Abstract

The application of the recently developed core doped ceramic Nd:YAG rods has the potential to provide better beam qualities compared to conventional rods since the hard aperture of the rod’s boundary can be made wider while the width of the gain region remains the same. Thus, beam truncation and consequential diffraction can be reduced. We apply a finite elements model to calculate the resulting refractive index profiles in conventional and core doped rods. Propagating a Gaussian beam through both rod geometries the impact of aberrations and diffraction is compared for different side pumped scenarios. The potential advantage of the core doped geometry is discussed.

© 2005 Optical Society of America

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References

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  1. Baikowski Chimie, BP501, F-74339 La Balme de Sillingy cedex, France
  2. L. Jianren, M. Prabhu, X. Jianqiu, K. Ueda, H. Yagi, T. Yanagitani and A. A. Kaminski, "High efficient 2% Nd:yttrium aluminum garnet ceramic laser," Appl. Phys. Lett. 78, 3707-3709 (2000)
  3. J. Lu, M. Prabhu, K, Ueda, H. Yagi, T. Yanagitani, A. Kudryashov and A. A. Kaminski, "Potential of Ceramic YAG Lasers," Laser Phys. 78, 1053-1057 (2001)
  4. D. Kracht, M. Frede, D. Freiburg, R. Wilhelm and C. Fallnich, "Diode End-Pumped Core-Doped Ceramic Nd:YAG Laser," ASSP 2005
  5. Femlab 3.1, Comsol, 1994-2004
  6. Q. Lu, N. Kugler, H. Weber, S. Dong, N. Muller and U. Wittrock, "A novel approach for compensation of birefringence in cylindrical Nd:YAG rods," Opt. Quantum Electron. 28, 57-69 (1996)
    [CrossRef]
  7. M. Ostermeyer, G. Klemz, P. Kubina and R. Menzel, "Quasi-continuous-wave birefringence-compensated single-and double-rod Nd:YAG lasers," Appl. Opt. 41, 7573 - 7582 (2002)
    [CrossRef]
  8. D.C. Brown, "Nonlinear Thermal Distortion in YAG Rod Amplifiers," IEEE J. Quantum Electron. 34, 2383-2392 (1998)
    [CrossRef]
  9. W. Koechner, "Solid-State Laser Engineering" (Springer, 1999), Chapter 2.3
  10. R.Wilhelm, "Numerical Modeling of Solid State Lasers," Talk at Laser working group session, 15 Aug 2001, <a href= "http://www.ligo.caltech.edu/docs/G/G010362-00.pdf">http://www.ligo.caltech.edu/docs/G/G010362-00.pdf</a>
  11. W. Koechner, Solid-State Laser Engineering (Springer, 1999), Chapter 7.1
  12. J. Marcou et. al., Opt. Fiber Technol. 5, 105-118 (1999)
    [CrossRef]
  13. N. Hodgson, H. Weber, Optical Resonators, (Springer 1997), Chapter 2.6
  14. G. Cousin, Baikowski Chimie, BP501, F-74339 La Balme de Sillingy cedex, France, (private communication, 2005)

Appl. Opt.

Appl. Phys. Lett.

L. Jianren, M. Prabhu, X. Jianqiu, K. Ueda, H. Yagi, T. Yanagitani and A. A. Kaminski, "High efficient 2% Nd:yttrium aluminum garnet ceramic laser," Appl. Phys. Lett. 78, 3707-3709 (2000)

IEEE J. Quantum Electron.

D.C. Brown, "Nonlinear Thermal Distortion in YAG Rod Amplifiers," IEEE J. Quantum Electron. 34, 2383-2392 (1998)
[CrossRef]

Laser Phys.

J. Lu, M. Prabhu, K, Ueda, H. Yagi, T. Yanagitani, A. Kudryashov and A. A. Kaminski, "Potential of Ceramic YAG Lasers," Laser Phys. 78, 1053-1057 (2001)

Opt. Quantum Electron.

Q. Lu, N. Kugler, H. Weber, S. Dong, N. Muller and U. Wittrock, "A novel approach for compensation of birefringence in cylindrical Nd:YAG rods," Opt. Quantum Electron. 28, 57-69 (1996)
[CrossRef]

Talk at Laser working group session, 15

R.Wilhelm, "Numerical Modeling of Solid State Lasers," Talk at Laser working group session, 15 Aug 2001, <a href= "http://www.ligo.caltech.edu/docs/G/G010362-00.pdf">http://www.ligo.caltech.edu/docs/G/G010362-00.pdf</a>

Other

W. Koechner, Solid-State Laser Engineering (Springer, 1999), Chapter 7.1

J. Marcou et. al., Opt. Fiber Technol. 5, 105-118 (1999)
[CrossRef]

N. Hodgson, H. Weber, Optical Resonators, (Springer 1997), Chapter 2.6

G. Cousin, Baikowski Chimie, BP501, F-74339 La Balme de Sillingy cedex, France, (private communication, 2005)

Baikowski Chimie, BP501, F-74339 La Balme de Sillingy cedex, France

W. Koechner, "Solid-State Laser Engineering" (Springer, 1999), Chapter 2.3

D. Kracht, M. Frede, D. Freiburg, R. Wilhelm and C. Fallnich, "Diode End-Pumped Core-Doped Ceramic Nd:YAG Laser," ASSP 2005

Femlab 3.1, Comsol, 1994-2004

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Figures (7)

Fig. 1.
Fig. 1.

