Influence of a ring-shaped pump beam on temperature distribution and thermal lensing in end-pumped solid state lasers

D. J. Kim; S. H. Noh; S. M. Ahn; J. W. Kim

doi:10.1364/OE.25.014668

1. Introduction

Diode-end-pumped solid state lasers are used in a variety of applications due to its excellent laser characteristics including high efficiency, good beam quality, compactness, and flexibility in mode of operation. These advantages are primarily due to the ability to selectively excite the fundamental mode, i.e. the TEM₀₀ mode, by matching the applied pump beam profile to the targeted laser mode in the laser medium. In addition, the use of a fiber-coupled diode laser source provides the pump beam with relatively high brightness allowing for construction of a very compact laser resonator with low loss in a simple configuration. These advantages enable the laser resonator to achieve low threshold pump power and high optical efficiency. However, scaling to higher power levels whilst maintaining high efficiency and good beam quality is quite challenging in diode-pumped solid state lasers since the deposited heat due to pumping causes spatial temperature variation in the laser medium leading to detrimental thermal effects such as highly aberrated thermal lensing, stress-induced birefringence, and catastrophic damage of the laser rod [1–5]. These thermal problems limit the power scalability of the laser output due to significant reduction in beam quality and laser efficiency. Particularly in end-pumped solid state lasers [6–15], the requirement for a small focused pump beam size leads to a very high pump deposition density that causes a high thermal loading density, which exacerbates these thermal problems. A number of techniques have been developed to mitigate the thermal problems, for example, in-band pumping for reducing the quantum defect [16–19], a master-oscillator power-amplifier configuration for enlarging a pump beam and distributing the generated heat into multiple laser mediums [20], and a thin disk or slap laser geometry for maximizing the cooling capacity [21–24]. These approaches have demonstrated improved laser performance, but at the expense of increased complexity and cost. Recently, there was another approach to employ a ring-shaped pumping configuration for reducing thermal effects, reported by our group [25] and D. Lin et al [26], and their preliminary works showed the possibility of power scaling over the conventionalquasi-top-hat pumping configuration.

Here, we report the detailed theoretical and experimental studies for reducing thermal lensing in a conventional diode-end-pumped solid state laser using a ring-shape pump beam, which offers the prospect of further power scaling while retaining high efficiency and good beam quality. Extending the preliminary works, we derive simple analytical expressions for the temperature distribution and the thermal lensing focal length in the laser medium due to the ring-shaped pump intensity distribution. The measured thermal lens power and power amplification in a Nd:YVO₄ amplifier support the theoretical expectations confirming the validity of the use of the ring-shaped pump beam.

2. Theoretical model

The analytical expression of the steady-state temperature distribution in a cylindrical rod can be derived by solving the following heat conduction Eq. (1):

\frac{\partial}{\partial r} (r \frac{\partial T}{\partial r}) + \frac{\partial^{2} T}{\partial z^{2}} = - \frac{Q (r, z)}{K_{c}}

where K_c is the thermal conductivity of the laser material and Q(r, z) is the dissipated heat density [1]. When we assume that the pump beam in the laser medium has an annular step-like profile with inner radius, w_a, and outer radius, w_b, as illustrated in Fig. 1, Q(r, z) is given by

Q (r, z) = {\begin{matrix} 0, 0 \leq r < w_{a} \\ \frac{P_{h}}{π (w_{b}^{2} - w_{a}^{2})} \frac{α}{1 - e^{- α l}} e^{- α z}, w_{a} \leq r \leq w_{b} \\ 0, w_{a} < r \end{matrix}

where P_h is the total heat load, l is the length of the rod, and α is the absorption coefficient for pump radiation. With the boundary condition, T(r₀) = T₀, where r₀ is the radius of the rod, we can obtain the following analytical expression for the temperature distribution in the crystal:

\begin{array}{l} Δ T (r, z) = T (r, z) - T (0, z) \\ = \frac{P_{h}}{4 π K_{c}} \frac{α}{1 - e^{- α l}} e^{- α z} \times {\begin{matrix} 1 + \frac{w_{a}^{2}}{w_{b}^{2} - w_{a}^{2}} \ln (\frac{w_{a}^{2}}{w_{b}^{2}}) + \ln (\frac{r_{0}^{2}}{w_{b}^{2}}), 0 \leq r < w_{a} \\ \frac{w_{b}^{2} - r^{2}}{w_{b}^{2} - w_{a}^{2}} + \frac{w_{a}^{2}}{w_{b}^{2} - w_{a}^{2}} \ln (\frac{r^{2}}{w_{b}^{2}}) + \ln (\frac{r_{0}^{2}}{w_{b}^{2}}), w_{a} \leq r \leq w_{b} \\ \ln (\frac{r_{0}^{2}}{r^{2}}), w_{b} < r \end{matrix} \end{array}

