Monolithic thin-disk laser and amplifier concept

Thin-disk lasers are indispensable in photonics research as well as in a multitude of industrial applications. They represent a unique class of laser and amplifier architecture that provides kW output power with excellent properties concerning beam quality, long-term stability, thermal management, and power scalability. For many applications, a reduced complexity of the laser and its size would be highly beneficial. The necessary multipass transitions in thin-disk lasers and amplifiers typically require sophisticated multi-mirror arrangements. Here, we present a monolithic version of the pump concept for thin-disk lasers and amplifiers, where the thin disk is replaced by a thin, wedged gain medium acting as a wedged optical trap. The wedge is coated in a peculiar manner in order to allow for efficient inand out-coupling of the pump and laser radiation from the wedge. This concept transfers the complexity of the multi-mirror optics into the thin disk itself in a monolithic fashion. With this concept, we achieved 890 W of CW output power, 59% slope efficiency, optical-to-optical efficiency of 50%, and a gain factor greater than 10 for small signals. This demonstrates that this new concept is capable of reaching the kW power regime with minimum complexity and size.


INTRODUCTION
Solid state lasers and amplifiers enable a plethora of applications in basic research and industry. Fiber lasers, slab lasers, and thin-disk lasers exhibit excellent beam quality at kW power levels in CW and pulsed modes [1].
All three concepts achieve efficient thermal management by using a large surface-to-volume ratio. In the case of the thin-disk laser-invented in the 1990s especially to enable high-power operation of ytterbium-doped laser crystals-this is reached by cooling the relatively large (back) surface of the thin disk [2,3]. The cooled surface is coated highly reflective (HR) for the laser wavelength and acts as a resonator mirror, so the cooling will not interfere with the laser, and the main temperature gradients will be parallel to the laser beam. Pump radiation is applied from the front side. This design was quickly transferred to industrial applications: in 1997, Jenoptik produced the first commercial thin-disk laser, a 10 W Nd:YVO system; in 1999, Trumpf presented the first 1 kW thin-disk laser. In the following decades, thin-disk lasers addressed a large range of laser concepts and laser applications for science and industry-from high-power CW operation to sub-ps oscillators and amplifiers [4][5][6]. Currently, high-power thin-disk lasers with more than 10 kW out of one disk and good beam quality (sufficient for welding applications) are available [7]. One specific benefit of the thin-disk laser is the large gain area-this allows for large beam diameters and low fluences. Working at a low fluence is especially useful for the amplification of short pulses. Additionally, the thin disk combines these low fluences with a small amount of material inside the resonator. This results in low nonlinearities that, e.g., enable chirped pulse amplification (CPA)-free amplification of 750 fs pulses [8]. Many commercial and scientific thin-disk amplifiers are realized as regenerative amplifiers using electro-optical switches. The suitability of the thin disk for high efficiencies at high power also inspired the development of geometrical multipass amplifiers to overcome the power and energy limitations of the electro-optical switches. The comparably low single-pass gain of the thin disk (due to the small thickness) is challenging for multipass amplification, but several concepts were developed, including methods to control the beam quality. One example is the concept described in Ref. [9] that allowed after adaption to larger beam sizes for pulse energies of more than 300 mJ at low repetition rates [10]. A variation of this multipass concept was realized during the last years, achieving more than 1.4 kW with ps pulses and high repetition rate, using 80 passes through the thin disk [11]. For many applications, more compact multipass amplifier arrangements would be beneficial. Additionally, the optical multipass geometry usually necessary for pumping due to the small single-pass absorption of the thin disk also prevents compact solutions.
Here, we demonstrate a new concept for thin-disk lasers and amplifiers that allows reduction of the number of folding optics for pumping and amplification to an absolute minimum.
We introduce a wedge to the thin disk, which breaks its rotational symmetry and introduces a new plane of symmetry. This Close-up sketch of wedged thin-disk geometry. Indicated are the wedge angle α, the two incidence angles for pump ( P ) and lasing ( E ) radiation, as well as the local thickness d and beam displacement r . The upper surface is coated as a long pass, while the bottom (back) side is coated with a wide-angle highly reflective coating glued onto a diamond heat sink.
converts the gain medium into a wedged optical trap for the pump light. Optical wedge traps have been investigated as an optimization method for detectors [12,13]. Nevertheless, these trap detectors are illuminated from the edge of the wedge, which is undesirable in the case of a thin-disk laser. For application in a thin-disk laser, it is necessary to introduce a specialized multilayer dielectric coating on top of the wedge. This top coating-as any dielectric coating-exhibits an angle-dependent reflectivity [14] and is designed as a long-pass (LP) filter. The rear side of the thin disk is coated with an HR coating. Due to the wedge, the reflected angle of incidence (AOI) after the reflection is reduced slightly, which suffices to change the reflectivity experienced by the beam at the LP surface significantly. As depicted in Fig. 1, this allows coupling of laser radiation into the wedge trap at any given point on the surface.
With this approach, we demonstrate a CW output power of 890 W, 59% slope efficiency, 50% optical-to-optical efficiency, and a small signal gain factor of 10 in an extremely compact design.

