Abstract

The gain and the saturation intensity of optimized cw 337-μm lasers are shown empirically to vary inversely as tube diameter. An expression is then derived for the power of a waveguide laser as a function of geometrical parameters, losses, and coupling. For optimized coupling the power is a strong function of tube diameter with a well defined maximum. Optimum diameter depends on tube length and losses only. The results agree well with the measured powers of three waveguide lasers delivering 30 mW, 100 mW, and 170 mW from discharges of 1-m, 2-m, and 3-m lengths. Such lasers are competitive with optically pumped submillimeter lasers.

© 1976 Optical Society of America

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  1. P. Belland, D. Véron, Opt. Commun. 9, 146 (1973).
    [CrossRef]
  2. P. Belland, A. I. Ciura, L. B. Whitbourn, Opt. Commun. 11, 21 (1974).
    [CrossRef]
  3. P. Belland, D. Veron, L. B. Whitbourn, J. Phys. D 8, 2113 (1975).
    [CrossRef]
  4. T. Y. Chang, IEEE Trans. Microwave Theory Tech. MTT-22, 983 (1974).
    [CrossRef]
  5. D. C. Sinclair, W. E. Bell, Gas Laser Technology (Holt, Rinehart and Winston, New York, 1969).
  6. N. R. Heckenberg, G. D. Tait, L. B. Whitbourn, J. Appl. Phys. 44, 4522 (1973).
    [CrossRef]
  7. P. Belland, L. B. Whitbourn, to be published.
  8. J. P. Lesieur, M. C. Sexton, D. Véron, J. Phys. D 5, 1212 (1972).
    [CrossRef]
  9. H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
    [CrossRef]
  10. E. A. J. Marcatili, R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
  11. R. Ulrich, T. J. Bridges, M. A. Pollack, Appl. Opt. 9, 2511 (1970).
    [CrossRef] [PubMed]
  12. J. R. Birch, C. C. Bradley, Infrared Phys. 13, 99 (1973).
    [CrossRef]
  13. P. Belland, D. Véron, L. B. Whitbourn, J. Phys. E 8, 866 (1975).
    [CrossRef]
  14. E. M. Dianov, N. A. Irisova, V. N. Timofeev, Sov. Phys. Solid State 8, 2113 (1967).
  15. J. R. Birch, N. W. B. Stone, J. Phys. E 6, 1001 (1973).
    [CrossRef]
  16. W. Bagdade, R. Stolen, J. Phys. Chem. Solids 29, 2001 (1968).
    [CrossRef]
  17. J. R. Birch, R. J. Cook, A. F. Harding, R. G. Jones, G. D. Price, J. Phys. D 8, 1353 (1975).
    [CrossRef]
  18. D. Véron, Opt. Commun. 10, 95 (1974).
    [CrossRef]
  19. D. Véron, J. Certain, J. P. Crenn, Report EUR-CEA-FC-799 (December1975).
  20. T. A. DeTemple, E. J. Danielewicz, IEEE J. Quantum Electron. QE-12, 40 (1976).
    [CrossRef]
  21. D. T. Hodges, J. R. Tucker, T. S. Hartwick, Infrared Phys. 16, 175 (1976).
    [CrossRef]
  22. C. C. Bradley, Infrared Phys. 12, 287 (1972).
    [CrossRef]

1976 (2)

T. A. DeTemple, E. J. Danielewicz, IEEE J. Quantum Electron. QE-12, 40 (1976).
[CrossRef]

D. T. Hodges, J. R. Tucker, T. S. Hartwick, Infrared Phys. 16, 175 (1976).
[CrossRef]

1975 (3)

J. R. Birch, R. J. Cook, A. F. Harding, R. G. Jones, G. D. Price, J. Phys. D 8, 1353 (1975).
[CrossRef]

P. Belland, D. Véron, L. B. Whitbourn, J. Phys. E 8, 866 (1975).
[CrossRef]

P. Belland, D. Veron, L. B. Whitbourn, J. Phys. D 8, 2113 (1975).
[CrossRef]

1974 (3)

T. Y. Chang, IEEE Trans. Microwave Theory Tech. MTT-22, 983 (1974).
[CrossRef]

P. Belland, A. I. Ciura, L. B. Whitbourn, Opt. Commun. 11, 21 (1974).
[CrossRef]

D. Véron, Opt. Commun. 10, 95 (1974).
[CrossRef]

1973 (4)

J. R. Birch, N. W. B. Stone, J. Phys. E 6, 1001 (1973).
[CrossRef]

P. Belland, D. Véron, Opt. Commun. 9, 146 (1973).
[CrossRef]

J. R. Birch, C. C. Bradley, Infrared Phys. 13, 99 (1973).
[CrossRef]

N. R. Heckenberg, G. D. Tait, L. B. Whitbourn, J. Appl. Phys. 44, 4522 (1973).
[CrossRef]

1972 (2)

J. P. Lesieur, M. C. Sexton, D. Véron, J. Phys. D 5, 1212 (1972).
[CrossRef]

C. C. Bradley, Infrared Phys. 12, 287 (1972).
[CrossRef]

1970 (1)

1968 (1)

W. Bagdade, R. Stolen, J. Phys. Chem. Solids 29, 2001 (1968).
[CrossRef]

1967 (1)

E. M. Dianov, N. A. Irisova, V. N. Timofeev, Sov. Phys. Solid State 8, 2113 (1967).

1966 (1)

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

1964 (1)

E. A. J. Marcatili, R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).

Bagdade, W.

