Radiation-balanced Yb:YAG disk laser

Zhou Yang; Junwei Meng; Alexander R. Albrecht; Mansoor Sheik-Bahae

doi:10.1364/OE.27.001392

1. Introduction

Almost all lasers will suffer modal and efficiency (thermal rollover) degradation at some level as the pump excitation is increased and heat generated from various exothermic processes accumulates in the gain media. Such thermal degradation particularly affects the operation of high power solid-state lasers. Heat is generated primarily due to quantum defect, although the non-radiative decay of the population also contributes. By increasing the surface-to-volume ratio of the gain medium (as in fiber and thin-disk lasers), and exploiting low quantum defect transitions, drastic improvement in thermal management has been achieved leading to high-power (multi-kilowatt) continuous wave (CW) operation in such lasers [1–3]. Thermal degradation and beam breakup, however, remain the limiting factors at high powers [4–6].

Shortly after the first demonstration of solid-state laser cooling (optical refrigeration) using anti-Stokes fluorescence [7], Bowman proposed the concept of a radiation-balanced laser (RBL) where the fluorescence-induced cooling power compensates the heat load arising from the quantum defect and non-radiative decay [8]. As an example, a diagram of this process is depicted in Fig. 1 for the 4f transitions of Yb³⁺ ions in a solid host, which is considered the workhorse of high-power solid-state lasers [9]. By selecting the pump wavelength λ_P longer than the mean fluorescence wavelength λ_f, but shorter than the laser wavelength λ_L, one can effectively balance the exothermic quantum defect with the endothermic spontaneous emission. Bowman et al. subsequently demonstrated this concept experimentally in high quality Yb:YAG rods where powers exceeding 500 W were reported under RBL condition [10], which is to date the only experimental work on RBL.

Fig. 1 Energy diagram of Yb:YAG. λ_f, λ_P, and λ_L represent the mean fluorescence wavelength, the wavelength of pump and laser photon, respectively.

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It is, however, difficult to establish the RBL condition in every point along a rod, as the ratio of the pump and laser intensities may vary substantially, causing local thermal gradients even when the RBL condition is globally satisfied. Therefore, it is highly desirable to extend the RBL operation to disk architectures. Moreover, disk lasers are more suitable for diode-pumping since it is easier, compared to rod lasers, to maintain good modal overlap between the pump and laser beams. Compared to typical thin-disk lasers, without the limitation of thermal diffusion, RBL gain disks can be thicker. Considering its power scaling potential by increasing the transverse mode size much larger than the longitudinal scale, we believe this feasibility study paves the way for the realization of a high-power radiation balanced disk laser.

Bowman et al. [11] reported a Yb:KGW based disk laser with reduced heating in quasi-CW operation. Since then, there have been only theoretical studies [12,13]. In this letter, we report the first CW disk RBL operation, present a detailed performance analysis, and discuss its promising potential for power scaling. Since the single-pass pump absorbance is low in such thin structures, efficient pump absorption in typical thin-disk lasers is achieved by adopting multi-pass pumping schemes [14,15]. In our study, we exploited an intracavity pumping scheme using an optically-pumped vertical-external-cavity surface-emitting laser (VECSEL) to enhance the pump absorption, which is not necessarily the optimal laser geometry. The broad wavelength tunability and good beam quality of VECSELs provide additional parametric freedom in our investigation [16].

2. Experiments

2.1 Material characterization

A necessary condition for demonstrating RBL action is that the gain material must be of cooling grade. That is, it should be of sufficiently high purity and high optical quality to exhibit net cooling at room temperature. The cooling efficiency defined as the ratio between the heat-lift and absorbed pump power at a given pump wavelength λ can be shown to be $η_{c} = η_{e x t} η_{a b s} \frac{λ}{λ_{f}} - 1$ , where the external quantum efficiency $η_{e x t} = τ_{f} / τ_{r a d}$ , and the absorption efficiency $η_{a b s} \approx 1 - α_{b} / α_{0} (λ)$ are the critical material parameters. Here $τ_{f}$ and $τ_{r a d}$ denote the escaped fluorescence and radiative recombination lifetimes, while α_b and α₀(λ) represent the parasitic (background) and resonant absorption coefficients, respectively. For a high-quality cooling-grade material (η_c>0), one needs $η_{e x t} η_{a b s} \approx 1$ . A candidate material can be screened by measuring its cooling efficiency using laser-induced thermal modulation spectroscopy (LITMoS), where fractional heating of the sample normalized to the absorbed laser power is recorded (e.g. using a thermal camera) as the excitation laser wavelength λ is varied in the vicinity of the mean fluorescence wavelength λ_f [17].

