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Abstract
We report on a simple method for reduction of the depolarization loss in an end-pumped Tm:Y2O3 ceramic laser by using a near-field ring-shaped pump beam. Initially, we theoretically derive the expression of the depolarization loss in a bulk laser end-pumped with a near-field flat-top-hat or ring-shaped beam, where a significant reduction of depolarization loss in the latter case is presented. Experimental verification is thereafter carried out with a Tm:Y2O3 ceramic laser employing these two different pump configurations. It shows that the experimentally measured depolarization losses are close to the simulated values; the loss in the case of the annular-beam pump is almost 18 times lower than that with a quasi-top-hat beam at a same absorption pump power of 7.4 W. This work, as a proof-of-principle study, indicates that depolarization loss in the end-pumped bulk lasers can be significantly reduced simply by using a ring-shaped pump beam.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Yttrium aluminum garnet (YAG) and sesquioxides hosts doped with rare-earth active ions are widely used in high-power solid-state lasers due to their excellent optical, mechanical and thermal properties [1,2]. To date, end-pumping scheme is the most common method for solid-state lasers since their high efficiency and high beam quality [3]. However, when it comes to power scaling, high pump power densities even in the level of several kW/cm2 [4–7] give rise to a very high pump deposition and further leading to a thermal birefringence. The unwanted thermal induced birefringence on one hand can result in a degradation of laser beam quality due to double focusing of linearly polarized beams, and on the other depolarization of a linearly polarized beam [8]. For the latter, if the depolarization loss is too large, it may affect its potential applications in electro-optic Q-switched, material processing, frequency doubling and nonlinear optics [9–13]. A number of techniques have been used to reduce depolarization losses mainly through making depolarization effects from different optical elements canceling each other out. These techniques include employing a Faraday rotator to rotate the polarization direction of the light beam by a specific angle [14–16], utilizing a λ/4 wave plate to adjust the polarization state of the light beam [17–19], employing a Gran-Taylor polarizer to selectively transmit or absorb light with a specific polarization [20], selecting an appropriate tangent crystal to adjust the polarization state of the beam [21], or adjusting the design and construction of the laser resonator to introduce a Gouy phase shift of suitable magnitude [22].
Here, we theoretically and experimentally show that the depolarization loss in an end-pumped solid-state laser can be significantly reduced by using a spatially ring-shaped pump beam. The ring pump scheme allows for the attainment of a more uniform laser gain distribution in the laser materials, which means further reduction of the depolarization losses arising from non-uniform thermal distribution in lasing process is still possible simply by in combination with inserting a compensating element like Faraday rotators, λ/4 wave plates, and Glan-Taylor polarizers in the cavity. Therefore, this scheme in principle can be employed together with the above mentioned methods in the solid-state oscillators or amplifiers for further power scaling with high efficiency and good beam quality.
2. Theoretical analysis
In order to analyze the effect of ring-shaped and top-hat pump beams on the depolarization loss, we assume that the azimuthal intensity distribution of the pump beam is uniform across the transverse cross section within the gain media for both ring-shaped and top-hat beams, and that the coolant temperature remains constant along the Z-axis. The end effect (refers to the influence of the ends or edges of the gain medium on the heat flow and resulting temperature distribution [23]) was ignored and the heat flow was limited to radial flow [18]. In this case, the depolarization loss can be expressed as [23,24]:
If only p- polarization laser considered, the total depolarization loss in the laser crystal cross-section is:
Figure 1 shows the calculated depolarization losses as a function of the absorbed pump power for the top-hat and ring-shaped pump beams. It can be seen from Fig. 1 that the depolarization loss of the ring-shaped pump is significantly reduced than that with the top-hat pump beam under the same pump power. When the absorption pump power is 7.4 W, the depolarization losses of the ring-shaped and top-hat pump beam are 0.018% and 0.25%, respectively.
Fig. 1. Theoretical calculation of depolarization loss of Gaussian p linearly polarized beam from a Tm:Y2O3 ceramic laser pumping with top-hat and ring-shaped beams (a). Inset: the zoom-in view of the depolarization loss with the absorbed pump power in the range of 10 W.
