Abstract

A fraction of pump power has been converted to TEM00 mode laser power for a side-pumped solid-state laser by use of a space-dependent rate equation. We investigated the pump-to-mode (TEM00) ratio when scaling laser-diode side-pumped solid-state lasers to high-power levels by including the thermal effect in the space-dependent rate equation. Based on the assumption that Gaussian pump power is the same at any cross section of a laser rod, we resolved the output power with a space-dependent rate equation; temperature distribution in the laser rod was obtained; the optical path difference distribution was derived, and we estimated the diffraction losses that result from thermally induced spherical aberration by use of the Strehl intensity ratio. We determined that thermally induced diffraction losses are strongly dependent on pump power and on the pump-to-mode ratio.

© 2000 Optical Society of America

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References

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  1. W. Xie, Y-L. Lam, Y-C. Chan, S-C. Tam, J. Gu, F. Zhou, H. Yang, G. Zhao, “Fluorescence feedback control of an active Q-switched diode-pumped Nd:YVO4 laser,” Appl. Opt. 39, 978–981 (2000).
    [CrossRef]
  2. B. J. Comaskey, R. Beach, G. Albrecht, W. J. Benett, B. L. Freitas, C. Petty, D. Mundinger, R. W. Solarz, “High average power diode pump slab laser,” IEEE J. Quantum Electron. 28, 992–996 (1992).
    [CrossRef]
  3. N. Hodgson, S. Dong, Q. Lu, “Performance of a 2.3-kW Nd:YAG slab laser system,” Opt. Lett. 18, 1727–1729 (1993).
    [CrossRef] [PubMed]
  4. R. J. St. Pierre, D. W. Mordaunt, H. Injeyanetc, “Diode array pumping kilowatt laser,” IEEE J. Sel. Top. Quantum Electron. 3, 53–58 (1997).
    [CrossRef]
  5. T. Y. Fan, R. L. Byer, “Diode laser-pumped solid-state lasers,” IEEE J. Quantum Electron. 24, 895–912 (1988).
    [CrossRef]
  6. M. J. F. Digonnet, C. J. Gaeta, “Theoretical analysis of optical fiber laser amplifiers and oscillators,” Appl. Opt. 24, 333–342 (1985).
    [CrossRef] [PubMed]
  7. P. Laporta, M. Brussard, “Design criteria for mode size optimization in diode-pumped solid-state lasers,” IEEE J. Quantum Electron. 27, 2319–2326 (1991).
    [CrossRef]
  8. Y. F. Chen, T. S. Liao, C. F. Kao, T. M. Huang, K. H. Lin, S. C. Wang, “Optimization of fiber-coupled laser-diode end-pumped lasers: influence of pump-beam quality,” IEEE J. Quantum Electron. 32, 2010–2016 (1996).
    [CrossRef]
  9. Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33, 1424–1429 (1997).
    [CrossRef]
  10. S. B. Sutton, G. F. Albrecht, “Simple analytical method to calculate the radial energy deposition profile in an isotropic diode-pumped solid-state laser rod,” Appl. Opt. 35, 5937–5948 (1996).
    [CrossRef] [PubMed]
  11. M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965), pp. 227.
  12. A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1069 (1992).
    [CrossRef]
  13. C. Pfistner, R. Weber, H. P. Weber, “Thermal beam distortion in longitudinally pumped solid-state lasers,” IEEE J. Quantum Electron. 30, 1605–1616 (1994).
    [CrossRef]
  14. W. Koechner, Solid-State Laser Engineering, 3rd ed. (Springer-Verlag, Berlin, 1992), Chap. 5.
    [CrossRef]
  15. S. Konno, S. Fujikawa, K. Yasui, “80 W cw TEM00 1064 nm beam generation by use of a laser-diode-side-pumped Nd:YAG rod laser,” Appl. Phys. Lett. 70, 2650–2651 (1997).
    [CrossRef]
  16. A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 5, 80–89 (1963).
    [CrossRef]
  17. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 460–464.
  18. P. A. Schulz, S. R. Henion, “Liquid-nitrogen-cooled Ti:Al2O3 laser,” IEEE J. Quantum Electron. 27, 1039–1047 (1991).
    [CrossRef]