We used a 5% doped Yb:YAG crystal (Scientific Materials Inc.) having dimensions of d = 0.5 mm thick and 4 × 5 mm² cross section with a mean fluorescence wavelength λ_f of 1019 nm. The LITMoS data for this crystal is shown in Fig. 2(a) exhibiting a large cooling spectral window between 1021 nm ( $λ_{c}$ ) and 1053 nm. The best fit to the data η_c(λ) is also shown using η_ext = 99.6% and α_b = 3 × 10⁻³ cm⁻¹ indicating the suitability of this crystal for RBL investigation. Figure 2(b) shows the measured absorption spectrum $α_{0} (λ)$ for this crystal. To exploit a large absorption peak, we choose λ_P = 1030 nm (corresponding to E₃-E₅ transition in Fig. 1), and calculate the gain spectrum using the expression [10]:

γ (λ) = α_{0} (λ) \frac{i_{P} (\frac{β_{P}}{β_{L}} - 1) - 1}{1 + i_{P} + i_{L}},

Where

β_{P} (λ_{P}) = {[1 + \frac{Z_{1}}{Z_{2}} e^{\frac{E_{15} - h c / λ_{P}}{k T}}]}^{- 1}

and

β_{L} (λ) = {[1 + \frac{Z_{1}}{Z_{2}} e^{\frac{E_{15} - h c / λ}{k T}}]}^{- 1}

with Z₁ and Z₂ describing the partition functions in lower and upper manifolds, respectively.

i_{P} = I_{P} / I_{S P}

,

i_{L} = I_{L} / I_{S L}

are the pump and laser (when present) pump intensities normalized to their saturation intensities

I_{S P} = \frac{h c}{λ_{P} σ (λ_{P}) τ_{f}} β_{P}

,

I_{S L} = \frac{h c}{λ_{L} σ (λ_{L}) τ_{f}} β_{L}

and the absorption cross section

σ (λ)

=

α_{0} (λ) / N_{0}

with N₀ being the dopant (Yb³⁺) density. The small signal gain spectrum (I_L = 0) calculated using I_P = 20 kW/cm² at 1030 nm is shown in Fig. 2(b). It exhibits a gain peak at λ∼1050 nm which corresponds to the E₅-E₄ transition of Yb:YAG. For comparison, the unsaturated (I_P = 0) absorption spectrum

α_{0} (λ)

is also shown.

Fig. 2 (a) Measurement (circles) and fitting (solid curve) of the laser cooling efficiency η_c of the Yb:YAG disk at room temperature. The blue-shaded area represents the cooling regime. (b) Absorption $α_{0} (λ)$ (dotted curve) and $α (λ) = - γ (λ, I_{P} = 20 k W / c m^{2}, I_{L} = 0)$ (solid curve) spectra of 5% Yb:YAG. The small signal gain spectrum is calculated with 20 kW/cm² incident pump intensity at 1030 nm. The yellow-shaded area represents the regime with optical gain.

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2.2 Disk RBL experimental setup

The experimental arrangement for the VECSEL intracavity pumped Yb:YAG disk laser is shown in Fig. 3. The detailed structure and fabrication information of the VECSEL has been described in [16]. It uses a standard active mirror gain chip consisting of 12 InGaAs quantum wells grown on a 25 pair AlAs/GaAs semiconductor distributed Bragg reflector (DBR). The VECSEL cavity is formed between the active mirror and a concave dielectric high reflector (HR) with a 25 cm radius of curvature. The gain chip is pumped by a high-power diode laser at 808 nm. Using a 2-mm thick quartz birefringent filter (BRF) inside the cavity, the operation wavelength of the VECSEL can be tuned from 1010 to 1040 nm, covering a significant portion of the cooling window for the Yb:YAG disk.

