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Abstract
Beam quality and average output power are two long-sought parameters of continuous-wave lasers. The operating characteristics of a Yb:YAG thin-disk laser based on a 72-pass pump module using output couplers with continuously variable coupling rates are reported. When the pump power is 450 W, the average power of more than 210 W is obtained, and the corresponding optical-optical efficiency is about 46.67%. The output beam is near diffraction limited with M2=1.20 and 1.18 on the horizontal and vertical directions respectively. The thin-disk laser maintains the beam quality near diffraction limited within the whole pump power range by continuously changing the coupling rate of the output coupler (the combination of thin film polarizer and quarter-wave plate) according to the incident pump power. The experimental results show that by continuously changing the coupling rate, combined with the dynamic change of thermal lens effect, the laser beam quality factor M2 can be reduced from 2.0 to 1.2, and the beam quality can be improved by about 40%. The improvement of and increase of average output power confirm that resonators with continuously variable coupling rate are a promising method for enhancing output performance of thin-disk lasers.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High average power Yb:YAG solid-state lasers are widely used in military field (such as laser ranging [1], lidar [2], blinding [3] and optoelectronic countermeasure [4]) and civil field (such as cutting [5], welding [6], heat treatment [7] and marking [8]) because of their short wavelength, easy transmission, high peak power, compact and solid structure.
The problem of poor beam quality is the main factor restricting its development. With the continuous improvement of the output power of solid-state laser, this problem is becoming more and more prominent and is attracting more and more attention. While researchers all over the world pay attention to the increment of output power, the improvement of beam quality is rapidly drawing attention. Deep cutting, drilling and efficient frequency doubling require several times of the diffraction limit beam, while for optical fiber transmission, it requires 40$\sim$200 times the diffraction limited beam [9–12]. Depending on the numerical aperture of optical fiber, the requirement for beam quality also differs. The higher the beam quality factor, fibers with the finer, softer, and better bending performance can be used, which brings convenience to the application and improves the processing quality.
The laser beam quality is closely related to the structure of the laser resonator and the thermal characteristics of the gain medium. In order to obtain high power output, high average power solid-state lasers are characterized by large gain cross section and large Fresnel number, and are generally in the state of multimode oscillation. The thermal lens effect of the laser medium under the high power pump makes the output beam quality vary with the pump power. The beam quality is further reduced by the thermal birefringence effect, the thermal lens aberration caused by the temperature dependence of the thermal conductivity of the medium and the asymmetric aberration caused by uneven pumping.
However, the emergence of thin-disk lasers has effectively improved the situation. In 1994, Adolf Giesen of the University of Stuttgart in Germany proposed a thin-disk laser scheme [13]. In this scheme, the laser crystal is processed into a as thin as 200 $\mathrm{\mu} \mathrm {m}$ disk, and the antireflective film is coated on the front surface of the crystal for the pump laser and oscillating laser, and the back surface is coated with a high reflective film at pumping and lasing wavelength. The rear surface is then welded to the heat sink, so the surface also acts as a mirror for the thin-disk laser. Under the influence of the longitudinal near-flat-top pump beam, this geometric structure can form a uniform one-dimensional heat flux distribution which is perpendicular to the surface of the gain medium, so the temperature gradient direction can be coaxial with the output laser direction [14]. Therefore, the unique design can mitigate the thermal lens effect to a great extent and obtain high beam quality and high power laser output. In addition, the multi-pass pumping technology makes up for the low single-pass absorption efficiency of the gain medium and improves the pump absorption efficiency, while the backward cooling of the front pump further reduces the thermal lens effect of the gain crystal. Thus, the scheme achieves excellent beam quality in both continuous and pulsed fields [15–19].
In a conventional thin-disk laser, the coupling rate of the output coupler (OC) is fixed. In a specific laser system, the OC with a fixed coupling rate can only achieve the best beam quality in a small range of incident pump power. The optimal value of the output coupling rate is different under different pump power. At low pump power, the laser gain is small, thus, the output coupling rate should be small so as to reduce the loss and the lasing threshold, enhance the laser feedback, and obtain a higher output power. Under the condition of high pump power, the laser gain is larger and the optical feedback in the cavity is strong. The output coupling rate should be large to extract laser energy more effectively and prevent the laser in the resonant cavity from damaging the dielectric mirror and laser working medium. Therefore, it is difficult to achieve the best output performance of the laser under different pump power at a fixed OC rate.
