Abstract

We present theoretical modeling that makes it possible to compute the output characteristics of a laser-pumped codoped Tm, Ho microchip laser and the experimental results already obtained with a Tm, Ho:YLiF4 crystal. By taking into account the match of the pump beam to the self-induced eigenmode of the cavity, we find good agreement between theory and experiment when the pump beam size is properly adjusted relative to the absorbed pump power and the crystal characteristics.

© 1999 Optical Society of America

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  1. T. Y. Fan, G. Huber, R. L. Byer, P. Mitzscherlich, “Spectroscopy and diode-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
    [CrossRef]
  2. G. Rustad, K. Stenersen, “Modeling of laser-pumped Tm and Ho lasers accounting for upconversion and ground-state depletion,” IEEE J. Quantum Electron. 32, 1645–1655 (1996).
    [CrossRef]
  3. V. E. Hartwell, H. Nakajima, N. Djeu, “Pump interference and optical bistability effects in a Tm, Ho:YAG micro-laser,” Opt. Lett. 20, 2210–2212 (1995).
    [CrossRef]
  4. N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. I. Theoretical,” IEEE J. Quantum Electron. 32, 92–103 (1996).
    [CrossRef]
  5. N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. II. Experiments,” IEEE J. Quantum Electron. 32, 104–111 (1996).
    [CrossRef]
  6. H. Hemmati, “2.07-µm cw diode-laser-pumped Tm, Ho:YLiF4 room temperature laser,” Opt. Lett. 14, 435–437 (1989).
    [CrossRef] [PubMed]
  7. G. J. Koch, J. P. Deyst, M. E. Storm, “Single-frequency lasing of monolithic Ho, Tm:YLF,” Opt. Lett. 18, 1235–1237 (1993).
    [CrossRef] [PubMed]
  8. I. F. Elder, M. T. P. Payne, “Lasing diode pumped Tm:YAP, Tm, Ho:YAP and Tm, Ho:YLF,” Opt. Commun. 145, 329–339 (1998).
    [CrossRef]
  9. J. J. Zayhowski, “Thermal guiding in microchip lasers,” in Advanced Solid-State Lasers, Vol. 6 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1990), p. 121.
  10. G. L. Bourdet, G. Lescroart, “Theoretical modelling of mode formation in Tm3+:YVO4 microchip lasers,” Opt. Commun. 150, 136–140 (1998).
    [CrossRef]
  11. W. P. Risk, “Modeling of longitudinally pumped solid state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am B 5, 1412–1423 (1988).
    [CrossRef]
  12. T. Y. Fan, “Aperture guiding in quasi-three-level lasers,” Opt. Lett. 19, 554–556 (1994).
    [CrossRef] [PubMed]
  13. G. L. Bourdet, G. Lescroart, “Theoretical modelling and design of a Tm:YVO4 microchip laser,” Opt. Commun. 149, 404–414 (1998).
    [CrossRef]
  14. G. Rustad, Norwegian Defence Research Establishment, Postboks 25, 2007 Kjeller, Norway (Personal communication, 1997).
  15. W. W. Rigrod, “Gain saturation and output power of optical masers,” J. Appl. Phys. 34, 2602–2609 (1963).
    [CrossRef]
  16. M. E. Storm, “Holmium YLF amplifier performances and the prospects for multi-joule energy using diode-laser pumping,” IEEE J. Quantum Electron. 29, 440–451 (1993).
    [CrossRef]
  17. H. P. Jenssen, A. Linz, R. P. Leavitt, C. A. Morisson, D. E. Wortman, “Analysis of the optical spectrum of Tm3+ in LiYF4,” Phys. Rev. B 11, 92–101 (1975).
    [CrossRef]
  18. G. Lescroart, R. Muller, G. Bourdet, “Experimental investigations and theoretical modeling of a Tm:YVO4 microchip laser,” Opt. Commun. 143, 147–155 (1997).
    [CrossRef]
  19. G. L. Bourdet, G. Lescroart, R. Muller, “Spectral characteristics of 2 µm microchip Tm:YVO4 and Tm, Ho:YLF lasers,” Opt. Commun. 150, 141–146 (1998).
    [CrossRef]

1998

I. F. Elder, M. T. P. Payne, “Lasing diode pumped Tm:YAP, Tm, Ho:YAP and Tm, Ho:YLF,” Opt. Commun. 145, 329–339 (1998).
[CrossRef]

G. L. Bourdet, G. Lescroart, “Theoretical modelling of mode formation in Tm3+:YVO4 microchip lasers,” Opt. Commun. 150, 136–140 (1998).
[CrossRef]

