Abstract

A method is presented for estimating the transfer efficiency of laser pumping cavities that have diffusely reflecting walls. The method is based on the assumption that the light inside the cavity is approximately isotropic. It is demonstrated that such a simplification leads to estimates of transfer efficiency that agree well with estimates obtained by Monte Carlo methods. Curves are given for the proportion of isotropic light absorbed by a cylindrical absorbing crystal as a function of the product of radius and absorption coefficient. This proportion is an important parameter in the transfer efficiency estimation.

© 1966 Optical Society of America

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References

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  1. D. R. Skinner, J. Tregellas-Williams, Australian J. Phys. 19, 1 (1966).
  2. C. H. Cooke, J. McKenna, J. G. Skinner, Appl. Opt. 3, 957 (1964).
    [CrossRef]
  3. Y. A. Ananev, E. A. Korolev, Opt. Spectry. 16, 381 (1963).

1966 (1)

D. R. Skinner, J. Tregellas-Williams, Australian J. Phys. 19, 1 (1966).

1964 (1)

1963 (1)

Y. A. Ananev, E. A. Korolev, Opt. Spectry. 16, 381 (1963).

Ananev, Y. A.

Y. A. Ananev, E. A. Korolev, Opt. Spectry. 16, 381 (1963).

Cooke, C. H.

Korolev, E. A.

Y. A. Ananev, E. A. Korolev, Opt. Spectry. 16, 381 (1963).

McKenna, J.

Skinner, D. R.

D. R. Skinner, J. Tregellas-Williams, Australian J. Phys. 19, 1 (1966).

Skinner, J. G.

Tregellas-Williams, J.

D. R. Skinner, J. Tregellas-Williams, Australian J. Phys. 19, 1 (1966).

Appl. Opt. (1)

Australian J. Phys. (1)

D. R. Skinner, J. Tregellas-Williams, Australian J. Phys. 19, 1 (1966).

Opt. Spectry. (1)

Y. A. Ananev, E. A. Korolev, Opt. Spectry. 16, 381 (1963).

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Figures (5)

Fig. 1
Fig. 1

Transfer efficiency estimated by Monte Carlo (A) calculations plotted against efficiency predicted by the formula. The line represents perfect agreement.

Fig. 2
Fig. 2

Percentage of photons absorbed by cavity wall estimated by Monte Carlo (A) calculations plotted against absorption predicted by the formula. The line represents perfect agreement.

Fig. 3
Fig. 3

Capture efficiency of a cylindrical crystal exposed to isotropic light: ×, n = 1.5; +, n = 1.75; ⊙, n = 2.0. The solid lines represent an empirical expression given in the text and the dashed line represents the results of Ananev and Korolev3 for n = 1.77. The horizontal lines represent asymptotic values of capture efficiency for high αR0, as described in the text.

Fig. 4
Fig. 4

Percentage of photons undergoing first and second internal reflections in the laser crystal.

Fig. 5
Fig. 5

Comparison of Monte Carlo (B) estimates of energy density inside a laser crystal under isotropic illumination with the curves given by Cooke et al.2 (solid lines).

Tables (1)

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Table I Pumping Cavity Details

Equations (3)

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β 1 = ( 1.1146 - 0.1376 n ) { 1 - exp [ ( - 1.868 - 0.2104 n ) α R 0 + ( 0.3246 - 0.1180 n ) α 2 R 0 2 ] }
lim β 1 α R 0 = 1 - 1 2 0 1 ( A - B ) 2 ( A + B ) 2 [ 1 + ( A B + χ ) 2 ( A B + χ ) 2 ] d χ ,
lim β 1 α R 0 = 1.0711 - 0.1221 n + 0.0166 / ( n - 0.67 ) .

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