Abstract

The total cavity loss in several ruby lasers has been determined experimentally from a set of threshold measurements. Scattering loss and end-mirror reflectance were measured separately and the difference between these losses and the total attributed to diffraction. Both plane-parallel and confocal resonators were employed. Diffraction loss in the plane-parallel cavities was 25 ± 8% per pass while diffraction loss in the confocal cavity was 8 ± 8%. These values are in agreement with theoretical analysis within experimental error.

© 1963 Optical Society of America

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References

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  1. T. H. Maiman, Nature 187, 493 (1960).
    [Crossref]
  2. R. J. Collins, D. F. Nelson, A. L. Schawlow, W. Bond, C. G. B. Garrett, and W. Kaiser, Phys. Rev. Letters 5, 303 (1960).
    [Crossref]
  3. A. L. Schawlow, Solid State 2, 21 (1961).
  4. A. G. Fox and T. Li, Proc. IRE 48, 1904 (1960).
  5. A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).
    [Crossref]
  6. G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
    [Crossref]
  7. L. Tonks, J. Appl. Phys. 33, 1980 (1962).
    [Crossref]
  8. V. Evtuhov and J. K. Neeland, Appl. Opt. 1, 517 (1962).
    [Crossref]
  9. M. S. Lipsett and M. W. P. Strandberg, Appl. Opt. 1, 343 (1962).
    [Crossref]
  10. E. S. Dayhoff and B. Kessler, Appl. Opt. 1, 339 (1962).
    [Crossref]
  11. E. S. Dayhoff, Proc. IRE 50, 1684 (1962).
  12. W. Kaiser and M. J. Keck, J. Appl. Phys. 33, 762 (1962).
    [Crossref]
  13. This apparatus is described in A. S. D. Tech. Rept. by J. E. Janssen, R. H. Torborg, J. R. Luck, and R. N. Schmidt.
  14. J. F. Ready and D. L. Hardwick, Proc. IRE (to be published).
  15. N. B. Piper, Electronics 34, 66 (1961).
  16. C. F. Luck (private communication).
  17. T. H. Maiman, R. H. Hoskins, I. J. D. Haenens, C. K. Asawa, and V. Evtuhov, Phys. Rev. 123, 1151 (1961).
    [Crossref]
  18. A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (The MacMillan Company, New York, 1934).
  19. I. D. Abella and H. Z. Cummins, J. Appl. Phys. 32, 1177 (1961).
    [Crossref]
  20. A. L. Schawlow, “Fine Structure and Properties of Chromium Fluorescence in Aluminum and Magnesium Oxide,” Advances in Quantum Electronics, edited by J. R. Singer (Columbia University Press, New York, 1961), p. 50.
  21. F. Varsanyi, D. A. Wood, and A. L. Schawlow, Phys. Rev. Letters 3, 544 (1959).
    [Crossref]
  22. J. E. Geusic and H. E. D. Scovil, Bell System Tech. J. 41, 1371 (1962).
    [Crossref]
  23. R. L. Aagard, J. Appl. Phys. 33, 2842 (1962).
    [Crossref]
  24. D. F. Nelson and R. J. Collins, Proceedings of the 1961 Conference on Optics, London.

1962 (8)

L. Tonks, J. Appl. Phys. 33, 1980 (1962).
[Crossref]

V. Evtuhov and J. K. Neeland, Appl. Opt. 1, 517 (1962).
[Crossref]

M. S. Lipsett and M. W. P. Strandberg, Appl. Opt. 1, 343 (1962).
[Crossref]

E. S. Dayhoff and B. Kessler, Appl. Opt. 1, 339 (1962).
[Crossref]

E. S. Dayhoff, Proc. IRE 50, 1684 (1962).

W. Kaiser and M. J. Keck, J. Appl. Phys. 33, 762 (1962).
[Crossref]

J. E. Geusic and H. E. D. Scovil, Bell System Tech. J. 41, 1371 (1962).
[Crossref]

R. L. Aagard, J. Appl. Phys. 33, 2842 (1962).
[Crossref]

1961 (6)