G. L. Bourdet, G. Lescroart, “Theoretical modelling and design of a Tm:YVO4 microchip laser,” Opt. Commun. 149, 404–414 (1998).
[CrossRef]

G. L. Bourdet, G. Lescroart, R. Muller, “Spectral characteristics of 2 µm microchip Tm:YVO4 and Tm, Ho:YLF lasers,” Opt. Commun. 150, 141–146 (1998).
[CrossRef]

1997

G. Lescroart, R. Muller, G. Bourdet, “Experimental investigations and theoretical modeling of a Tm:YVO4 microchip laser,” Opt. Commun. 143, 147–155 (1997).
[CrossRef]

1996

G. Rustad, K. Stenersen, “Modeling of laser-pumped Tm and Ho lasers accounting for upconversion and ground-state depletion,” IEEE J. Quantum Electron. 32, 1645–1655 (1996).
[CrossRef]

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. I. Theoretical,” IEEE J. Quantum Electron. 32, 92–103 (1996).
[CrossRef]

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. II. Experiments,” IEEE J. Quantum Electron. 32, 104–111 (1996).
[CrossRef]

1995

1994

1993

M. E. Storm, “Holmium YLF amplifier performances and the prospects for multi-joule energy using diode-laser pumping,” IEEE J. Quantum Electron. 29, 440–451 (1993).
[CrossRef]

G. J. Koch, J. P. Deyst, M. E. Storm, “Single-frequency lasing of monolithic Ho, Tm:YLF,” Opt. Lett. 18, 1235–1237 (1993).
[CrossRef] [PubMed]

1989

1988

T. Y. Fan, G. Huber, R. L. Byer, P. Mitzscherlich, “Spectroscopy and diode-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
[CrossRef]

W. P. Risk, “Modeling of longitudinally pumped solid state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am B 5, 1412–1423 (1988).
[CrossRef]

1975

H. P. Jenssen, A. Linz, R. P. Leavitt, C. A. Morisson, D. E. Wortman, “Analysis of the optical spectrum of Tm3+ in LiYF4,” Phys. Rev. B 11, 92–101 (1975).
[CrossRef]

1963

W. W. Rigrod, “Gain saturation and output power of optical masers,” J. Appl. Phys. 34, 2602–2609 (1963).
[CrossRef]

Barnes, N. P.

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. I. Theoretical,” IEEE J. Quantum Electron. 32, 92–103 (1996).
[CrossRef]

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. II. Experiments,” IEEE J. Quantum Electron. 32, 104–111 (1996).
[CrossRef]

Bourdet, G.

G. Lescroart, R. Muller, G. Bourdet, “Experimental investigations and theoretical modeling of a Tm:YVO4 microchip laser,” Opt. Commun. 143, 147–155 (1997).
[CrossRef]

Bourdet, G. L.

G. L. Bourdet, G. Lescroart, R. Muller, “Spectral characteristics of 2 µm microchip Tm:YVO4 and Tm, Ho:YLF lasers,” Opt. Commun. 150, 141–146 (1998).
[CrossRef]

G. L. Bourdet, G. Lescroart, “Theoretical modelling of mode formation in Tm3+:YVO4 microchip lasers,” Opt. Commun. 150, 136–140 (1998).
[CrossRef]

G. L. Bourdet, G. Lescroart, “Theoretical modelling and design of a Tm:YVO4 microchip laser,” Opt. Commun. 149, 404–414 (1998).
[CrossRef]

Byer, R. L.

T. Y. Fan, G. Huber, R. L. Byer, P. Mitzscherlich, “Spectroscopy and diode-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
[CrossRef]

Deyst, J. P.

Djeu, N.

Elder, I. F.

I. F. Elder, M. T. P. Payne, “Lasing diode pumped Tm:YAP, Tm, Ho:YAP and Tm, Ho:YLF,” Opt. Commun. 145, 329–339 (1998).
[CrossRef]

Fan, T. Y.

T. Y. Fan, “Aperture guiding in quasi-three-level lasers,” Opt. Lett. 19, 554–556 (1994).
[CrossRef] [PubMed]

T. Y. Fan, G. Huber, R. L. Byer, P. Mitzscherlich, “Spectroscopy and diode-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
[CrossRef]

Filer, E. D.

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. I. Theoretical,” IEEE J. Quantum Electron. 32, 92–103 (1996).
[CrossRef]

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. II. Experiments,” IEEE J. Quantum Electron. 32, 104–111 (1996).
[CrossRef]

Hartwell, V. E.

Hemmati, H.

