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Abstract
A compact Kerr-lens mode-locked thin-disk oscillator reproducibly delivering 110 MW output peak power, the highest among all oscillators, is reported. This simple and stable femtosecond oscillator delivering a unique combination of high average power (202 W) and peak power, is an ideal driver and an important milestone for the development of extreme ultraviolet transportable frequency comb sources.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Recent rapid advances in the development of femtosecond thin-disk oscillators indicated a simple empirical mechanism for average and peak power scalability [1], essentially relying on scaling the mode size inside the Kerr medium (KM) and, thus, opening the path to gigawatt-level peak power directly out of the oscillator. However, as of now, there is no theoretical or experimental proof that this concept is power scalable beyond the previously demonstrated highest 62 MW for a Kerr-lens mode-locked (KLM) oscillator [2] and 66 MW for a SESAM mode-locked oscillator [3]. Interestingly, a KLM oscillator with 102 MW peak power and 50 fs output pulse duration was recently demonstrated [4], relying on the use of enhanced intra-cavity nonlinear effects. However, due to an overheating pump delivery system, the laser operates for only a few minutes, which makes it somewhat impractical for real-world applications. Here we experimentally show that the above-stated peak and average power values do not represent a fundamental limitation for soliton mode-locking in the negative dispersion regime. We experimentally verify the geometrical procedure behind this concept which implies a simple modification of a cavity resulting in increased mode sizes in the KM without significantly changing any other parameters. This concept provides nearly unlimited scalability of KLM thin-disk oscillators. Moreover, due to its simple design, robustness, and reliability, as well as its ability to utilize the entire gain bandwidth, the KLM Yb:YAG thin-disk oscillator is a favorable laser source for delivering high peak power and femtosecond long pulses at MHz repetition rates with excellent beam quality. The oscillator delivers a unique combination of high average and peak power (summarized in Fig. S4 in Supplement 1) which is important for driving low-efficiency processes like high harmonic generation. Subsequent efficient (up to 95%) nonlinear broadening and pulse compression in multipass cells [5] would result in a 1 GW level laser system delivering sub-15 fs long pulses at a repetition rate of a few megahertz. This oscillator, when CEP stabilized, is an ideal driver to efficiently generate high-order harmonics down to the XUV and deep UV ranges, favoring a coherent optical comb for high-precision spectroscopy [6–10].
2. Setup and experimental results
In this paper, we report on a compact femtosecond Yb:YAG KLM thin-disk oscillator. This type of oscillator includes an active gain medium, a thin disk, a set of highly dispersive mirrors (HD), a telescope with the KM in its focus, and a hard aperture (HA). The cavity is usually designed such that the mode size is slightly smaller than the pump spot on the thin disk. The repetition rate of the cavity can be easily scaled along with the telescope size and varies from a few megahertz [3,11] to a couple of hundred megahertz [12]. Nevertheless, while the upper limit arises from spatial constraints applied to the intra-cavity optics, fundamentally, there is no lower limit dictating the extension of the cavity to at least a few tens of meters, for example, using multipass cells [3].
Our thin-disk oscillator design is shown in Fig. 1. A 0.1 mm thick Yb:YAG thin-disk provided by Trumpf served as a gain medium and was pumped by laser diodes at 940 nm. The collimated pump beam was focused onto the thin disk into a spot diameter of approximately 3.3 mm, achieving a pump intensity of up to ∼10 kW/cm2 at the full pump power of 840 W and the disk water flow of approximately 3 l/min. The cavity design was selected in a way such that the average laser mode size across the cavity (defined at the 1/e2 level) was slightly less than the pump spot and maintained a 2.9 mm diameter (see Fig. 2(a)). In this oscillator configuration, a double-pass geometry was realized (see Fig. 1) to increase the overall gain, resulting in a total of 8 passes through the gain medium per round trip. Interestingly, cavity designs with a higher number of passes were demonstrated [11,13], yielding even higher gain. However, when future XUV frequency comb generation applications are considered, a repetition rate over 10 MHz is highly desirable.
Fig. 1. Optical layout of the KLM thin-disk oscillator. OC, 19% output coupler; TD, Yb:YAG thin-disk; KM, 5 mm thick crystalline quartz; HA, 5 mm diameter HA; HD, highly dispersive mirror with -2400 fs2 group delay dispersion (GDD); HR, high reflective mirror; M1 and M2, a pair of plano-concave mirrors. The footprint of the layout is 0.7 × 1.3 m2. Two insets represent the output beam profile and the laser mode on the pump spot, respectively. The imaging settings of the camera were adjusted to increase the contrast between the pump spot and the laser mode for better visualization.