In this paper, we demonstrate a Yb:YAG thin-disk laser with an output coupler of continuously variable output coupling rate. By continuously changing the output coupling rate, we obtain the maximum average output power and the best beam quality without replacing the optical components. Based on the 72-pass pump module, when the output beam is near diffraction-limited with 1.20 and 1.18 on the horizontal and vertical directions, the average output power reaches 210.3 W at the pump power of 450 W. It is worth mentioning that the laser is the first Yb:YAG thin-disk laser with a variable coupling rate output coupler (VCROC) to the best of our knowledge. And the near-diffraction-limited beam quality is obtained at any incident pump power. Moreover, based on the Yb:YAG quasi-three-level rate equation and laser mode theory, the expression of average output power and output coupling rate and the simplified calculation method of diffraction loss of laser stable resonator are obtained under approximate conditions. This method provides theoretical support for the subsequent design of high-beam-quality laser resonators. In our opinion, the demonstrated good-beam-quality Yb:YAG thin-disk laser with a VCROC provides an alternative technique for improving beam quality and increasing output power.
2. Experimental setup
As shown in Fig. 1, the thin-disk gain medium used throughout the experiment is a 200-$\mathrm{\mu} \mathrm {m}$ Yb:YAG disk with a $\mathrm {Yb^{3+}}$-doping concentration of 7 at.% and a diameter of 15 mm. The radius of curvature (RoC) of the thin disk is 3.7 m at room temperature. The thin disk was welded onto a diamond heat sink with a diameter of 17 mm and a thickness of 3 mm. A physical diagram of the final thin-disk module is shown in Fig. 1(b). In order to efficiently absorb the pump radiation, we designed and manufactured a thin-disk pump unit, providing 72 passes of the pump radiation through the active medium, ensuring a extremely high pump absorption of 99.19% [19].
Fig. 1. (a)Schematic diagram of simulated pump light of the 72-pass pump module. (b)Physical diagram of the 72-pass pump module. (c)Pump spot of the 72-pass pump module.
The disk is pumped with a commercial laser diode from EVERBRIGHT Photoelectric emitting up to 500 W at 968.8 nm based on volume Bragg gratings (VBG). This type of pumping at 969 nm is known as "zero-phonon line" (ZPL) pumping. Compared to the conventional pumping at 940 nm, further reduction of the quantum defect to 5.8% can be achieved by ZPL pumping, which reduces the heat load by more than one-third [20,21]. The output of the pump collimator was coupled to the pumping unit system through a home-made free-space imaging system. As shown in Fig. 1(c), because the homogenized fiber is square, the pump spot after collimation has several protuberances. The flat-top part is hexagonal, and its inner tangent circle diameter is 4.0 mm, implying a pump intensity of $\mathrm {3581\: W/cm^2}$ when pumped at 450 W.
The experimental setup for the laser experiment in fundamental-mode operation is shown in Fig. 2(a). A V-shaped laser cavity was formed by a convex end mirror with a RoC of 1.7 m, the Yb:YAG thin disk acting as a folding mirror, and a plane fixed coupling rate output coupler. In order to optimize the output coupling rate for fundamental-mode operation at pump power level of 450 W, the output coupling rate of 1.5%/2.5%/3.4%/5.4% was applied in the experiment. The total cavity length is 2.68 m. As shown in Fig. 2(b), the parameters of the VCROC cavity are basically the same as the former, except that the output coupler with fixed coupling rate is replaced by a continuous variable coupling rate output coupler (VCROC) composed of TFP and QWP. To ensure fundamental-mode operation of the TDL, the resonator was designed by ABCD matrix formalism to provide a 1.8-mm beam radius on the disk, as shown in Fig. 3.
Fig. 2. (a) Schematic of the Yb:YAG thin-disk laser and measuring set-up. V-shaped laser cavity with fixed-coupling-rate output couplers (OC, T=1.5%/2.5%/3.4%/5.4%) and highly reflective (HR) end-mirror. (b) Schematic of the Yb:YAG thin-disk laser with variable-coupling-rate output coupler (VCROC). (c) Diagram of the angle $\theta$ between fast axis of QWP and S-polarization direction generated by TFP. QWP, quarter-wave plate; TFP, thin-film polarizer. M3 denotes a 1.7 m RoC convex mirror, and M2 is a plane HR with an incident angle of 50$^{\circ }$. All other mirrors are plane.