Huber, G.

T. Y. Fan, G. Huber, R. L. Byer, P. Mitzscherlich, “Spectroscopy and diode-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
[CrossRef]

Jenssen, H. P.

H. P. Jenssen, A. Linz, R. P. Leavitt, C. A. Morisson, D. E. Wortman, “Analysis of the optical spectrum of Tm3+ in LiYF4,” Phys. Rev. B 11, 92–101 (1975).
[CrossRef]

Koch, G. J.

Leavitt, R. P.

H. P. Jenssen, A. Linz, R. P. Leavitt, C. A. Morisson, D. E. Wortman, “Analysis of the optical spectrum of Tm3+ in LiYF4,” Phys. Rev. B 11, 92–101 (1975).
[CrossRef]

Lee, C. J.

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. II. Experiments,” IEEE J. Quantum Electron. 32, 104–111 (1996).
[CrossRef]

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. I. Theoretical,” IEEE J. Quantum Electron. 32, 92–103 (1996).
[CrossRef]

Lescroart, G.

G. L. Bourdet, G. Lescroart, “Theoretical modelling of mode formation in Tm3+:YVO4 microchip lasers,” Opt. Commun. 150, 136–140 (1998).
[CrossRef]

G. L. Bourdet, G. Lescroart, “Theoretical modelling and design of a Tm:YVO4 microchip laser,” Opt. Commun. 149, 404–414 (1998).
[CrossRef]

G. L. Bourdet, G. Lescroart, R. Muller, “Spectral characteristics of 2 µm microchip Tm:YVO4 and Tm, Ho:YLF lasers,” Opt. Commun. 150, 141–146 (1998).
[CrossRef]

G. Lescroart, R. Muller, G. Bourdet, “Experimental investigations and theoretical modeling of a Tm:YVO4 microchip laser,” Opt. Commun. 143, 147–155 (1997).
[CrossRef]

Linz, A.

H. P. Jenssen, A. Linz, R. P. Leavitt, C. A. Morisson, D. E. Wortman, “Analysis of the optical spectrum of Tm3+ in LiYF4,” Phys. Rev. B 11, 92–101 (1975).
[CrossRef]

Mitzscherlich, P.

T. Y. Fan, G. Huber, R. L. Byer, P. Mitzscherlich, “Spectroscopy and diode-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
[CrossRef]

Morisson, C. A.

H. P. Jenssen, A. Linz, R. P. Leavitt, C. A. Morisson, D. E. Wortman, “Analysis of the optical spectrum of Tm3+ in LiYF4,” Phys. Rev. B 11, 92–101 (1975).
[CrossRef]

Morrison, C. A.

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. I. Theoretical,” IEEE J. Quantum Electron. 32, 92–103 (1996).
[CrossRef]

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. II. Experiments,” IEEE J. Quantum Electron. 32, 104–111 (1996).
[CrossRef]

Muller, R.

G. L. Bourdet, G. Lescroart, R. Muller, “Spectral characteristics of 2 µm microchip Tm:YVO4 and Tm, Ho:YLF lasers,” Opt. Commun. 150, 141–146 (1998).
[CrossRef]

G. Lescroart, R. Muller, G. Bourdet, “Experimental investigations and theoretical modeling of a Tm:YVO4 microchip laser,” Opt. Commun. 143, 147–155 (1997).
[CrossRef]

Nakajima, H.

Payne, M. T. P.

I. F. Elder, M. T. P. Payne, “Lasing diode pumped Tm:YAP, Tm, Ho:YAP and Tm, Ho:YLF,” Opt. Commun. 145, 329–339 (1998).
[CrossRef]

Rigrod, W. W.

W. W. Rigrod, “Gain saturation and output power of optical masers,” J. Appl. Phys. 34, 2602–2609 (1963).
[CrossRef]

Risk, W. P.

W. P. Risk, “Modeling of longitudinally pumped solid state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am B 5, 1412–1423 (1988).
[CrossRef]

Rustad, G.

G. Rustad, K. Stenersen, “Modeling of laser-pumped Tm and Ho lasers accounting for upconversion and ground-state depletion,” IEEE J. Quantum Electron. 32, 1645–1655 (1996).
[CrossRef]

G. Rustad, Norwegian Defence Research Establishment, Postboks 25, 2007 Kjeller, Norway (Personal communication, 1997).

Stenersen, K.

G. Rustad, K. Stenersen, “Modeling of laser-pumped Tm and Ho lasers accounting for upconversion and ground-state depletion,” IEEE J. Quantum Electron. 32, 1645–1655 (1996).
[CrossRef]

Storm, M. E.

