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The effect of temperature on absorption in end-pumped Yb:YAG thin disk lasers
ARTICLE IN PRESS Optics & Laser Technology 41 (2009) 800–803
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
The effect of temperature on absorption in end-pumped Yb:YAG thin disk lasers Seyfollah Toroghi , Ahmad Khayat Jafari, Ala Hashemi Golpayegani Laser Science & Technology National Laboratory, 14665-567 Tehran, Iran
a r t i c l e in f o
a b s t r a c t
Article history: Received 26 July 2008 Received in revised form 25 November 2008 Accepted 5 December 2008 Available online 23 January 2009
In this paper, the dependence of the absorbed power on the temperature in an end-pumped CW quasithree-level Yb:YAG thin disk laser is calculated. Here, we have used the temperature-dependent form of the Boltzmann occupation factors, absorption cross-section and thermal conductivity of the Yb:YAG crystal. A Monte Carlo ray tracing code and a 2D finite element analysis (FEA) with the ANSYS package have been used to calculate the absorbed power and the temperature distribution inside the Yb:YAG thin disk laser, respectively. According to the model, the temperature-dependent absorbed power turns out to be 18% less than the temperature-independent absorbed power in the top center of the Yb:YAG thin disk laser for used parameters. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Thin-disk laser Temperature-dependent absorption Monte Carlo ray tracing
1. Introduction With the development of high-power laser diodes, quasi-threelevel laser media such as Yb:YAG have attracted a worldwide interest. The Yb3+ ion as a lasant ion has a simple electronic structure and contains only two energy-level manifolds, the ground 2F7/2 state and an excited 2F5/2 state, which are separated by approximately 10,000 cm1. So, detrimental effects such as concentration quenching, excited-state absorption, and upconversion are absent from this lasant [1,2]. Because of the high concentration of the Yb3+ ions in the YAG crystal, the laser active medium can be a thin disk and thus the ratio of cooling surface to the pumped volume is increased compared to rod and slab lasers, which is an important key to the extraction of high output power from a small volume [3]. With the emergence of powerful InGaAs laser diodes that emit at 941 nm, the picture has changed. Several research groups such as Brusselbach et al. [4,5], Rutherford et al. [6], and Chen et al. [7] employed the Yb:YAG gain medium in high-power slab lasers. In addition, Yu et al. [8] used Yb:YAG gain medium in the pulsed highpower disk lasers. In all research mentioned above, the temperatureindependent absorption coefficient of the Yb:YAG has been used for calculation of the absorption power through the laser medium. However, it is clear that the absorption coefficient is strongly influenced by the ambient temperature under real experimental conditions. This temperature-dependency of the absorption coefficient leads to a modification in performance of the laser. Recently, the dependence of the absorption coefficient of the Yb:YAG on the temperature has been investigated by Liu et al. [9].
In this paper, we focus on the modeling in which the absorption power in the end-pumped Yb:YAG thin disk laser is temperature-dependent. We have used a combination of the Monte Carlo ray tracing and the finite element method with an iterative method to fulfill our goal. 2. Numerical method 2.1. Monte Carlo ray tracing The optical setup used for end-pumped Yb:YAG thin disk laser is shown schematically in Fig. 1. The Monte Carlo ray tracing code developed by our group is used to predict the absorbed pump beam in the crystal. The paths of a large number of photons through the optical system are traced. The orientation of photons and the absorption of them in the optical system are being considered as a statistical process. The wavelength of pumped photons is equal to 941 nm. The path of every photon is traced through the optical system until it is lost at one of the optical component, is absorbed inside the crystal, or has exited the system after the designated number of passes through the crystal. The transmission of the crystal along the photon path is calculated taking into account the temperature-dependent form of Boltzmann occupation factors and absorption cross-section. The temperature-dependency of absorption cross-section and absorption coefficient in pump wavelength is given by the following formulae [9]:
sabs ðTÞ ¼ ½2:07 þ 6:37 expððT 273Þ=288Þ1021 cm2 0
Corresponding author.