A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).
[Crossref]

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
[Crossref]

A. L. Schawlow, Solid State 2, 21 (1961).

N. B. Piper, Electronics 34, 66 (1961).

T. H. Maiman, R. H. Hoskins, I. J. D. Haenens, C. K. Asawa, and V. Evtuhov, Phys. Rev. 123, 1151 (1961).
[Crossref]

I. D. Abella and H. Z. Cummins, J. Appl. Phys. 32, 1177 (1961).
[Crossref]

1960 (3)

A. G. Fox and T. Li, Proc. IRE 48, 1904 (1960).

T. H. Maiman, Nature 187, 493 (1960).
[Crossref]

R. J. Collins, D. F. Nelson, A. L. Schawlow, W. Bond, C. G. B. Garrett, and W. Kaiser, Phys. Rev. Letters 5, 303 (1960).
[Crossref]

1959 (1)

F. Varsanyi, D. A. Wood, and A. L. Schawlow, Phys. Rev. Letters 3, 544 (1959).
[Crossref]

Aagard, R. L.

R. L. Aagard, J. Appl. Phys. 33, 2842 (1962).
[Crossref]

Abella, I. D.

I. D. Abella and H. Z. Cummins, J. Appl. Phys. 32, 1177 (1961).
[Crossref]

Asawa, C. K.

T. H. Maiman, R. H. Hoskins, I. J. D. Haenens, C. K. Asawa, and V. Evtuhov, Phys. Rev. 123, 1151 (1961).
[Crossref]

Bond, W.

R. J. Collins, D. F. Nelson, A. L. Schawlow, W. Bond, C. G. B. Garrett, and W. Kaiser, Phys. Rev. Letters 5, 303 (1960).
[Crossref]

Boyd, G. D.

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
[Crossref]

Collins, R. J.

R. J. Collins, D. F. Nelson, A. L. Schawlow, W. Bond, C. G. B. Garrett, and W. Kaiser, Phys. Rev. Letters 5, 303 (1960).
[Crossref]

D. F. Nelson and R. J. Collins, Proceedings of the 1961 Conference on Optics, London.

Cummins, H. Z.

I. D. Abella and H. Z. Cummins, J. Appl. Phys. 32, 1177 (1961).
[Crossref]

Dayhoff, E. S.

E. S. Dayhoff, Proc. IRE 50, 1684 (1962).

E. S. Dayhoff and B. Kessler, Appl. Opt. 1, 339 (1962).
[Crossref]

Evtuhov, V.

V. Evtuhov and J. K. Neeland, Appl. Opt. 1, 517 (1962).
[Crossref]

T. H. Maiman, R. H. Hoskins, I. J. D. Haenens, C. K. Asawa, and V. Evtuhov, Phys. Rev. 123, 1151 (1961).
[Crossref]

Fox, A. G.

A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).
[Crossref]

A. G. Fox and T. Li, Proc. IRE 48, 1904 (1960).

Garrett, C. G. B.

R. J. Collins, D. F. Nelson, A. L. Schawlow, W. Bond, C. G. B. Garrett, and W. Kaiser, Phys. Rev. Letters 5, 303 (1960).
[Crossref]

Geusic, J. E.

J. E. Geusic and H. E. D. Scovil, Bell System Tech. J. 41, 1371 (1962).
[Crossref]

Gordon, J. P.

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
[Crossref]

Haenens, I. J. D.

T. H. Maiman, R. H. Hoskins, I. J. D. Haenens, C. K. Asawa, and V. Evtuhov, Phys. Rev. 123, 1151 (1961).
[Crossref]

Hardwick, D. L.

J. F. Ready and D. L. Hardwick, Proc. IRE (to be published).

Hoskins, R. H.

T. H. Maiman, R. H. Hoskins, I. J. D. Haenens, C. K. Asawa, and V. Evtuhov, Phys. Rev. 123, 1151 (1961).
[Crossref]

Janssen, J. E.

