Thermal-birefringence-induced depolarization in a 450 W Ho:YAG MOPA system

Shuyi Mi; Jinwen Tang; Disheng Wei; Baoquan Yao; Junhui Li; Ke Yang; Tongyu Dai; Xiaoming Duan

doi:10.1364/OE.462617

1. Introduction

High-power 2 µm solid-state lasers have various applications in remote sensing, laser surgery, and industrial processing. In addition, they are also an efficient pump source for mid-infrared optical parametric oscillators [1]. The Ho:YAG crystal is the most popular gain medium for generating high-power, high-repetition-rate laser due to its high heat conductivity (as high as twice that of YLF), excellent mechanical property, and the long upper lifetime [2]. The 1.9 µm laser in-band pumped Ho:YAG lasers have the advantages of small quantum defect loss and high pump utilization, and the 1.9 µm lasers generated from bulk or fiber have reached hundreds of watts [3,4]. Moreover, the Ho:YAG crystal can be dual-end-pumped by two linearly polarized lasers with orthometric polarization benefits from the isotropy of its optical property [5]. These advantages make Ho:YAG the most promising candidate for obtaining a high-power 2 µm laser.

Recently, the Ho:YAG lasers have been deeply investigated and developed rapidly. The output power has easily reached 100 W only via an oscillator structure [5,6]. The master oscillator power amplifier (MOPA) configuration is a mature and effective method to obtain a higher power and better beam quality [7,8]. In 2018, our group reported a two-stage Ho:YAG MOPA system pumped by Tm:YLF lasers. The MOPA system achieved 231 W laser output at 2090 nm with a beam quality of near diffraction-limit [9]. Soon after, we increased the output power of the Ho:YAG laser to 332 W by the similar two-stage MOPA structure [10]. The thermal effects, including thermal focusing, distortion, and birefringence, have a more pronounced influence on the output performance with the increase of laser power in the solid-state laser. Among them, thermal-induced birefringence has a severe effect on YAG crystal, which breaks the isotropy of YAG and results in depolarization, defined as the ratio of depolarized power to the total output power. This depolarization in a Ho:YAG oscillator can be eliminated by inserting a quarter-wave plate into the cavity or adopting the specially coated mirrors as cavity mirrors [10,11]. These methods are effective for oscillators but not suitable for single-pass amplifier structures. There is plenty of research about the depolarization of the YAG amplifier, but most is about the Nd:YAG amplifier [12–14]. This situation is because Nd:YAG laser uses lamps or commercial laser diodes that can easily reach several kilowatts as the pump source [15]. Thus, the depolarization is evident and considerable. However, in previously reported Ho:YAG amplifiers, the total pump power was usually only 150 W [9,10], so the weak depolarization was often ignored. However, in the higher power Ho:YAG MOPA system, especially in a three-stage amplifiers system, depolarization should be valued.

In this paper, we demonstrated a three-stage Ho:YAG MOPA system and provided a theoretical model to predict the depolarization of the Ho:YAG amplifier. The depolarization in the oscillator was close to zero due to the unique cavity mirrors, which had high reflectivity for s-polarized light and high transmittance for p-polarized. The polarization in amplifier#1 and amplifier#2 was 0.018 and 0.023, respectively, and the depolarized power was 2.98 W and 6.20 W. The effects of beam sizes and different types of Ho:YAG rods on depolarization were verified in amplifier#3. The depolarization and depolarized power were 0.07 and 32 W at the maximum output power. These experimental results were in good agreement with the numerical simulations. Besides, the maximum output power was 450 W with an overall optical-to-optical efficiency of 60%. To our knowledge, this is the highest power output with a Ho:YAG MOPA system. The beam quality M² factors were measured to be ∼ 1.8 at 400 W.

2. Theory and numerical simulations

Nonuniform temperature distribution in the laser crystal will cause thermal strain, which leads photoelastic effect and makes the original isotropic material anisotropic [16]. Here, we discuss the depolarization loss in the dual-end-pumped Ho:YAG power amplifier with rod structure. The seed light is an s-polarized laser with a wavelength of 2090 nm. The pump light wavelength is 1908 nm, one direction is p-polarized, and the other is s-polarized, and the detail polarization isolation device can be found in [5]. In this paper, depolarization is defined as the ratio of the p-polarized light power generated from the amplifier to the total output power of the amplifier. The dual-end-pumped Ho:YAG amplifier structure is shown in Fig. 1.

