Abstract

The laser performance at 491 and 635 nm of praseodymium-doped fluorozirconate fiber pumped at 1.01 μm and 835 nm is described and is interpreted with analytical solutions to the rate equations. Spectroscopic measurements of the absorption and the emission cross sections are presented, and the values are shown to be consistent with the observed lasing performance. The analytical model is shown to be a reliable indication of the optimum length of fiber for operation on the three-level 491-nm transition.

© 1994 Optical Society of America

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  1. J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 26, 166–168 (1990).
    [Crossref]
  2. J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 26, 261–263 (1990).
    [Crossref]
  3. J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 27, 189–191 (1991).
    [Crossref]
  4. R. G. Smart, J. N. Carter, A. C. Tropper, D. C. Hanna, S. F. Carter, and D. Szebesta, Opt. Commun. 86, 333–340 (1991).
    [Crossref]
  5. J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 27, 1156–1157 (1991).
    [Crossref]
  6. R. G. Smart, A. C. Tropper, D. C. Hanna, S. T. Davey, S. F. Carter, and D. Szebesta, Electron. Lett. 27, 1307–1308 (1991).
    [Crossref]
  7. T. J. Whitley, C. A. Millar, R. Wyatt, M. C. Brierley, and D. Szebesta, Electron. Lett. 27, 1785–1786 (1991).
    [Crossref]
  8. J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 28, 111–113 (1992).
    [Crossref]
  9. S. G. Grubb, K. W. Bennett, R. S. Cannon, and W. F. Humer, Electron. Lett. 28, 1243–1244 (1992).
    [Crossref]
  10. P. W. France, ed., Fluoride Glass Optical Fibres (Blackie, London, 1990).
    [Crossref]
  11. Y. Ohishi, T. Kanamori, T. Kitagawa, S. Takahashi, E. Snitzer, and G. H. Sigel, Opt. Lett. 16, 1747–1749 (1991).
    [Crossref] [PubMed]
  12. R. S. Quimby and B. Zheng, Appl. Phys. Lett. 60, 1055–1057 (1992).
    [Crossref]
  13. D. E. McCumber, Phys. Rev. A 134, A299–A306 (1964).
  14. W. J. Miniscalco and R. S. Quimby, Opt. Lett. 16, 258–260 (1991).
    [Crossref] [PubMed]
  15. J. L. Adam and W. A. Sibley, J. Non-Cryst. Solids 76, 267–279 (1985).
    [Crossref]

1992 (3)

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 28, 111–113 (1992).
[Crossref]

S. G. Grubb, K. W. Bennett, R. S. Cannon, and W. F. Humer, Electron. Lett. 28, 1243–1244 (1992).
[Crossref]

R. S. Quimby and B. Zheng, Appl. Phys. Lett. 60, 1055–1057 (1992).
[Crossref]

1991 (7)

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 27, 189–191 (1991).
[Crossref]

R. G. Smart, J. N. Carter, A. C. Tropper, D. C. Hanna, S. F. Carter, and D. Szebesta, Opt. Commun. 86, 333–340 (1991).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 27, 1156–1157 (1991).
[Crossref]

R. G. Smart, A. C. Tropper, D. C. Hanna, S. T. Davey, S. F. Carter, and D. Szebesta, Electron. Lett. 27, 1307–1308 (1991).
[Crossref]

T. J. Whitley, C. A. Millar, R. Wyatt, M. C. Brierley, and D. Szebesta, Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

W. J. Miniscalco and R. S. Quimby, Opt. Lett. 16, 258–260 (1991).
[Crossref] [PubMed]

Y. Ohishi, T. Kanamori, T. Kitagawa, S. Takahashi, E. Snitzer, and G. H. Sigel, Opt. Lett. 16, 1747–1749 (1991).
[Crossref] [PubMed]

1990 (2)

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 26, 166–168 (1990).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 26, 261–263 (1990).
[Crossref]

1985 (1)

J. L. Adam and W. A. Sibley, J. Non-Cryst. Solids 76, 267–279 (1985).
[Crossref]

1964 (1)

D. E. McCumber, Phys. Rev. A 134, A299–A306 (1964).

Adam, J. L.