2000 (1)

1997 (3)

S. Konno, S. Fujikawa, K. Yasui, “80 W cw TEM00 1064 nm beam generation by use of a laser-diode-side-pumped Nd:YAG rod laser,” Appl. Phys. Lett. 70, 2650–2651 (1997).
[CrossRef]

R. J. St. Pierre, D. W. Mordaunt, H. Injeyanetc, “Diode array pumping kilowatt laser,” IEEE J. Sel. Top. Quantum Electron. 3, 53–58 (1997).
[CrossRef]

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33, 1424–1429 (1997).
[CrossRef]

1996 (2)

Y. F. Chen, T. S. Liao, C. F. Kao, T. M. Huang, K. H. Lin, S. C. Wang, “Optimization of fiber-coupled laser-diode end-pumped lasers: influence of pump-beam quality,” IEEE J. Quantum Electron. 32, 2010–2016 (1996).
[CrossRef]

S. B. Sutton, G. F. Albrecht, “Simple analytical method to calculate the radial energy deposition profile in an isotropic diode-pumped solid-state laser rod,” Appl. Opt. 35, 5937–5948 (1996).
[CrossRef] [PubMed]

1994 (1)

C. Pfistner, R. Weber, H. P. Weber, “Thermal beam distortion in longitudinally pumped solid-state lasers,” IEEE J. Quantum Electron. 30, 1605–1616 (1994).
[CrossRef]

1993 (1)

1992 (2)

A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1069 (1992).
[CrossRef]

B. J. Comaskey, R. Beach, G. Albrecht, W. J. Benett, B. L. Freitas, C. Petty, D. Mundinger, R. W. Solarz, “High average power diode pump slab laser,” IEEE J. Quantum Electron. 28, 992–996 (1992).
[CrossRef]

1991 (2)

P. Laporta, M. Brussard, “Design criteria for mode size optimization in diode-pumped solid-state lasers,” IEEE J. Quantum Electron. 27, 2319–2326 (1991).
[CrossRef]

P. A. Schulz, S. R. Henion, “Liquid-nitrogen-cooled Ti:Al2O3 laser,” IEEE J. Quantum Electron. 27, 1039–1047 (1991).
[CrossRef]

1988 (1)

T. Y. Fan, R. L. Byer, “Diode laser-pumped solid-state lasers,” IEEE J. Quantum Electron. 24, 895–912 (1988).
[CrossRef]

1985 (1)

1963 (1)

A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 5, 80–89 (1963).
[CrossRef]

Albrecht, G.

B. J. Comaskey, R. Beach, G. Albrecht, W. J. Benett, B. L. Freitas, C. Petty, D. Mundinger, R. W. Solarz, “High average power diode pump slab laser,” IEEE J. Quantum Electron. 28, 992–996 (1992).
[CrossRef]

Albrecht, G. F.

Beach, R.

B. J. Comaskey, R. Beach, G. Albrecht, W. J. Benett, B. L. Freitas, C. Petty, D. Mundinger, R. W. Solarz, “High average power diode pump slab laser,” IEEE J. Quantum Electron. 28, 992–996 (1992).
[CrossRef]

Benett, W. J.

B. J. Comaskey, R. Beach, G. Albrecht, W. J. Benett, B. L. Freitas, C. Petty, D. Mundinger, R. W. Solarz, “High average power diode pump slab laser,” IEEE J. Quantum Electron. 28, 992–996 (1992).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 460–464.

Brussard, M.

P. Laporta, M. Brussard, “Design criteria for mode size optimization in diode-pumped solid-state lasers,” IEEE J. Quantum Electron. 27, 2319–2326 (1991).
[CrossRef]

Byer, R. L.

T. Y. Fan, R. L. Byer, “Diode laser-pumped solid-state lasers,” IEEE J. Quantum Electron. 24, 895–912 (1988).
[CrossRef]

Chan, Y-C.

Chen, Y. F.

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33, 1424–1429 (1997).
[CrossRef]

Y. F. Chen, T. S. Liao, C. F. Kao, T. M. Huang, K. H. Lin, S. C. Wang, “Optimization of fiber-coupled laser-diode end-pumped lasers: influence of pump-beam quality,” IEEE J. Quantum Electron. 32, 2010–2016 (1996).
[CrossRef]

Comaskey, B. J.

