Abstract

A resonator with toroidal mirrors is described. This resonator behaves like an off-axis unstable confocal resonator in one transverse dimension and like an on-axis concave–convex stable resonator in the other orthogonal dimension. Some experimental results are reported for a fast flow high power cw-CO2 laser whose transverse cross section is restricted in the stable-resonator direction. These cavities allow an output laser beam with a fully illuminated cross section which is well suited for focusing. Moreover, the fraction of the available laser power which may be concentrated in the central lobe of the focal plane intensity distribution is 2.5–4.5 times higher than other unstable resonators with similarly restricted modal volumes. Finally the alignment requirements are examined.

© 1981 Optical Society of America

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References

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  1. HPL LASER manufactured by AVCO, 32 Cobble Hill Road, Somerville, Mass. 02143.
  2. G. W. Sutton, M. M. Weiner, S. A. Mani, Appl. Opt. 15, 2228 (1976).
    [CrossRef] [PubMed]
  3. M. M. Weiner, Appl. Opt. 16, 1790 (1977).
    [CrossRef] [PubMed]
  4. E. A. Phillips, J. P. Reilly, D. B. Northam, Appl. Opt. 15, 2159 (1976).
    [CrossRef] [PubMed]
  5. V. N. Mahajan, J. Opt. Soc. Am, 68, 742 (1978).
    [CrossRef]
  6. M. M. Weiner, Appl. Opt. 18, 1828 (1979).
    [CrossRef] [PubMed]
  7. Yu. A. Ananev, V. N. Chernov, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 403 (1972).
    [CrossRef]
  8. P. E. Dyer, D. J. James, Opt. Commun. 15, 20 (1975).
    [CrossRef]
  9. O. L. Bourne, P. E. Dyer, Opt. Commun. 31, 193 (1979).
    [CrossRef]
  10. H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
    [CrossRef]
  11. W. W. Rigrod, J. Appl. Phys. 36, 2487 (1965).
    [CrossRef]
  12. W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
    [CrossRef]
  13. A. L. Bloom, Spectra-Physics Laser Technical Bulletin No. 2 (1963).

1979 (2)

M. M. Weiner, Appl. Opt. 18, 1828 (1979).
[CrossRef] [PubMed]

O. L. Bourne, P. E. Dyer, Opt. Commun. 31, 193 (1979).
[CrossRef]

1978 (1)

V. N. Mahajan, J. Opt. Soc. Am, 68, 742 (1978).
[CrossRef]

1977 (1)

1976 (2)

1975 (1)

P. E. Dyer, D. J. James, Opt. Commun. 15, 20 (1975).
[CrossRef]

1972 (1)

Yu. A. Ananev, V. N. Chernov, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 403 (1972).
[CrossRef]

1969 (1)

W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

1966 (1)

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

1965 (1)

W. W. Rigrod, J. Appl. Phys. 36, 2487 (1965).
[CrossRef]

1963 (1)

A. L. Bloom, Spectra-Physics Laser Technical Bulletin No. 2 (1963).

Ananev, Yu. A.

Yu. A. Ananev, V. N. Chernov, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 403 (1972).
[CrossRef]

Bloom, A. L.

A. L. Bloom, Spectra-Physics Laser Technical Bulletin No. 2 (1963).

Bourne, O. L.

O. L. Bourne, P. E. Dyer, Opt. Commun. 31, 193 (1979).
[CrossRef]

Chernov, V. N.

Yu. A. Ananev, V. N. Chernov, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 403 (1972).
[CrossRef]

Dyer, P. E.

O. L. Bourne, P. E. Dyer, Opt. Commun. 31, 193 (1979).
[CrossRef]

P. E. Dyer, D. J. James, Opt. Commun. 15, 20 (1975).
[CrossRef]

James, D. J.

P. E. Dyer, D. J. James, Opt. Commun. 15, 20 (1975).
[CrossRef]

Kogelnik, H.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Krupke, W. F.

W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

Li, T.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Mahajan, V. N.

V. N. Mahajan, J. Opt. Soc. Am, 68, 742 (1978).
[CrossRef]

Mani, S. A.

Northam, D. B.

Phillips, E. A.

Reilly, J. P.

Rigrod, W. W.

W. W. Rigrod, J. Appl. Phys. 36, 2487 (1965).
[CrossRef]

Sherstobitov, V. E.

Yu. A. Ananev, V. N. Chernov, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 403 (1972).
[CrossRef]

Sooy, W. R.

W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

Sutton, G. W.

Weiner, M. M.