J. L. Adam and W. A. Sibley, J. Non-Cryst. Solids 76, 267–279 (1985).
[Crossref]

Allain, J. Y.

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 28, 111–113 (1992).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 27, 189–191 (1991).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 27, 1156–1157 (1991).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 26, 166–168 (1990).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 26, 261–263 (1990).
[Crossref]

Bennett, K. W.

S. G. Grubb, K. W. Bennett, R. S. Cannon, and W. F. Humer, Electron. Lett. 28, 1243–1244 (1992).
[Crossref]

Brierley, M. C.

T. J. Whitley, C. A. Millar, R. Wyatt, M. C. Brierley, and D. Szebesta, Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

Cannon, R. S.

S. G. Grubb, K. W. Bennett, R. S. Cannon, and W. F. Humer, Electron. Lett. 28, 1243–1244 (1992).
[Crossref]

Carter, J. N.

R. G. Smart, J. N. Carter, A. C. Tropper, D. C. Hanna, S. F. Carter, and D. Szebesta, Opt. Commun. 86, 333–340 (1991).
[Crossref]

Carter, S. F.

R. G. Smart, J. N. Carter, A. C. Tropper, D. C. Hanna, S. F. Carter, and D. Szebesta, Opt. Commun. 86, 333–340 (1991).
[Crossref]

R. G. Smart, A. C. Tropper, D. C. Hanna, S. T. Davey, S. F. Carter, and D. Szebesta, Electron. Lett. 27, 1307–1308 (1991).
[Crossref]

Davey, S. T.

R. G. Smart, A. C. Tropper, D. C. Hanna, S. T. Davey, S. F. Carter, and D. Szebesta, Electron. Lett. 27, 1307–1308 (1991).
[Crossref]

Grubb, S. G.

S. G. Grubb, K. W. Bennett, R. S. Cannon, and W. F. Humer, Electron. Lett. 28, 1243–1244 (1992).
[Crossref]

Hanna, D. C.

R. G. Smart, J. N. Carter, A. C. Tropper, D. C. Hanna, S. F. Carter, and D. Szebesta, Opt. Commun. 86, 333–340 (1991).
[Crossref]

R. G. Smart, A. C. Tropper, D. C. Hanna, S. T. Davey, S. F. Carter, and D. Szebesta, Electron. Lett. 27, 1307–1308 (1991).
[Crossref]

Humer, W. F.

S. G. Grubb, K. W. Bennett, R. S. Cannon, and W. F. Humer, Electron. Lett. 28, 1243–1244 (1992).
[Crossref]

Kanamori, T.

Kitagawa, T.

McCumber, D. E.

D. E. McCumber, Phys. Rev. A 134, A299–A306 (1964).

Millar, C. A.

T. J. Whitley, C. A. Millar, R. Wyatt, M. C. Brierley, and D. Szebesta, Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

Miniscalco, W. J.

Monerie, M.

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 28, 111–113 (1992).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 27, 1156–1157 (1991).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 27, 189–191 (1991).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 26, 261–263 (1990).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 26, 166–168 (1990).
[Crossref]

Ohishi, Y.

Poignant, H.

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 28, 111–113 (1992).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 27, 189–191 (1991).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 27, 1156–1157 (1991).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 26, 166–168 (1990).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 26, 261–263 (1990).
[Crossref]

Quimby, R. S.

R. S. Quimby and B. Zheng, Appl. Phys. Lett. 60, 1055–1057 (1992).
[Crossref]

W. J. Miniscalco and R. S. Quimby, Opt. Lett. 16, 258–260 (1991).
[Crossref] [PubMed]

Sibley, W. A.

J. L. Adam and W. A. Sibley, J. Non-Cryst. Solids 76, 267–279 (1985).
[Crossref]

Sigel, G. H.

Smart, R. G.

R. G. Smart, J. N. Carter, A. C. Tropper, D. C. Hanna, S. F. Carter, and D. Szebesta, Opt. Commun. 86, 333–340 (1991).
[Crossref]

R. G. Smart, A. C. Tropper, D. C. Hanna, S. T. Davey, S. F. Carter, and D. Szebesta, Electron. Lett. 27, 1307–1308 (1991).
[Crossref]

Snitzer, E.

Szebesta, D.

