded resonator is 130 mm long with a concave output coupler (OC) with a radius of curvature 300 mm and reflectivity of 60 %, a flat high-reflector (HR), and two flat mirrors M1 tilted by 32°, with high transmission at the pump and high reflection at the laser wavelengths. A 17 mm Brewster-cut acousto-optic modulator (AOM) (Gooch & Housego model QS041-4M(BR)-IS3) was used for Q-switched operation with a repetition rate of 10 kHz. Radio-frequency power was 20 W at 41 MHz. The AOM forces oscillation on $\sigma$-polarization and amplification is done on $\sigma$-polarization, too. The middle of the oscillator crystal is imaged 1 to 1 to the center of the composite amplifier crystal with lens L6 (f = 150 mm).
The graphs in Fig. 1 show average laser power (a) and spectral output (b) of the system. It delivers 68.7 W at 2065 nm in TEM$_{00}$ operation at a repetition rate of 10 kHz with an optical-to-optical efficiency of 61.5 %. The second telescope was adjusted to obtain temporally stable pulses. Afterward, a pump spot diameter of 609 $\mu$m was measured. The output beam quality is diffraction-limited at a maximum pulse energy of 6.87 mJ.
2.2 ZGP OPO experimental setup
The experimental setup of the ZGP OPO is presented in Fig. 2. The 300 mm lens focuses the output from Ho:LLF onto the ZGP crystal with a measured spot diameter of $1.1$ mm. The spot size was chosen not to exceed the damage threshold of the ZGP (< 1 J/cm$^2$). A half-wave plate in combination with a polarizer allows polarization rotation and, by this means, pulse energy and power adjustment without changes in spatial and temporal pulse properties. A Pockels cell allows voltage-controlled polarization rotation for power adjustment and pulse picking. We can set the pump repetition rate to the values: 0.1 kHz, 0.5 kHz, 1 kHz, 2.5 kHz, 5 kHz, and 10 kHz without affecting pulse properties. Behind the cavity, the depleted pump is filtered out by a dichroic mirror. A wedge is used to reflect a small portion of the OPO beams for $M^2$-analysis. It is carried out with f = 500 mm focusing lens. The respective power of the beams is monitored with water-cooled thermal sensors (mks Ophir L250W).
Fig. 2. The experimental setup with a mirror configuration of the RISTRA OPO cavity used in this study.
Brightness determination was done by inspection of the signal and idler beams with infrared pyroelectric array sensor (mks Ophir Pyrocam IV Beam Profiling Camera) using the test method for laser beam parameters: beam widths, divergence angle, and beam propagation factor $M^2$ (EN ISO 11146). The camera resolution is 320x320 pixels with the pixel pitch 80 $\mu$m. This camera was used in chopped (50 Hz) or triggered (100 Hz) modes for all the beam images presented here. The 50 Hz frame rate offers 20 ms time resolution for the acquisition of beam images. The mechanical, remotely controlled beam shutter allows the pump beam blocking before the OPO cavity.
The ZGP crystal used in this study has an aperture of 6x6 mm$^2$ and a length of 20 mm, it is cut at 55° with respect to the optical axis for type-I phase matching at 2 $\mu$m, its end faces are AR-coated for the pump and 3 – 5 $\mu$m (Harbin Huigong Science & Technology Co., Ltd.). We determined its absorption coefficient by measuring absorptance $\alpha =0.044~\textrm {cm}^{-1}$ at 2.065 $\mu$m. It is transversely centered on the pump beam and adjusted in a phase-matching angle for maximum OPO output pulse energy, resulting in a signal wavelength around 3.85 µm and an idler around 4.45 µm. The crystal is wrapped in indium foil and mounted inside the optical cavity in a copper holder, serving as a heat sink. The crystal holder was not water-cooled.
The singly signal resonant RISTRA cavity is composed of four flat mirrors in a non-planar ring configuration. The output coupler (OC) of the RISTRA is partially reflective for the signal beam ($R \approx 50\%$) and highly transmitting ($T>95\%$) for the pump and the idler. The input coupling mirror (IC) and the two other mirrors (M1, M2) are identical and have high transmission for the pump ($T=86.3\%$) and the idler ($T>94\%$), and high reflectivity for the signal ($R>99\%$). The uncoated, zero-order MgF$_2$ half-wave plate compensates for polarization rotations in the resonator and keeps it unchanged after a round trip. The physical length of the resonator is 130 mm, which corresponds to the optical path of the signal beam per round trip around 172 mm.