Fig. 2. Simulated cavity characteristics. (a) Caustics of the cavity in continuous wavelength (CW) and mode-locked (ML) regimes. The positions of the hard aperture (HA) and thin disk (TD) are indicated. (b) Cavity mode radius at the HA vs distance between KM and mirror M2. The dependence represents one of the stability zones. The oscillator is mode-locked at the edge of the stability zone corresponding to the area between two grey lines. See Fig. S1 in Supplement 1 for supporting information.
The 5 mm thick Kerr plate was placed in the center of the 2.5 m long telescopic system consisting of a pair of plano-concave mirrors (see M1 and M2 in Fig. 1). Based on the numerical simulation of the beam caustics inside the cavity, the laser mode had a diameter of approximately 400 µm in the KM in its optimal position during mode-locking (see Fig. 2(a)). The oscillator ran with both soft and HA mode-locking. The soft aperture was placed in the thin-disk gain medium. The HA was placed close to the end mirror to enhance the overall self-amplitude modulation (SAM) effect and make the mode-locking start-up more reproducible. The HA represented a few-millimeter thick water-cooled copper plate with a 5 mm diameter hole. The Kerr plate placed under Brewster's angle, along with the HA and soft aperture in the disk, formed a mode-locker that induced sufficient self-phase modulation (SPM) and SAM for the stable pulsed operation.
The formation of a stable soliton pulse in the cavity is possible when anomalous GDD compensates for the frequency chirp due to SPM. Using this simplified model, a solitary solution can be derived from the nonlinear Schrödinger equation [14]. A more rigorous analysis can be performed based on a complex Ginzburg-Landau equation [15], which includes crucial parameters of real oscillators such as SAM, spectral filtering, gain, and loss. A complex interplay between those parameters defines the performance of the KLM regime. In this work, the intra-cavity dispersion management was governed by a pair of HD mirrors, resulting in a round trip GDD of approximately -10000 fs2. Thus, by operating in the anomalous dispersion regime, the oscillator delivered bandwidth-limited sech2 soliton pulses. The value of the GDD was adjusted to achieve the minimum possible pulse duration. The maximum peak power was set by the resonator configuration. The separation distance between the focusing mirrors M1 and M2 was increased to reach the far edge of the first stability zone (see Fig. 2(b)). Approaching the stability edge in continuous wave operation is a requirement for starting KLM in our oscillator. TEM00 mode size of the oscillator operating close to the stability edge is much more sensitive to intensity fluctuations introduced by external perturbations. Thus, pushing the translation stage with the output-coupler mirror mounted to it made it possible to mode-lock the oscillator reproducibly. Notably, the mode-locked oscillator operates close to the center of the stability zone, in “a stable cavity configuration,” not at the stability edge anymore.
The optical cavity was placed inside a monolithic temperature-stabilized aluminum housing in a clean, dust-free environment to enable reliable and stable long-term operation. Importantly, the housing was partially evacuated to provide a low-pressure ambient air environment. It was previously empirically shown [1] that the peak power in thin-disk oscillators can be scaled up by increasing the mode area inside the KM in the focal area of the telescope. Along with the increased intra-cavity peak power, nonlinear effects in ambient air, such as self-focusing and SPM, become more prominent. These can prevent further increases in peak power or lead to unstable pulses [16] since nonlinear effects in the air are spatially distributed (mainly within the telescope's Rayleigh range) and start competing with the induced SPM and self-focusing of the KM. Nonetheless, under slight vacuum conditions or in the presence of buffer gas, the impact of ambient air on the total nonlinearity per round trip becomes negligible [16,17], enabling further efficient peak power scaling. Therefore, at some point in the scaling procedure, operating the oscillator in a low-pressure environment is necessary. In the present experiment, the housing had to be evacuated, and the residual air pressure in the range of 150 mbar to 600 mbar showed stable mode-locked operation. It was shown [2] that output peak power strongly depends on air pressure. Due to its non-negligible contribution to the overall dispersion, fine-tuning generally leads to an optimal value corresponding to maximum peak power. In this experiment, a residual pressure of 180 mbar was found to be optimal for providing an output peak power of 110 MW.