Most of the output power was directed to a power meter (LaserPoint, Italy) by a wedged beams plitter with a high transmission of 92%. The remaining reflected beam was used for different measurements (spectrometer and BEAMAGE-$\mathrm {M^2}$).
3. Model and theory
Due to the effect of strong crystal field, Stokes splitting occurs in both the ground state energy level $\mathrm {^2F_{5/2}}$ and the excited state energy level $\mathrm {^2F_{7/2}}$. The energy level $\mathrm {^2F_{7/2}}$ is split into four sub-levels: 0 $\mathrm {cm^{-1}}$, 565 $\mathrm {cm^{-1}}$, 612 $\mathrm {cm^{-1}}$ and 785 $\mathrm {cm^{-1}}$, while the energy level $\mathrm {^2F_{5/2}}$ is divided into three sub-levels: 10327 $\mathrm {cm^{-1}}$, 10624 $\mathrm {cm^{-1}}$ and 10941 $\mathrm {cm^{-1}}$. Among them, the fluorescence lifetime of the 10327 $\mathrm {cm^{-1}}$ Stokes level in the excited state level $\mathrm {^2F_{5/2}}$ is as long as 0.95 ms, which means it can store energy effectively. Meanwhile the Stark level energy in the ground state level $\mathrm {^2F_{7/2}}$ is relatively large, so the laser radiation of the main 1030 nm occurs between these two sub-levels making that the Yb:YAG crystal a quasi-three-level structure.
The rate equation of Yb:YAG quasi-three-level system [13] is
For the thin-disk laser, because of the special structure of the thin-disk crystal, the thickness of the disk is much smaller than the length of the cavity, so the integral interval is strictly restricted in the thin-disk crystal. The flat-top distribution of the pump spot on the thin disk can be expressed as $r_p=\dfrac {1}{\pi \omega _p^2 l}$.
When the resonator is in steady state, the rate equation can be simplified as follows:
The pump rate can be expressed as: $R=\dfrac {\eta _p P_{in}\eta _{abs}}{h\nu _p}$.
For the multi-pass pumping module, $\eta _{abs}$ can be iterated according to the paper [19].
The above formula can be solved by substituting the above formula into Eq. (4), (5), $P_{in}$ is the threshold power.
Among them, $\delta =T+2L_i$, $T$ is the transmittance of the output coupler, $L_i$ is the total additional single-trip loss due to scattering and absorption. In addition, according to the derived results of Jafari [22], the continuous-wave output power of Yb:YAG thin disk laser can be derived by the following formula:
Fig. 4. (a)Average output power versus coupling rate under different intracavity loss. (b)Threshold pump power versus coupling rate under typical intracavity loss $L_i =0.002$.
3.1 Numerical simulation of beam quality affected by coupling rate
In a typical thin-disk laser, the spatial distribution of the laser beam mainly depends on the laser transverse mode, and different laser modes have different losses. Generally speaking, there are two kinds of loss in the laser resonator, one is the non-selective loss independent of the order of the laser transverse mode, such as the loss caused by the incomplete reflection of the mirror, the inactive absorption and scattering in the material, the loss caused by inserts in the cavity (such as Q-switched components and Brewster windows), and the other is the diffraction loss which is closely related to the order of laser transverse mode. The diffraction loss has a major influence on the oscillation of each order transverse mode of the laser, which is an important physical basis for realizing the selection of laser transverse mode and obtaining high beam quality laser output.
From the laser principle, it is known that the laser oscillation is formed by the feedback of the resonant cavity and the laser gain medium, and only the laser mode with low loss can form a stable laser oscillation in the cavity and produce laser output through the output coupler. Because the geometric size of the laser resonator mirror is limited, when the laser propagates back and forth between the mirrors, the loss caused by the diffraction effect at the edge of the resonant mirror is inevitable. In this process, the diffraction loss is related not only to the size of the mirror but also to the coupling rate of the output coupler.
As shown in [23], after multiple round-trip propagation, the steady-state light wave field of on mirror M1 is $E_1(x,y)$, and the field on M2 mirror is $E_2(x,y)$. The following self-consistent relationship should be established between the two steady-state fields:
In formula (8), $\gamma$ is a complex constant factor, which represents the diffraction loss of the laser resonator and reflects the change of the amplitude and phase of the light field after a single roundtrip propagation.
