Abstract

Waste heat generation is a generic problem in high-power solid-state laser systems. One way to reduce heat loading while improving efficiency is to reduce the laser’s quantum defect. This paper presents a simple analysis of low quantum defect laser materials. In these laser materials, the effects of fluorescent cooling and weak loss processes should not be ignored. Simple expressions are developed for efficiency and heating in a steady-state purely radiative material. These expressions are then extended to include weak losses and fluorescence reabsorption. Evaluation of these relations using ytterbium-doped YAG is used to illustrate several optimization schemes and the impact of realistic losses.

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  8. S. Biswal, S. P. O’Connor, and S. R. Bowman, “Non-radiative losses in Yb:KGd(WO4)2 and Yb:Y3Al5O12,” Appl. Phys. Lett. 89, 0919111 (2006).
    [Crossref]
  9. S. R. Bowman, “Lasers without internal heat generation,” IEEE J. Quantum Electron. 35, 115–122 (1999).
    [Crossref]
  10. S. R. Bowman, N. W. Jenkins, S. O’Connor, and B. J. Feldman, “Sensitivity and stability of a radiation balanced laser system,” IEEE J. Quantum Electron. 38, 1339–1348 (2002).
    [Crossref]
  11. J. Wright, “Up-conversion and excited state energy transfer in rare-earth doped materials,” in Radiationless Processes in Molecules and Condensed Phases, F. K. Fong, ed., Vol. 15 of Topics in Applied Physics (Springer, 1976), Chap. 4, pp. 239–295.
  12. S. R. Bowman and C. Mungan, “New materials for optical cooling,” Appl. Phys. B 71, 807–811 (2000).
    [Crossref]
  13. M. P. Hehlen, R. I. Epstein, and H. Inoue, “Model of laser cooling in the Yb3+-doped fluorozirconate glass ZBLAN,” Phys. Rev. B 75, 144302 (2007).
  14. S. R. Bowman, S. O’Connor, and S. Biswal, “Ytterbium laser with reduced thermal heating,” IEEE J. Quantum Electron. 41, 1510–1517 (2005).
    [Crossref]
  15. S. Matsubara, T. Ueda, S. Kawato, and T. Kobayashi, “Highly efficient continuous-wave laser oscillation in microchip Yb:YAG laser at room temperature,” Jpn. J. Appl. Phys. 46, 132–134 (2007).
  16. S. Bowman, S. O’Connor, S. Biswal, and N. Condon, “Demonstration and analysis of a high power radiation balanced laser,” in Proceedings of 2011 Conference on Lasers and Electro-Optics (2011), paper CMH4.

2014 (1)

S. R. Bowman, J. Ganem, and C. G. Brown, “Optical cooling in multi-level systems,” Proc. SPIE 9000, 90000G (2014).

2012 (1)

2011 (2)

2010 (1)

S. R. Bowman, S. P. O’Connor, S. Biswal, N. J. Condon, and A. Rosenberg, “Minimizing heat generation in solid-state lasers,” IEEE J. Quantum Electron. 46, 1076–1085 (2010).
[Crossref]

2007 (2)

M. P. Hehlen, R. I. Epstein, and H. Inoue, “Model of laser cooling in the Yb3+-doped fluorozirconate glass ZBLAN,” Phys. Rev. B 75, 144302 (2007).

S. Matsubara, T. Ueda, S. Kawato, and T. Kobayashi, “Highly efficient continuous-wave laser oscillation in microchip Yb:YAG laser at room temperature,” Jpn. J. Appl. Phys. 46, 132–134 (2007).