Fig. 3 Schematic of the intracavity-pumped radiation balanced disk laser setup. On the right, the mounting of the Yb:YAG disk is shown where it is glued onto two bare fibers, which are in turn supported by a glass slide to reduce the heat load.

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At the current stage, no high reflectivity dielectric mirror is deposited on the disk for cost reason. The disk is placed at Brewster’s angle with respect to the VECSEL beam to minimize the Fresnel reflection losses. To minimize thermal contact, the disk is glued onto two bare optical fibers, which are mounted onto a glass slide, without heatsink. The fundamental mode of the VECSEL, projected onto the Brewster angle gain disk is estimated to be an ellipse having semi-major and semi-minor lengths of 1.00 and 0.50 mm. The disk laser cavity is formed with its axis also at Brewster condition, to lower internal cavity losses for the RBL, and with two concave HR mirrors, with radii of curvature of 50 and 100 mm. The combined transmission of both mirrors is measured to be 0.3%, acting as the output coupling of the RBL. The elliptical RBL cavity mode’s radial dimensions inside the Yb:YAG crystal is estimated to be 0.60 × 0.30 mm. As will be discussed laser, the actual beam parameters of the VECSEL and RBL cavities may differ slightly from the calculated values due to uncertainties arising, for example, from thermal lensing and gain-guiding effects [18].

3. Results and discussion

The VECSEL is tuned to 1030 nm (λ_P), which is both the gain peak of the VECSEL chip and an absorption peak of the Yb:YAG disk. The free-running disk laser operates at 1050 nm (λ_L), as shown in Fig. 4 at 57 W of diode power incident on the VECSEL chip. Both the VECSEL and RBL operate in near fundamental mode, as shown in Fig. 4 inset. The VECSEL and RBL power stabilize within 1-5 minutes after turning on the pump diode, which is the time-scale for VECSEL temperature stabilization.

Fig. 4 Side-scattered fluorescence spectrum from the Yb:YAG disk laser. The zero-crossing wavelength at 1021 nm along with the scattered VECSEL pump at 1030 nm and the laser line at 1050 nm are also shown. Inset is the measured beam profile at the RBL condition.

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The temperature profile of the gain disk was monitored using a thermal camera (Nanocore 640, L3 Communications Corporation, Garland, TX, USA) with 0.05 K resolution as the VECSEL power was varied. Recorded thermal images of the disk at room temperature (unpumped), and under pump are shown in Fig. 5 (a) and (b), respectively. In order to display the temperature dynamics, the line distribution along the center of the disk in the vertical direction is plotted versus time for the RBL case in Fig. 5 (c).

Fig. 5 (a) and (b) are the thermal images of the mounted gain disk at room temperature and radiation balancing condition after 30 minutes, with darker shades representing lower temperatures. The red lines in (a) represent the outline of the disk. (c) The line-integrated time-evolution of the temperature change along the vertical white dash line in (a) after the VECSEL cavity is unblocked at t = 1 minute. The black dashed lines represent the pump beam position. The estimated Gaussian profiles of the pump (green) and laser (red) beams are depicted on the right.

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After turning on the pump diode, the VECSEL lases and the Yb:YAG fluorescence emission process starts right away, while the Yb:YAG laser takes time to initiate. Therefore, net cooling is observed from the very beginning. After the Yb:YAG laser reaches the steady state, the disk is slowly warmed up and its temperature stabilizes. In experiments, we observed about 10% power fluctuation in the first 5 minutes. The radiation balancing condition is realized with 57 W of incident pump power at 808 nm, or 32 W of absorbed power. Based on the leakage VECSEL power (through the high reflector), a total intracavity power of 130 W is estimated to be circulating in the VECSEL at λ_P = 1030 nm. This in turn results in approximately 7 W of absorbed power in the Yb:YAG disk. A total output power of 1.05 W is collected from the disk laser (from both ends of the cavity) which translates to approximately 15% optical-to-optical conversion efficiency from 1030 nm to 1050 nm. This is lower than the maximum theoretical efficiency $η_{m} = \frac{λ_{P} - λ_{c}}{λ_{L} - λ_{c}} = 31 %$ [19] due to the suboptimal output coupling efficiency, as well as the mode-mismatch between pump and laser in this experiment, as will be addressed later.