E-mail address: [email protected] (S. Toroghi). 0030-3992/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2008.12.004
a0 ðTÞ ¼ sabs ðTÞN dopant
1
1
0
1
0
f p ðTÞ f l ðTÞ f p ðTÞ f l ðTÞ f l ðTÞ þ f l ðTÞ
(1) (2)
ARTICLE IN PRESS S. Toroghi et al. / Optics & Laser Technology 41 (2009) 800–803
801
Fig. 1. Shematic optical setup for an end-pumped Yb:YAG thin disk laser.
where T is the temperature in Kelvin, Ndopant is the Yb3+ dopant concentration, fl0 and fl1 are the terminal and initial laser Stark level Boltzmann occupation factors, and fp0 and fp1 are the initial and final pump Stark level Boltzmann occupation factors, respectively. Moreover, the absorption saturation has been considered for more accurate calculation of absorption
aðTÞ ¼
a0 ðTÞ 1 þ ðIP =IPsat Þ
(3)
where IPsat is pump saturation intensity which is about 28 kW/cm2 for Yb:YAG lasers. The absorbed photons are counted in the corresponding element of mesh. 2.2. Thermal Modeling of the thin disk laser Since the absorbed power has symmetric distribution around the axial axis of the crystal, the 2D axisymmetric model is used for the temperature calculation. The Yb:YAG end-pumped geometry, the corresponding orientation of axes and thermal boundary conditions are shown in Fig. 2. The Yb:YAG crystal is fixed with a layer of indium onto a heat sink, which is a CuW disk of 1 mm thickness. The front side of the crystal is AR-coated, whereas the back side is HR-coated, for both the pump and the laser wavelengths. The CuW disk is cooled by a coolant fluid from the back side with a heat exchange coefficient of h1. The front and perimeter surface of the crystal is in an air environment with a heat exchange coefficient of h2. A 2D finite element analysis (FEA) with the ANSYS package is used for computation, the temperature distribution inside the disk [10]. We used FEA to solve the heat conduction equation
r2 T ¼
Pth kðTÞ
(4)
with the following boundary conditions:
qT h1 ðT ¼ T s1 Þ in S1 surface qn1 kðTÞ coolant qT h2 ðT T si Þ in Si surface; ¼ qni kðTÞ air
i ¼ 2; 3; 4
where k(T) is temperature-dependent thermal conductivity of Yb:YAG crystal, Pth is the heat generated inside Yb:YAG crystal, and ni is perpendicular direction to surface Si. The heat load is calculated according to the distribution of the absorbed pump power in the disk. Generally, thermal load inside the Yb:YAG crystal is result of two mechanisms. Firstly, there is 8.7% of quantum defect or Stokes shift between the energy of the pump and the laser photon. Secondly, the absorption of pump and laser radiation along with fluorescence by the HR-coated surfaces which amount to about 6% of absorbed pump power [11]. A Yb:YAG crystal with 10% Yb3+ doped concentration is considered as the active medium of laser. This crystal has been bonded on 1 mm CuW (20%–80%) surface with a 20 mm thin layer of indium. This ratio (20–80) has been selected in order to match
Fig. 2. Two-dimensional geometry, the corresponding orientation of axes and thermal boundary conditions.
with YAG mechanical characteristics. For more accurate calculation, we used the temperature-dependent thermal conductivity of Yb:YAG. The following function represents the dependence of the thermal conductivity k on the doping concentration cYb and the temperature T [3]: 204 K 0:480:46cYb kðT; cYb Þ ¼ kth ð300 K; cYb Þ (5) T 96 K kth ð300 K; cYb Þ ¼ ð7:28 7:3cYb Þ
W mK
(6)
According to Eq. (5), there is about 20% decrease in thermal conductivity of Yb:YAG with increasing temperature in the range 127 K (273–400 K). This variation in the thermal conductivity causes more realistic prediction of the thermal flow in the thin disk with large increase in the temperature. Therefore, in present work, the temperature-dependent of thermal conductivity has been employed. 2.3. Numerical iterative method The iterative method employed here, is composed of three steps. First of all, we calculate the absorption power at room temperature. In the second step, we use this absorbed power to achieve the thermal loading inside the thin disk medium. Using this thermal loading distribution, we can calculate the temperature distribution. In final step, we use the temperature distribution to calculate the temperature-dependent absorption power. We iterate the second and third steps until the difference of temperature in elements becomes less than 0.1 K. So, we can assume that the absorption distribution inside the medium becomes stable.
