Abstract

A comparison of composite Nd:YAG laser rod crystals with one, two and three doped segments for high-power diode end-pumping is presented. An approach based on an expansion of the heat generation density and temperature distributions into a Fourier-Bessel basis set for solving the stationary heat conduction equation is used for choosing adequate segment lengths and dopant concentrations. A maximum laser output power of 167.5 W at an optical-to-optical efficiency of 53.6 % was achieved by longitudinal pumping a crystal with three doped segments with fibre-coupled laser diodes.

©2009 Optical Society of America

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References

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  1. S. C. Tidwell, J. F. Seamans, M. S. Bowers, and A. K. Cousins, “Scaling CW Diode-End-Pumped Nd:YAG Lasers to High Average Powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
    [Crossref]
  2. W. Koechner, Solid-State Laser Engineering (Springer, New York, 1996).
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    [Crossref] [PubMed]
  4. D. Kracht, R. Wilhelm, M. Frede, K. Dupré, and L. Ackermann, “407 W End-Pumped Multi-Segmented Nd:YAG Laser,” Opt. Express 13, 10140–10144 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-25-10140.
    [Crossref] [PubMed]
  5. M. Frede, R. Wilhelm, and D. Kracht, “250 W end-pumped Nd:YAG laser with direct pumping into the upper laser level,” Opt. Lett. 31, 3618–3619 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-24-3618.
    [Crossref] [PubMed]
  6. D. Kracht, M. Frede, R. Wilhelm, and C. Fallnich, “Comparison of crystalline and ceramic composite Nd:YAG for high power diode end-pumping,” Opt. Express 13, 6212–6216 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-16-6212.
    [Crossref] [PubMed]
  7. R. Wilhelm, M. Frede, and D. Kracht, “Power Scaling of End-Pumped Solid-State Rod Lasers by Longitudinal Dopant Concentration Gradients,” IEEE J. Quantum Electron. 44, 232–244 (2008).
    [Crossref]
  8. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Oxford University Press, New York, 1959).
  9. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (Dover, New York, 1964).
  10. R. Wilhelm, M. Frede, D. Freiburg, D. Kracht, and C. Fallnich, “Thermal Design of Segmented Rod Laser Crystals,” in Advanced Solid-State Photonics 2005 Technical Digest on CD-ROM (The Optical Society of America, Washington, DC, 2005), MB46.
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  16. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1970).
  17. R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
    [Crossref]
  18. M. Tsunekane, N. Taguchi, T. Kasamatsu, and H. Inaba, “Analytical and Experimental Studies on the Characteristics of Composite Solid-State Laser Rods in Diode-End-Pumped Geometry,” IEEE J. Sel. Top. Quantum Electron. 3, 9–18 (1998).
  19. K. Contag, Modellierung und numerische Auslegung des Yb:YAG-Scheibenlasers (Munich, Herbert Utz Verlag, 2002).

2008 (2)

R. Wilhelm, D. Freiburg, M. Frede, and D. Kracht, “End-pumped Nd:YAG laser with a longitudinal hyperbolic dopant concentration profile,” Opt. Express 16, 20106–20116 (2008) http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-24-20106
[Crossref] [PubMed]

R. Wilhelm, M. Frede, and D. Kracht, “Power Scaling of End-Pumped Solid-State Rod Lasers by Longitudinal Dopant Concentration Gradients,” IEEE J. Quantum Electron. 44, 232–244 (2008).
[Crossref]

2006 (1)

2005 (2)

2004 (1)

1998 (3)

L. Yu, M. Huang, M. Chen, W. Chen, W. Huang, and Z. Zhu, “Quasi-Discrete Hankel Transform,” Opt. Lett. 23, 409–411 (1998).
[Crossref]

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[Crossref]

M. Tsunekane, N. Taguchi, T. Kasamatsu, and H. Inaba, “Analytical and Experimental Studies on the Characteristics of Composite Solid-State Laser Rods in Diode-End-Pumped Geometry,” IEEE J. Sel. Top. Quantum Electron. 3, 9–18 (1998).

1992 (1)

S. C. Tidwell, J. F. Seamans, M. S. Bowers, and A. K. Cousins, “Scaling CW Diode-End-Pumped Nd:YAG Lasers to High Average Powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[Crossref]

1981 (1)

1977 (1)

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (Dover, New York, 1964).

Ackermann, L.

Agrawal, G. P.

Bowers, M. S.