Fig. 1. Schematics of the pumping and cooling of Ho:YAG amplifiers. The inset shows the pump beam profile.

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The temperature distribution of the crystal is related to the distribution of the pump source and the cooling mode of the crystal. The pump sources are the high-power Tm:YLF slab lasers, and the pump profiles approximately follow the ‘top-hat’ distribution, which can be seen in the inset of Fig. 1. The Ho:YAG rod is traditional [111]-oriented. As shown in Fig. 1, the seed light and pump light propagate along the z-axis or in the [111] direction. To simplify the model, we assume that the heat source is only from the quantum defect losses of the in-band-pumped Ho:YAG process. The heat is removed by a water-cooled copper heat sink along the cylindrical rod surface. The temperature distribution inside the cylindrically symmetric rod can be obtained by solving the heat conduction equation [17]

(1)$$\frac{1}{r}\frac{\partial }{{\partial r}}\left( {r\frac{{\partial \Delta T(r,z)}}{{\partial r}}} \right) + \frac{{{\partial ^2}\Delta T(r,z)}}{{\partial {z^2}}} ={-} \frac{1}{{{K_\textrm{c}}}}\frac{{2{\eta _\textrm{h}}{P_{\textrm{ab}}}}}{{\pi \omega _\textrm{p}^2}}\frac{{\alpha [\exp ( - \alpha z) + \exp ( - \alpha (L - z))]}}{{1 - \exp ( - \alpha L)}}\Theta (\omega _\textrm{p}^2 - {r^2})$$

where ΔT is the temperature difference between point (r, z) and point (R_c, z), and R_c is the radius of the YAG rod. K_c is the thermal conductivity (0.014 W/(mm·K) for YAG) [16], P_ab is the one-side absorbed pump power, η_h is the fractional thermal loading, which is written as η_h= 1-λ_p/λ_s (λ_p, λ_s are the wavelength of pump light and seed light, respectively). ω_p is the pump light radius, α is the absorption coefficient for the 1.9 µm laser, L is the length of the rod, and Θ is the Heaviside function. Here, since the pump beam has a small divergence angle, we assume that the pump radius in the rod remains constant to simplify the calculation. With the approximation mentioned in Ref. [17], the solution in Eq. (1) is

(2)$$\begin{aligned} \Delta T(r,z) &= \frac{{{P_\textrm{h}}}}{{2\pi {K_\textrm{c}}}}\frac{{\alpha [\exp ( - \alpha z) + \exp ( - \alpha (L - z))]}}{{1 - \exp ( - \alpha L)}}\{ [(1 - \frac{{{r^2}}}{{\omega _\textrm{p}^2}})\\ &+ \ln (\frac{{R_\textrm{c}^2}}{{\omega _\textrm{p}^2}})]\Theta [\omega _\textrm{p}^2 - {r^2}] + \ln (\frac{{R_\textrm{c}^2}}{{{r^2}}})\Theta [{r^2} - \omega _\textrm{p}^2]\} \end{aligned}$$

where P_h = η_hP_ab. The thermal distribution can determine the stresses under Snitzer’s approach [18]. Then, the elastic strains can be calculated. For an isotropic material, the elastic strain difference between the radial and the tangential is given by

(3)$${\varepsilon _\textrm{r}} - {\varepsilon _\mathrm{\phi }} = \frac{{{\alpha _\textrm{T}}(\nu + 1)}}{{1 - \nu }}\Delta T - \frac{{2{\alpha _\textrm{T}}(\nu + 1)}}{{1 - \nu }}\frac{1}{{{r^2}}}\int_{r = 0}^r {\Delta T} \cdot rdr$$

where ε_r and ε_ϕ are the thermal strains in the r and ϕ directions, respectively, α_T is the linear expansion coefficient (7.5 × 10⁻⁶ K^-1 for YAG), ν is the Poisson’s ratio (0.25) [16]. Then, the thermal birefringence in [111]-direction is given by [19]