3. Numerical results In the previous sections, the method used to calculate the temperature-dependent absorption power and temperature distribution inside the Yb:YAG thin disk laser medium, has been elaborated. In our modeling, we have used parameters for the end-pumped Yb:YAG thin disk laser depicted in Table 1. Fig. 3a shows the temperature distributions for the constant temperature case and the iterated cases along the radial direction at the top surface of the disk. It has been confirmed that more iterations cannot lead to modifications less than 0.1 K. Hence, we stop the process after the fifth iteration and consider the obtained result as the final and stable one. Fig. 3b shows the temperature distributions for the constant temperature case and the iterated cases in axial direction at the center of the disk. It can be inferred from Fig. 3b that the temperature along the thickness is high at the center and top surface of the disk and low at the bottom surface of the disk due to its contact with the coolant fluid. As the disk laser medium absorbs power and heat from the pump source, the temperature-dependent
ARTICLE IN PRESS 802
S. Toroghi et al. / Optics & Laser Technology 41 (2009) 800–803
Table 1 Design parameters for end-pumped Yb:YAG thin disk laser. Parameter
Value
Units
Radius of disk Thickness Yb concentration Thermal exchange coefficient in bottom surface (h1) Thermal exchange coefficient in top surface (h2) Coolant Temperature (Tcoolant) Air Temperature (Tair) Parabolic and folding mirrors reflectivity Number of pass through disk Pump power Pump profile Pump radius Heat fraction
5 200 10 106 10 289 300 99.5 16 500 Top hat 2 14.6
mm mm % W/m2 K W/m2 K K K % – W – mm %
cross-section becomes smaller than its value at the constant temperature. Consequently, the temperature at the top surface of the disk in the temperature-dependent calculations becomes less than the temperature-independent one. The difference of 14 K occurs in our modeling. Fig. 4a and b shows the thermal load generated in the disk radial cross-section in the temperature-independent and the temperature-dependent simulations, respectively. There is a decrease in the absorption power and the thermal load in higher temperature regions and an increase in the absorption power and the thermal load in lower temperature regions. Moreover, the temperature-dependent absorption power and the thermal load turn out to be 18% less than the temperature-independent ones at the top center of the disk. In addition, integration over the whole volume of the thin disk crystal shows that the total absorption power decreases
Fig. 3. (a) Temperature distribution along the radial direction at top surface and (b) temperature distribution in the axial direction at the center of disk; initial distribution and results after iterations are also shown in both figures.
ARTICLE IN PRESS S. Toroghi et al. / Optics & Laser Technology 41 (2009) 800–803
803
Fig. 4. Cross-sectional view of the thermal load distribution in the disk (a) with temperature-independent absorption coefficient and (b) with the temperature-dependent absorption coefficient (steady state distribution after iterations).
about 5% in the temperature-dependent case. The total absorption power in the temperature-independent modeling is about 90% in comparison with 85% in the temperature-dependent one.
4. Conclusion Using the temperature-dependent formulae for modeling the performance of the Yb:YAG thin disk laser leads us to accurate prediction of the thermal behavior in such type of lasers. The numerical modeling showed that there is an essential difference between the temperature-independent and the temperaturedependent absorption power amount and profile. This absorption power difference causes a decrease in the heat load and so in the disk temperature. This amendment of the absorption power amount and profile causes realistic improvement in the thermal effects and consequences like thermal lensing, thermal stress, optical phase distortion (OPD), and so on. In fact, the temperature-dependent absorption results in increasing the effective heat conduction along the thin disk thickness and consequently smoothing the temperature distribution.