R. G. Smart, J. N. Carter, A. C. Tropper, D. C. Hanna, S. F. Carter, and D. Szebesta, Opt. Commun. 86, 333–340 (1991).
[Crossref]

T. J. Whitley, C. A. Millar, R. Wyatt, M. C. Brierley, and D. Szebesta, Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

R. G. Smart, A. C. Tropper, D. C. Hanna, S. T. Davey, S. F. Carter, and D. Szebesta, Electron. Lett. 27, 1307–1308 (1991).
[Crossref]

Takahashi, S.

Tropper, A. C.

R. G. Smart, J. N. Carter, A. C. Tropper, D. C. Hanna, S. F. Carter, and D. Szebesta, Opt. Commun. 86, 333–340 (1991).
[Crossref]

R. G. Smart, A. C. Tropper, D. C. Hanna, S. T. Davey, S. F. Carter, and D. Szebesta, Electron. Lett. 27, 1307–1308 (1991).
[Crossref]

Whitley, T. J.

T. J. Whitley, C. A. Millar, R. Wyatt, M. C. Brierley, and D. Szebesta, Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

Wyatt, R.

T. J. Whitley, C. A. Millar, R. Wyatt, M. C. Brierley, and D. Szebesta, Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

Zheng, B.

R. S. Quimby and B. Zheng, Appl. Phys. Lett. 60, 1055–1057 (1992).
[Crossref]

Appl. Phys. Lett. (1)

R. S. Quimby and B. Zheng, Appl. Phys. Lett. 60, 1055–1057 (1992).
[Crossref]

Electron. Lett. (8)

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 26, 166–168 (1990).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 26, 261–263 (1990).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 27, 189–191 (1991).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 27, 1156–1157 (1991).
[Crossref]

R. G. Smart, A. C. Tropper, D. C. Hanna, S. T. Davey, S. F. Carter, and D. Szebesta, Electron. Lett. 27, 1307–1308 (1991).
[Crossref]

T. J. Whitley, C. A. Millar, R. Wyatt, M. C. Brierley, and D. Szebesta, Electron. Lett. 27, 1785–1786 (1991).
[Crossref]

J. Y. Allain, M. Monerie, and H. Poignant, Electron. Lett. 28, 111–113 (1992).
[Crossref]

S. G. Grubb, K. W. Bennett, R. S. Cannon, and W. F. Humer, Electron. Lett. 28, 1243–1244 (1992).
[Crossref]

J. Non-Cryst. Solids (1)

J. L. Adam and W. A. Sibley, J. Non-Cryst. Solids 76, 267–279 (1985).
[Crossref]

Opt. Commun. (1)

R. G. Smart, J. N. Carter, A. C. Tropper, D. C. Hanna, S. F. Carter, and D. Szebesta, Opt. Commun. 86, 333–340 (1991).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (1)

D. E. McCumber, Phys. Rev. A 134, A299–A306 (1964).

Other (1)

P. W. France, ed., Fluoride Glass Optical Fibres (Blackie, London, 1990).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1

Energy-level diagram for the Pr3+ ion showing the optical pumping cycle for infrared-pumped visible laser emission and the labeling scheme used for the rate-equation model.

Fig. 2
Fig. 2

Room-temperature absorption spectrum of a 13-mm-thick ZBLAN glass sample doped with 5000 parts in 106 wt. of Pr.

Fig. 3
Fig. 3

Logs of intensity of 586-nm sidelight fluorescence from a length of fiber B pumped at 1.015 μm as a function of distance along the fiber.

Fig. 4
Fig. 4

Experimentally measured intensity of visible sidelight fluorescence from fiber A as a function of intracore power at 835 nm (circles) for three values of intracore power at 1.01 μm. The curves are calculated from Eq. (1) with the parameter values given in Table 1.

Fig. 5
Fig. 5

Experimentally measured intensity of 1.3-μm sidelight fluorescence from fiber A as a function of intracore power at 835 nm (circles) during pumping with 500 mW of intracore power at 1.01 μm. The curve is calculated from Eqs. (1) and (2) with σ23 = 8 × 10−25 m2.

Fig. 6
Fig. 6

Measured room-temperature absorption cross section of a Pr3+ ion in a ZBLAN glass host as a function of energy (solid curve) in the region of the 3H43P0, 3P1, 1I6 absorption bands. The dashed curve represents the sum of a Lorentzian and a Gaussian band with parameters given in the text.