M. E. Storm, “Holmium YLF amplifier performances and the prospects for multi-joule energy using diode-laser pumping,” IEEE J. Quantum Electron. 29, 440–451 (1993).
[CrossRef]

G. J. Koch, J. P. Deyst, M. E. Storm, “Single-frequency lasing of monolithic Ho, Tm:YLF,” Opt. Lett. 18, 1235–1237 (1993).
[CrossRef] [PubMed]

Wortman, D. E.

H. P. Jenssen, A. Linz, R. P. Leavitt, C. A. Morisson, D. E. Wortman, “Analysis of the optical spectrum of Tm3+ in LiYF4,” Phys. Rev. B 11, 92–101 (1975).
[CrossRef]

Zayhowski, J. J.

J. J. Zayhowski, “Thermal guiding in microchip lasers,” in Advanced Solid-State Lasers, Vol. 6 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1990), p. 121.

IEEE J. Quantum Electron.

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. I. Theoretical,” IEEE J. Quantum Electron. 32, 92–103 (1996).
[CrossRef]

N. P. Barnes, E. D. Filer, C. A. Morrison, C. J. Lee, “Ho, Tm lasers. II. Experiments,” IEEE J. Quantum Electron. 32, 104–111 (1996).
[CrossRef]

T. Y. Fan, G. Huber, R. L. Byer, P. Mitzscherlich, “Spectroscopy and diode-pumped operation of Tm, Ho:YAG,” IEEE J. Quantum Electron. 24, 924–933 (1988).
[CrossRef]

G. Rustad, K. Stenersen, “Modeling of laser-pumped Tm and Ho lasers accounting for upconversion and ground-state depletion,” IEEE J. Quantum Electron. 32, 1645–1655 (1996).
[CrossRef]

M. E. Storm, “Holmium YLF amplifier performances and the prospects for multi-joule energy using diode-laser pumping,” IEEE J. Quantum Electron. 29, 440–451 (1993).
[CrossRef]

J. Appl. Phys.

W. W. Rigrod, “Gain saturation and output power of optical masers,” J. Appl. Phys. 34, 2602–2609 (1963).
[CrossRef]

J. Opt. Soc. Am B

W. P. Risk, “Modeling of longitudinally pumped solid state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am B 5, 1412–1423 (1988).
[CrossRef]

Opt. Commun.

G. L. Bourdet, G. Lescroart, “Theoretical modelling and design of a Tm:YVO4 microchip laser,” Opt. Commun. 149, 404–414 (1998).
[CrossRef]

G. L. Bourdet, G. Lescroart, “Theoretical modelling of mode formation in Tm3+:YVO4 microchip lasers,” Opt. Commun. 150, 136–140 (1998).
[CrossRef]

I. F. Elder, M. T. P. Payne, “Lasing diode pumped Tm:YAP, Tm, Ho:YAP and Tm, Ho:YLF,” Opt. Commun. 145, 329–339 (1998).
[CrossRef]

G. Lescroart, R. Muller, G. Bourdet, “Experimental investigations and theoretical modeling of a Tm:YVO4 microchip laser,” Opt. Commun. 143, 147–155 (1997).
[CrossRef]

G. L. Bourdet, G. Lescroart, R. Muller, “Spectral characteristics of 2 µm microchip Tm:YVO4 and Tm, Ho:YLF lasers,” Opt. Commun. 150, 141–146 (1998).
[CrossRef]

Opt. Lett.

Phys. Rev. B

H. P. Jenssen, A. Linz, R. P. Leavitt, C. A. Morisson, D. E. Wortman, “Analysis of the optical spectrum of Tm3+ in LiYF4,” Phys. Rev. B 11, 92–101 (1975).
[CrossRef]

Other

G. Rustad, Norwegian Defence Research Establishment, Postboks 25, 2007 Kjeller, Norway (Personal communication, 1997).

J. J. Zayhowski, “Thermal guiding in microchip lasers,” in Advanced Solid-State Lasers, Vol. 6 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1990), p. 121.

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Figures (8)

Fig. 1
Fig. 1

Lower-energy manifolds, atomic transitions, and energy transfer processes in a codoped Tm, Ho system.

Fig. 2
Fig. 2

Experimental apparatus.

Fig. 3
Fig. 3

Variation of the occupation factors for the upper (f u ) and lower (f l ) levels of the laser transition and the energy transfer rate for the 3 F 4 manifold of the Tm3+ ion to the 5 I 7 manifold of the Ho3+ ion versus temperature.