If the inner radius is zero (i.e., w_a = 0), Eq. (3) becomes the well-known expression of the temperature distribution for the top-hat pump beam, as expected [4–8]. Figure 2 shows the calculated temperature distributions as a function of the normalized radius, r/r₀, for the pump beams with different ring-shape parameters (i.e. w_a/w_b and w_b/r₀). We normalized all the temperature data with respect to the maximum temperature (i.e. center temperature) of the top-hat pump beam for comparison. Surprisingly, the temperature is uniform in the unpumped inner hole region (r < w_a), and, even in the pumped region (w_a ≤ r ≤ w_b), the induced temperature gradient is much smaller than that of the top-hat beam. In the outer region (w_b ≤ r), its temperature distribution becomes equal to that of the top-hat beam. Considering that the size of the excited laser mode is typically smaller than the pump beam in the laser material, these results clearly suggest that thermal effects including thermal lensing can be significantly reduced for the ring-shaped pump beam, compared to the conventional Gaussian/top-hat pump beams.

Fig. 1 Geometry of the end-pumped rod and the ring-shaped intensity distribution.

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Fig. 2 Normalized temperature distribution along the radial direction for the ring-shaped pump beams (a) with different values of w_a/w_b, (b) an enlarged picture of (a), and (c) different values of w_b/r₀.

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The focal length of the thermal lensing [2] can be calculated from

f_{t h} (r) = \frac{2 π r}{λ (d Δ φ / d r)}

where λ is the signal wavelength and Δϕ(r) = ϕ(0)-ϕ(r) is the phase difference due to the temperature dependence of the refractive index, which is given by

Δ φ (r) = \frac{2 π}{λ} \int_{0}^{l} Δ T (r, z) \frac{d n}{d T} d z

Equation (5) can be readily solved by using Eq. (3). In this paper, we only consider the contribution of the refractive index on the thermal lensing due to the temperature gradient, not the optical path length change induced by thermal expansion or stress of the crystal [27,28]. The contribution from the latter is known to be ~20% of the total thermal lensing power [1] and hence, we believe that our modeling is enough to show the reduced thermal effects due to a ring-shape pump beam. The focal length of the induced thermal lens becomes

\begin{array}{l} f_{t h} (r) = {\begin{matrix} \infty, 0 \leq r < w_{a} \\ \frac{2 π K_{c} (w_{b}^{2} - w_{a}^{2})}{P_{h} (d n / d T)} \frac{r^{2}}{r^{2} - w_{a}^{2}}, w_{a} \leq r \leq w_{b} \\ \frac{2 π K_{c} r^{2}}{P_{h} (d n / d T)}, w_{b} < r \end{matrix} \end{array}

As expected from Eq. (3), there is no thermal lensing in the inner hole region, and a much longer focal length in the pumped region compared to the top-hat pump beam. That is, the overall thermal lensing is considerably reduced for the ring-shaped pump beam. In practice, a typical focused pump beam from a fiber-coupled diode pump laser has a quasi-top-hat intensity profile between the Gaussian and the top-hat profile [4], making it experience stronger thermal lensing than the ideal top-hat profile. Therefore, the thermal lensing effects for pumping with a ring-shaped beam are considerably weaker than the conventional fiber- coupled diode pumping leading to a better beam quality at high power levels. However, the ring-shaped pump beam has the drawbacks of high threshold pump power and low slope efficiency due to an imperfect spatial overlap with the fundamental transverse Gaussian mode [25, 26], which will be investigated in the experiments and results. Therefore, it requires careful adjustment of the ring intensity profile to compromise the reduced thermal effects and the low spatial overlap efficiency.