3. Results and discussion
3.1 Beam quality at a constant repetition rate of 10 kHz
The beam quality factor $M^2$ of the OPO signal and idler beams as a function of the pump pulse energy at a constant repetition rate of 10 kHz is shown in Fig. 3 (upper left). It is nearly diffraction-limited near threshold at pump energy of 1 mJ and increases to a value of $M^2\sim 1.8$ at maximum pump pulse energy of 6 mJ (60 W). The inset depicts corresponding conversion efficiency and the OPO output pulse energy and power. The graphs on the right in Fig. 3 show the change of the focused signal beam between the highest (top) and the lowest (bottom) laser power after a positive 500 mm focal length CaF$_2$ lens. The beam quality factors were determined by fitting the standard Gaussian beam propagation expression to the measured data. A shift of the waist position of around 2.5 cm is visible. The rows of images in the bottom are the near-field beam images taken at the position 80 cm after the focusing lens. Higher-order modes contribute to beam profiles, which is the result of a decrease in the fundamental mode size of the signal. Because the idler beam has a much larger divergence than the signal beam, it was clipped by the 1-inch optics. The $M^2$ measurement at the highest power could not be performed, that is the reason for a lack of the last 3 data points for the idler in the graph. There is no reason for a deviation from the trend, thus similar behavior can be anticipated.
Fig. 3. The main graph shows how the beam quality factor scales with the pump pulse energy at a fixed repetition rate of 10 kHz. The inset shows the conversion efficiency with output pulse energy associated with the left axis and total output power with the right axis. Below are near-field beam images (taken 80 cm after the focusing lens) corresponding to each data point. The graphs on the right-hand-side show signal beam focusing behavior as measured for two extreme pump power levels.
3.2 Calculation of the fundamental mode size
Since all the cavity mirrors are flat, the question remains, what makes it stable? On one hand, a portion of the pump radiation is converted into heat inside the crystal and forms a positive thermal lens. As depicted in Fig. 4(a), the signal fundamental mode beam radius $w$ decreases with increasing thermal lens ($n_2$ parameter) which makes the resonator stable. Calculations are done with laser cavity analysis and design software (LAS-CAD GmbH, http://www.las-cad.com). From the relation between the real spot size of a laser beam, which in our case is the pump spot size $w_{pump}$, and its corresponding fundamental mode spot size $w$, the $M^2 = ({w_{pump}}/{w})^2$ [34] increases with increasing thermal lens. At increasing values of $n_2$, the resonator approaches its stability limit and the fundamental mode spot size increases again, resulting in a decrease of $M^2$ value. On the other hand, a quadratic variation of the gain parameter $\alpha (r) = \alpha _0 - \frac {1}{2}\alpha _2r^2$ makes the cavity stable too, its influence on the fundamental mode signal beam size and expected $M^2$ value is shown in Fig. 4(b). The parametric gain coefficient $\alpha$ can be found e.g. in [18].
Fig. 4. Calculation of the fundamental mode signal radius $w$ and corresponding expected $M^2$ value as a function of (a) the quadratically varying index of refraction parameter $n_2$ and (b) the quadratically varying gain parameter $\alpha _2$. In (a), respective focal lengths of the thermal lens are displayed on the radius curve.
Taking into account a Gaussian intensity distribution with pump spot radius $w_{pump} = 0.55$ mm, pump pulse energy $E = 6$ mJ, pulse duration $t = 25$ ns (FWHM), and an effective nonlinear coefficient $d_{eff} = 80$ pm/V, the calculated gain distribution is shown in the inset of Fig. 4(b). By curve fitting, the quadratic gain parameter $\alpha _2$ turns out to be $2.6$ mm$^{-3}$. This simple calculation shows that gain guiding can make the signal beam narrower than the pump beam, increasing the $M^2$. Therefore, both effects of thermal lensing and gain guiding lead to deterioration of the beam quality. To discriminate between them, we investigated the beam quality as a function of the repetition rate.
3.3 Evolution of beam quality with pump repetition rate
We controlled the repetition rate of the pump by pulse picking without affecting pulse properties. This way, we isolated the influence of the repetition frequency from other factors affecting beam quality. Figure 5(a) shows the results of the measurement of the beam quality factor as a function of the repetition rate of the pump. The pulse energy was kept at 6 mJ and other pulse properties were not changed between measurements. At the maximum rate of 10 kHz, corresponding to the maximum output power of 25 W in our setup, we measured $M^2=1.8$ (Fig. 5(b)). As one could expect when lowering the repetition rate, the beam quality should improve as it does when the pulse energy is lowered. However, the actual behavior deviates from expected. The $M^2$ data show a minimum value of $1.2$ at 1 kHz, starting from 1.3 at a low repetition rate of 0.1 kHz and rising to 1.8 at 10 kHz. The observed minimum suggests a trade-off between the thermal lens and the gain guiding, as in this case only the thermal lens is varied while the gain is fixed. It is different from the behavior observed previously when both pulse energy (gain) and thermal lens (average pump power) were varied.
Fig. 5. (a) Evolution of beam quality with the pump repetition rate for RISTRA cavity at constant pump pulse energy of 6 mJ and (b) an example of the caustic registered to retrieve $M^2$ for signal beam corresponding to the maximum output power at 10 kHz.