Fig. 4
Fig. 4

Laser intensity versus pump intensity normalized to the corresponding saturation intensity.

Fig. 5
Fig. 5

Pump reflectivity of the crystal when it is lasing versus the reflectivity of the front face at pump wavelength.

Fig. 6
Fig. 6

Experimental and theoretical laser output power versus pump power (w p = 49 µm).

Fig. 7
Fig. 7

Experimental and theoretical laser output power versus pump power (w p = 75 µm).

Fig. 8
Fig. 8

Experimental and theoretical laser output power versus pump power (w p = 96 µm).

Equations (35)

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dN2dt=σpcΦpRNTm-N2-N2τ2-kΣN22-k2156N2N5+k6512N6N1-ATmN2N6,dN6dt=k2156N2N5-k6512N6N1-N6τ6-AHoN2N6-σlcΦlfu+flN6-flNHo,
fj=gj exp-EjkBTi gi exp-EikBT,
R=2η4+1-η4β4+β43η3,
kΣ=k21231-η3+k21242-β4-β43η31-η4,
ATm=k21681-η71-η81+η3β87-η82,
AHo=k21681-1-η8β86+1-η8β87β76-2η86-η82,
η82=k8612N1k8612N1+k8656N5+τ8-1,η86=k8656N5k8612N1+k8656N5+τ8-1.
b=2NTmτ2kΣ,  f=flfu+fl,  r=NHoNTm, ρ=τ2τ6,  XTm=N2NTm,  XHo=N6NHo.
A=k21682-1-η8η71+η3β87+β86+1-η8β87β76-2η8,
σpcΦpRτ21-XTm-XTm-b2 XTm2-Aτ2NHoXTmXHo-rρXHo-σlcΦlrτ2fu+flXHo-f=0.
Φi=Iichνi,  Ii=IiIsati,  i=l, p,
Isatl=hν1fu+flσlτ6, Isatp=hνp2η4+1-η4β4+β43η3σpτ2
Ipz1-XTm-XTm-b2 XTm2-Aτ2NHoXTmXHo-rρXHo-rρIlzXHo-f=0.
θ=k2156k6512=N6N1N2N5.
N1=NTm-N2,  N5=NHo-N6,
XHo=θXTm1+θ-1XTm.
θ=i5I7 gi exp-EikBTj5I8 gj exp-EjkBTk3H6 gk exp-EkkBTl3F4 gl exp-ElkBT,
-b2θ-1XTm3-b2+Ipz+1θ-1+Aτ2NHoθ×XTm2-Ipz2-θ+Ilzrρθ-fθ-1+rρθ+1XTm+Ipz+frρIlz=0,
dIlεzIlεz=εg0XHo-fdz=εg0θXTm1+θ-1XTm-fdz,
dIpεzIpεz=-εα01-XTmdz,
g0=σlNHofu+fl,  α0=σpNTm,
εdIpεzα0Ipεzdz=-ξ 1-f-εdIlεzg0Ilεzdz1-ξ θ-1θεdIlεzg0Ilεzdz, ξ=11-f θ-1θ.
dIpεzα0Ipεzdz=-εξ1-f-ξθεdIlεzg0Ilεzdz,
ξ2θεg0dIlεzIlεz-εα0dIpεzIpεz=ξ1-fdz.
Ipεz=CεεIlεzεε α0g0ξ2θ exp-εα0ξ1-fz.
D=α0g0ξ2θ,  δ=α0ξ1-f.
Ipz=TspRspRmp-D1/2X+1X×Iinj1+RspΓ-2RspΓcos φexp-δL,
X=Rmp1RmlIl+zIl-zD/2 exp-δz,
Γ=RmpRslRml-D exp-2δL,
Iref=Rsp+RmpRmlRsl-D exp-2δL-2RspRmpRmlRsl-D1/2 exp-δLcos φ1+RspRmpRmlRsl-D exp-2δL-2RspRmpRmlRsl-D1/2 exp-δLcos φ Iinj.
σp=0.65×10-20 cm2,  σ1=15×10-20 cm2,α0=5.4 cm-1,  g0=0.94 cm-1, r=0.067,  ρ=2,  τ2=12 ms.
A=k21682-β86-β87β76k2168=2.515×10-18 cm3/s.
Ilρ=ηiIp0exp-2ρ/wp2-Ith>0,ηi=Il0Ip0-Ith,
Pl=Isatl02π0ρth Ilρρdρdα=ηiIsatlIsatp Pp1-1+lnXX,  X=Ip0Ith1.
Isatp=1.7 kW/cm2,  Isatl=0.99 kW/cm2

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