Abstract

Results are presented of a computer-based study on the rate of excitation in the active cores of two types of optically pumped lasers as a function of a number of parameters of the active core. The absorption bands of the active materials are generated by Lorentzian and Gaussian functions. The excitation rate of the active core is proportional to the width of the absorption band at all depths of penetration. The plots of excitation rate as a function of frequency show curves similar to line reversal spectra and emphasize the importance of excitation some distance from the center of the absorption band in the slab model. In the cylindrical model, this wing pumping is even more important due to focusing. The effect of refractive index on the excitation rate is also described.

© 1967 Optical Society of America

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References

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N. F. Borrelli, M. L. Charters, J. Appl. Phys. 36, 2172 (1965).
[CrossRef]

W. Jekeli, J. Opt. Soc. Am. 55, 1442 (1965).
[CrossRef]

1964 (3)

1963 (1)

1962 (1)

1961 (1)

W. Kaiser, C. G. B. Garrett, D. L. Wood, Phys. Rev. 123, 766 (1961).
[CrossRef]

Borrelli, N. F.

N. F. Borrelli, M. L. Charters, J. Appl. Phys. 36, 2172 (1965).
[CrossRef]

Brecher, C.

H. Samelson, A. Lempicki, C. Brecher, J. Chem. Phys. 40, 2553 (1964).
[CrossRef]

Charters, M. L.

N. F. Borrelli, M. L. Charters, J. Appl. Phys. 36, 2172 (1965).
[CrossRef]

Cooke, C. H.

Devlin, G. E.

Garrett, C. G. B.

W. Kaiser, C. G. B. Garrett, D. L. Wood, Phys. Rev. 123, 766 (1961).
[CrossRef]

Jekeli, W.

Kaiser, W.

W. Kaiser, C. G. B. Garrett, D. L. Wood, Phys. Rev. 123, 766 (1961).
[CrossRef]

Lempicki, A.

H. Samelson, A. Lempicki, C. Brecher, J. Chem. Phys. 40, 2553 (1964).
[CrossRef]

May, A. D.

McKenna, J.

Samelson, H.

H. Samelson, A. Lempicki, C. Brecher, J. Chem. Phys. 40, 2553 (1964).
[CrossRef]

Schawlow, A. L.

Skinner, J. G.

Wood, D. L.

W. Kaiser, C. G. B. Garrett, D. L. Wood, Phys. Rev. 123, 766 (1961).
[CrossRef]

Appl. Opt. (4)

J. Appl. Phys. (1)

N. F. Borrelli, M. L. Charters, J. Appl. Phys. 36, 2172 (1965).
[CrossRef]

J. Chem. Phys. (1)

H. Samelson, A. Lempicki, C. Brecher, J. Chem. Phys. 40, 2553 (1964).
[CrossRef]

J. Opt. Soc. Am. (1)

Phys. Rev. (1)

W. Kaiser, C. G. B. Garrett, D. L. Wood, Phys. Rev. 123, 766 (1961).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Integrated pumping rate as a function of absorption bandwidth for both slab and cylindrical models at various depths of penetration. L = Lorentzian generated absorption band, G = Gaussian generated absorption band. The cylindrical plots refer to the left-hand axis, the slab plots to the right-hand axis.

Fig. 2
Fig. 2

Excitation rate reversal in the slab model. N(x)/P0 as a function of wavenumber for various depths of penetration. Lorentzian generated absorption band. a0 = 5 cm−1, Δ v ˜ = 1000 cm−1.

Fig. 3
Fig. 3

Excitation rate reversal in the cylindrical model. Only half of the symmetrical excitation rate curve is shown. a ( ν ˜ ) [ V ( r , a ( ν ˜ ) ) ] vs v ˜ at various values of r. R0 = 0.5 cm, n = 1.7, a0 = 5 cm−1.

Fig. 4
Fig. 4

Cumulative fraction of integrated pumping rate as a function of position in the absorption band at two depths in the cylindrical rod. r in cm. Gaussian absorption band. R0 = 1 cm, n = 1.7, a0 = 4 cm−1, Δ v ˜ = 3000 cm−1.

Fig. 5
Fig. 5

Effect of refractive index on the integrated pumping rate at various radii in the cylindrical rod. Lorentzian generated absorption band. R0 = 1 cm, Δ v ˜ = 3000 cm−1, a0 = 5 cm−1.

Fig. 6
Fig. 6

Cylindrical model integrated pumping rates as a function of r/R0 for two different rods. Upper curve: Lorentzian generated absorption band. R0 = 0.2 cm, a0 = 4 cm−1, n = 1.7. Lower curve: Lorentzian generated absorption band. R0 = 1.0 cm, a0 = 5 cm−1, n = 1.3. Δ v ˜ = 3,000 cm−1 in both cases.

Equations (8)

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a = c .
N ( X ) = a P 0 e - a x ,
P 0 a ( v ˜ ) exp whole band [ - a ( ν ˜ ) x ] d ν ˜ .
N ( r ) t = ( c / n ) U 0 ν ˜ 1 ν ˜ 2 a ( ν ˜ ) h ν ˜ v [ r , a ( ν ¯ ) ] d ν ¯ ,
Gaussian a = a 0 exp [ - 4 ln 2 ( ν ˜ - ν ˜ 0 ) 2 / ( Δ ν ˜ ) 2 ] ,
Lorentzian a = a 0 ( Δ ν ˜ / 2 ) 2 ( ν ˜ - ν ˜ 0 ) 2 + ( Δ ν ˜ / 2 ) 2 ,
d N ( r ) = ( c / n ) ( U 0 / h ν ˜ 0 ) { a ( ν ˜ ) v [ r , a ( ν ˜ ) ] } .
f = 2 ν ˜ 0 - 2 Δ ν ˜ ν ˜ a ( ν ˜ ) v [ r , a ( ν ˜ ) ] d ν ˜ ν ˜ 0 - 2 Δ ν ˜ ν ˜ 0 + 2 Δ ν ˜ a ( ν ˜ ) v [ r , a ( ν ˜ ) ] d ν ˜ .

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