(4)$$\Delta n(r,z) = \frac{{n_0^3}}{6}({p_{11}} - {p_{12}} + 4{p_{44}})({\varepsilon _\textrm{r}} - {\varepsilon _\mathrm{\phi }})$$

where n₀ is the refractive index (1.82), p₁₁, p₁₂, and p₄₄ are the elastooptical coefficients with the approximate values of -0.029, 0.0091, and -0.0615 [20], respectively. Due to refractive index change, a laser with wavelength λ_s single pass a crystal with the length of L would produce a phase difference ψ(r), which is given by

(5)$$\psi (r) = \frac{{2\pi }}{{{\lambda _\textrm{s}}}}\int_0^L {\Delta n} (r,z)dz$$

After the phase difference is obtained, the depolarization D_pol can be calculated by [21]

(6)$${D_{\textrm{pol}}} = \frac{1}{{r_\textrm{a}^2}}\int_{r = 0}^{{r_\textrm{a}}} {\int_{\theta = 0}^{2\pi } {{{\sin }^2}} } (2\theta ){\sin ^2}(\frac{{\psi (r)}}{2})rd\theta dr$$

where r_a is the seed light radius. Ignoring the thermal focusing effect inside the crystal, we believe the seed light radius does not change during the amplification process, i.e., r_a is a constant here. Substituting Eqs. (2), (3), (4), (5) into Eq. (6) gives

(7)$${D_{\textrm{pol}}} = \left\{ \begin{array}{cc} &\frac{1}{{r_\textrm{a}^2}}\int_0^{{r_\textrm{a}}} {{{\sin }^2}( - \frac{A}{{4\omega_\textrm{p}^2}}{r^2})} \cdot rdr,{r_\textrm{a}} \le {\omega_\textrm{p}}\\ \frac{{\omega_\textrm{p}^2}}{{r_\textrm{a}^2}}[\frac{1}{4} - \frac{{\sin ({A / 2})}}{{2A}}] + &\frac{1}{{r_\textrm{a}^2}}\int_{{\omega_\textrm{p}}}^{{r_\textrm{a}}} {{{\sin }^2}(\frac{B}{{{r^2}}} - \frac{A}{2}) \cdot rdr} ,{r_\textrm{a}} > {\omega_\textrm{p}} \end{array} \right.$$

where

(8)$$\begin{array}{l} A = \frac{{n_0^3({p_{11}} - {p_{12}} + 4{p_{44}})}}{6}\frac{{2{P_\textrm{h}}{\alpha _\textrm{T}}(\nu + 1)}}{{{\lambda _\textrm{s}}(1 - \nu ){K_\textrm{c}}}}\\ B = \frac{{A\omega _\textrm{p}^2[\ln ({{R_\textrm{c}^2} / {\omega _\textrm{p}^2}}) + 1]}}{2} \end{array}$$

From Eq. (7), the depolarization in the Ho:YAG amplifier is related to the radius of seed light and pump light. Figure 2(a) shows a calculation for a dual-end-pumped 140 mm, 0.3 at.% Ho:YAG rod with different pump radii. In this case, the seed light radius is constant at 0.6 mm. When the incident pump power is less than 500 W, the depolarization decreases with the increase of pump radius, which indicates that the pump radius less than the seed radius can weaken depolarization. However, according to the design criteria of mode matching in solid-state laser, the laser has a high output power when the seed light is slightly larger than the pump light [22]. To balance the above two situations, we would adopt the beam transformation system to make the pump light and seed light have the same beam radius inside the amplifier crystal. At this time, r_a = ω_p, and the Eq. (7) becomes

(9)$${D_{\textrm{pol}}} = \frac{1}{4} - \frac{{\sin ({A / 2})}}{{2A}}$$

Fig. 2. Simulation results: (a) depolarization of three pump light radii versus pump power, the inset shows the depolarization when the incident pump power is below 500 W; (b) depolarization of three Ho:YAG rods versus pump power, the inset shows the depolarization when the incident pump power is below 500 W.