Appl. Opt. (4)

IEEE J. Quantum Electron. (1)

W. F. Krupke, W. R. Sooy, IEEE J. Quantum Electron. QE-5, 575 (1969).
[CrossRef]

J. Appl. Phys. (1)

W. W. Rigrod, J. Appl. Phys. 36, 2487 (1965).
[CrossRef]

J. Opt. Soc. Am (1)

V. N. Mahajan, J. Opt. Soc. Am, 68, 742 (1978).
[CrossRef]

Opt. Commun. (2)

P. E. Dyer, D. J. James, Opt. Commun. 15, 20 (1975).
[CrossRef]

O. L. Bourne, P. E. Dyer, Opt. Commun. 31, 193 (1979).
[CrossRef]

Proc. IEEE (1)

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Sov. J. Quantum Electron. (1)

Yu. A. Ananev, V. N. Chernov, V. E. Sherstobitov, Sov. J. Quantum Electron. 1, 403 (1972).
[CrossRef]

Spectra-Physics Laser Technical Bulletin No. 2 (1)

A. L. Bloom, Spectra-Physics Laser Technical Bulletin No. 2 (1963).

Other (1)

HPL LASER manufactured by AVCO, 32 Cobble Hill Road, Somerville, Mass. 02143.

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Figures (9)

Fig. 1
Fig. 1

Off-axis toroidal unstable resonator: 1, concave mirror; 2, convex mirror.

Fig. 2
Fig. 2

(a) Off-axis confocal unstable cavity in the vertical plane (y,z); (b) on-axis concave–convex stable cavity in the horizontal plane (x,z).

Fig. 3
Fig. 3

Laser cavity geometry cross sections in the planes (y,z) (a) and (x,z) (b).

Fig. 4
Fig. 4

Near-field burn patterns on Plexiglas of the off-axis unstable resonators: (a) 1.4-kW optical output power; (b) 300-W optical output power.

Fig. 5
Fig. 5

Resonators tested: (a) circular cross-section spherical mirror unstable telescope resonator; (b) rectangular cross-section toroidal mirror resonators.

Fig. 6
Fig. 6

Experimental configuration for the measure of the intensity distribution in the focal plane: C1C2, calorimeters; M1, 2.5-m focal length spherical mirror; A, variable aperture slit.

Fig. 7
Fig. 7

Fraction ηA of total power transmitted through the line slit A: (a) slit opening along the y axis of focal plane; (b) slit opening along the x axis of focal plane.

Fig. 8
Fig. 8

Modal volume cross section of the compared cavities: (a) spherical mirror aligned confocal unstable resonator; (b) spherical mirror off-axis confocal unstable resonator; (c) toroidal mirror off-axis unstable resonator.

Fig. 9
Fig. 9

Effect of angular sensitivity mx on TEM0 transverse mode size 2ω1 and on optical axis displacement Δ1x.

Tables (1)

Tables Icon

Table I Important Features of the Compared Cavities

Equations (22)

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γ x 1 ,
γ y 1 / M ,
δ = 1 - γ x · γ y 1 - ( 1 / M ) ,
I ( x , y ) = I x ( x ) · I y ( y ) .
I y ( y ) = I y 0             rect ( y D y / 2 ) ,
rect ( y D y / 2 ) = { 1 , 2 y / D y < 1 , 0 , otherwise .
cross - section size : 50 × 90 mm , R 1 y = + 10.0 m R 1 x = + 9.4 m ;
cross - section size :             50 × 72 mm , R 2 y = - 8.0 m             R 2 x = - 8.6 m ; M = 1.25             δ = 0.20             L = 1 m .
R 1 = + 16.0 m             R 2 = - 14.0 m             L = 1 m δ = 1 - ( 1 / M 2 ) = 0.23             beam diameter = 45 mm ,
cross - section size :             30 × 80 mm R 1 y = + 13.40 m             R 1 x = + 12.80 m ;
cross - section size :             30 × 68 mm R 2 y = - 11.40 m             R 2 x = - 12.00 m ; M = 1.18             δ = 0.15             L = 1 m .
η 0 = P out / P avail ,
η F = P F / P out ,
Q = P F / P avail
Q = η 0 × η F .
and for case ( c )             δ = 1 - ( 1 / M 2 ) δ = 1 - ( 1 / M ) } .
V = L × S = 1000 - cm 3 active medium volume , with L = 1 m and S = 10 cm 2 , g 0 = 0.01 cm - 1 ( typical value for cw - CO 2 fast flowing lasers ) and round - trip passive losses , ~ 0.03.
m = ϕ σ = R 1 R 1 + R 2 - L ,
Δ 1 R 1 ( R 2 - L ) σ R 1 + R 2 - L ,             Δ 2 = R 1 R 2 σ R 1 + R 2 - L .
m x = - 64             m y = 13.4
Δ 1 x = 8.3 mm Δ 1 y = 1.7 mm Δ 2 x = 7.7 mm Δ 2 y = 1.5 mm .
R av = R 1 + R 2 2 = 12.4 m .

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