3. Cavity design and result analysis
To generate the TEM00 mode, the inner (wa) and outer (wb) radius of the ring pump beam, as well as the laser cavity have to be carefully designed for suppressing the oscillation of other Laguerre-Gaussian (LG) modes which have the similar spatial intensity distribution to the annular pump beam [25]. It should be noted that since the values of wa and wb were variable along the propagation direction of z-axis, the propagation functions of wa,z and wb,z need to be obtained by fitting the measured values along z-axis [26]. With the propagation functions of the annular pump beam, the cavity factors for producing the fundamental mode (TEM00) was thereafter calculated following the relationship of Pth ∝ Veff, where Pth is the threshold power and Veff can be considered as the effective volume of the pump beam and laser mode taking into account their spatial overlap [26]. With a smaller Veff, the laser mode that exhibits the lowest pumping threshold will oscillate preferentially. Figure 2(a) shows the calculated Veff of different modes with respect to the ω0, which is the beam waist radius of the TEM00 mode in the cavity. By employing the 2-mm center-hollowed plane mirror, conditions for excitation of the TEM00 mode is to set ω0 > 268 µm, see Fig. 2(a). In the following experiment, the cavity mode was designed to be ∼ 280 µm based on the above simulated results.
Fig. 2. Calculated Veff of different LG0,l modes with l = 0, 1, and 2 (a). Schematic diagram of Tm:Y2O3 ceramic laser (b). (c) The normalized intensity distribution of the ring-shaped pump beam (inner diameter of 320 µm and outer diameter of 700 µm at the focal plane) in the X and Y directions and its corresponding beam profile, and (d) for the case of quasi-top-hat pump beams (diameter of 724 µm). LD: laser diode; L1-L2: lens; M: hollow mirror; M1: input mirror; M2-M3: cavity mirror; OC: output coupler; P1 and P2 are the reflected laser by the YAG plate.
Using an end-pumped Tm:Y2O3 ceramic laser, see Fig. 2(b), the depolarization losses and the laser performance were experimentally investigated with pump beam exhibiting different near-field spatial intensity distributions. A multi-transverse-mode fiber-coupled diode laser emitted at 790 nm (100 µm fiber core and 0.22 numerical aperture) was employed as a pump source. After collimation by a lens (L1, f = 25.4 mm), the pump beam was thereafter reshaped by using a center-hollowed plane mirror (M) and focused into the crystal with a near-field ring-shaped intensity profile through a focusing lens (L2, f = 150 mm). The beam size at the focal plane (Z = 0 mm) of the ring-shaped pump beam was the inner radius wa = 160 µm and the outer radius wb = 350 µm and the normalized intensities in the X and Y directions were shown by the Fig. 2(c), the beam quality (M2 factor) was measured to be 84.5. The beam profile could maintain a ring-shape over the entire gain range along the laser crystal. The Y2O3 ceramic doped with 2 at.% Tm3+ ions had a dimension of 3 mm × 3 mm × 3 mm, and both of its end faces were polished but uncoated. To mitigate the thermal load, the Tm:Y2O3 ceramic was wrapped with 0.1 mm thick indium foil and tightly mounted in a copper holder with water cooling to 7.5°C. A Z-type folded cavity was employed, which consists of a plane pump mirror (M1), two plano-concave cavity mirrors M2 and M3 with the radius of curvature of 200 mm and 500 mm, and a plane output coupling mirror OC (TOC = 5%). A 1 mm-thick YAG plate was inserted into the cavity to obtain the linearly polarized laser. To ensure the optimized mode matching between the desired TEM00 mode and reduce the loss caused by astigmatism [27], the total physical cavity length of the resonant cavity was 648 mm, and the folding angle of the concave mirror M3 was less than 10 degree.
Without the YAG plate, the slope efficiency of the Tm:Y2O3 ceramic laser pumped with the two different spatial profile beams is shown in Fig. 3(a). At a 7.4 W absorbed pump power, the slope efficiencies of the quasi-top-hat and ring-shaped pump were 31.8% and 29.8%, respectively, both exhibiting a multi-peak optical spectra at a center wavelength of 2051 nm. The slightly larger lasing threshold and lower slope efficiency in the case of ring-shaped beam pumping was because of the imperfect spatial overlap with the fundamental transverse Gaussian mode [27,28]. Figure 3(b) shows the laser performance in the case of inserting the YAG plate in the cavity. At the highest absorption pump power of 7.4 W, the laser performance for the both cases was much similar, giving a slope efficiency of 29.3% and a maximum output power of 1.9 W for the ring-shaped pump beam. The optical spectrum with a central wavelength of 2050nm exhibited a much clean profile than that without the YAG plate. Figure 3(c) shows the measured depolarization losses of the Tm:Y2O3 ceramic laser at different absorbed pump powers. Due to the thermally induced birefringence effect of the Tm:Y2O3 ceramic, the linearly polarized laser would become elliptically polarized one after passing through the ceramic, thus reflecting part of the laser beams at the YAG surface. It can be seen from Fig. 3(c) that the depolarization losses gradually increased and the rate of such increase gradually accelerated as the absorbed pump power. At the highest absorbed pump power, the depolarization losses of the Tm:Y2O3 ceramic laser were 0.347% and 0.020% for the case of quasi-top-hat and the ring-shaped pump beams, respectively. These experimentally measured values are larger than the theoretical values (the depolarization losses of the top-hat and ring-shaped pump beam are 0.25% and 0.018% as can be seen in section 2) due to the quasi-top-hat pump beam in the experiment rather than the ideal top-hat intensity profile, which makes it experience stronger depolarization loss than the ideal flat top-hat beam.