As shown in Fig.6, the laser resonator is a symmetrical spherical confocal resonator. The radius of curvature of the end mirrors M1 and M2 is $R$, and the length of the cavity is $L$. The two mirrors are circular with a radius of $a$. From Fresnel Kirchhoff diffraction integral formula in the cylindrical coordinate system, the light field distribution from M1 to the M2 can be obtained as follows:
In order to calculate the diffraction loss of laser resonator more conveniently, the integral equation can be solved by approximate method. Combined with the Laguerre-Gaussian modal decomposition, the diffraction loss formula of laser in resonant cavity can be obtained.
It can be seen from the Eq. (10) that the single-pass diffraction loss factor of the laser $\delta _{mn}$ is related to the order of the laser transverse mode. If the corresponding laguerre polynomial $L_n^m (x)$ is substituted respectively and calculated by formula (10), the analytical formula for calculating the diffraction loss of each order laser mode expressed by Fresnel number $N$ can be obtained.
According to the calculation results above, each order of laser modes can be sorted according to the magnitude of diffraction loss. The intensity distribution of the first nine laser modes with the lowest diffraction loss in a confocal cavity is shown in Fig. 5(b). As can be seen from Fig. 5(a), it is known that is the easiest for the fundamental mode $\mathrm {TEM_{00}}$ to establish laser oscillation because of its minimum diffraction loss. The intensity distribution of this laser mode is Gaussian and divergence angle is the smallest. However, considering that the fundamental mode laser spot size is too small, and the laser output power is relatively low, it is often unable to meet the needs of high output power and good beam quality at the same time. From the above calculation results, compared with $\mathrm {TEM_{00}}$, the diffraction losses of the $\mathrm {TEM_{10}}$ and $\mathrm {TEM_{20}}$ laser mode is relatively high, so the fundamental mode $\mathrm {TEM_{00}}$ can be obtained by changing the output coupling rate of the resonator or decreasing the radius of the hard aperture for the mode selection in the cavity.
Fig. 5. (a) Relationship between diffraction loss and Fresnel number $N$ under different laser modes of $\mathrm {TEM_{00}}$, $\mathrm {TEM_{01}}$, $\mathrm {TEM_{02}}$, $\mathrm {TEM_{03}}$, $\mathrm {TEM_{21}}$, $\mathrm {TEM_{30}}$ in the confocal resonator. (b) Simulated near-field beam intensity distribution of different laser modes sorted by diffraction loss (from small to large).
4. Results and discussion
In order to measure the optimal output coupling rate of a resonator under CW operation of a thin-disk laser, the traditional method is to measure the output power at different coupling rates. Then when the output power is the highest, the coupling rate is set to be the optimal output coupling rate, as shown in Fig. 2(a). In order to match the pump spot with the laser spot pattern, a flat-convex cavity was designed. The length of the cavity is 2.68 m, and the length of the arm near the OC is 0.98 m. Without changing the cavity parameters, we replace the output couplers with output coupling rates of 1.5%, 2.5%, 3.4% and 5.4% respectively and measure the average output power under the incident pump power of 0$\sim$450 W.
The variation curve of the average output power versus the incident pump power at different coupling rates is shown in Fig. 6(a). It can be seen from Fig. 6(a) that at the maximum pump power of 450 W, the maximum average output power is obtained for the OCs with coupling rates of 3.4% and 5.4%, and the output power of the other coupling rates is significantly smaller than that of the former. Therefore, we conclude that the optimal output coupling rate of the cavity is between 3.4% and 5.4%. This experimental result is in good agreement with the theoretical derivation of Fig. 4(a). Because the intracavity loss is closely related to the output coupling rate, the coupling rate indirectly affects the threshold pump power. From the fitting results of Fig. 6 (a), it can be seen that the higher the coupling rate is, the higher the threshold pump power is. When the coupling rate is 5.4%, the measured threshold pump power is 108.2W, which is very close to the simulation result in Fig. 4(b). At the same time, we also measured the beam quality factor $\mathrm {M^2}$ when the coupling rate is 5.4%, and its maximum value is close to 2.0, as shown in Fig. 6(b).
Fig. 6. (a) Average output power versus incident pump power under different coupling rates. (b) Beam quality factor $\mathrm {M^2}$ versus incident pump power at the coupling rate of 5.4%.