2006 (1)

S. Biswal, S. P. O’Connor, and S. R. Bowman, “Non-radiative losses in Yb:KGd(WO4)2 and Yb:Y3Al5O12,” Appl. Phys. Lett. 89, 0919111 (2006).
[Crossref]

2005 (1)

S. R. Bowman, S. O’Connor, and S. Biswal, “Ytterbium laser with reduced thermal heating,” IEEE J. Quantum Electron. 41, 1510–1517 (2005).
[Crossref]

2002 (1)

S. R. Bowman, N. W. Jenkins, S. O’Connor, and B. J. Feldman, “Sensitivity and stability of a radiation balanced laser system,” IEEE J. Quantum Electron. 38, 1339–1348 (2002).
[Crossref]

2000 (1)

S. R. Bowman and C. Mungan, “New materials for optical cooling,” Appl. Phys. B 71, 807–811 (2000).
[Crossref]

1999 (1)

S. R. Bowman, “Lasers without internal heat generation,” IEEE J. Quantum Electron. 35, 115–122 (1999).
[Crossref]

1964 (1)

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136, A954–A957 (1964).
[Crossref]

1962 (1)

W. B. Fowler and D. L. Dexter, “Relation between absorption and emission probabilities in luminescent centers in ionic solids,” Phys. Rev. 128, 2154–2165 (1962).
[Crossref]

Biswal, S.

S. R. Bowman, S. P. O’Connor, S. Biswal, N. J. Condon, and A. Rosenberg, “Minimizing heat generation in solid-state lasers,” IEEE J. Quantum Electron. 46, 1076–1085 (2010).
[Crossref]

S. Biswal, S. P. O’Connor, and S. R. Bowman, “Non-radiative losses in Yb:KGd(WO4)2 and Yb:Y3Al5O12,” Appl. Phys. Lett. 89, 0919111 (2006).
[Crossref]

S. R. Bowman, S. O’Connor, and S. Biswal, “Ytterbium laser with reduced thermal heating,” IEEE J. Quantum Electron. 41, 1510–1517 (2005).
[Crossref]

S. Bowman, S. O’Connor, S. Biswal, and N. Condon, “Demonstration and analysis of a high power radiation balanced laser,” in Proceedings of 2011 Conference on Lasers and Electro-Optics (2011), paper CMH4.

Bowman, S.

S. Bowman, S. O’Connor, S. Biswal, and N. Condon, “Demonstration and analysis of a high power radiation balanced laser,” in Proceedings of 2011 Conference on Lasers and Electro-Optics (2011), paper CMH4.

Bowman, S. R.

S. R. Bowman, J. Ganem, and C. G. Brown, “Optical cooling in multi-level systems,” Proc. SPIE 9000, 90000G (2014).

S. R. Bowman, S. P. O’Connor, S. Biswal, N. J. Condon, and A. Rosenberg, “Minimizing heat generation in solid-state lasers,” IEEE J. Quantum Electron. 46, 1076–1085 (2010).
[Crossref]

S. Biswal, S. P. O’Connor, and S. R. Bowman, “Non-radiative losses in Yb:KGd(WO4)2 and Yb:Y3Al5O12,” Appl. Phys. Lett. 89, 0919111 (2006).
[Crossref]

S. R. Bowman, S. O’Connor, and S. Biswal, “Ytterbium laser with reduced thermal heating,” IEEE J. Quantum Electron. 41, 1510–1517 (2005).
[Crossref]

S. R. Bowman, N. W. Jenkins, S. O’Connor, and B. J. Feldman, “Sensitivity and stability of a radiation balanced laser system,” IEEE J. Quantum Electron. 38, 1339–1348 (2002).
[Crossref]

S. R. Bowman and C. Mungan, “New materials for optical cooling,” Appl. Phys. B 71, 807–811 (2000).
[Crossref]

S. R. Bowman, “Lasers without internal heat generation,” IEEE J. Quantum Electron. 35, 115–122 (1999).
[Crossref]

Brown, C. G.

S. R. Bowman, J. Ganem, and C. G. Brown, “Optical cooling in multi-level systems,” Proc. SPIE 9000, 90000G (2014).

Condon, N.

S. Bowman, S. O’Connor, S. Biswal, and N. Condon, “Demonstration and analysis of a high power radiation balanced laser,” in Proceedings of 2011 Conference on Lasers and Electro-Optics (2011), paper CMH4.

Condon, N. J.

S. R. Bowman, S. P. O’Connor, S. Biswal, N. J. Condon, and A. Rosenberg, “Minimizing heat generation in solid-state lasers,” IEEE J. Quantum Electron. 46, 1076–1085 (2010).
[Crossref]

Dajani, I.