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By Eq. (9), it can be found that the depolarization is independent of the pump radius and seed radius but only related to the heat load of the rod. Hence, the rod parameters, including length, radius, and Ho-doped concentration, will determine the depolarization of an amplifier. The depolarization can be calculated by Eq. (9) with the following three types of Ho:YAG rods which will be used in section 3. One is 100 mm long with 0.3 at.% Ho³⁺ concentration, another is 140 mm long with 0.3 at.% Ho³⁺ concentration, and the last is 100 mm long with 0.5 at.% Ho³⁺ concentration, the diameter of all crystals is 5 mm. The absorption coefficient of three rods is measured to be 0.17 cm^-1, 0.18 cm^-1, and 0.36 cm^-1, respectively. When r_a = ω_p = 0.6 mm, the simulation results are shown in Fig. 2(b). The depolarization curves are monotonically increasing when the pump power is less than 500 W, as shown in the inset of Fig. 2(b). The depolarization of three Ho:YAG rods with pump power of 300 W, the highest pump power in later experiments, is 0.065, 0.078, and 0.088, respectively.

3. Experimental setup

The schematic diagram of the Ho:YAG MOPA system is shown in Fig. 3, which includes one master oscillator and three power amplifiers. Every Ho:YAG rod was dual-end-pumped by home-built modular linearly polarized Tm:YLF lasers with a wavelength of 1908nm (Tm1 ∼ Tm8). The output powers of Tm1 ∼ Tm6 were ∼ 80 W, and the maximum powers of Tm7 and Tm8 could reach 150 W. The Ho:YAG crystal in the master oscillator was a 60 mm long rod with a diameter of 4 mm and a Ho³⁺ concentration of 0.8 at.%. The 140 mm, 0.3 at.% rods with 5 mm diameter were used in amplifiers #1 and #2. There were three kinds of Ho:YAG rods available in amplifier#3, introduced in section 2. All Ho:YAG rods were wrapped in indium foil and placed in water-cooled heat sinks, and the temperatures of circulating water were 289 K. The oscillator consisted of a convex mirror with a radius of 300 mm (with high reflection at 2.1 µm), two plane mirrors M1 and M2 (R > 99% at 2.1 µm s-polarized light, T > 70% at 2.1 µm p-polarized light, T > 95% at 1.9 µm light), and an output coupler (OC) with a transmittance of 70% at 2.1 µm and a curvature radius of - 300 mm. In addition, a 0.05 mm thickness etalon was inserted into the master oscillator to limit the output wavelength at 2.09 µm. The TFP1 ∼ TFP7 were thin-film polarizers (TFPs) with T > 96% at 2.1 µm p-polarized light and R > 99% at 2.1 µm s-polarized light. TFP1 and TFP2 ensured that the seed light entering amplifier#1 was pure s-polarization. Likewise, two TFPs were utilized after each amplifier. The first TFP was used to separate depolarized light from total output light so that the depolarization could be measured. Because the TFP still had a weak reflectivity for p-polarized light, the second TFP ensured the 2.1 µm laser entering the next amplifier was completely s-polarized light. The DM1 ∼ DM6 were 45° dichroic mirrors with R > 98% at 2.1 µm laser and T > 97% at 1.9 µm laser. The waist spot of Tm3 ∼ Tm6 was at the end face of Ho:YAG rods with a radius of ∼ 0.5 mm and divergence angle of ∼ 3 mrad. The oscillator’s output laser was coupled into amplifier#1 by a convex lens L1. The beam radius at the incident and exit surfaces of the Ho:YAG rod were 0.5 mm and 0.8 mm, respectively. Similarly, the s-polarized light generated from amplifier#1 was coupled to amplifier#2 with a beam radius of 0.5 mm (incident surface) and 0.9 mm (exit surface) by a convex lens L2. For amplifier#3, three beam radii of 0.5 mm, 0.6 mm, and 0.7 mm at the incident surface, corresponding to 1.0 mm, 1.1 mm, and 1.2 mm at the exit surface, were adopted to compare the influence of beam size on thermally induced depolarization. In this process, the pump light radius always remained similar to that of the seed light by adjusting the beam transformation system of the pump light. In order to simplify the description, we used a beam radius of 0.5 mm to represent the radii of seed light and pump light at the incident plane of Ho:YAG crystal was 0.5 mm. This description also applied to beam radii of 0.6 mm and 0.7 mm. A power meter (PM1K, Coherent) and a beam analyzer camera (Pyrocam IV, Ophir) was used to measure the power and beam profile of the output laser.

