Abstract

Determinations of optical loss in unpumped ruby laser crystals from measurements of the transmissivity vs optical path length (as changed by temperature) using an amplitude regulated, single mode, He–Ne laser beam probe are described. Excellent agreement between these measurements and the theory of Dufour and Picca was obtained for a flux-grown ruby using as-grown feedback surfaces. The essentially zero loss per pass β (apart from end reflector losses) deduced from this comparison is in excellent agreement with a previous determination of the loss in this crystal from laser threshold measurements. The reduction of the effective surface roughness by deposition of multilayer zinc sulfide–cryolite reflectors was observed in these experiments. For a high quality, 7.5-cm long, 0.05 wt% Cr2O3, 60° orientation ruby rod, β was found to be 0.03 ± 0.03. For a 90° orientation, 2.2-cm long, trumpet-shaped ruby used for continuous operation threshold studies, β was found to be about 0.14. The problems of this type of loss measurement when index of refraction variations are present are discussed, and observations connecting the crystal quality and laser mode characteristics are presented.

© 1967 Optical Society of America

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References

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  1. R. J. Collins, D. F. Nelson in Proceedings of the Conference on Optical Instruments, 1961 (Chapman and Hall Ltd., London, 1962), p. 441.
  2. R. L. Aagard, J. Opt. Soc. Am. 53, 911 (1963).
    [Crossref]
  3. J. I. Masters, Nature 199, 442 (1963).
    [Crossref]
  4. M. M. Hercher, Doctoral Dissertation, Institute of Optics, The University of Rochester, 1963 (unpublished).
  5. D. F. Nelson, J. P. Remeika, J. Appl. Phys. 35, 522 (1964).
    [Crossref]
  6. V. Daneu, C. A. Sacchi, O. Svelto, Appl. Opt. 4, 863 (1965).
    [Crossref]
  7. D. C. Hanna, W. A. Gambling, R. C. Smith, J. Quantum Electron. QE-2, 507 (1966).
    [Crossref]
  8. D. F. Nelson, D. E. McCumber, in Quantum Electronics, III, P. Grivet, N. Bloembergen, Eds. (Columbia University Press, New York, 1964), p. 1037.
  9. A. J. Rack, M. R. Biazzo, Bell System Tech. J. 63, 1563 (1964).
  10. V. N. Del Piano, A. F. Quesada, Appl. Opt. 4, 1386 (1965).
    [Crossref]
  11. J. A. Giordmaine, R. C. Miller, Phys. Rev. Letters 14, 973 (1965).
    [Crossref]
  12. D. G. Peterson, A. Yariv, Appl. Opt. 5, 469 (1966); Appl. Opt. 5, 985 (1966).
    [Crossref] [PubMed]
  13. G. D. Boyd, A. Ashkin, Phys. Rev. 146, 187 (1966).
    [Crossref]
  14. M. Born, E. Wolf, Principles of Optics (The Macmillan Company, New York, 1964), p. 323.
  15. C. Dufour, R. Picca, Rev. Opt. 24, 19 (1945).
  16. R. Chabbal, J. Rech. Cent. Nat. Rech. Sci., Labs. Bellevue (Paris) 24, 138 (1953).
  17. J. Kotik, M. C. Newstein, J. Appl. Phys. 32, 178 (1961).
    [Crossref]
  18. A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
    [Crossref]
  19. J. W. Hansen, K. F. Rodgers, D. E. Thomas, private communication.
  20. I. H. Malitson, F. V. Murphy, W. S. Rodney, J. Opt. Soc. Am. 48, 72 (1958).
    [Crossref]
  21. D. L. Perry, Appl. Opt. 4, 987 (1965).
    [Crossref]
  22. D. F. Nelson, W. S. Boyle, Appl. Opt. 1, 181 (1962).
    [Crossref]
  23. R. L. Aagard, R. A. Dufault, Appl. Phys. Letters 4, 102 (1964).
    [Crossref]
  24. Y. C. Kiang, J. F. Stephany, F. C. Unterleitner, J. Quantum Electron. QE-2, 295 (1965).
    [Crossref]
  25. T. Kushida, J. Quantum Electron. QE-2, 524 (1966).
    [Crossref]
  26. D. F. Nelson, M. D. Sturge, Phys. Rev. 137, A11117 (1965).
    [Crossref]
  27. A. D. White, J. D. Rigden, Appl. Phys. Letters 2, 211 (1963).
    [Crossref]

1966 (4)

D. C. Hanna, W. A. Gambling, R. C. Smith, J. Quantum Electron. QE-2, 507 (1966).
[Crossref]

D. G. Peterson, A. Yariv, Appl. Opt. 5, 469 (1966); Appl. Opt. 5, 985 (1966).
[Crossref] [PubMed]

G. D. Boyd, A. Ashkin, Phys. Rev. 146, 187 (1966).
[Crossref]

T. Kushida, J. Quantum Electron. QE-2, 524 (1966).
[Crossref]

1965 (6)