3. Experiments and Results

In order to investigate the influence of the pump beam with ring-shaped intensity distribution on thermal lensing and laser performance, we constructed a simple end-pumped Nd:YVO₄ laser amplifier, as shown in Fig. 3. Pump light was provided by two diode lasers at 808 nm coupled to multimode step-index delivery fibers with a 105 μm diameter core and a 0.22 numerical aperture (NA) yielding an output beam with a typical quasi-top-hat intensity profile. To produce the ring-shaped intensity distribution, a silica capillary fiber with a length of ~50 cm was carefully tapered and spliced to one of the diode delivery fibers. The capillary fiber had a 200 μm diameter pure silica inner cladding and a 130 μm diameter air hole in the center and was coated with a low refractive index (n = 1.375) fluorinated polymer outer cladding, giving a calculated NA of 0.49 for the inner-cladding waveguide [29, 30]. The coupling efficiency from the delivery fiber to the capillary fiber was measured to be ~97%. The inset picture in Fig. 3 shows the transmitted (ring-shaped) near-field output beam profile from the capillary fiber, recorded with a silicon CCD camera (Spiricon Inc.) at the position of the image plane. Further details for making a ring-shape pump beam and its beam characteristics can be found in [29] and [30]. Two pump beams were aligned to co-propagate along the same path with the aid of a polarizing beam splitter.

Fig. 3 Experimental setup for measurement of the thermal lens power and power amplification.

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First, we measured the thermal lens power in the gain medium due to the pump beam profiles. We used an antireflection coated 0.3 at.% Nd:YVO₄ crystal with a cross section of 3 × 3 mm² and a length of 8 mm as the gain medium. The crystal was mounted in a water-cooled aluminum heat-sink maintained at 19 °C. The pump beam exiting the capillary fiber was collimated and focused to yield a ring-shaped pump beam with a waist outer radius of ~390 μm and an inner hole radius of ~253 μm inside the Nd:YVO₄ crystal. The pump beam exiting the step-index delivery fiber was also focused to have the same waist beam radius of ~390 μm in the laser crystal. To determine the thermal lens power of the Nd:YVO₄ crystal due to pumping, a fundamental Gaussian laser beam from a single-mode diode laser at 975 nm was launched into the crystal via a plane dichroic mirror with high reflectivity (>95%) at the pump wavelength (808 nm) and high transmission (>95%) at the probe beam and lasing wavelengths (~1 μm). Since the laser signal at 975 nm did not have a gain in Nd:YVO₄ and has diffraction-limited beam quality (M²≈1.0), it was used as a probe beam for measuring the thermal lens power, i.e. 1/f_th(r). This probe beam was carefully aligned to propagate with thepump beam collinearly and was reduced by a factor of 1.0, 0.6, and 0.3 using a simple telescope to yield a waist radius of ~390 μm, ~230 μm, and ~120 μm in the crystal, respectively, for investigating the dependence of the thermal lens power on beam size. The thermal lens power could be directly determined by measuring the beam size and the focusing position of the probe beam after the crystal.

Figure 4 shows the measured thermal lens power as a function of the absorbed pump power for the quasi-top-hat and ring-shaped pump beams. For the quasi-top-hat pump beam, the slopes of the thermal lens power were measured to be 0.18 m⁻¹⋅W⁻¹ and 0.21 m⁻¹⋅W⁻¹ for the probe beam sizes of 390 μm and 230 μm, respectively. The smaller probe beam experiences stronger thermal lensing, which is well-known for the quasi-top-hat pump beam [8]. For the ring-shaped pump beam, the slopes of the thermal lens power were determined to be 0.15 m⁻¹⋅W⁻¹, 0.12 m⁻¹⋅W⁻¹, and 0.03 m⁻¹⋅W⁻¹ for the probe beam sizes of 390 μm, 230 μm, and 120 μm, respectively. Unlike the quasi-top-hat pump beam, the thermal lens power decreases as the probe beam size decreases and becomes negligible for the smallest beam size, 120 μm. These experimental results fit very well with the theoretical expectation that the focal length of the thermal lensing becomes longer at a smaller radial position and infinite in the unpumped hole region. However, there was still thermal lensing even in the inner hole region (ratio 0.3), which should be disappeared. Theoretical calculation for the slope of the thermal lens power and the small thermal lens power in the inner hole region are the subject of ongoing investigation. Nevertheless, these results confirm that the ring-shaped pump beam can significantly reduce detrimental thermal effects including thermal lensing, which will be beneficial for high power laser operation. However, in contrast to the case of a Gaussian or top-hat pump beam, a ring-shaped pump beam has a worse spatial overlap with the fundamental Gaussian beam, leading to a higher threshold and a lower slope efficiency.