Principal sketch for FEA-model.

Fig. 2.
Fig. 2.

Pump profiles for an absorbed pump power of 378W

Fig. 3.
Fig. 3.

Refractive index profiles for 378 W of absorbed pump power for Nd:YAG-rod with radius rrod = 4.5 mm.

Fig. 4.
Fig. 4.

Caustics of a 6 mm diameter Gaussian input beam behind the 9 mm diameter laser rod pumped with 378 W of absorbed pump power arising for the 4 different cases.

Fig. 5.
Fig. 5.

Profiles from the caustics in Fig. 4 at different distances z. Rows 1-4 present the corresponding cases 1-4.

Fig. 6.
Fig. 6.

Refractive index profiles for the core doped Nd:YAG-rod with a radius of rrod = 2.5 mm, a doped core with rdoped = 1.5 mm, and a length of 12 cm for 378 W of absorbed pump power.

Fig. 7.
Fig. 7.

Refractive index profiles for the core doped Nd:YAG-rod with a radius of r = 2.5 mm, a doped core with rdoped = 2 mm, and a length of 12 cm for 378 W of absorbed pump power.

Tables (9)

Tables Icon

Table 1. Nd:YAG-Parameters used in FEA-Modeling

Tables Icon

Table 2. Coefficients from equation 1, resulting focal length f, and temperature at the rod’s boundary and center for Nd:YAG rod with radius of rrod = 4.5 mm and length Lrod = 12 cm corresponding to the refractive index profiles shown in Fig. 3 for 378 W of absorbed pump power.

Tables Icon

Table 3. Coefficients from equation 1, resulting focal length f, and temperature at the rod’s boundary and center for Nd:YAG rod with radius of rrod = 2.5 mm and length Lrod = 12 cm compared to extrapolated values for a rod with 4.5 mm radius for 378 W of absorbed pump power (compare to Table 2).

Tables Icon

Table 4. Results for Nd:YAG-rod with a radius of rrod = 2.5 mm and a length of 12 cm. The coefficients for the refractive index profiles, the focal length f and the temperatures at the rod’s boundary and center are given at three different cooling water temperatures for 378 W of absorbed pump power.

Tables Icon

Table 5. Coefficients of the refractive index profiles of the core doped rod with rdoped = 1.5 mm core radius, rrod = 2.5 mm outer radius, and a length of 12 cm as depicted in Fig. 6 for 378 W of absorbed pump power.

Tables Icon

Table 6. Coefficients of the refractive index profiles of a 12 cm long crystalline Nd:YAG rod with a radius of rrod = 1.5 mm, for 378 W of absorbed pump power.

Tables Icon

Table 7. Coefficients of the refractive index profiles of the core doped rod with rdoped = 2 mm core radius rrod = 2.5 mm outer radius, and a length of 12 cm as depicted in Fig. 7 for 378 W of absorbed pump power.

Tables Icon

Table 8. Coefficients of the refractive index profiles of a 12 cm long crystalline Nd:YAG rod with a radius of rrod = 2 mm, for 378 W of absorbed pump power.

Tables Icon

Table 9. Calculated beam qualities for a collimated Gaussian beam with different beam radii passing through the core doped Nd:YAG-rods with 1.5 mm and 2 mm core radius and 2.5 mm outer radius in comparison to a crystalline rod with 2.5 mm radius. All examples are calculated for the pump distribution case 1. M 2 C4 denotes the beam propagation factor for a propagation with 4th-order aberrations, M 2 is the beam quality for propagation without 4th-order aberration term C4 in the refractive index profiles shown in Fig. 6 and Fig. 7.

Equations (4)

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n ( r ) = n 0 + C 2 * r 2 + C 4 * r 4
n ( r ) = n 0 ( 1 r 2 2 n 0 f L rod )
Φ ( r ) = n ( r ) L rod λ
E i ( r 2 ) = i e ik L i 2 πF 0 r rod E in ( r ) e F i ( L i ) ( r 1 2 + r 2 2 ) e i Φ ( r 1 ) J 0 [ 2 π F i ( L i ) r 1 r 2 ] d r 1

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