A. Wedged Thin-Disk Properties
The wedge under test was analyzed in great detail in order to understand the dependencies of the relevant parameters. If not stated otherwise, the angles related to laser radiation are given in air. The wedge is designed with a wedge angle of α = 1 • starting at a thickness of 100 µm and over a diameter of 15 mm, reaching a thickness of 360 µm. The wedge is made from an 7 at-% Yb:LuAG crystal. The HR coating (NANEO, Germany) is designed to reflect more than 99.99% at 969 nm for an AOI between 0 • and 52 • , as well as 99.99% at 1030 nm for an AOI between 0 • to 38 • . Therefore, the coating is HR for all relevant angles and will be treated as a perfect mirror for the following considerations. The angle-dependent front coating is supposed to start transmitting s -polarized laser radiation at 1030 nm at 27.5 • and unpolarized pump radiation of 969 nm at 45.5 • AOI. In blocking regions, the coating is expected to exceed 99% reflectivity while transmitting more than 99% in the passband.
This results in the angle-dependent reflective behavior of the front coating displayed in Fig. 2. The reflection curves in Fig. 2 were measured with unpolarized Fourier-transform infrared (FTIR) spectroscopy. Due to the unpolarized pump radiation, the coating was specifically optimized to have reduced polarization effects. S-polarized radiation is expected to experience a slightly steeper LP edge. For details on the procedures and results, see Supplement 1.
The wedged thin disk with these dielectric coatings works as follows: the angle-sensitive LP coating faces the laser and pump radiation, as depicted in Fig. 1. Figure 3 shows the corresponding LPedge shift depending on the AOI.
The monochromatic laser light is highly reflected at an AOI of 0 • to 23 • , and at a threshold AOI of 27 • , the same wavelength is transmitted ( Fig. 2 purple and brown line). Given that the laser radiation is introduced from the thicker end of the wedge, the angle relative to the HR surface introduces a reduction of the AOI below the threshold angle after one reflection, and the laser beam is trapped for multiple reflections (compare Fig. 1) [16,17]. This is also true for the pump radiation indicated in green and red in Fig. 2.
The number N of reflections at the HR coating of the wedge can be estimated by dividing the internal AOI internal = arcsin(sin( )/n) by the wedge angle [16]: with n as the refractive index within the laser crystal. These values obviously are delicately connected to the actual wedge angle, which we assume to have a tolerance of 0.1 • . Therefore, the number of reflections for the seed and pump laser beams may be estimated to N λ=969 = 22 ± 2 and N λ=1030 = 14 ± 2, respectively. The average spatial displacement r due to the larger AOI and multiple reflections as indicated in Fig. 1 may be estimated with [16] with d as the average wedge thickness experienced by the beam. This results in r λ=969 ≈ 4.5 d and r λ=1030 ≈ 1.8 d .