Because the conventional output coupling rates are discrete, in order to find the optimal output coupling rate of the resonator, the OCs with different coupling rates have to be replaced again and again. However, this method is not elegant. It not only takes a lot of time, but also cannot obtain the optimal output coupling rate accurately. Therefore, we design an OC with continuous variable coupling rate, which is composed of a TFP and a QWP, as shown in Fig. 2(b) and Fig. 2(c). The basic principle of VCROC is that the coupling rate of the cavity is related to the angle $\theta$ between the fast axis of the QWP and the polarization direction of s-polarized light generated by TFP. So the output coupling rate can be expressed as $T=\mathrm {cos}^2(2\theta )$. Therefore, we only need to rotate the QWP to realize continuous variable coupling rate of the cavity. With the increase of pump power, the deformation and thermal lens effect of thin-disk crystal are also enhanced, which leads to dynamic change of intracavity diffraction loss with incident pump power. Therefore, different pump power corresponds to different optimal output coupling rates. However, due to the small size of the fundamental transverse mode and the low ability of transverse mode identification, it is difficult to achieve high power output and fundamental mode operation at the same time.
As is shown in Fig. 2(b) and Fig. 7(a), the highest output power and the best beam quality are obtained by monitoring the power meter and Beamage beam quality analyzer (Gentec-EO, Canada) at the same time and changing the angle $\theta$ in real time. When the pump power is 450 W, we get the highest output power of 243.2 W, which is obviously higher than the results at the coupling rate of 5.4% and 3.4%. As shown in Fig. 7(b) and Fig. 8(b), we have obtained the best beam quality under every pump power, and the beam quality factors $\mathrm {M^2}$ are kept below 1.2 all the time. Compared with Fig. 6(b), by using VCROC, the beam quality factor $\mathrm {M^2}$ is reduced by 40%, and the laser beam quality is significantly improved.
Fig. 7. (a) Average output power versus incident pump power at the highest output power or the best beam quality. (b) Beam quality factor $\mathrm {M^2}$ versus incident pump power at the best beam quality.
Fig. 8. (a) Spectra of the output laser. (b) The best beam quality of the output beam by using VCROC measured at 450 W pump power. The inset shows the beam shape at the waist. The measured values are $M_x^2=1.209$ and $M_y^2=1.185$.
The beam profiles of different coupling rates at the pump power of 135 W and 450 W are shown in Table 1. As can be seen from Table 1, with low -power pumping, the laser beam intensity distribution of all coupling rates is the Gaussian distribution, and the beam quality is close to diffraction-limited. However, as the pump power increases, the deformation and thermal lens effect of the thin-disk crystal will be enhanced, leading to the intracavity loss change. Meanwhile, for the output couplers of fixed coupling rate, the beam quality begins to deteriorate. The laser transverse mode begins to change from $\mathrm {TEM_{00}}$ to $\mathrm {TEM_{01}}$, and the near-field beam profile has a doughnut-shaped spatial intensity distribution. However, for the resonator with VCROC, we can continuously change the output coupling rate, so that the fundamental mode operation can still be achieved under high power pumping.
Table 1. Beam profiles with different coupling rates at incident pump power of 135 W Table 1. and 450 W, respectively.
As shown in Fig. 8(a), we have measured the spectrum of the output laser. The central wavelength of the output laser is 1031.292 nm, and its linewidth (FWHM) is as narrow as 0.031 nm, which lays a foundation for our next step of in-band pumping. At the maximum pump power of 450 W, the beam quality close to diffraction limited is obtained.
5. Conclusion and outlook
In conclusion, we demonstrate a Yb:YAG thin-disk laser based on a 72-pass pump module with an output coupler of continuously variable output coupling rate. The near-diffraction-limited beam quality at full range of incident pump power was obtained by continuously changing the coupling rate of the resonator. In other words, the resonator can achieve not only the maximum output power, but also the best beam quality. Moreover, the optimal output coupling rate and the threshold pump power is theoretically calculated, and it is in good agreement with the experimental results. In order to enhance the versatility of the VCROC, we plan to upgrade the quarter-wave plate to a electric one in the future, and make the electric quarter-wave plate control software establish feedback with the power meter and the $\mathrm {M^2}$ measurement system. So that we can automatically achieve the best beam quality and maximum output power in the resonator with VCROC. Therefore, the thin-disk laser with continuous variable coupling rate output coupler has a good prospect in enhancing output performance of thin-disk lasers.
Funding
Dalian Institute of Chemical Physics Innovation Fund (DICP I202034); Dalian Science and Technology Innovation Fund (2018J11CY013).
Acknowledgments
We are very grateful for the 72-pass pump module provided by Key Laboratory of Chemical Lasers, Dalian Institute of Chemical Physics.
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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