Fig. 3. Schematic diagram of the Ho:YAG MOPA system.

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4. Results and discussion

4.1 Master oscillator, amplifier#1, amplifier#2

This section studied the continuous-wave (CW) output characteristics of the oscillator, amplifier#1, and amplifier#2. The output characteristics of the master oscillator are shown in Fig. 4. The maximum output power was 81.8 W with a total pump power of 139.7 W, corresponding to a slope and optical-to-optical efficiency of 62.5% and 58.6%, respectively. The power transmitted through TFP1 was only 0.12 W, and the beam profile was also recorded. As shown in Fig. 4(d), the beam profile was not a cloverleaf-like pattern which was the image that should be produced by depolarization, so this was weak s-polarized light rather than depolarized light. This result indicated that the polarization selectivity of M1 and M2 play an important role in depressing the depolarization in the master oscillator. In addition, the beam radius of s-polarized light was measured by 90/10 knife-edge technology at the maximum output power, and the M² factors were calculated to be 1.40 and 1.14 in x and y directions, respectively. The output laser wavelength was 2090.5 nm with a linewidth of 0.19 nm.

Fig. 4. The output characteristics of the master oscillator: (a) output power, (b) beam quality of s-polarized light, (c) beam profile of s-polarized light, and (d) beam profile of transmitted light.

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Next, adopting the oscillator s-polarized output as seed light, the output power of amplifier#1 is shown in Fig. 5(a). The maximum output power was 165 W with a total pump power of 144.5 W, corresponding to a slope of 68.8%. The extraction efficiency, defined as (output power – seed power)/pump power, was 57.6%. The maximum power transmitted through TFP3 was 2.98 W, and the beam profiles are shown in Fig. 6. Amplifier#1 produced a cloverleaf-like image even at lower power, verifying that depolarization did occur during the amplification. The depolarization becomes worse with the increase of pump power, and the maximum depolarization was 0.018, as shown in Fig. 5(c). For amplifier#2, the maximum output power was 267 W with the seed light of 162 W and the total pump power of 160 W, as shown in Fig. 5(b). The slope of the output power curve was 76.1%, and the extraction efficiency was 65.5%. Among output power, s-polarized light and p-polarized light were 261 W and 6.20 W, respectively, and the corresponding depolarization was 0.023. Besides, the beam profile of depolarized light was closely similar to the patterns shown in Fig. 6. In Fig. 5(c), amplifier#2’s depolarization was slightly larger than amplifier#1. The main reason was that higher power lasers interacted in amplifier#2’ rod, which intensified the thermal birefringence. The solid line in Fig. 5(c) is the numerical calculation of depolarization according to Eq. (7) in section 2. The depolarization of the rod was independent of the size of the beam when the size of the seed light and the pump light was the same. Therefore, the simulation results under different beam radii were the same, so there was only one simulation curve in Fig. 5(c). It can be seen that the experiment results are in good agreement with the theory simulation. Moreover, the gain of amplifiers #1 and #2, defined as the ratio of amplifier’s output power to seed light, was 2.02 and 1.65, respectively.

Fig. 5. The output characteristics of amplifiers #1 and #2: (a) output power of amplifier#1 with seed light of 81.8 W, (b) output power of amplifier#2 with seed light of 162 W, and (c) depolarization in amplifiers #1 and #2.

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Fig. 6. Beam profiles of depolarized laser in amplifier#1.