To initiate the mode-locked operation, the output coupling mirror was disturbed by a magnetic pusher. A specific balance between the induced SPM, SAM, and GDD resulted in the formation of a stable sech2-shaped pulse train. The 10.7 m cavity length defined the pulse repetition rate of 14 MHz. It was beneficial to start the KLM operation when the KM was placed in the telescope's focus, and then the plate was moved out of focus during the mode-locked operation. During this procedure, the output peak and average powers increased proportionally to increases in pump power. The oscillator configuration was initially pumped at approximately 500 W when the KM was in focus. The output power in the continuous-wave regime at the mode-locking threshold was 60 W. After mode-locking, the average power increased to 100 W. Then, it reached 200 W while shifting the plate outside the focus and gradually increasing the pump power to ∼840 W. The corresponding optical-to-optical efficiency is 24%. In other words, mode-locking commenced in one configuration where the system easily started, and then the system was gradually moved to the optimal configuration with increased SAM depth. Starting the oscillator in this optimal configuration was either impossible or barely reproducible due to the damage to the KM and optics during oscillator start-up.
A limited range of materials was preferred for utilization as KMs in the experiments. The material needed to have a reasonable nonlinear refractive index, high thermal conductivity, and low linear absorption for reliable and reproducible high average power KLM operation. In the present experiment, crystalline quartz was used, which fully met these requirements. The choice of KM thickness was based on the following empirical implications. On the one hand, one way to increase induced SPM is to use a relatively thick KM. For such plates, the process of pulse build-up ran smoothly and reliably. However, the thicker the KM, the lower the mode-locking threshold and, thus, the less peak power the oscillator provided. Once the oscillator was mode-locked, the subsequent procedure of moving the thick KM out of focus and the proportional increase of pump power resulted in the appearance of a second or even a third pulse but not an increase in peak power. On the other hand, for thin Kerr plates, the mode-locking threshold is higher, allowing for high peak power pulses that preserve the single-pulsed regime. However, the mode-locking process became more unpredictable, less reproducible, and frequently led to the damage of the KM and intra-cavity optics. Based on these considerations and previous experience with these types of oscillators, a 5 mm thickness was determined to be optimal for the current resonator configuration. This value ensured both stable, reliable operation and high intra-cavity peak power of 585 MW.
The single-pulsed operation was proven by a 1 m long (corresponding to 3.4 ns delay), home-built autocorrelator combined with a fast photodiode with a 175 ps rise time and 2 GHz bandwidth. The 15 ps range was verified by a commercial autocorrelator. The intensity autocorrelation trace, the corresponding optical spectrum, and the RF spectrum of the output pulses are shown in Fig. 3. The oscillator delivered 115 fs long, 10 nm (FWHM) bandwidth-limited pulses with the time-bandwidth product of approximately 0.32. The output beam had an excellent beam quality and was measured in accordance with ISO 11146 to be M2 = 1.1 × 1.1 (Fig. 4(a)). The output power stability measurement is shown in Fig. 4(b). During the first 25 minutes of warming up, the oscillator was slowly drifting.
Fig. 3. (a) Output optical spectrum (orange) and GDD curve of HD mirrors (grey). (b) Intensity autocorrelation trace of output pulses. (c) and (d) Oscillator repetition rate measured with a radio-frequency spectrum analyzer. The resolution bandwidths are 10 Hz and 100 Hz, respectively. Orange lines indicate the noise floor. See Fig. S2 and S3 in Supplement 1 for supporting measurements.
Fig. 4. (a) Measurement of the beam quality M2. The inset represents the beam profile on the focal plane of a focusing lens. (b) Average output power stability measurement. The power fluctuation and drift are attributed to drifts in cooling water temperature.
This record-high output peak power of 110 MW was achieved mainly due to the following reasons. The beam size in the KM was enlarged by extending the telescope to 2.5 m, whereas the previous work used a 2.0 m long telescope. After this procedure, the intra-cavity peak power was scaled from 420 MW to 585 MW. Considering the value of intra-cavity peak power, the SPM coefficient for this cavity was estimated to be 0.0041 MW-1. Moreover, in the current experiment, the pump power density on the thin disk was increased from 9 kW/cm2 to ∼10 kW/cm2 by increasing the overall gain, making it possible to operate the oscillator with a higher output coupling rate of 19% compared to 15% [2] without sacrificing a pulse duration. These experimental steps resulted in a 110 MW peak power and 202 W average power directly from the oscillator.
