Abstract

The effect of a radially varying gain in tightly focused lasers is investigated with a generalized ABCD matrix formalism in a nonparabolic approximation. It is shown that the beam sizes can differ strongly from the theoretical with a constant gain or with radially varying gain in a parabolic approximation. Geometrical threshold zones are defined and studied and, instead action for a given cavity design.

© 1994 Optical Society of America

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References

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  1. H. Kogelnik, Appl. Opt. 4, 1562 (1965).
    [CrossRef]
  2. L. W. Casperson, A. Yariv, Appl. Phys. Lett. 12, 355 (1968).
    [CrossRef]
  3. L. W. Casperson, Appl. Opt. 12, 2434 (1973).
    [CrossRef] [PubMed]
  4. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  5. F. Salin, J. Squier, Opt. Lett. 17,1352 (1992).
    [CrossRef] [PubMed]
  6. J. Herrmann, J. Opt. Soc. Am. B 11,498 (1994).
    [CrossRef]

1994 (1)

1992 (1)

1973 (1)

1968 (1)

L. W. Casperson, A. Yariv, Appl. Phys. Lett. 12, 355 (1968).
[CrossRef]

1965 (1)

Casperson, L. W.

L. W. Casperson, Appl. Opt. 12, 2434 (1973).
[CrossRef] [PubMed]

L. W. Casperson, A. Yariv, Appl. Phys. Lett. 12, 355 (1968).
[CrossRef]

Herrmann, J.

Kogelnik, H.

Salin, F.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Squier, J.

Yariv, A.

L. W. Casperson, A. Yariv, Appl. Phys. Lett. 12, 355 (1968).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

L. W. Casperson, A. Yariv, Appl. Phys. Lett. 12, 355 (1968).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Other (1)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

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Figures (3)

Fig. 1
Fig. 1

Power amplification factor Γ versus the variable ξ for the parameters c = 85 cm, d = 95 cm, a = b, f = 5 cm, wp = 75 μm, and L = 2 cm for different gain coefficients: g0 = 0.2 cm−1 (curve 1), g0 = 0.38 cm−1 (curve 2), g0 = 0.5 cm−1 (curve 3). Inset: four-mirror cavity with internal gain element.

Fig. 2
Fig. 2

Spot size w2 at the outcouple mirror M2 versus ξ (solid curve) for g0 = 0.38 cm−1. The long-dashed curve represents w2 in the parabolic approximation, and the short-dashed curve represents w2 in the bare-resonator theory (g0 = 0 or wp → ∞). Inset: plot of the inner region with a larger scale.

Fig. 3
Fig. 3

Beam profiles in the gain medium for ξ = 2.09 in (a) the forward direction and (b) the backward direction; spot sizes for ξ = 2.059 in (c) the forward direction and (d) the backward direction. Dotted-dashed curves, pump beam waist wp; solid curves, nonparabolic approximation; short-dashed curves, parabolic approximation.

Equations (6)

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d A x + d z = C c + n 0 ,             d B c + d z = D c + n 0 , d C c + d z = - 2 k h + A c + ,             d D c + d z = - 2 k h + B c + ,
d G + d z = W p 2 g 0 ( 1 + S ) ( W p 2 + 2 W l 2 ) ( W p 2 + W l 2 ) 2 ,
h + ( z ) = 2 i g 0 W p 2 ( i + S ) ( W p 2 + W l 2 ) 2 .
1 q 2 = 1 2 B ^ [ D ^ - A ^ ± ( A ^ + D ^ ) 2 - 4 ] , α 2 = 1 M = 2 A ^ + D ^ ± ( A ^ + D ^ ) 2 - 4 .
Γ = 1 M 2 exp ( G + + G - ) ,
Γ ( P = 0 ) * R 1 * R 2 = 1

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