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Moreover, the beam quality M² factors of the s-polarized light in these amplifiers were measured. The results are shown in Fig. 7. For amplifier#1, the M² factors of s-polarized light were measured to be 1.48 in x-direction and 1.21 in y-direction at the maximum output power. For amplifier#2, the M² factors were 1.63 and 1.34 in the x and y directions, respectively. The inset of Fig. 7 shows the beam profiles in the far-field. Obviously, the M² factors in both directions deteriorated after each amplification, which was related to thermally induced phase aberration [23].

Fig. 7. Beam quality measurement: (a) the beam quality of amplifier#1, the inset shows the beam profile; (b) the beam quality of amplifier#2, the inset shows the beam profile.

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Fig. 8. The output characteristics of amplifier#3 with different beam radii: (a) output powers, (b) depolarized powers, and (c) depolarizations.

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4.2 Amplifier#3

In this section, the output characteristics of amplifier#3 with different beam radii and types of Ho:YAG rods are studied, and the depolarization in different situations is discussed.

Figure 8(a) shows the output powers of amplifier#3 with different beam radii. A 140 mm long Ho:YAG rod with 0.3 at.% doped concentration was used here. With the total pump power of 307 W, the maximum output power with the beam radius of 0.5 mm, 0.6 mm, and 0.7 mm was 448.4 W, 450.1 W, and 436.1 W, respectively. The corresponding slope was 69.3%, 72.9%, and 69.9%, respectively, with the extraction efficiency of 61.0%, 61.6%, and 57.0%. The increase of the beam size would lead to an increase in the population of Ho³⁺ involved in the amplification process. Then, the absorption power of seed light by the amplifier’s crystal also increased accordingly, which decreased the output power when the beam was larger, even though the slope were closely similar in all three cases. As the beam radius increased, the power of p-polarized light transmitted through the TFP7 was measured to be 34.4 W, 32.1 W, and 31.1 W. As shown in Fig. 8(b), the depolarized power curves were approximately linear when the incident pump power was more than 200 W. The depolarized power increased with a slope of 17.7%, 16.7%, and 14.8% for three beam radii, respectively. It is worth mentioning that the depolarizations in the three conditions were very close, around 0.07. This result showed that the thermal-birefringence-induced depolarization of the rod was independent of the size of the beam when the size of the seed light and the pump light was the same, i.e., r_a = ω_p, which was consistent with the result of Eq. (9) in section 2. In addition, as shown in Fig. 8(c), the experimental results agreed well with the numerical simulation result.

The beam radius remained 0.6 mm, and the output characteristics of amplifier#3 with three types of Ho:YAG rods are shown in Fig. 9. The maximum pump power was also 307 W. For the 100 mm, 0.3 at.% Ho:YAG rod, the absorption power of seed light was 27 W, and the maximum output power was 441.7 W with a slope of 58.9%. The output performances has been described for the 140 mm, 0.3% Ho:YAG rod in the previous paragraph. For the 100 mm, 0.5 at.% Ho:YAG rod, the absorption of seed light was up to 40 W, which denoted the low output power of 438.5 W. The most severe depolarization also occurs in the 100 mm, 0.5 at.% crystal with the depolarized power of 46 W, and the depolarization was up to 0.106.

Fig. 9. The output characteristics of amplifier#3 with different Ho:YAG rods: (a) output powers, (b) depolarized powers, and (c) depolarizations.

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In contrast to the case of a 0.5 at.% rod, the lowest depolarization was 0.062 by adopting the 100 mm, 0.3% Ho:YAG rod. Furthermore, the slope of depolarized power in the 100 mm, 0.3 at.% rod was 13.9% which was half of a 100 mm, 0.5 at.% rod. As expected, reducing Ho³⁺ concentrations can effectively weaken the thermal-birefringence effect, and the depolarization of the shorter rod was weaker under the same concentrations. As shown in Fig. 9(c), the numerical calculation results of 0.3 at.% rods (including the 100 mm long and 140 mm long) followed the experimental results. However, the 0.5 at.% rod simulation curve was lower than the actual result (Fig. 9(c), blue solid line). The main reason was that the thermal conductivity and the linear expansion coefficient had defaulted as the constants in the above simulations. In fact, the former is inversely proportional to temperature, while the latter is proportional to temperature [24]. Therefore, the simulation results could agree with the real results by slightly adjusting the two parameters to 0.013 W/(mm·K) and 7.9 × 10⁻⁶ K^-1 [18,19], as shown in Fig. 9(c), black short dot line. In addition, the depolarized beam patterns of the 140 mm, 0.3 at.% rod at different depolarized powers was recorded in Fig. 10, and the beam distribution was no longer a uniform four-leaf-like pattern due to the increasing thermal birefringence and perhaps thermal focusing.