B. J. Comaskey, R. Beach, G. Albrecht, W. J. Benett, B. L. Freitas, C. Petty, D. Mundinger, R. W. Solarz, “High average power diode pump slab laser,” IEEE J. Quantum Electron. 28, 992–996 (1992).
[CrossRef]

Cousins, A. K.

A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1069 (1992).
[CrossRef]

Digonnet, M. J. F.

Dong, S.

Fan, T. Y.

T. Y. Fan, R. L. Byer, “Diode laser-pumped solid-state lasers,” IEEE J. Quantum Electron. 24, 895–912 (1988).
[CrossRef]

Fox, A. G.

A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 5, 80–89 (1963).
[CrossRef]

Freitas, B. L.

B. J. Comaskey, R. Beach, G. Albrecht, W. J. Benett, B. L. Freitas, C. Petty, D. Mundinger, R. W. Solarz, “High average power diode pump slab laser,” IEEE J. Quantum Electron. 28, 992–996 (1992).
[CrossRef]

Fujikawa, S.

S. Konno, S. Fujikawa, K. Yasui, “80 W cw TEM00 1064 nm beam generation by use of a laser-diode-side-pumped Nd:YAG rod laser,” Appl. Phys. Lett. 70, 2650–2651 (1997).
[CrossRef]

Gaeta, C. J.

Gu, J.

Henion, S. R.

P. A. Schulz, S. R. Henion, “Liquid-nitrogen-cooled Ti:Al2O3 laser,” IEEE J. Quantum Electron. 27, 1039–1047 (1991).
[CrossRef]

Hodgson, N.

Huang, T. M.

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33, 1424–1429 (1997).
[CrossRef]

Y. F. Chen, T. S. Liao, C. F. Kao, T. M. Huang, K. H. Lin, S. C. Wang, “Optimization of fiber-coupled laser-diode end-pumped lasers: influence of pump-beam quality,” IEEE J. Quantum Electron. 32, 2010–2016 (1996).
[CrossRef]

Injeyanetc, H.

R. J. St. Pierre, D. W. Mordaunt, H. Injeyanetc, “Diode array pumping kilowatt laser,” IEEE J. Sel. Top. Quantum Electron. 3, 53–58 (1997).
[CrossRef]

Kao, C. F.

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33, 1424–1429 (1997).
[CrossRef]

Y. F. Chen, T. S. Liao, C. F. Kao, T. M. Huang, K. H. Lin, S. C. Wang, “Optimization of fiber-coupled laser-diode end-pumped lasers: influence of pump-beam quality,” IEEE J. Quantum Electron. 32, 2010–2016 (1996).
[CrossRef]

Koechner, W.

W. Koechner, Solid-State Laser Engineering, 3rd ed. (Springer-Verlag, Berlin, 1992), Chap. 5.
[CrossRef]

Konno, S.

S. Konno, S. Fujikawa, K. Yasui, “80 W cw TEM00 1064 nm beam generation by use of a laser-diode-side-pumped Nd:YAG rod laser,” Appl. Phys. Lett. 70, 2650–2651 (1997).
[CrossRef]

Lam, Y-L.

Laporta, P.

P. Laporta, M. Brussard, “Design criteria for mode size optimization in diode-pumped solid-state lasers,” IEEE J. Quantum Electron. 27, 2319–2326 (1991).
[CrossRef]

Li, T.

A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 5, 80–89 (1963).
[CrossRef]

Liao, T. S.

Y. F. Chen, T. S. Liao, C. F. Kao, T. M. Huang, K. H. Lin, S. C. Wang, “Optimization of fiber-coupled laser-diode end-pumped lasers: influence of pump-beam quality,” IEEE J. Quantum Electron. 32, 2010–2016 (1996).
[CrossRef]

Lin, K. H.

Y. F. Chen, T. S. Liao, C. F. Kao, T. M. Huang, K. H. Lin, S. C. Wang, “Optimization of fiber-coupled laser-diode end-pumped lasers: influence of pump-beam quality,” IEEE J. Quantum Electron. 32, 2010–2016 (1996).
[CrossRef]

Lu, Q.