No fundamental limits were observed for further scaling of KLM thin-disk oscillators towards the gigawatt level of output peak power. As shown in Fig. 5, the result of this work perfectly follows the trend line of the scaling law previously demonstrated in [1]. Interestingly, the oscillator spectrum was very close to the emission bandwidth of the Yb:YAG gain medium, which is about 9 nm FHWM. In principle, it is possible to overcome this limitation by further increasing the SAM using a distributed KLM technique [18], or in a way, it was recently shown [4] which already demonstrated 50 fs long output pulses directly from a Yb:YAG thin-disk oscillator.
Fig. 5. Intra-cavity peak power vs telescope length. Triangle represents the result of this work. Rectangles correspond to the results from [1]. Dashed line is a fit of the data [1].
As previously mentioned, the average pump power density in the oscillator reached 10 kW/cm2, which was close to the critical value when thermal lens distortions in the disk might get pronounced. Those effects typically change the stability of the cavity [19]. Depending on the resonator configuration, they may even favor the mode-locked operation, for instance, by pushing the cavity towards the stability edge due to the induced thermal lens. Thereby, one of the ways to avoid such unpredictable scenarios is to maintain a pump power density for the thin disk by enlarging the pump spot, which is also a key to further average power scaling. Further scaling can also be accomplished by increasing the number of passes through the disk. Both approaches were previously demonstrated [11,16,20].
Furthermore, because of the fundamental soliton mode-locking regime and its low noise characteristics [21,22], CEP stabilization of this type of oscillator no longer presents a great challenge. Moreover, the stabilization performance can be further improved if technical noises such as flicker noise can be overcome, which may be drastically suppressed by minimizing the repetition rate and maximizing the intra-cavity peak power [23]. Thus, this oscillator is expected to be CEP stabilizable with excellent short and long-term performance.
To ensure a good conversion efficiency of 10−7–10−6 in the upcoming experiments on direct deep UV and XUV generation in a gas jet, a high peak power laser favoring ultrashort pulses of a few tens of femtoseconds would be required [24,25]. Both requirements can be fulfilled in a single step with nonlinear broadening and pulse compression in a multipass cell [26,27]. Depending on the configuration, for a cell filled with nonlinear gas, a compression factor of no more than 10 [28,29], and possibly even more than 10 [30,31], can be achieved, preserving a relatively clean shape of the pulse with over 80% power in the main peak [27,29,32]. Moreover, due to their simplicity, robustness, and high transmission (up to 95%), these multipass cells can be stacked consecutively to yield an overall broadening and compression factor greater than 20 with approximately 1 GW, sub-10 fs pulses. Further amplification of the oscillator output by factors 5-10 may be necessary to increase XUV flux. Thus, starting even with longer pulses from the oscillator can be advantageous since amplification for pulses significantly exceeding the bandwidth of the gain media is very problematic.
3. Summary and outlook
In summary, we have demonstrated a compact table-top solid-state Yb:YAG femtosecond thin-disk oscillator delivering 110 MW output peak power. The spectral FWHM of the generated output pulses was close to the emission bandwidth of the Yb:YAG gain medium and resulted in 115 fs long soliton pulses containing 14.4 µJ of energy directly from the oscillator without any external amplification. Additionally, we have experimentally verified that the geometric power scaling works in the 100-MW-level output peak powers range. A subsequent spectral broadening and pulse compression of oscillator pulses down to sub-15 fs in gas-filled multipass cells is feasible with the upcoming experiments, possibly resulting in a gigawatt-level amplification-free laser-oscillator system. As shown previously, CEP stabilization of this type of oscillator with an intra-cavity acoustic-optic modulator is possible with a performance at levels as low as 90 mrad of integrated phase noise [22]. Even better values are expected for the current system. Therefore, this compact and simple oscillator is a promising driver for XUV frequency combs and consequent high-precision XUV spectroscopy experiments.
Acknowledgments
Considering the difficulty in setting up the new professorship in combination with typical university bureaucratic procedures, we would like to sincerely acknowledge a few facilitators: A. Borchers, D. Kiesewetter, and A. Puckhaber.
Disclosures
The authors declare no conflict of interest.
Data availability
Data underlying the results presented in this paper are available upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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