References [1] Giesen A, Hugel H, Voss A, Wittig K, Brauch U, Opower H. Scalable concept for diode-pumped high-power solid-state lasers. Appl Phys B 1994;58:365–72. [2] Dong J, Bass M, Mao Y, Deng P, Gan F. Dependence of the Yb3+ emission cross section and lifetime on temperature and concentration in yttrium aluminum garnet. J Opt Soc Am B 2003;20:1975–9. [3] Stewen C, Contag K, Larionov M, Giesen A, Hugel H. A 1-kW CW thin disk laser. IEEE J Select Top Quantum Electron 2000;6:650–7. [4] Bruesselbach HW, Sumida DS, Reeder RA, Byren RW. Low-heat high-power scaling using InGaAs-diodepumped Yb:YAG lasers. IEEE J Select Top Quantum Electron 1997;3:105–16. [5] Bruesselbach HW. Power scaling issues for Yb:YAG lasers. Annual Meeting of OSA, Long Beach, California, October 14–18, 2001. [6] Rutherford TS, Tulloch WM, Gustafson EK, Byer RL. Edge-pumped quasithree-level slab lasers: design and power scaling. IEEE J Quantum Electron 2000;36:205–19. [7] Chen B, Dong J, Patel M, Chen Y, Kar A, Bass M. Modeling of high power solidstate slab lasers. Proc SPIE 2003;4968:1–10. [8] Yu H, Bourdet G, Ferre S. Comprehensive modeling of the temperature-related laser performance of the amplifiers of the LUCIA laser. Appl Opt 2005;44:6412–8. [9] Liu Q, Fu X, Gong M, Huang L. Effects of the temperature dependence of absorption coefficients in edge-pumped Yb:YAG slab lasers. J Opt Soc Am B 2007;24:2081–9. [10] ANSYS Heat Flow Analysis Guide, Chapter 6. [11] Contag K, Karszewski M, Stewen C, Giesen A, Hugel H. Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser. Kvantovaya Elektronika and Turpion Ltd. Quantum Electron 1999;29:697–703.
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
The effect of temperature on absorption in end-pumped Yb:YAG thin disk lasers Seyfollah Toroghi , Ahmad Khayat Jafari, Ala Hashemi Golpayegani Laser Science & Technology National Laboratory, 14665-567 Tehran, Iran
a r t i c l e in f o
a b s t r a c t
Article history: Received 26 July 2008 Received in revised form 25 November 2008 Accepted 5 December 2008 Available online 23 January 2009
In this paper, the dependence of the absorbed power on the temperature in an end-pumped CW quasithree-level Yb:YAG thin disk laser is calculated. Here, we have used the temperature-dependent form of the Boltzmann occupation factors, absorption cross-section and thermal conductivity of the Yb:YAG crystal. A Monte Carlo ray tracing code and a 2D finite element analysis (FEA) with the ANSYS package have been used to calculate the absorbed power and the temperature distribution inside the Yb:YAG thin disk laser, respectively. According to the model, the temperature-dependent absorbed power turns out to be 18% less than the temperature-independent absorbed power in the top center of the Yb:YAG thin disk laser for used parameters. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Thin-disk laser Temperature-dependent absorption Monte Carlo ray tracing
1. Introduction With the development of high-power laser diodes, quasi-threelevel laser media such as Yb:YAG have attracted a worldwide interest. The Yb3+ ion as a lasant ion has a simple electronic structure and contains only two energy-level manifolds, the ground 2F7/2 state and an excited 2F5/2 state, which are separated by approximately 10,000 cm1. So, detrimental effects such as concentration quenching, excited-state absorption, and upconversion are absent from this lasant [1,2]. Because of the high concentration of the Yb3+ ions in the YAG crystal, the laser active medium can be a thin disk and thus the ratio of cooling surface to the pumped volume is increased compared to rod and slab lasers, which is an important key to the extraction of high output power from a small volume [3]. With the emergence of powerful InGaAs laser diodes that emit at 941 nm, the picture has changed. Several research groups such as Brusselbach et al. [4,5], Rutherford et al. [6], and Chen et al. [7] employed the Yb:YAG gain medium in high-power slab lasers. In addition, Yu et al. [8] used Yb:YAG gain medium in the pulsed highpower disk lasers. In all research mentioned above, the temperatureindependent absorption coefficient of the Yb:YAG has been used for calculation of the absorption power through the laser medium. However, it is clear that the absorption coefficient is strongly influenced by the ambient temperature under real experimental conditions. This temperature-dependency of the absorption coefficient leads to a modification in performance of the laser. Recently, the dependence of the absorption coefficient of the Yb:YAG on the temperature has been investigated by Liu et al. [9].