The small residual thermal gradient of 2 K between the center and the edge is due to radial intensity distribution (Gaussian) of the modes. This prevents achieving a local RBL condition at every radial point. Various approaches based on beam-shaping of the pump have been suggested [10] to mitigate such thermal gradients. This gradient also depends on the physical size of the gain disk since the thermal diffusion process is involved. The heating near the edges can be attributed to fluorescence being absorbed due to surface imperfections and contamination of the unpolished edges. Because of the relatively large refractive index of YAG, a significant amount of fluorescence could be trapped by total internal reflection, reabsorbed and partially converted to heat via the non-radiative recombination. As has been practiced in the implementation of thin-disk lasers, radiation trapping can be remedied by sandwiching the gain between windows of similar index of refraction, while roughening the edges facilitates more efficient fluorescence escape [20]. This will also help to suppress amplified spontaneous emission [21] and, as a result, reduce losses.

4. Data analysis

To further gain insight into the operation of disk RBL, we use the expression for saturated gain from Eq. (1) to obtain the total steady-state intracavity laser intensity by balancing the roundtrip gain and losses assuming a low-loss linear cavity:

γ (λ_{L}) = \frac{T_{2} + l_{i}}{2 d},

where T₂(∼0.3%) and

l_{i}

are output coupling and the unknown internal cavity losses, respectively. Equation (2) gives the input-output curve of the laser:

i_{L} = (1 + 1 / θ) [\frac{i_{P}}{i_{P}^{t h}} - 1],

with the normalized loss factor

θ = \frac{T_{2} + l_{i}}{2 d α_{0} (ν_{L})}

and the laser threshold

i_{P}^{t h} = (1 + θ) / (\frac{β_{P}}{β_{L}} - 1 - θ)

. The generated heat power density Q can be written as [10]:

Q = (β_{P} - β_{L}) \frac{N_{T} h (ν_{P} - ν_{L})}{τ_{2}} \cdot \frac{i_{L} i_{P} - i_{L}^{\min} i_{P} - i_{L} i_{P}^{\min}}{1 + i_{P} + i_{L}},

The local RBL condition, ignoring the radial intensity variations, was found by Bowman by setting Q = 0, which leads to

\frac{i_{P}^{\min}}{i_{P}} + \frac{i_{L}^{\min}}{i_{L}} = 1,

where

i_{P}^{m i n} = \frac{λ_{P}}{λ_{c}} \frac{λ_{L} - λ_{c}}{λ_{L} - λ_{P}} \frac{β_{L}}{β_{P - β_{L}}}

and

i_{L}^{m i n} = \frac{λ_{L}}{λ_{c}} \frac{λ_{P} - λ_{c}}{λ_{L} - λ_{P}} \frac{β_{P}}{β_{P} - β_{L}},

with

λ_{c} = λ_{f} / η_{e x t} η_{a b s}

denoting the zero-crossing wavelength. Note that we have included the effect of parasitic absorption in the definition of the zero-crossing wavelength. This simple treatment, however, ignores the saturation of resonant absorption (and gain) at RBL points. That is, α_b/α(λ) will effectively increase by the saturation factor

1 + i_{L} + i_{P}

at the pump and laser wavelengths, thus potentially further red-shifting λ_c.

The RBL condition given by Eq. (5) also ignores the radial distribution of pump and laser modes. Assuming TEM₀₀ Gaussian beams, $i_{P, L} (r) = i_{P 0, L 0} (r) exp (- 2 r^{2} / w_{P, L}^{2})$ , the effects of radial variation and mode-mismatch can be taken into account by balancing the total dissipated power which leads to the modified RBL condition:

H \approx π d \int Q (r) d r^{2} = 0 .