D. F. Nelson, M. D. Sturge, Phys. Rev. 137, A11117 (1965).
[Crossref]

Y. C. Kiang, J. F. Stephany, F. C. Unterleitner, J. Quantum Electron. QE-2, 295 (1965).
[Crossref]

D. L. Perry, Appl. Opt. 4, 987 (1965).
[Crossref]

V. N. Del Piano, A. F. Quesada, Appl. Opt. 4, 1386 (1965).
[Crossref]

J. A. Giordmaine, R. C. Miller, Phys. Rev. Letters 14, 973 (1965).
[Crossref]

V. Daneu, C. A. Sacchi, O. Svelto, Appl. Opt. 4, 863 (1965).
[Crossref]

1964 (3)

D. F. Nelson, J. P. Remeika, J. Appl. Phys. 35, 522 (1964).
[Crossref]

A. J. Rack, M. R. Biazzo, Bell System Tech. J. 63, 1563 (1964).

R. L. Aagard, R. A. Dufault, Appl. Phys. Letters 4, 102 (1964).
[Crossref]

1963 (4)

A. D. White, J. D. Rigden, Appl. Phys. Letters 2, 211 (1963).
[Crossref]

R. L. Aagard, J. Opt. Soc. Am. 53, 911 (1963).
[Crossref]

J. I. Masters, Nature 199, 442 (1963).
[Crossref]

A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
[Crossref]

1962 (1)

1961 (1)

J. Kotik, M. C. Newstein, J. Appl. Phys. 32, 178 (1961).
[Crossref]

1958 (1)

1953 (1)

R. Chabbal, J. Rech. Cent. Nat. Rech. Sci., Labs. Bellevue (Paris) 24, 138 (1953).

1945 (1)

C. Dufour, R. Picca, Rev. Opt. 24, 19 (1945).

Aagard, R. L.

R. L. Aagard, R. A. Dufault, Appl. Phys. Letters 4, 102 (1964).
[Crossref]

R. L. Aagard, J. Opt. Soc. Am. 53, 911 (1963).
[Crossref]

Ashkin, A.

G. D. Boyd, A. Ashkin, Phys. Rev. 146, 187 (1966).
[Crossref]

Biazzo, M. R.

A. J. Rack, M. R. Biazzo, Bell System Tech. J. 63, 1563 (1964).

Born, M.

M. Born, E. Wolf, Principles of Optics (The Macmillan Company, New York, 1964), p. 323.

Boyd, G. D.

G. D. Boyd, A. Ashkin, Phys. Rev. 146, 187 (1966).
[Crossref]

Boyle, W. S.

Chabbal, R.

R. Chabbal, J. Rech. Cent. Nat. Rech. Sci., Labs. Bellevue (Paris) 24, 138 (1953).

Collins, R. J.

R. J. Collins, D. F. Nelson in Proceedings of the Conference on Optical Instruments, 1961 (Chapman and Hall Ltd., London, 1962), p. 441.

Daneu, V.

Del Piano, V. N.

Dufault, R. A.

R. L. Aagard, R. A. Dufault, Appl. Phys. Letters 4, 102 (1964).
[Crossref]

Dufour, C.

C. Dufour, R. Picca, Rev. Opt. 24, 19 (1945).

Fox, A. G.

A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
[Crossref]

Gambling, W. A.

D. C. Hanna, W. A. Gambling, R. C. Smith, J. Quantum Electron. QE-2, 507 (1966).
[Crossref]

Giordmaine, J. A.

J. A. Giordmaine, R. C. Miller, Phys. Rev. Letters 14, 973 (1965).
[Crossref]

Hanna, D. C.

D. C. Hanna, W. A. Gambling, R. C. Smith, J. Quantum Electron. QE-2, 507 (1966).
[Crossref]

Hansen, J. W.

J. W. Hansen, K. F. Rodgers, D. E. Thomas, private communication.

Hercher, M. M.

M. M. Hercher, Doctoral Dissertation, Institute of Optics, The University of Rochester, 1963 (unpublished).

Kiang, Y. C.

Y. C. Kiang, J. F. Stephany, F. C. Unterleitner, J. Quantum Electron. QE-2, 295 (1965).
[Crossref]

Kotik, J.

J. Kotik, M. C. Newstein, J. Appl. Phys. 32, 178 (1961).
[Crossref]

Kushida, T.

T. Kushida, J. Quantum Electron. QE-2, 524 (1966).
[Crossref]

Li, T.

A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
[Crossref]

Malitson, I. H.

Masters, J. I.

J. I. Masters, Nature 199, 442 (1963).
[Crossref]

McCumber, D. E.

D. F. Nelson, D. E. McCumber, in Quantum Electronics, III, P. Grivet, N. Bloembergen, Eds. (Columbia University Press, New York, 1964), p. 1037.

Miller, R. C.

J. A. Giordmaine, R. C. Miller, Phys. Rev. Letters 14, 973 (1965).
[Crossref]

Murphy, F. V.

Nelson, D. F.