Fig. 3. The output power of the laser without (a) or with YAG plate (b) with respect to the absorbed pump power, pumping with ring-shaped and quasi-top-hat beams. The measured depolarization losses of the Tm:Y2O3 ceramic laser pumping with different spatial profile beams under different absorbed pump powers (c). Insets (a) and (b) are the corresponding optical spectra of the ring-beam pumped Tm:Y2O3 ceramic laser at the highest output power. Inset (d) is the zoom-in view of the depolarization losses in the case of the ring-shaped beam pumping.
Apart from the depolarization losses, thermal lens focal length and the beam propagation factor were also analyzed. Figure 4(a) shows the measured thermal lens focal length as a function of the absorbed pump power in the both cases, the focal length was slightly longer in the case of ring-shaped beam pumping, i.e., 35 mm versus 30 mm for the case of quasi-top-hat pumping, at the highest pump power of 7.4 W. So, we may recognize that the overall thermal effect in the Tm:Y2O3 ceramic laser with the two different pump configurations is serious, and in particular for quasi-top-hat pumping. This also results in a difference in depolarization loss between quasi-top-hat and ring pumped lasers. Finally, the beam propagation factors were evaluated at different power level, see Figs. 4(b) and (d) for the case of quasi-top-hat and ring-shaped beam pump, respectively. There are two main reasons why ring-shaped pumping can achieve excellent beam quality. Firstly, by optimizing the beam sizes of the ring-shaped pump light and cavity modes, it allows for larger spatial gain distribution for the fundamental TEM00 mode compared to high-order modes (as shown in Fig. 2(a)), thus theoretically resulting in the generation of single TEM00 mode. Secondly, the gain was transferred away from the optical axis towards the outer regions of the beam due to the zero central intensity of the ring-shaped pump, which helps to smooth the gain curve and reduce spatial variations in gain and depolarization effects, thus reducing the effects of thermal focusing and distortion and enhancing beam quality. No obvious difference was found with good beam quality of less than 1.1 in the both cases, thanks to the well-designed mode matching and low pumping power. Typical measurements for the beam propagation factors and the beam intensity profiles for these two cases were shown in Figs. 4(c) and 4(e), giving M2-factors of 1.09 and 1.08, respectively. Nevertheless, we believe that the effect at high pumping power will make a great difference as what has been demonstrated in the Nd:YVO4 laser at 1 µm [28].
Fig. 4. The measured thermal lensing of the Tm:Y2O3 ceramic laser pumping with different spatial profile beams under different absorbed pump powers (a). The measured M2 values of Tm:Y2O3 ceramic lasers end-pumped with quasi-top-hat (b) and ring-shaped beams (d) at different absorbed pump powers. (c) and (e) are typical M2-measurements and the corresponding beam profiles at the highest output power.
4. Conclusion
In conclusion, we have demonstrated that the depolarization losses of the end-pumped bulk lasers can be reduced by employing a near-field ring-shaped pump beam. At first, we theoretically analyzed the depolarization losses of the Tm:Y2O3 ceramic laser in the case of two different pump beams with ring-shaped or top-hat intensity profiles. Taking into account the experimentally measured propagation features of the reshaped ring-shaped pump light, we thereafter constructed a mode-matched “Z”-shaped Tm:Y2O3 solid-state laser to analyze the difference in depolarization loss with different pumping configurations. The measured depolarization loss under ring-shaped beam pump was found to be 18 times lower than that pumping with the top-hat beam, the deviation to the theoretical value of 14 times was attributed to the quasi-top-hat rather than the ideal top-hat intensity profile of the focused pumped beam from a fiber-coupled laser diode. This work, as a proof of principle study, shows that the ring-shaped pumping can be employed as an effective method for reducing depolarization loss in an end-pumped Tm:Y2O3 ceramic laser. This new method of reducing depolarization loss can in principle be used together with the existing methods. This provides one more choices to compensate depolarization loss for end-pumped solid-state lasers.
Funding
National Natural Science Foundation of China (52032009, 62075090).
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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