W. Bagdade, R. Stolen, J. Phys. Chem. Solids 29, 2001 (1968).
[CrossRef]

Bell, W. E.

D. C. Sinclair, W. E. Bell, Gas Laser Technology (Holt, Rinehart and Winston, New York, 1969).

Belland, P.

P. Belland, D. Veron, L. B. Whitbourn, J. Phys. D 8, 2113 (1975).
[CrossRef]

P. Belland, D. Véron, L. B. Whitbourn, J. Phys. E 8, 866 (1975).
[CrossRef]

P. Belland, A. I. Ciura, L. B. Whitbourn, Opt. Commun. 11, 21 (1974).
[CrossRef]

P. Belland, D. Véron, Opt. Commun. 9, 146 (1973).
[CrossRef]

P. Belland, L. B. Whitbourn, to be published.

Birch, J. R.

J. R. Birch, R. J. Cook, A. F. Harding, R. G. Jones, G. D. Price, J. Phys. D 8, 1353 (1975).
[CrossRef]

J. R. Birch, N. W. B. Stone, J. Phys. E 6, 1001 (1973).
[CrossRef]

J. R. Birch, C. C. Bradley, Infrared Phys. 13, 99 (1973).
[CrossRef]

Bradley, C. C.

J. R. Birch, C. C. Bradley, Infrared Phys. 13, 99 (1973).
[CrossRef]

C. C. Bradley, Infrared Phys. 12, 287 (1972).
[CrossRef]

Bridges, T. J.

Certain, J.

D. Véron, J. Certain, J. P. Crenn, Report EUR-CEA-FC-799 (December1975).

Chang, T. Y.

T. Y. Chang, IEEE Trans. Microwave Theory Tech. MTT-22, 983 (1974).
[CrossRef]

Ciura, A. I.

P. Belland, A. I. Ciura, L. B. Whitbourn, Opt. Commun. 11, 21 (1974).
[CrossRef]

Cook, R. J.

J. R. Birch, R. J. Cook, A. F. Harding, R. G. Jones, G. D. Price, J. Phys. D 8, 1353 (1975).
[CrossRef]

Crenn, J. P.

D. Véron, J. Certain, J. P. Crenn, Report EUR-CEA-FC-799 (December1975).

Danielewicz, E. J.

T. A. DeTemple, E. J. Danielewicz, IEEE J. Quantum Electron. QE-12, 40 (1976).
[CrossRef]

DeTemple, T. A.

T. A. DeTemple, E. J. Danielewicz, IEEE J. Quantum Electron. QE-12, 40 (1976).
[CrossRef]

Dianov, E. M.

E. M. Dianov, N. A. Irisova, V. N. Timofeev, Sov. Phys. Solid State 8, 2113 (1967).

Harding, A. F.

J. R. Birch, R. J. Cook, A. F. Harding, R. G. Jones, G. D. Price, J. Phys. D 8, 1353 (1975).
[CrossRef]

Hartwick, T. S.

D. T. Hodges, J. R. Tucker, T. S. Hartwick, Infrared Phys. 16, 175 (1976).
[CrossRef]

Heckenberg, N. R.

N. R. Heckenberg, G. D. Tait, L. B. Whitbourn, J. Appl. Phys. 44, 4522 (1973).
[CrossRef]

Hodges, D. T.

D. T. Hodges, J. R. Tucker, T. S. Hartwick, Infrared Phys. 16, 175 (1976).
[CrossRef]

Irisova, N. A.

E. M. Dianov, N. A. Irisova, V. N. Timofeev, Sov. Phys. Solid State 8, 2113 (1967).

Jones, R. G.

J. R. Birch, R. J. Cook, A. F. Harding, R. G. Jones, G. D. Price, J. Phys. D 8, 1353 (1975).
[CrossRef]

Kogelnik, H.

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

Lesieur, J. P.

J. P. Lesieur, M. C. Sexton, D. Véron, J. Phys. D 5, 1212 (1972).
[CrossRef]

Li, T.

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

Marcatili, E. A. J.

E. A. J. Marcatili, R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).

Pollack, M. A.