Dexter, D. L.

W. B. Fowler and D. L. Dexter, “Relation between absorption and emission probabilities in luminescent centers in ionic solids,” Phys. Rev. 128, 2154–2165 (1962).
[Crossref]

Eidam, T.

Epstein, R. I.

M. P. Hehlen, R. I. Epstein, and H. Inoue, “Model of laser cooling in the Yb3+-doped fluorozirconate glass ZBLAN,” Phys. Rev. B 75, 144302 (2007).

Feldman, B. J.

S. R. Bowman, N. W. Jenkins, S. O’Connor, and B. J. Feldman, “Sensitivity and stability of a radiation balanced laser system,” IEEE J. Quantum Electron. 38, 1339–1348 (2002).
[Crossref]

Fowler, W. B.

W. B. Fowler and D. L. Dexter, “Relation between absorption and emission probabilities in luminescent centers in ionic solids,” Phys. Rev. 128, 2154–2165 (1962).
[Crossref]

Ganem, J.

S. R. Bowman, J. Ganem, and C. G. Brown, “Optical cooling in multi-level systems,” Proc. SPIE 9000, 90000G (2014).

Hehlen, M. P.

M. P. Hehlen, R. I. Epstein, and H. Inoue, “Model of laser cooling in the Yb3+-doped fluorozirconate glass ZBLAN,” Phys. Rev. B 75, 144302 (2007).

Inoue, H.

M. P. Hehlen, R. I. Epstein, and H. Inoue, “Model of laser cooling in the Yb3+-doped fluorozirconate glass ZBLAN,” Phys. Rev. B 75, 144302 (2007).

Jauregui, C.

Jenkins, N. W.

S. R. Bowman, N. W. Jenkins, S. O’Connor, and B. J. Feldman, “Sensitivity and stability of a radiation balanced laser system,” IEEE J. Quantum Electron. 38, 1339–1348 (2002).
[Crossref]

Kawato, S.

S. Matsubara, T. Ueda, S. Kawato, and T. Kobayashi, “Highly efficient continuous-wave laser oscillation in microchip Yb:YAG laser at room temperature,” Jpn. J. Appl. Phys. 46, 132–134 (2007).

Kobayashi, T.

S. Matsubara, T. Ueda, S. Kawato, and T. Kobayashi, “Highly efficient continuous-wave laser oscillation in microchip Yb:YAG laser at room temperature,” Jpn. J. Appl. Phys. 46, 132–134 (2007).

Limpert, J.

Matsubara, S.

S. Matsubara, T. Ueda, S. Kawato, and T. Kobayashi, “Highly efficient continuous-wave laser oscillation in microchip Yb:YAG laser at room temperature,” Jpn. J. Appl. Phys. 46, 132–134 (2007).

McCumber, D. E.

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136, A954–A957 (1964).
[Crossref]

Mungan, C.

S. R. Bowman and C. Mungan, “New materials for optical cooling,” Appl. Phys. B 71, 807–811 (2000).
[Crossref]

O’Connor, S.

S. R. Bowman, S. O’Connor, and S. Biswal, “Ytterbium laser with reduced thermal heating,” IEEE J. Quantum Electron. 41, 1510–1517 (2005).
[Crossref]

S. R. Bowman, N. W. Jenkins, S. O’Connor, and B. J. Feldman, “Sensitivity and stability of a radiation balanced laser system,” IEEE J. Quantum Electron. 38, 1339–1348 (2002).
[Crossref]

S. Bowman, S. O’Connor, S. Biswal, and N. Condon, “Demonstration and analysis of a high power radiation balanced laser,” in Proceedings of 2011 Conference on Lasers and Electro-Optics (2011), paper CMH4.

O’Connor, S. P.