In this paper, we focus on the modeling in which the absorption power in the end-pumped Yb:YAG thin disk laser is temperature-dependent. We have used a combination of the Monte Carlo ray tracing and the finite element method with an iterative method to fulfill our goal. 2. Numerical method 2.1. Monte Carlo ray tracing The optical setup used for end-pumped Yb:YAG thin disk laser is shown schematically in Fig. 1. The Monte Carlo ray tracing code developed by our group is used to predict the absorbed pump beam in the crystal. The paths of a large number of photons through the optical system are traced. The orientation of photons and the absorption of them in the optical system are being considered as a statistical process. The wavelength of pumped photons is equal to 941 nm. The path of every photon is traced through the optical system until it is lost at one of the optical component, is absorbed inside the crystal, or has exited the system after the designated number of passes through the crystal. The transmission of the crystal along the photon path is calculated taking into account the temperature-dependent form of Boltzmann occupation factors and absorption cross-section. The temperature-dependency of absorption cross-section and absorption coefficient in pump wavelength is given by the following formulae [9]:
sabs ðTÞ ¼ ½2:07 þ 6:37 expððT 273Þ=288Þ1021 cm2 0
Corresponding author.
E-mail address: [email protected] (S. Toroghi). 0030-3992/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2008.12.004
a0 ðTÞ ¼ sabs ðTÞN dopant
1
1
0
1
0
f p ðTÞ f l ðTÞ f p ðTÞ f l ðTÞ f l ðTÞ þ f l ðTÞ
(1) (2)
ARTICLE IN PRESS S. Toroghi et al. / Optics & Laser Technology 41 (2009) 800–803
801
Fig. 1. Shematic optical setup for an end-pumped Yb:YAG thin disk laser.
where T is the temperature in Kelvin, Ndopant is the Yb3+ dopant concentration, fl0 and fl1 are the terminal and initial laser Stark level Boltzmann occupation factors, and fp0 and fp1 are the initial and final pump Stark level Boltzmann occupation factors, respectively. Moreover, the absorption saturation has been considered for more accurate calculation of absorption
aðTÞ ¼
a0 ðTÞ 1 þ ðIP =IPsat Þ
(3)
where IPsat is pump saturation intensity which is about 28 kW/cm2 for Yb:YAG lasers. The absorbed photons are counted in the corresponding element of mesh. 2.2. Thermal Modeling of the thin disk laser Since the absorbed power has symmetric distribution around the axial axis of the crystal, the 2D axisymmetric model is used for the temperature calculation. The Yb:YAG end-pumped geometry, the corresponding orientation of axes and thermal boundary conditions are shown in Fig. 2. The Yb:YAG crystal is fixed with a layer of indium onto a heat sink, which is a CuW disk of 1 mm thickness. The front side of the crystal is AR-coated, whereas the back side is HR-coated, for both the pump and the laser wavelengths. The CuW disk is cooled by a coolant fluid from the back side with a heat exchange coefficient of h1. The front and perimeter surface of the crystal is in an air environment with a heat exchange coefficient of h2. A 2D finite element analysis (FEA) with the ANSYS package is used for computation, the temperature distribution inside the disk [10]. We used FEA to solve the heat conduction equation
r2 T ¼
Pth kðTÞ
(4)
with the following boundary conditions:
qT h1 ðT ¼ T s1 Þ in S1 surface qn1 kðTÞ coolant qT h2 ðT T si Þ in Si surface; ¼ qni kðTÞ air
i ¼ 2; 3; 4
where k(T) is temperature-dependent thermal conductivity of Yb:YAG crystal, Pth is the heat generated inside Yb:YAG crystal, and ni is perpendicular direction to surface Si. The heat load is calculated according to the distribution of the absorbed pump power in the disk. Generally, thermal load inside the Yb:YAG crystal is result of two mechanisms. Firstly, there is 8.7% of quantum defect or Stokes shift between the energy of the pump and the laser photon. Secondly, the absorption of pump and laser radiation along with fluorescence by the HR-coated surfaces which amount to about 6% of absorbed pump power [11]. A Yb:YAG crystal with 10% Yb3+ doped concentration is considered as the active medium of laser. This crystal has been bonded on 1 mm CuW (20%–80%) surface with a 20 mm thin layer of indium. This ratio (20–80) has been selected in order to match
Fig. 2. Two-dimensional geometry, the corresponding orientation of axes and thermal boundary conditions.