Price, G. D.

J. R. Birch, R. J. Cook, A. F. Harding, R. G. Jones, G. D. Price, J. Phys. D 8, 1353 (1975).
[CrossRef]

Schmeltzer, R. A.

E. A. J. Marcatili, R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).

Sexton, M. C.

J. P. Lesieur, M. C. Sexton, D. Véron, J. Phys. D 5, 1212 (1972).
[CrossRef]

Sinclair, D. C.

D. C. Sinclair, W. E. Bell, Gas Laser Technology (Holt, Rinehart and Winston, New York, 1969).

Stolen, R.

W. Bagdade, R. Stolen, J. Phys. Chem. Solids 29, 2001 (1968).
[CrossRef]

Stone, N. W. B.

J. R. Birch, N. W. B. Stone, J. Phys. E 6, 1001 (1973).
[CrossRef]

Tait, G. D.

N. R. Heckenberg, G. D. Tait, L. B. Whitbourn, J. Appl. Phys. 44, 4522 (1973).
[CrossRef]

Timofeev, V. N.

E. M. Dianov, N. A. Irisova, V. N. Timofeev, Sov. Phys. Solid State 8, 2113 (1967).

Tucker, J. R.

D. T. Hodges, J. R. Tucker, T. S. Hartwick, Infrared Phys. 16, 175 (1976).
[CrossRef]

Ulrich, R.

Veron, D.

P. Belland, D. Veron, L. B. Whitbourn, J. Phys. D 8, 2113 (1975).
[CrossRef]

Véron, D.

P. Belland, D. Véron, L. B. Whitbourn, J. Phys. E 8, 866 (1975).
[CrossRef]

D. Véron, Opt. Commun. 10, 95 (1974).
[CrossRef]

P. Belland, D. Véron, Opt. Commun. 9, 146 (1973).
[CrossRef]

J. P. Lesieur, M. C. Sexton, D. Véron, J. Phys. D 5, 1212 (1972).
[CrossRef]

D. Véron, J. Certain, J. P. Crenn, Report EUR-CEA-FC-799 (December1975).

Whitbourn, L. B.

P. Belland, D. Véron, L. B. Whitbourn, J. Phys. E 8, 866 (1975).
[CrossRef]

P. Belland, D. Veron, L. B. Whitbourn, J. Phys. D 8, 2113 (1975).
[CrossRef]

P. Belland, A. I. Ciura, L. B. Whitbourn, Opt. Commun. 11, 21 (1974).
[CrossRef]

N. R. Heckenberg, G. D. Tait, L. B. Whitbourn, J. Appl. Phys. 44, 4522 (1973).
[CrossRef]

P. Belland, L. B. Whitbourn, to be published.

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

E. A. J. Marcatili, R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).

IEEE J. Quantum Electron. (1)

T. A. DeTemple, E. J. Danielewicz, IEEE J. Quantum Electron. QE-12, 40 (1976).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

T. Y. Chang, IEEE Trans. Microwave Theory Tech. MTT-22, 983 (1974).
[CrossRef]

Infrared Phys. (3)

J. R. Birch, C. C. Bradley, Infrared Phys. 13, 99 (1973).
[CrossRef]

D. T. Hodges, J. R. Tucker, T. S. Hartwick, Infrared Phys. 16, 175 (1976).
[CrossRef]

C. C. Bradley, Infrared Phys. 12, 287 (1972).
[CrossRef]

J. Appl. Phys. (1)

N. R. Heckenberg, G. D. Tait, L. B. Whitbourn, J. Appl. Phys. 44, 4522 (1973).
[CrossRef]

J. Phys. Chem. Solids (1)

W. Bagdade, R. Stolen, J. Phys. Chem. Solids 29, 2001 (1968).
[CrossRef]

J. Phys. D (3)

J. R. Birch, R. J. Cook, A. F. Harding, R. G. Jones, G. D. Price, J. Phys. D 8, 1353 (1975).
[CrossRef]

J. P. Lesieur, M. C. Sexton, D. Véron, J. Phys. D 5, 1212 (1972).
[CrossRef]

P. Belland, D. Veron, L. B. Whitbourn, J. Phys. D 8, 2113 (1975).
[CrossRef]

J. Phys. E (2)

J. R. Birch, N. W. B. Stone, J. Phys. E 6, 1001 (1973).
[CrossRef]

P. Belland, D. Véron, L. B. Whitbourn, J. Phys. E 8, 866 (1975).
[CrossRef]

Opt. Commun. (3)

D. Véron, Opt. Commun. 10, 95 (1974).
[CrossRef]

P. Belland, D. Véron, Opt. Commun. 9, 146 (1973).
[CrossRef]

P. Belland, A. I. Ciura, L. B. Whitbourn, Opt. Commun. 11, 21 (1974).
[CrossRef]

Proc. IEEE (1)