Fig. 10. Depolarized beam patterns with different depolarized power in amplifier#3.

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The ultimate goal for the Ho:YAG MOPA system was to obtain a high-power linearly polarized laser. Table 1 lists the output power of the s-polarized laser under the above conditions. The maximum s-polarized laser of 418 W can be obtained with the beam radius of 0.6 mm and the Ho:YAG rod of 140 mm long and 0.3 at.% concentration, even the depolarization was not the smallest in this condition. The overall optical-to-optical efficiency of the MOPA system was defined as the ratio of amplifier#3’s total output power to the total pump power (the sum of Tm1 to Tm8 power was ∼ 751 W). The highest optical-to-optical efficiency of this system was close to 60% with the gain of ∼ 1.7. Moreover, the M² factors in the x and y directions were measured to be 1.85 and 1.60 at the output power of 400 W. The inset of Fig. 11 shows the beam distribution in the far-field.

Fig. 11. Beam quality measurement at the output power of 400 W after amplifier#3. The inset shows the beam profile.

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Table 1. Output characteristics of amplifier#3

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In addition, inserting an acoustic optical modulator (AOM) in the master-oscillator could achieve pulse laser output conveniently as in Ref. [10]. At the pulse repetition frequency of 40 kHz, the Ho:YAG MOPA system could produce ∼ 11 mJ pulse laser with the pulse width of 51 ns, and the corresponding peak power was 220 kW. This system was run in pulse mode for two hours without damage, the output power range of s-polarized light was 414 W to 420 W.

5. Conclusion

In summary, we demonstrated a 450 W Ho:YAG MOPA system with efficient optical-to-optical efficiency of ∼ 60%. In the theory section, the numerical calculations for the depolarization of dual-end-pumped Ho:YAG amplifier with the pump profile of ‘top-hat’ were derived. In the experiment section, the result of the master oscillator showed that the depolarization could be effectively suppressed by adopting specially coated mirrors as the cavity mirror in the oscillator. Moreover, the actual depolarizations of each amplifier were well consistent with the theoretical result, which proved that the simplified theoretical model could calculate the depolarization of the Ho:YAG amplifier conveniently and quickly. Moreover, our experimental results verified the theoretical conclusion that the depolarization of the amplifier mainly depended on the thermal loading, which was involved with the length and concentration of the amplifier’s crystal when the size of seed light was equal to that of pump light was correct. Finally, we obtained a 418 W s-polarized laser with a fine beam quality M² of ∼ 1.8.

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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Thermal-birefringence-induced depolarization in a 450 W Ho:YAG MOPA system

Abstract

1. Introduction

2. Theory and numerical simulations

3. Experimental setup

4. Results and discussion

4.1 Master oscillator, amplifier#1, amplifier#2

4.2 Amplifier#3

5. Conclusion

Disclosures

Data availability

References

Data availability

Cited By

Figures (11)

Tables (1)

Equations (9)

Optics Express

Crystal length (mm)	100	140	140	140	100
Ho³⁺ concentration (at. %)	0.3	0.3	0.3	0.3	0.5
Beam radius (mm)	0.6	0.5	0.6	0.7	0.6
S- polarized power (W)	414	414	418	405	392
P-polarized power (W)	27.7	34.4	32.1	31.1	46.5
Total output power (W)	441.7	448.4	450.1	436.1	438.5
Depolarization	0.062	0.077	0.071	0.071	0.106
Gain	1.69	1.72	1.72	1.67	1.68
Optical-to-optical efficiency of the whole system (%)	58.8	59.7	59.9	58.0	58.3