S. R. Bowman, S. P. O’Connor, S. Biswal, N. J. Condon, and A. Rosenberg, “Minimizing heat generation in solid-state lasers,” IEEE J. Quantum Electron. 46, 1076–1085 (2010).
[Crossref]

S. Biswal, S. P. O’Connor, and S. R. Bowman, “Non-radiative losses in Yb:KGd(WO4)2 and Yb:Y3Al5O12,” Appl. Phys. Lett. 89, 0919111 (2006).
[Crossref]

Robin, C.

Rosenberg, A.

S. R. Bowman, S. P. O’Connor, S. Biswal, N. J. Condon, and A. Rosenberg, “Minimizing heat generation in solid-state lasers,” IEEE J. Quantum Electron. 46, 1076–1085 (2010).
[Crossref]

Smith, A. V.

Smith, J. J.

Tunnermann, A.

Ueda, T.

S. Matsubara, T. Ueda, S. Kawato, and T. Kobayashi, “Highly efficient continuous-wave laser oscillation in microchip Yb:YAG laser at room temperature,” Jpn. J. Appl. Phys. 46, 132–134 (2007).

Ward, B.

Wright, J.

J. Wright, “Up-conversion and excited state energy transfer in rare-earth doped materials,” in Radiationless Processes in Molecules and Condensed Phases, F. K. Fong, ed., Vol. 15 of Topics in Applied Physics (Springer, 1976), Chap. 4, pp. 239–295.

Appl. Phys. B (1)

S. R. Bowman and C. Mungan, “New materials for optical cooling,” Appl. Phys. B 71, 807–811 (2000).
[Crossref]

Appl. Phys. Lett. (1)

S. Biswal, S. P. O’Connor, and S. R. Bowman, “Non-radiative losses in Yb:KGd(WO4)2 and Yb:Y3Al5O12,” Appl. Phys. Lett. 89, 0919111 (2006).
[Crossref]

IEEE J. Quantum Electron. (4)

S. R. Bowman, “Lasers without internal heat generation,” IEEE J. Quantum Electron. 35, 115–122 (1999).
[Crossref]

S. R. Bowman, N. W. Jenkins, S. O’Connor, and B. J. Feldman, “Sensitivity and stability of a radiation balanced laser system,” IEEE J. Quantum Electron. 38, 1339–1348 (2002).
[Crossref]

S. R. Bowman, S. O’Connor, and S. Biswal, “Ytterbium laser with reduced thermal heating,” IEEE J. Quantum Electron. 41, 1510–1517 (2005).
[Crossref]

S. R. Bowman, S. P. O’Connor, S. Biswal, N. J. Condon, and A. Rosenberg, “Minimizing heat generation in solid-state lasers,” IEEE J. Quantum Electron. 46, 1076–1085 (2010).
[Crossref]

Jpn. J. Appl. Phys. (1)

S. Matsubara, T. Ueda, S. Kawato, and T. Kobayashi, “Highly efficient continuous-wave laser oscillation in microchip Yb:YAG laser at room temperature,” Jpn. J. Appl. Phys. 46, 132–134 (2007).

Opt. Express (3)

Phys. Rev. (2)

D. E. McCumber, “Einstein relations connecting broadband emission and absorption spectra,” Phys. Rev. 136, A954–A957 (1964).
[Crossref]

W. B. Fowler and D. L. Dexter, “Relation between absorption and emission probabilities in luminescent centers in ionic solids,” Phys. Rev. 128, 2154–2165 (1962).
[Crossref]

Phys. Rev. B (1)

M. P. Hehlen, R. I. Epstein, and H. Inoue, “Model of laser cooling in the Yb3+-doped fluorozirconate glass ZBLAN,” Phys. Rev. B 75, 144302 (2007).

Proc. SPIE (1)

S. R. Bowman, J. Ganem, and C. G. Brown, “Optical cooling in multi-level systems,” Proc. SPIE 9000, 90000G (2014).

Other (2)

J. Wright, “Up-conversion and excited state energy transfer in rare-earth doped materials,” in Radiationless Processes in Molecules and Condensed Phases, F. K. Fong, ed., Vol. 15 of Topics in Applied Physics (Springer, 1976), Chap. 4, pp. 239–295.