Mordaunt, D. W.

R. J. St. Pierre, D. W. Mordaunt, H. Injeyanetc, “Diode array pumping kilowatt laser,” IEEE J. Sel. Top. Quantum Electron. 3, 53–58 (1997).
[CrossRef]

Mundinger, D.

B. J. Comaskey, R. Beach, G. Albrecht, W. J. Benett, B. L. Freitas, C. Petty, D. Mundinger, R. W. Solarz, “High average power diode pump slab laser,” IEEE J. Quantum Electron. 28, 992–996 (1992).
[CrossRef]

Petty, C.

B. J. Comaskey, R. Beach, G. Albrecht, W. J. Benett, B. L. Freitas, C. Petty, D. Mundinger, R. W. Solarz, “High average power diode pump slab laser,” IEEE J. Quantum Electron. 28, 992–996 (1992).
[CrossRef]

Pfistner, C.

C. Pfistner, R. Weber, H. P. Weber, “Thermal beam distortion in longitudinally pumped solid-state lasers,” IEEE J. Quantum Electron. 30, 1605–1616 (1994).
[CrossRef]

Schulz, P. A.

P. A. Schulz, S. R. Henion, “Liquid-nitrogen-cooled Ti:Al2O3 laser,” IEEE J. Quantum Electron. 27, 1039–1047 (1991).
[CrossRef]

Solarz, R. W.

B. J. Comaskey, R. Beach, G. Albrecht, W. J. Benett, B. L. Freitas, C. Petty, D. Mundinger, R. W. Solarz, “High average power diode pump slab laser,” IEEE J. Quantum Electron. 28, 992–996 (1992).
[CrossRef]

St. Pierre, R. J.

R. J. St. Pierre, D. W. Mordaunt, H. Injeyanetc, “Diode array pumping kilowatt laser,” IEEE J. Sel. Top. Quantum Electron. 3, 53–58 (1997).
[CrossRef]

Sutton, S. B.

Tam, S-C.

Wang, C. L.

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33, 1424–1429 (1997).
[CrossRef]

Wang, S. C.

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33, 1424–1429 (1997).
[CrossRef]

Y. F. Chen, T. S. Liao, C. F. Kao, T. M. Huang, K. H. Lin, S. C. Wang, “Optimization of fiber-coupled laser-diode end-pumped lasers: influence of pump-beam quality,” IEEE J. Quantum Electron. 32, 2010–2016 (1996).
[CrossRef]

Weber, H. P.

C. Pfistner, R. Weber, H. P. Weber, “Thermal beam distortion in longitudinally pumped solid-state lasers,” IEEE J. Quantum Electron. 30, 1605–1616 (1994).
[CrossRef]

Weber, R.

C. Pfistner, R. Weber, H. P. Weber, “Thermal beam distortion in longitudinally pumped solid-state lasers,” IEEE J. Quantum Electron. 30, 1605–1616 (1994).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 460–464.

Xie, W.

Yang, H.

Yasui, K.

S. Konno, S. Fujikawa, K. Yasui, “80 W cw TEM00 1064 nm beam generation by use of a laser-diode-side-pumped Nd:YAG rod laser,” Appl. Phys. Lett. 70, 2650–2651 (1997).
[CrossRef]

Zhao, G.

Zhou, F.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

S. Konno, S. Fujikawa, K. Yasui, “80 W cw TEM00 1064 nm beam generation by use of a laser-diode-side-pumped Nd:YAG rod laser,” Appl. Phys. Lett. 70, 2650–2651 (1997).
[CrossRef]

IEEE J. Quantum Electron. (8)

P. A. Schulz, S. R. Henion, “Liquid-nitrogen-cooled Ti:Al2O3 laser,” IEEE J. Quantum Electron. 27, 1039–1047 (1991).
[CrossRef]

A. K. Cousins, “Temperature and thermal stress scaling in finite-length end-pumped laser rods,” IEEE J. Quantum Electron. 28, 1057–1069 (1992).
[CrossRef]

C. Pfistner, R. Weber, H. P. Weber, “Thermal beam distortion in longitudinally pumped solid-state lasers,” IEEE J. Quantum Electron. 30, 1605–1616 (1994).
[CrossRef]