S. C. Tidwell, J. F. Seamans, M. S. Bowers, and A. K. Cousins, “Scaling CW Diode-End-Pumped Nd:YAG Lasers to High Average Powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[Crossref]

Carslaw, H. S.

H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Oxford University Press, New York, 1959).

Chen, M.

Chen, W.

Contag, K.

K. Contag, Modellierung und numerische Auslegung des Yb:YAG-Scheibenlasers (Munich, Herbert Utz Verlag, 2002).

Cousins, A. K.

S. C. Tidwell, J. F. Seamans, M. S. Bowers, and A. K. Cousins, “Scaling CW Diode-End-Pumped Nd:YAG Lasers to High Average Powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[Crossref]

Donald, M. Mac

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[Crossref]

Dupré, K.

Fallnich, C.

D. Kracht, M. Frede, R. Wilhelm, and C. Fallnich, “Comparison of crystalline and ceramic composite Nd:YAG for high power diode end-pumping,” Opt. Express 13, 6212–6216 (2005) http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-16-6212.
[Crossref] [PubMed]

R. Wilhelm, M. Frede, D. Freiburg, D. Kracht, and C. Fallnich, “Thermal Design of Segmented Rod Laser Crystals,” in Advanced Solid-State Photonics 2005 Technical Digest on CD-ROM (The Optical Society of America, Washington, DC, 2005), MB46.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in PASCAL (Cambridge, New York, 1989).

Frede, M.

Freiburg, D.

R. Wilhelm, D. Freiburg, M. Frede, and D. Kracht, “End-pumped Nd:YAG laser with a longitudinal hyperbolic dopant concentration profile,” Opt. Express 16, 20106–20116 (2008) http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-24-20106
[Crossref] [PubMed]

R. Wilhelm, M. Frede, D. Freiburg, D. Kracht, and C. Fallnich, “Thermal Design of Segmented Rod Laser Crystals,” in Advanced Solid-State Photonics 2005 Technical Digest on CD-ROM (The Optical Society of America, Washington, DC, 2005), MB46.

Goodier, J. N.

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1970).

Guizar-Sicairos, M.

Gutiérrez-Vega, J. C.

Huang, M.

Huang, W.

Inaba, H.

M. Tsunekane, N. Taguchi, T. Kasamatsu, and H. Inaba, “Analytical and Experimental Studies on the Characteristics of Composite Solid-State Laser Rods in Diode-End-Pumped Geometry,” IEEE J. Sel. Top. Quantum Electron. 3, 9–18 (1998).

Jaeger, J. C.

H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Oxford University Press, New York, 1959).

Kasamatsu, T.

M. Tsunekane, N. Taguchi, T. Kasamatsu, and H. Inaba, “Analytical and Experimental Studies on the Characteristics of Composite Solid-State Laser Rods in Diode-End-Pumped Geometry,” IEEE J. Sel. Top. Quantum Electron. 3, 9–18 (1998).

Koechner, W.

W. Koechner, Solid-State Laser Engineering (Springer, New York, 1996).

Kracht, D.

Lax, M.

Neuenschwander, B.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[Crossref]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in PASCAL (Cambridge, New York, 1989).

Roos, M. B.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[Crossref]

Seamans, J. F.

S. C. Tidwell, J. F. Seamans, M. S. Bowers, and A. K. Cousins, “Scaling CW Diode-End-Pumped Nd:YAG Lasers to High Average Powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[Crossref]

Siegman, A. E.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (Dover, New York, 1964).

Taguchi, N.

M. Tsunekane, N. Taguchi, T. Kasamatsu, and H. Inaba, “Analytical and Experimental Studies on the Characteristics of Composite Solid-State Laser Rods in Diode-End-Pumped Geometry,” IEEE J. Sel. Top. Quantum Electron. 3, 9–18 (1998).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in PASCAL (Cambridge, New York, 1989).

Tidwell, S. C.

S. C. Tidwell, J. F. Seamans, M. S. Bowers, and A. K. Cousins, “Scaling CW Diode-End-Pumped Nd:YAG Lasers to High Average Powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[Crossref]

Timoshenko, S. P.

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1970).

Tsunekane, M.

M. Tsunekane, N. Taguchi, T. Kasamatsu, and H. Inaba, “Analytical and Experimental Studies on the Characteristics of Composite Solid-State Laser Rods in Diode-End-Pumped Geometry,” IEEE J. Sel. Top. Quantum Electron. 3, 9–18 (1998).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in PASCAL (Cambridge, New York, 1989).

Weber, P.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[Crossref]

Weber, R.

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[Crossref]

Wilhelm, R.