with YAG mechanical characteristics. For more accurate calculation, we used the temperature-dependent thermal conductivity of Yb:YAG. The following function represents the dependence of the thermal conductivity k on the doping concentration cYb and the temperature T [3]: 204 K 0:480:46cYb kðT; cYb Þ ¼ kth ð300 K; cYb Þ (5) T 96 K kth ð300 K; cYb Þ ¼ ð7:28 7:3cYb Þ
W mK
(6)
According to Eq. (5), there is about 20% decrease in thermal conductivity of Yb:YAG with increasing temperature in the range 127 K (273–400 K). This variation in the thermal conductivity causes more realistic prediction of the thermal flow in the thin disk with large increase in the temperature. Therefore, in present work, the temperature-dependent of thermal conductivity has been employed. 2.3. Numerical iterative method The iterative method employed here, is composed of three steps. First of all, we calculate the absorption power at room temperature. In the second step, we use this absorbed power to achieve the thermal loading inside the thin disk medium. Using this thermal loading distribution, we can calculate the temperature distribution. In final step, we use the temperature distribution to calculate the temperature-dependent absorption power. We iterate the second and third steps until the difference of temperature in elements becomes less than 0.1 K. So, we can assume that the absorption distribution inside the medium becomes stable.
3. Numerical results In the previous sections, the method used to calculate the temperature-dependent absorption power and temperature distribution inside the Yb:YAG thin disk laser medium, has been elaborated. In our modeling, we have used parameters for the end-pumped Yb:YAG thin disk laser depicted in Table 1. Fig. 3a shows the temperature distributions for the constant temperature case and the iterated cases along the radial direction at the top surface of the disk. It has been confirmed that more iterations cannot lead to modifications less than 0.1 K. Hence, we stop the process after the fifth iteration and consider the obtained result as the final and stable one. Fig. 3b shows the temperature distributions for the constant temperature case and the iterated cases in axial direction at the center of the disk. It can be inferred from Fig. 3b that the temperature along the thickness is high at the center and top surface of the disk and low at the bottom surface of the disk due to its contact with the coolant fluid. As the disk laser medium absorbs power and heat from the pump source, the temperature-dependent
ARTICLE IN PRESS 802
S. Toroghi et al. / Optics & Laser Technology 41 (2009) 800–803
Table 1 Design parameters for end-pumped Yb:YAG thin disk laser. Parameter
Value
Units
Radius of disk Thickness Yb concentration Thermal exchange coefficient in bottom surface (h1) Thermal exchange coefficient in top surface (h2) Coolant Temperature (Tcoolant) Air Temperature (Tair) Parabolic and folding mirrors reflectivity Number of pass through disk Pump power Pump profile Pump radius Heat fraction
5 200 10 106 10 289 300 99.5 16 500 Top hat 2 14.6
mm mm % W/m2 K W/m2 K K K % – W – mm %
cross-section becomes smaller than its value at the constant temperature. Consequently, the temperature at the top surface of the disk in the temperature-dependent calculations becomes less than the temperature-independent one. The difference of 14 K occurs in our modeling. Fig. 4a and b shows the thermal load generated in the disk radial cross-section in the temperature-independent and the temperature-dependent simulations, respectively. There is a decrease in the absorption power and the thermal load in higher temperature regions and an increase in the absorption power and the thermal load in lower temperature regions. Moreover, the temperature-dependent absorption power and the thermal load turn out to be 18% less than the temperature-independent ones at the top center of the disk. In addition, integration over the whole volume of the thin disk crystal shows that the total absorption power decreases
Fig. 3. (a) Temperature distribution along the radial direction at top surface and (b) temperature distribution in the axial direction at the center of disk; initial distribution and results after iterations are also shown in both figures.