B. Lasing Setup and Rigrod Analysis
In order to demonstrate the new concept and verify the kW scalability, a simple multimode I-resonator was chosen. This resonator is established with concave output couplers of 1 m radius of curvature (custom coatings, Laseroptik, Germany) and the thin-disk wedge at an incidence angle optimized for the lasing wavelength of 1030 nm. The basic setup is displayed in Fig. 4. By changing the output coupler, different output coupling ratios were evaluated. As the pump source, a 969 nm fiber coupled laser diode array was chosen (IS57.1, DILAS, Germany). The system is wavelength stabilized and allows optical pumping with up to 2 kW via a 1 mm, NA 0.2 high-power fiber system. The fiber output was re-imaged via a cooled collimation lens ( f = 50 mm) and a mirror (BB1-E03, Thorlabs, USA) onto the wedged thin disk with an approximate AOI of 45 • . The pump spot reached  The Rigrod analysis is an established method for determination of laser efficiency. Slope efficiencies η slope for the I-resonator were evaluated for different transmission values of the concave out-coupling mirrors.
The Rigrod model as described in Ref. [18] is given in Eq. (3): with R 1 = 1 − T and R 2 = 1 − L. The remaining fitting parameters are internal losses L and single-pass small signal gain G 0 . The transmission T of the output coupler was determined by reference laser transmission measurements at 1030 nm.
To utilize the well-determinable slope efficiencies instead of the available lasing power P avail , which is not available from measurements, we did alter Eq. (3) slightly.
For moderate degrees of output coupling and output powers well above the lasing threshold, the relation between output power P out and pump power P pump may be approximated by which for full equality results in the relationship Since η L as well as η slope are constants, η in must be constant, too. Introducing Eq. (5) into Eq. (3) then results in the measurable relation where η in is introduced as a new fit parameter. Equation (6) unfortunately, due to the approximation in Eq. (4), is not suitable to determine G 0 any longer. Therefore, emphasis will be on the results concerning the loss L of the system.

C. Small Signal Gain of Wedged Thin Disk
The small signal gain of the wedged thin disk was determined in the setup depicted in Fig. 5. By introducing an additional angle β relative to the plane of mirror symmetry of the wedge, the returning light may be separated from the incoming seed laser light. The seed laser beam was extended to 6 mm in diameter to match the diameter of the pump spot. The incident (P in ) and emitted (P out ) radiation powers were measured with the same power meter (PD300-3 W, Ophir Optronics, Israel); background fluorescence (P fluo ) was measured separately and subtracted before calculating the gain factor G of the emitted over the incident radiation power: The seed laser (Matchbox 1030-15B, Integrated Optics, Lithuania) produced 1030 nm CW emission at approx. 160 mW. The amplification factor with respect to the pump power was determined for a pump spot on two positions, as indicated in Fig. 5. Position 1 is 5 mm apart from the thin edge with thickness d ≈ 190 µm, and position 2 is 5 mm apart from the thick edge with thickness d ≈ 270 µm. Furthermore, the seed laser was attenuated to 9.6 mW and 3.2 mW for comparison.

A. Lasing Test and Rigrod Analysis
In the high-power lasing test, the system reached 890 W of output power (Fig. 6). At output powers below 700 W, it appears feasible to achieve 1 kW of output power with 2 kW of pump power. Nevertheless, saturation effects are observed above 700 W of output power, currently limiting the system to 890 W. During the test, temperatures of up to 130 • C were reached. High temperatures are known to have a fundamental influence on the efficiency of quasi-three-level laser materials such as Yb:YAG [3] due to the thermal population of the lower laser level. Gain and absorption coefficients are reduced at higher temperatures [19].
Since the core temperature of the thin-disk wedge is not accessible, a contactless thermal camera was chosen to document surface temperature of the wedge. To generate plausible readings, the setting for the thermal camera was chosen as 0.8. With pump radiation turned off, this gave a reading of 13 • C, as determined by the known coolant temperature.
The slope efficiency reaches 59 ± 3%, while the optical-tooptical efficiency of the system peaks at 50 ± 3%. These results were achieved with a concave output coupler (R = 1 m) and a transmission of 36%.
Multiple measurements of the optical-to-optical properties of the I-resonator setup have been performed to deduce system  losses and optical-to-optical efficiency. By changing the output transmission, different slope efficiencies were determined and used to evaluate the fitting parameters of the adapted Rigrod model in Eq. (6). The fit result is shown in Fig. 7 and suggests internal losses of 4.1 ± 0.7% and a maximum achievable system slope efficiency of 70 ± 5% if no internal losses were present.