P. Laporta, M. Brussard, “Design criteria for mode size optimization in diode-pumped solid-state lasers,” IEEE J. Quantum Electron. 27, 2319–2326 (1991).
[CrossRef]

Y. F. Chen, T. S. Liao, C. F. Kao, T. M. Huang, K. H. Lin, S. C. Wang, “Optimization of fiber-coupled laser-diode end-pumped lasers: influence of pump-beam quality,” IEEE J. Quantum Electron. 32, 2010–2016 (1996).
[CrossRef]

Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, S. C. Wang, “Optimization in scaling fiber-coupled laser-diode end-pumped lasers to higher power: influence of thermal effect,” IEEE J. Quantum Electron. 33, 1424–1429 (1997).
[CrossRef]

B. J. Comaskey, R. Beach, G. Albrecht, W. J. Benett, B. L. Freitas, C. Petty, D. Mundinger, R. W. Solarz, “High average power diode pump slab laser,” IEEE J. Quantum Electron. 28, 992–996 (1992).
[CrossRef]

T. Y. Fan, R. L. Byer, “Diode laser-pumped solid-state lasers,” IEEE J. Quantum Electron. 24, 895–912 (1988).
[CrossRef]

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

R. J. St. Pierre, D. W. Mordaunt, H. Injeyanetc, “Diode array pumping kilowatt laser,” IEEE J. Sel. Top. Quantum Electron. 3, 53–58 (1997).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 5, 80–89 (1963).
[CrossRef]

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 460–464.

W. Koechner, Solid-State Laser Engineering, 3rd ed. (Springer-Verlag, Berlin, 1992), Chap. 5.
[CrossRef]

M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965), pp. 227.

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Figures (9)

Fig. 1
Fig. 1

Cavity geometry for one side-pumping module.

Fig. 2
Fig. 2

Cross-sectional geometry of the laser rod pumped by only one laser diode.

Fig. 3
Fig. 3

Pump energy distribution for a four-side-pumped solid-state laser with w po = 0.3 mm.

Fig. 4
Fig. 4

Pump energy distribution for a side-pumped solid-state laser having four sides with w po = 1 mm.

Fig. 5
Fig. 5

Comparisons of (a) the axial x plane and (b) the y = x plane with the overlap pump profile (solid curve) and a Gaussian profile (dashed curve).

Fig. 6
Fig. 6

Threshold mode volume V eff as a function of pump beam waist.

Fig. 7
Fig. 7

Overlap efficiency η0 as a function of pump beam waist.

Fig. 8
Fig. 8

Thermally induced diffraction loss as a function of assumed Gaussian pump power for several pump beam sizes.

Fig. 9
Fig. 9

Optimum pump-to-mode ratio as a function of assumed Gaussian pump power.

Equations (23)

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

Ix, y=2πI0wexp-2x2w2,
w2=wpo21+λyπwpo22.
Ix, y=2πI0wpoexp-2π2wpo2x2π2wpo4+λ2y2-αdπ2wpo4+λ2y21/2.
d=AB=r02-x2+y.
Pout=Toδ ηpη0Pin-Isatηplδ2 Veff,
Veff= slr, zrpr, zdV-1,
η0= slr, zrpr, zdV2 sl2r, zrpr, zdV,
slr, z=2πwl2zexp-2 r2wl2z,
wlz=w01+zλl/πw022w0,
rpr, z=2πwp2zexp-2 r2wp2z,
Veff=πwl2+wp22l,
η0=wl2z2wp2z+wl2zwp2z+wl2z2.
·hr, z=Qr, z,
hr, z=-KTr, z,
2πrh=or Q2πrdr,
Ihr, z=I0h exp-2r2wp2,
hr=Sph2π1-exp-2r2wp2r,
ΔTr=Sph4πKlnr02r2+E12r02wp2-E12r2wp2,
dϕr, zdz=nT ΔTr, z+n-1zz+i,j=13nij ij,
ϕr=2 0lnT ΔTr, zdz.
δ=δd+δf+To,
δd=1-R=1-0roexpikΔϕexp-r2w02rdr20exp-r2w02rdr2,
Δϕ=ϕr-ϕ0-ξr2,

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