ARTICLE IN PRESS S. Toroghi et al. / Optics & Laser Technology 41 (2009) 800–803
803
Fig. 4. Cross-sectional view of the thermal load distribution in the disk (a) with temperature-independent absorption coefficient and (b) with the temperature-dependent absorption coefficient (steady state distribution after iterations).
about 5% in the temperature-dependent case. The total absorption power in the temperature-independent modeling is about 90% in comparison with 85% in the temperature-dependent one.
4. Conclusion Using the temperature-dependent formulae for modeling the performance of the Yb:YAG thin disk laser leads us to accurate prediction of the thermal behavior in such type of lasers. The numerical modeling showed that there is an essential difference between the temperature-independent and the temperaturedependent absorption power amount and profile. This absorption power difference causes a decrease in the heat load and so in the disk temperature. This amendment of the absorption power amount and profile causes realistic improvement in the thermal effects and consequences like thermal lensing, thermal stress, optical phase distortion (OPD), and so on. In fact, the temperature-dependent absorption results in increasing the effective heat conduction along the thin disk thickness and consequently smoothing the temperature distribution.
References [1] Giesen A, Hugel H, Voss A, Wittig K, Brauch U, Opower H. Scalable concept for diode-pumped high-power solid-state lasers. Appl Phys B 1994;58:365–72. [2] Dong J, Bass M, Mao Y, Deng P, Gan F. Dependence of the Yb3+ emission cross section and lifetime on temperature and concentration in yttrium aluminum garnet. J Opt Soc Am B 2003;20:1975–9. [3] Stewen C, Contag K, Larionov M, Giesen A, Hugel H. A 1-kW CW thin disk laser. IEEE J Select Top Quantum Electron 2000;6:650–7. [4] Bruesselbach HW, Sumida DS, Reeder RA, Byren RW. Low-heat high-power scaling using InGaAs-diodepumped Yb:YAG lasers. IEEE J Select Top Quantum Electron 1997;3:105–16. [5] Bruesselbach HW. Power scaling issues for Yb:YAG lasers. Annual Meeting of OSA, Long Beach, California, October 14–18, 2001. [6] Rutherford TS, Tulloch WM, Gustafson EK, Byer RL. Edge-pumped quasithree-level slab lasers: design and power scaling. IEEE J Quantum Electron 2000;36:205–19. [7] Chen B, Dong J, Patel M, Chen Y, Kar A, Bass M. Modeling of high power solidstate slab lasers. Proc SPIE 2003;4968:1–10. [8] Yu H, Bourdet G, Ferre S. Comprehensive modeling of the temperature-related laser performance of the amplifiers of the LUCIA laser. Appl Opt 2005;44:6412–8. [9] Liu Q, Fu X, Gong M, Huang L. Effects of the temperature dependence of absorption coefficients in edge-pumped Yb:YAG slab lasers. J Opt Soc Am B 2007;24:2081–9. [10] ANSYS Heat Flow Analysis Guide, Chapter 6. [11] Contag K, Karszewski M, Stewen C, Giesen A, Hugel H. Theoretical modeling and experimental investigations of the diode-pumped thin-disk Yb:YAG laser. Kvantovaya Elektronika and Turpion Ltd. Quantum Electron 1999;29:697–703.