Yu, L.

Zhu, Z.

IEEE J. Quantum Electron. (3)

S. C. Tidwell, J. F. Seamans, M. S. Bowers, and A. K. Cousins, “Scaling CW Diode-End-Pumped Nd:YAG Lasers to High Average Powers,” IEEE J. Quantum Electron. 28, 997–1009 (1992).
[Crossref]

R. Wilhelm, M. Frede, and D. Kracht, “Power Scaling of End-Pumped Solid-State Rod Lasers by Longitudinal Dopant Concentration Gradients,” IEEE J. Quantum Electron. 44, 232–244 (2008).
[Crossref]

R. Weber, B. Neuenschwander, M. Mac Donald, M. B. Roos, and P. Weber, “Cooling Schemes for Longitudinally Diode Laser-Pumped Nd:YAG Rods,” IEEE J. Quantum Electron. 34, 1046–1053 (1998).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Tsunekane, N. Taguchi, T. Kasamatsu, and H. Inaba, “Analytical and Experimental Studies on the Characteristics of Composite Solid-State Laser Rods in Diode-End-Pumped Geometry,” IEEE J. Sel. Top. Quantum Electron. 3, 9–18 (1998).

J. Opt. Soc. Am. A (1)

Opt. Express (3)

Opt. Lett. (4)

Other (7)

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in PASCAL (Cambridge, New York, 1989).

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1970).

K. Contag, Modellierung und numerische Auslegung des Yb:YAG-Scheibenlasers (Munich, Herbert Utz Verlag, 2002).

W. Koechner, Solid-State Laser Engineering (Springer, New York, 1996).

H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Oxford University Press, New York, 1959).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (Dover, New York, 1964).

R. Wilhelm, M. Frede, D. Freiburg, D. Kracht, and C. Fallnich, “Thermal Design of Segmented Rod Laser Crystals,” in Advanced Solid-State Photonics 2005 Technical Digest on CD-ROM (The Optical Society of America, Washington, DC, 2005), MB46.

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Figures (4)

Fig. 1.
Fig. 1. a) Difference in temperature distributions obtained from a finite element model and the described FOURIER–BESSEL approach. b) Comparison of the stress distributions obtained from the plain–strain approximation (dashed lines) and a finite element model (solid lines).
Fig. 2.
Fig. 2. Comparison of the three simulated rod designs at 300 W of pump power. A rod with single doped segment at 0.2 at. % Nd as been added for comparison. a) on-axis temperature and b) VON-MISES equivalent stress on barrel surface.
Fig. 3.
Fig. 3. Schematic setup of the short end-pumped multi-mode laser resonator. For details see text.
Fig. 4.
Fig. 4. Multi-mode laser output power versus absorbed pump power for the crystals with 1, 2 and 3 doped segments.

Tables (2)

Tables Icon

Table 1. Segment lengths and dopant concentrations of the different laser rod designs.

Tables Icon

Table 2. Laser performance for the studied three rod crystals.

Equations (13)

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Pmax=8πRLηh.
(2r2+1rr+2z2)T(r,z)=1k(T) {q(r,z)+kT[(Tr)2+(Tz)2]}Q̃(r,z)
q(r,z)=2Ppumpηhπw2(1exp(2R2/w2))αeff(z)×exp(0zαeff(z)dz)exp(2r2w2),
T(r,z)zz=0=T(r,z)zz=L=0andTrr=R+hk(T)(TTk)=0.
T(r,z)=T0(r)2+n=1Tn(r)cos(nπzL)andQ̃(r,z)=Q̃0(r)2+n=1Q̃n(r)cos(nπzL)
(2r2+1rr)T0(r)=Q̃0(r)and(2r2+1rrπ2n2L2)Tn(r)=Q̃n(r).
dTndrr=0=0anddTndrr=R+hnk(T)Tn=0.
Tn(r)=m=1Tn,mJ0(αm,nr)andQ̃n(r)=m=1Q̃n,mJ0(αm,nr)
withαm,nbeingarootofαm,n[ddrJ0(r)]r=R+hnkJ0(αm,nR)=0.
Tn,m=Q̃n,mαm,n2+π2n2L2.
σr(r,z)=αTE1ν (1R20RΔT(r,z)rdr1r20rΔT(r,z)rdr ) ,
σt(r,z)=αTE1ν (1R20RΔT(r,z)rdr+1r20rΔT(r,z)rdrΔT(r,z) ) ,
σz(r,z)=αTE1ν (2R20RΔT(r,z)rdrΔT(r,z)) .

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