S. Bowman, S. O’Connor, S. Biswal, and N. Condon, “Demonstration and analysis of a high power radiation balanced laser,” in Proceedings of 2011 Conference on Lasers and Electro-Optics (2011), paper CMH4.

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Figures (5)

Fig. 1.
Fig. 1. Plot of β(λP,T) (dotted lines) and βPL/βP (solid lines) for the Yb:YAG system. Values are calculated as discussed in the text for several temperatures assuming λL=1050nm; 300 K (red); 200 K (green); 100 K (blue).
Fig. 2.
Fig. 2. Plot of the material efficiency for an ideal Yb:YAG laser with λL=1050nm and several values of the scaled intensity. For the purpose of this illustration, the scaled pump and laser intensities are set equal. Solid curves are for 300 K and the dashed curves are for 100 K.
Fig. 3.
Fig. 3. Plot of laser material heating parameter for idealized Yb:YAG. Lasing is at 1050 nm and the temperature is 300 K. The vertical line marks the position of the mean fluorescence wavelength. As before, the scaled pump and laser intensities are set equal.
Fig. 4.
Fig. 4. Plot of the predicted laser material efficiency for the same conditions used in Fig. 2. Material parameters have been modified as described in the text.
Fig. 5.
Fig. 5. Plot of the realistic room temperature laser material heating parameter for the same conditions used in Fig. 4. The vertical dashed line marks the position of the effective crossover from fluorescent heating to fluorescent cooling, λC.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

β(λ,T)σA(λ,T)σA(λ,T)+σE(λ,T).
dN2dt=IPλPσA(λP,T)hc·[NTN2β(λP,T)]+ILλLσA(λL,T)hc·[NTN2β(λL,T)]N2τR.
H=IPσP·[NTN2βP]+ILσL·[NTN2βL]hcλFN2τR.
σPσA(λP,T),σLσA(λL,T),βPβ(λP,T),andβLβ(λL,T).
λFbandλ·IF(λ)dλbandIF(λ)dλ.
n2N2/NT,iPIP/IPsat,andiLIL/ILsat.
βPLβPβLβPβL.
β(λ,T)={1+Z1(T)Z2(T)exp[1kT(ε2hcλ)]}1andλF=bandσA(λ,T)exp(hc/λkT)dλ/λ4bandσA(λ,T)exp(hc/λkT)dλ/λ5.
n2=iPβP+iLβL1+iP+iL.
αP=σPNT·[1+iLβL/βPL1+iP+iL]andgL=σLNT·[iPβP/βPL11+iP+iL].
P=αPIPandL=gLIL.
H=NThcλFτR[λL(λFλP)βPiPλP(λLλF)βLiLλPλL(1+iP+iL)+λF(λLλP)iPiLβPβL/βPLλPλL(1+iP+iL)].
ηmLP=λPiL[iPβPL/βP]λLiP[iL+βPL/βL].
Ξm|H|L=|λF(λLλP)iPiLλFλPiL[iPβPL/βP]+λL(λFλP)iPβPL/βLλP(λLλF)iLβPL/βPλFλPiL[iPβPL/βP]|.
ηm=(λPλF)(λLλF).
Ξm=(1λL/λF),
dN2dt=IPλPσPhc·[NTN2βP]+ILλLσLhc·[NTN2βL]N2τFN22NYbτQ.
n2=n2·(1+δn)n2·[1+(1τR/τF)n2τR/τQ(iP+iL+τR/τF)].
ηmLmPm=λPiLλLiP[n2βLδαLβLβPn2+δαPβP].
ηmηm·[1+nmδnmβPδαPβPnm+nmδnmβLδαLnmβL].
δHQ=hcNTn2λP(1τF1τR+n2τQ)andδHA=hcNTτR(iPβPλPδαP+iLβLλLδαL).
Ξm=τFτF|[λF(λLλP)iPiLβP/βPL+λL(λFλP)iPβP/βLλP(λLλF)iL]|λFλPiL[iPβP/βPL1]+λLλP(τRτF1+n2τRτQ)[iPβP/iLβL+1iPβP/βPL1]+[iLβLδαL+iPβPδαPλL/λPn2βL]

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