This apparatus is described in A. S. D. Tech. Rept. by J. E. Janssen, R. H. Torborg, J. R. Luck, and R. N. Schmidt.

Kaiser, W.

W. Kaiser and M. J. Keck, J. Appl. Phys. 33, 762 (1962).
[Crossref]

R. J. Collins, D. F. Nelson, A. L. Schawlow, W. Bond, C. G. B. Garrett, and W. Kaiser, Phys. Rev. Letters 5, 303 (1960).
[Crossref]

Keck, M. J.

W. Kaiser and M. J. Keck, J. Appl. Phys. 33, 762 (1962).
[Crossref]

Kessler, B.

Li, T.

A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).
[Crossref]

A. G. Fox and T. Li, Proc. IRE 48, 1904 (1960).

Lipsett, M. S.

Luck, C. F.

C. F. Luck (private communication).

Luck, J. R.

This apparatus is described in A. S. D. Tech. Rept. by J. E. Janssen, R. H. Torborg, J. R. Luck, and R. N. Schmidt.

Maiman, T. H.

T. H. Maiman, R. H. Hoskins, I. J. D. Haenens, C. K. Asawa, and V. Evtuhov, Phys. Rev. 123, 1151 (1961).
[Crossref]

T. H. Maiman, Nature 187, 493 (1960).
[Crossref]

Mitchell, A. C. G.

A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (The MacMillan Company, New York, 1934).

Neeland, J. K.

Nelson, D. F.

R. J. Collins, D. F. Nelson, A. L. Schawlow, W. Bond, C. G. B. Garrett, and W. Kaiser, Phys. Rev. Letters 5, 303 (1960).
[Crossref]

D. F. Nelson and R. J. Collins, Proceedings of the 1961 Conference on Optics, London.

Piper, N. B.

N. B. Piper, Electronics 34, 66 (1961).

Ready, J. F.

J. F. Ready and D. L. Hardwick, Proc. IRE (to be published).

Schawlow, A. L.

A. L. Schawlow, Solid State 2, 21 (1961).

R. J. Collins, D. F. Nelson, A. L. Schawlow, W. Bond, C. G. B. Garrett, and W. Kaiser, Phys. Rev. Letters 5, 303 (1960).
[Crossref]

F. Varsanyi, D. A. Wood, and A. L. Schawlow, Phys. Rev. Letters 3, 544 (1959).
[Crossref]

A. L. Schawlow, “Fine Structure and Properties of Chromium Fluorescence in Aluminum and Magnesium Oxide,” Advances in Quantum Electronics, edited by J. R. Singer (Columbia University Press, New York, 1961), p. 50.

Schmidt, R. N.

This apparatus is described in A. S. D. Tech. Rept. by J. E. Janssen, R. H. Torborg, J. R. Luck, and R. N. Schmidt.

Scovil, H. E. D.

J. E. Geusic and H. E. D. Scovil, Bell System Tech. J. 41, 1371 (1962).
[Crossref]

Strandberg, M. W. P.

Tonks, L.

L. Tonks, J. Appl. Phys. 33, 1980 (1962).
[Crossref]

Torborg, R. H.

This apparatus is described in A. S. D. Tech. Rept. by J. E. Janssen, R. H. Torborg, J. R. Luck, and R. N. Schmidt.

Varsanyi, F.

F. Varsanyi, D. A. Wood, and A. L. Schawlow, Phys. Rev. Letters 3, 544 (1959).
[Crossref]

Wood, D. A.

F. Varsanyi, D. A. Wood, and A. L. Schawlow, Phys. Rev. Letters 3, 544 (1959).
[Crossref]

Zemansky, M. W.

A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (The MacMillan Company, New York, 1934).