Fig. 7
Fig. 7

Room-temperature emission cross-section spectrum of Pr3+ in ZBLAN glass near 21,000 cm−1 (solid curve). The absorption cross-section spectrum (dashed curve) is included for comparison.

Fig. 8
Fig. 8

Threshold power at 1.01 μm as a function of threshold power at 835 nm for lasing at 635 nm in a 10-m length of fiber A in a low-loss resonator; experimental values (circles) and theoretical curve are derived from Eq. (A12).

Fig. 9
Fig. 9

Total incident infrared power at threshold for lasing at 491 nm as a function of fiber length for fiber A (circles) and fiber B (squares).

Fig. 10
Fig. 10

Single-pass gain at 491 nm calculated from Eq. (A19) as a function of fiber length for fibers A and B.

Fig. 11
Fig. 11

Plot of Eq. (A9) relating the normalized pump intensity at 1.01 μm, i12, in the fiber core to the normalized pump intensity at 835 nm, i23. The origin of the i12 axis is set to give the hypothetical pump condition i12 = i23 = 2 at point A corresponding to the input end of a fiber. At some position farther down the fiber corresponding to point B the changes in pump intensity, Δi12 and Δi23, can be read from the curve. Point C, where the curve crosses the axis, corresponds to an infinite length of fiber and defines the maximum fraction of the 835-nm pump that will be absorbed, given the values for the pump intensities at the input end.

Tables (2)

Tables Icon

Table 1 Optical Pumping Cycle Parameters

Tables Icon

Table 2 Saturation Intensities and Powers

Equations (24)

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N 3 N = [ 1 + I 23 σ 23 τ 3 h ν 23 ( 1 + h ν 12 I 12 σ 12 τ 12 + I 23 ν 12 σ 23 τ 3 I 12 ν 23 σ 12 τ 2 ) ] - 1 .
N 3 = N 2 I 23 σ 23 τ 3 h ν 23 .
σ e ( ν ) = exp ( - h ν ) k T σ a ( ν ) ,
N = N 1 + N 2 + N 3 .
d N 2 d t = I 12 h ν 12 ( N 1 σ 12 - N 2 σ 21 ) - I 23 h ν 23 N 2 σ 23 - N 2 τ 2 ,
d N 3 d t = I 23 h ν 23 N 2 σ 23 - N 3 τ 3 ,
d I 12 I 12 = ( N 2 σ 21 - N 1 σ 12 ) d z ,
d I 23 I 23 = - N 2 σ 23 d z .
d I 12 I 23 d I 23 I 12 = N 1 σ 12 - N 2 σ 21 N 2 σ 23 .
N 1 = N 2 ( h ν 12 σ 12 τ 12 I 12 + σ 23 ν 12 I 23 σ 12 ν 23 I 12 + σ 21 σ 12 ) .
d I 12 = d I 23 ( h ν 12 τ 2 σ 23 I 23 + ν 12 ν 23 ) ,
i 12 = ln ( i 23 ) + η i 23 + K ,
i 12 = I 12 I 0 ,             i 23 = I 23 I 0 ,
I 0 = h ν 12 τ 2 σ 23 ,             η = ν 12 ν 23 .
Δ i 12 = ln [ i 23 ( 0 ) i 23 ( 0 ) - Δ i 23 ] + η Δ i 23 ,
Δ i j k = i j k ( 0 ) - i j k ( L )
Γ 34 = 0 L N 3 σ 34 d z .
Γ 34 = 0 L N 2 I 23 h ν 23 / σ 23 τ 3 σ 34 d z = L 0 d I 23 h ν 23 / σ 34 τ 3 .
Γ 34 = Δ P 23 W 34 ,
Δ P 23 = A co [ I 23 ( 0 ) - I 23 ( L ) ]
W 34 = A co h ν 23 / σ 34 τ 3 ,
Γ 31 = 0 L N 3 σ 31 d z - 0 L N 1 σ 13 d z .
Γ 31 = Δ P 23 W 31 - N σ 13 L ,
W 31 = A co h ν 23 / σ 31 τ 3 .

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