B. Small Signal Gain of Wedged Thin Disk
The amplification factor with respect to the pump power for a pump spot on position 1 and on position 2 is shown in Fig. 8.
A variation of the seed power by one order of magnitude results in similar gain values; this indicates that the results represent small signal gain. Without pump radiation, the wedge absorbs the seed radiation as described by the Beer-Lambert law. This relation allows testing the consistency between absorption and design geometry. The transmission of the non-pumped wedge is 0.47 at position 1 and 0.33 at position 2 for the 1030 nm seed laser. The ratio of optical extinction from both positions can be calculated from the measurements to be ln(0.47)/ ln(0.33) = 1.46. Assuming the design edge thickness of 100 µm increasing to 360 µm over 15 mm and an adjustment of the pump spot centers shifted 5 mm ± 1 mm

DISCUSSION
In the design phase of the experiment losses induced by the coating posted a major concern.
As discussed in Supplement 1, the spectral properties of the coating allow utilization of a total of 95% of the pump radiation. A direct measurement of the first surface reflected pump light results in 7% losses, which indicates that the divergence angle of the pump light is still larger as expected. Furthermore, it may be deduced that increasing the spot size would also reduce the divergence of the pump beam and therefore increase pump efficiency even further. A similar evaluation for the lasing wavelength results in a loss of 4.6% per round trip. Direct measurement yields reflective losses between 1.7% and 4.4%. The adapted Rigrod analysis suggests a loss of 4.1 ± 0.7%.
As can be seen in Fig. 2, the introduction of the monolithic design introduces beneficial internal angles in the high refractive index laser crystal. As indicated by Eq. (2), reducing the internal AOI and minimizing the wedge thickness also reduces shifting of the multiple reflected echoes and results in a sharp contrast pump spot compared to previous experiments [17] (compare Supplement 1, Fig. S5). Furthermore, this allows for a steeper separating LP edge compared to an LP-air interface at the same wedge angle. A smaller wedge angle leads to moderate thickness changes over the pump spot. With an LP-air interface, the wedge angle would need to be larger, and the thickness would vary significantly more.
To improve pump efficiency without changing the properties of the coating, it might be beneficial to introduce an asymmetric pump light source that has a reduced divergence angle in one direction. This is a typical property of laser diodes; therefore a direct attachment of the pump laser diodes in contrast to a delivery by fiber optics could improve the overall design. This could be improved even further by reimplementing the polarizationdependent properties of the front coating, which were minimized in the current design for the sake of compatibility to the available pump sources.
The monolithic thin-disk wedge approach is strongly dependent on the manufacturing capabilities for wedged thin laser amplifying media such as, e.g., Yb:YAG crystals as well as highcontrast angle-dependent and polarization-independent LP filters. All components are obliged to handle high pump radiation and laser radiation intensities. At this point, we can confirm that pump powers of 2 kW and internal resonator powers of approximately 3 kW are possible with the coatings deposited directly onto the laser crystal. Nevertheless, this does not allow a prediction for the use in pulsed operation yet, which will be the focus of future studies. The bandwidth implications of the demonstrated technology, which become relevant for ultra-short pulses of less than a few ps, are discussed in Supplement 1.
Remaining questions are the slope efficiency of the system, which did not reach literature standards of 80% [20], as well as optimization of the overall beam quality. The asymmetry of the wedge potentially leads to effects such as, e.g., astigmatism. Nevertheless, the monolithic nature of the system should allow for almost static compensations to restore beam quality. Further questions concern the ultimate power limitations, utilization in succeeding amplification stages or in parallel amplifiers, optimum AOIs, and variation of the coating as well as the crystal material itself.

CONCLUSION
In this paper, we were able to demonstrate that current manufacturing technologies are suitable to achieve all necessary prerequisites to reach 890 W of output power with the wedge disk concept. Due to the complex reflectivity nature of the wedge, reflective losses on the order of 4% are introduced into the system.
Multiple reflections within the wedge increase the amplification per pass, allowing for an output coupler transmission of 36%, strongly compensating for the internal losses.
We believe that improvements based on optimization of a variety of parameters in geometry, material properties, coating properties, and design will allow reducing the losses. Small signal gain was measured to reach an amplification factor of up to 10, and total optical-to-optical efficiency of 50% and slope efficiency of 59% in a multimode I-resonator were demonstrated.