Fig. 4 Thermal lens powers of the probe beams with different sizes for the quasi-top-hat (solid line) and ring-shaped (dashed line) pump beams.

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Laser amplification performance was investigated by replacing the probe beam with the seed beam at 1064 nm, as shown in Fig. 3. The seed beam was provided by a simple Nd:YVO₄ master-oscillator power-amplifier (MOPA) constructed in-house. The master oscillator employed a two-mirror cavity configuration comprising a plane pump in-coupling mirror with high reflectivity (>99.8%) at the lasing wavelength (1064 nm) and high transmission (>95%) at the pump wavelength (808 nm), an antireflection coated plano-convex lens with a focal length of 750 mm, and a plane output coupler with 5% transmission at the lasing wavelength. The laser beam from the master oscillator was amplified in a first Nd:YVO₄ amplifier end-pumped by a fiber-coupled diode laser at 808 nm yielding 4.6 W of output with beam quality (<M²) of 1.18. This beam was launched into the targeted second amplifier, as shown in Fig. 3, where its waist radius was 390 μm in the crystal.

The amplified laser output powers as a function of the absorbed pump power are shown in Fig. 5(a). The maximum output powers achieved were 12.6 W and 11.8 W at the absorbed pump power of 24.5 W, corresponding to the slope efficiencies of 33% and 29% for the quasi-top-hat and ring-shaped pump beams, respectively. Although the calculated overlap factor with the fundamental Gaussian intensity profile was 29.4% for the ring-shaped pump, which was nearly one third of the value for the top-hat pump, 86.4%, its slope efficiency was slightly reduced, only 4%. This small difference in efficiency was also observed in the laser oscillator [25, 26] and can be attributed to diffraction of the focused beam and energy transfer between the active ions filling the gain in the unpumped center region. The beam quality of the amplified output beam was also measured with the aid of the beam profiler (Dataray Inc. Beam scope-P8) and the silicon CCD camera confirming negligible degradation in beam quality for the ring-shaped pump beam, as shown in Fig. 5(a). To compare the laser performance including both the power and the beam quality, we used another parameter, the brightness of the output beam, defined by

B = \frac{C P}{λ^{2} {(M^{2})}^{2}}

where P is the power, λ is the wavelength, M² is the beam quality, and C is the constant that depends on the beam profile (for a Gaussian beam profile, C = 1) [1]. The results in Fig. 5(b) show that the brightness for the ring-shaped pumping was enhanced up to 32% over the conventional quasi-top-hat pumping at the maximum power level. Thus, it is clearly proved that a careful design of the ring-shaped intensity distribution should allow us to achieve a laser output with better brightness, i.e., power scaling while preserving good beam quality and high efficiency, due to reduced thermal lensing.

Fig. 5 (a) Amplified output power and beam quality as a function of absorbed pump power, and (b) calculated brightness for the quasi-top-hat and ring-shaped pump beams.

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4. Conclusion

We have developed a simple analytical expression for the temperature distribution in a solid state laser end-pumped by a beam with a ring-shaped intensity distribution. The analysis reveals that the overall temperature distribution is more uniform in the crystal for the ring-shaped pump beam, indicating significant reduction of the thermal effects. We have also derived an analytical expression for the focal length of thermal lensing showing that the laser beam would experience much weaker thermal lensing for the ring-shaped pump beam. We have applied this approach to the Nd:YVO₄ laser amplifier, confirming a ~33% reduction in the thermal lens power and, as a result, a 32% increase in the brightness at 11.8 W of the fundamental Gaussian output for the absorbed pump power of 24.5 W, compared to the conventional quasi-top-hat pumping. Good agreement between the theoretical and experimental results clearly proved the possibility of the ring-shaped pump beam for further power scaling. Therefore, this approach offers a route for achieving significantly higher output powers while preserving good beam quality simply by optimizing the intensity profile of the ring-shaped pump beam in the existing laser configuration.

Funding

National Research Foundation of Korea (NRF) (501100003725); Basic Science Research Program (NRF-2014R1A1A2A16053885); Korean National Police Agency (501100003600); Projects for Research and Development of Police science and Technology (Pa-B000001).

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Influence of a ring-shaped pump beam on temperature distribution and thermal lensing in end-pumped solid state lasers

Abstract

1. Introduction

2. Theoretical model

3. Experiments and Results

4. Conclusion

Funding

References and links

Cited By

Figures (5)

Equations (7)

Optics Express