Similarly, modal overlap effects can be applied to laser oscillation by rewriting Eq. (2) as

\int r (λ_{L}) i_{L} (r) d r^{2} / \int i_{L} (r) d r^{2} = (T_{2} + l_{i}) / 2 d .

Figure 6 presents the comparison of our theoretical and experimental results. The only parameters used in fitting the data are minor adjustments to the estimated beam radii and the zero-crossing wavelength. We use saturation intensities of I_SP = 7 kW/cm² and I_SL = 45.4 kW/cm² [22] at the pump and laser wavelengths, respectively. The laser output vs. pump power curve from Eq. (7) was obtained by reducing the pump beam radius by 26% from the calculated value, which is quite reasonable and expected due to thermal lensing in the VECSEL gain chip. The RBL mode however only needed minor adjustment (5% reduction) indicating the desired minimal thermal aberrations in this cavity. The RBL curve of Eq. (6) was calculated using λ_c = 1023 nm, representing a 2 nm redshift from the low pump power case measured in the LITMoS data of Fig. 2(a), which could be due to the parasitic absorption at the pump and laser wavelengths. Given the complexity of this laser system, the good agreement of the data and theory indicates that we have gained a thorough understanding of and predictive capability for the operation of these disk RBLs. While realizing that the current condition is far from optimum, we can make estimations for high power scaling. The RBL point in Fig. 6 corresponds to

i_{L 0} \approx 5.5

which in turn leads to

I_{L 0} \approx 5.5 I_{s L} = 250

kW/cm². With the current 0.3% output coupling, this gives 0.75 kW/cm² output intensity, implying that a CW RBL with more than 1 kW of output power is quite feasible using a 10 mm beam radius and further optimization and mode-matching. To increase the RBL conversion efficiency, an optimization of pump and laser conditions is needed, which will be discussed in detail in future publications. Use of other gain materials [23] and multiple gain disks [12] in series in a single cavity can further lead to multi-kilowatt output powers. Even though disk RBLs are advantageous in mitigating thermal gradient, the total efficiency of such devices could be lower than typical thin-disk lasers because a portion of the population is used to remove the heat.

Fig. 6 The five data points represent the measured intracavity Yb:YAG disk laser powers at λ_L = 1050 nm versus the intracavity VECSEL pump power at λ_P = 1030 nm. Open-squares are in the self-cooling regime (H<0), solid-square is in the heating regime (H>0) and the solid-circle is the RBL point (H∼0). The theoretical curves given by Eqs. (6) and (7) show an excellent agreement with the data; indicating the RBL point at the crossing of the two curves. For comparison, the RBL condition for plane-waves (or top-hat beams) as given by Eq. (5), is also shown.

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While we have simply exploited the intracavity VECSEL pumping as a tool for enhancing the pump absorption, such a scheme may also be found practical for scaling RBLs to high power operation. For instance, a cooling-grade Yb:YAG disk could be intracavity-pumped by another diode-pumped Yb:YAG thin-disk laser at 1030 nm as was shown in [24], but operating under RBL condition. Alternatively, a multi-pass pumping scheme [25] similar to those employed in commercial high-power thin-disk lasers [14,15] can be equally applied to disk RBLs. This pumping scheme offers a higher control of the pump intensity and mode-matching capability which in turn allows optimization of the overall efficiency and output powers.

5. Conclusions

We have demonstrated the first radiation-balanced disk laser in an intracavity-pumped Yb:YAG crystal. The detailed theoretical analysis in excellent agreement with the data provides a roadmap for advancing disk RBLs towards high beam quality, kilowatt power regimes with minimal adverse thermal degradation.

Funding.

Air Force Office of Scientific Research (AFSOR) FA9550-16-0362 (MURI).

Acknowledgment

The authors thank Dr. Steven R. Bowman for insightful discussion, and Dr. Markus P. Helen for providing the high quality Yb:YAG sample.

References

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Radiation-balanced Yb:YAG disk laser

Abstract

1. Introduction

2. Experiments

2.1 Material characterization

2.2 Disk RBL experimental setup

3. Results and discussion

4. Data analysis

5. Conclusions

Funding.

Acknowledgment

References

Cited By

Figures (6)

Equations (7)

Optics Express