The results of numerical simulations confirm the experimental data. The simulation tool OPODESIGN [18] solves the paraxial wave equations with fast Fourier transform and it propagates the signal, idler, and pump waves in the crystal, cavity, and outside to establish the caustic. The split-step method is applied to integrate the OPO equations, thus conversion and back conversion are accounted for. The simulation uses only single frequencies for all waves. The temporal evolution is realized by sampling slices of round-trip time in the cavity. At low repetition rate, the thermal lens is weak and the beam quality is dominantly governed by the gain guiding effect at the pump pulse energy of 6 mJ. When the repetition rate rises, the thermal lens gets stronger, causing the weakening of the gain guiding and slight improvement of the beam quality. Simulations with OPODESIGN indicate that this trend to better beam quality cannot be ascribed to an obvious change of a single parameter like, for instance, the diameter of the signal in the crystal. A further rise of the repetition rate makes the thermal lens stronger and stronger, thus causing a growing destabilizing effect on the OPO cavity. The beam quality factor leaves its minimum and rises again.
The effect of the pump repetition rate in such an OPO system has not been studied before. In [30] authors used the RISTRA and monitored conversion efficiency 1 – 500 Hz range, however they tuned Q-switching, thus varying the pump pulse duration along with the repetition frequency.
3.4 Time-resolved studies of a steady-state thermal lens
The transient evolution of beam quality correlates with a build-up of temperature gradient inside the crystal. Such a gradient leads to a steady-state thermal lens. To understand the process, we monitored the $M^2$ as a function of time after opening the pump with a mechanical shutter. The procedure to reconstruct the beam quality as a time function is as follows. The beam profiles at a certain position of the camera are captured with a 20 ms resolution. Then, the camera is moved to the next position along the signal beam, while the crystal is allowed to cool down and come back to the initial equilibrium conditions. The intervals required for this were determined experimentally. After data is collected for enough points to plot caustics, we retrieve the time evolution of the beam quality factor in post-processing by combining the profiles for the same time frame. The result of such procedure is shown in Fig. 6 over 8 s after the pump was unblocked. The inset graph shows an example of the build-up of temperature in the ZGP center calculated numerically by solving heat transport equations.
Fig. 6. The evolution of the beam quality factor $M^2$ for the RISTRA cavity registered with 20 ms time resolution (not all the points are plotted). The inset graph shows the numerical simulation of temperature evolution in the crystal center.
What we notice about the $M^2$ time dependency are two timescales of this process. The fast exponential growth is related to the steady-state thermal lens build-up with a time constant in a good agreement with a value calculated from heat diffusion equations for the steady-state thermal lens [35]. After this, we observe a drift in the $M^2$-value, which can be likely attributed to heat accumulation and a rise in the overall temperature of the crystal and its holder. The heat accumulation leads to a slow change of the boundary conditions for a temperature profile inside the crystal, thus a change in the shape of the thermal lens. As a consequence, we can see higher-order modes appearing as explained before. The beam shape during the evolution changes similarly to the dependency observed for pump pulse energy (compare Fig. 3). The slow drift in the $M^2$-value depends only on water cooling of the crystal holder, as its constant temperature ensures constant boundary conditions for the transient thermal lens [36].
4. Conclusions
In this paper, we investigated how the beam quality in a single-stage ZGP OPO changes under varying pumping conditions to determine the best parameters to further up-scale the output power while maintaining good beam quality. The maximum total output power in the mid-IR region between 3 and 5 $\mu$m from our system was 25 W with $M^2 = 1.8$ and it is only pump-power limited. The variation of $M^2$ with pump repetition rate is a manifestation of a trade-off between the thermal lens and gain guiding. To our knowledge, the effect of the pump repetition rate on $M^2$ has not been considered earlier. Our investigation revealed conditions for optimal beam quality. We supported our findings by numerical simulations of OPO pulse propagation relevant to our experimental conditions.
We also presented results of the time-resolved beam quality factor monitoring in our setup with the 20-ms resolution revealing the steady-state thermal lens build-up. Such studies provide new information about ZGP OPOs, being usually masked in other high-power experiments, where beam quality measurements show only the system performance at stationary conditions in equilibrium. The knowledge of dynamic behavior is useful when designing and optimizing the duty cycle for a particular application, e.g. the ability to focus the laser output over long ranges can be enhanced by appropriate timing control.
Funding
Direction Générale de l’Armement.
Acknowledgments
Portions of this work were presented at the OSA Laser Congress in 2019 [32], the OSA Laser Congress in 2020 [37], and the 9th EPS-QEOD Europhoton Conference on Solid-State, Fibre, and Waveguide Coherent Light Sources in 2020 [38].
Disclosures
The authors declare no conflicts of interest.
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