Appl. Opt. (3)

Bell System Tech. J. (3)

A. G. Fox and T. Li, Bell System Tech. J. 40, 453 (1961).
[Crossref]

G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961).
[Crossref]

J. E. Geusic and H. E. D. Scovil, Bell System Tech. J. 41, 1371 (1962).
[Crossref]

Electronics (1)

N. B. Piper, Electronics 34, 66 (1961).

J. Appl. Phys. (4)

W. Kaiser and M. J. Keck, J. Appl. Phys. 33, 762 (1962).
[Crossref]

I. D. Abella and H. Z. Cummins, J. Appl. Phys. 32, 1177 (1961).
[Crossref]

L. Tonks, J. Appl. Phys. 33, 1980 (1962).
[Crossref]

R. L. Aagard, J. Appl. Phys. 33, 2842 (1962).
[Crossref]

Nature (1)

T. H. Maiman, Nature 187, 493 (1960).
[Crossref]

Phys. Rev. (1)

T. H. Maiman, R. H. Hoskins, I. J. D. Haenens, C. K. Asawa, and V. Evtuhov, Phys. Rev. 123, 1151 (1961).
[Crossref]

Phys. Rev. Letters (2)

R. J. Collins, D. F. Nelson, A. L. Schawlow, W. Bond, C. G. B. Garrett, and W. Kaiser, Phys. Rev. Letters 5, 303 (1960).
[Crossref]

F. Varsanyi, D. A. Wood, and A. L. Schawlow, Phys. Rev. Letters 3, 544 (1959).
[Crossref]

Proc. IRE (2)

A. G. Fox and T. Li, Proc. IRE 48, 1904 (1960).

E. S. Dayhoff, Proc. IRE 50, 1684 (1962).

Solid State (1)

A. L. Schawlow, Solid State 2, 21 (1961).

Other (6)

A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (The MacMillan Company, New York, 1934).

A. L. Schawlow, “Fine Structure and Properties of Chromium Fluorescence in Aluminum and Magnesium Oxide,” Advances in Quantum Electronics, edited by J. R. Singer (Columbia University Press, New York, 1961), p. 50.

This apparatus is described in A. S. D. Tech. Rept. by J. E. Janssen, R. H. Torborg, J. R. Luck, and R. N. Schmidt.

J. F. Ready and D. L. Hardwick, Proc. IRE (to be published).

C. F. Luck (private communication).

D. F. Nelson and R. J. Collins, Proceedings of the 1961 Conference on Optics, London.

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Figures (1)

Fig. 1
Fig. 1

Threshold for laser action as a function of linewidth for two plane-parallel ruby lasers. The equation describing these data is given in the upper right corner. Et = threshold energy, an = cavity loss, and K = constant of proportionality between pumping energy and population of the metastable level. Δν = line-width in cm−1 and C = constant representing the amount of pumping energy required to equalize the populations of the metastable and ground levels. The nonlinear rise in threshold shown by the dotted lines is thought to be due to shortening of the mean fluorescence lifetime when coatings are removed from the rod. The relationship between linewidth and temperature is taken from measurements reported by A. L. Schawlow.20

Tables (2)

Tables Icon

Table I Rod specifications.a

Tables Icon

Table II Experimental results.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

α l = ln ( 1 / ξ [ R 1 R 2 ] 1 2 ) + β l ,
α = 2 Δ ν [ ln 2 π ] 1 2 λ 0 2 8 π g 2 g 1 ( g 1 / g 2 ) N 2 N 1 τ r .
α = ( g 1 / g 2 ) N 2 N 1 K 1 Δ ν ,
K 2 [ ( g 1 / g 2 ) N 2 N 1 ] = E t C ,
E t = K 3 Δ ν [ ln ( 1 / ξ [ R 1 R 2 ] 1 2 ) + β l ] + C ,
E t = K 3 a n Δ ν + C ,
a 1 = ln ( 1 / ξ R ) + β l ,
a 2 = ( S 2 / S 1 ) a 1 = ln [ 1 / ξ ( 0.075 R ) 1 2 ] + β l ,
a 3 = ( S 3 / S 1 ) a 1 = ln ( 1 / ξ 0.075 ) + β l .