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

Sov. Phys. Solid State (1)

E. M. Dianov, N. A. Irisova, V. N. Timofeev, Sov. Phys. Solid State 8, 2113 (1967).

Other (3)

D. Véron, J. Certain, J. P. Crenn, Report EUR-CEA-FC-799 (December1975).

P. Belland, L. B. Whitbourn, to be published.

D. C. Sinclair, W. E. Bell, Gas Laser Technology (Holt, Rinehart and Winston, New York, 1969).

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Figures (7)

Fig. 1
Fig. 1

Measured unsaturated gains of three optimized 337-μm HCN laser discharges as a function of the reciprocal of tube diameter. Also shown is an approximate value inferred from published data for a laser constructed at Bell Laboratories.11 The clear linear relationship is common for gas discharge lasers.

Fig. 2
Fig. 2

Measured saturation intensities of three optimized 337-μm HCN laser discharges as a function of the reciprocal of tube diameter. The point corresponding to a 2-cm diam tube is very approximate. Also shown is an approximate value inferred from published data for a laser constructed at Bell Laboratories.11 The linear relationsship between saturation intensity and reciprocal of tube diameter is a I new result for HCN lasers.

Fig. 3
Fig. 3

Output power as a function of tube diameter of a 337-μm waveguide laser with a fixed discharge length of 2 m in a 2.4-m long Pyrex tube for external loss a of 1%, 2%, 3%, and 4% per single pass. The values given by the curves correspond to optimum gas discharge conditions and cavity coupling for each combination of external loss and tube diameter. It is seen that there is an optimum tube diameter that decreases slowly with increasing external loss.

Fig. 4
Fig. 4

Output power as a function of tube diameter of a 337-μm waveguide laser with a fixed external loss of 2% per single pass for discharge lengths of 0.5 m, 1 m, 2 m, and 3 m. The Pyrex tube is assumed to be always 0.4 m longer than the discharge. The values given by the curves correspond to optimum gas conditions and cavity coupling for each combination of discharge length and tube diameter. The optimum tube diameter increases slowly with increasing discharge length.

Fig. 5
Fig. 5

Optimum tube diameter and corresponding optimum output power as a function of discharge length of a 337-μm waveguide laser for external losses of 1%, 2%, 3%, and 4% per single pass. Optimum discharge conditions and cavity coupling are assumed. The curves are extrapolated to show what would be required to produce powers of the order of 1 W at 337 μm.

Fig. 6
Fig. 6

Optimum output power as a function of discharge length of a 337-μm waveguide laser for external losses of 1%, 2%, 3%, and 4% per single pass. These are the same as the power curves of Fig. 5 but shown on a logarithmic scale to give better precision in designing lasers with discharge lengths up to 5 m. They agree quite well with the 30-mW, 100-mW, and 170-mW power levels obtained from waveguide lasers of lengths 1-m, 2-m, and 3-m lengths, respectively (a0 = 2%).

Fig. 7
Fig. 7

Optimum coupling as a function of discharge length of a 337-μm waveguide laser for external losses of 1%, 2%, 3%, and 4% per single pass. The values given by the curves correspond to the optimum tube diameter for each discharge length (Fig. 5).

Tables (1)

Tables Icon

Table I Geometrical Details, Operating Conditions, and Measured Parameters of the Four Lasers upon Which the Present Scaling Laws are Based

Equations (14)

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g ( W ) = ( g 0 ) / ( 1 + W / W s ) ,
W = W s ( g 0 L a + t - 1 ) .
P = t S W s ( g 0 L a + t - 1 ) .
t 0 = ( g 0 L a ) 1 / 2 - a ,
P 0 = S W s [ ( g 0 L ) 1 / 2 - ( a ) 1 / 2 ] 2 .
g 0 = 0.46 d ( cm ) m - 1
W s = 1350 d ( cm ) mW cm - 2 .
S = π 4 ( 0.555 d ) 2 .
2 α = ( 2.405 2 π ) 2 8 λ 2 d 3 Re [ η ^ 2 + 1 ( η ^ 2 - 1 ) 1 / 2 ] = k l ( η ^ , λ ) d 3 ,
2 α = 0.423 [ d ( cm ) ] 3 m - 1 .
a = a 0 + a 1 = a 0 + 0.423 ( L + L ) ( m ) [ d ( cm ) ] 3 .
P 0 = 327 ( [ 0.46 L ( m ) ] 1 / 2 - { a 0 d ( cm ) + 0.423 ( L + L ) ( m ) [ d ( cm ) ] 2 } 1 / 2 ) 2 mW .
d 0 = [ 2 × 0.423 ( L + L ) a 0 ] 1 / 3 ,
d 0 = [ 2 k l ( η ^ , λ ) ( L + L ) a 0 ] 1 / 3 .

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