D. F. Nelson, M. D. Sturge, Phys. Rev. 137, A11117 (1965).
[Crossref]

D. F. Nelson, J. P. Remeika, J. Appl. Phys. 35, 522 (1964).
[Crossref]

D. F. Nelson, W. S. Boyle, Appl. Opt. 1, 181 (1962).
[Crossref]

R. J. Collins, D. F. Nelson in Proceedings of the Conference on Optical Instruments, 1961 (Chapman and Hall Ltd., London, 1962), p. 441.

D. F. Nelson, D. E. McCumber, in Quantum Electronics, III, P. Grivet, N. Bloembergen, Eds. (Columbia University Press, New York, 1964), p. 1037.

Newstein, M. C.

J. Kotik, M. C. Newstein, J. Appl. Phys. 32, 178 (1961).
[Crossref]

Perry, D. L.

Peterson, D. G.

Picca, R.

C. Dufour, R. Picca, Rev. Opt. 24, 19 (1945).

Quesada, A. F.

Rack, A. J.

A. J. Rack, M. R. Biazzo, Bell System Tech. J. 63, 1563 (1964).

Remeika, J. P.

D. F. Nelson, J. P. Remeika, J. Appl. Phys. 35, 522 (1964).
[Crossref]

Rigden, J. D.

A. D. White, J. D. Rigden, Appl. Phys. Letters 2, 211 (1963).
[Crossref]

Rodgers, K. F.

J. W. Hansen, K. F. Rodgers, D. E. Thomas, private communication.

Rodney, W. S.

Sacchi, C. A.

Smith, R. C.

D. C. Hanna, W. A. Gambling, R. C. Smith, J. Quantum Electron. QE-2, 507 (1966).
[Crossref]

Stephany, J. F.

Y. C. Kiang, J. F. Stephany, F. C. Unterleitner, J. Quantum Electron. QE-2, 295 (1965).
[Crossref]

Sturge, M. D.

D. F. Nelson, M. D. Sturge, Phys. Rev. 137, A11117 (1965).
[Crossref]

Svelto, O.

Thomas, D. E.

J. W. Hansen, K. F. Rodgers, D. E. Thomas, private communication.

Unterleitner, F. C.

Y. C. Kiang, J. F. Stephany, F. C. Unterleitner, J. Quantum Electron. QE-2, 295 (1965).
[Crossref]

White, A. D.

A. D. White, J. D. Rigden, Appl. Phys. Letters 2, 211 (1963).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (The Macmillan Company, New York, 1964), p. 323.

Yariv, A.

Appl. Opt. (5)

Appl. Phys. Letters (2)

R. L. Aagard, R. A. Dufault, Appl. Phys. Letters 4, 102 (1964).
[Crossref]

A. D. White, J. D. Rigden, Appl. Phys. Letters 2, 211 (1963).
[Crossref]

Bell System Tech. J. (1)

A. J. Rack, M. R. Biazzo, Bell System Tech. J. 63, 1563 (1964).

J. Appl. Phys. (2)

J. Kotik, M. C. Newstein, J. Appl. Phys. 32, 178 (1961).
[Crossref]

D. F. Nelson, J. P. Remeika, J. Appl. Phys. 35, 522 (1964).
[Crossref]

J. Opt. Soc. Am. (2)

J. Quantum Electron. (3)

D. C. Hanna, W. A. Gambling, R. C. Smith, J. Quantum Electron. QE-2, 507 (1966).
[Crossref]

Y. C. Kiang, J. F. Stephany, F. C. Unterleitner, J. Quantum Electron. QE-2, 295 (1965).
[Crossref]

T. Kushida, J. Quantum Electron. QE-2, 524 (1966).
[Crossref]

J. Rech. Cent. Nat. Rech. Sci., Labs. Bellevue (Paris) (1)

R. Chabbal, J. Rech. Cent. Nat. Rech. Sci., Labs. Bellevue (Paris) 24, 138 (1953).

Nature (1)

J. I. Masters, Nature 199, 442 (1963).
[Crossref]

Phys. Rev. (2)

G. D. Boyd, A. Ashkin, Phys. Rev. 146, 187 (1966).
[Crossref]

D. F. Nelson, M. D. Sturge, Phys. Rev. 137, A11117 (1965).
[Crossref]

Phys. Rev. Letters (1)

J. A. Giordmaine, R. C. Miller, Phys. Rev. Letters 14, 973 (1965).
[Crossref]

Proc. IEEE (1)

A. G. Fox, T. Li, Proc. IEEE 51, 80 (1963).
[Crossref]

Rev. Opt. (1)

C. Dufour, R. Picca, Rev. Opt. 24, 19 (1945).

Other (5)

M. Born, E. Wolf, Principles of Optics (The Macmillan Company, New York, 1964), p. 323.

J. W. Hansen, K. F. Rodgers, D. E. Thomas, private communication.

D. F. Nelson, D. E. McCumber, in Quantum Electronics, III, P. Grivet, N. Bloembergen, Eds. (Columbia University Press, New York, 1964), p. 1037.

M. M. Hercher, Doctoral Dissertation, Institute of Optics, The University of Rochester, 1963 (unpublished).

R. J. Collins, D. F. Nelson in Proceedings of the Conference on Optical Instruments, 1961 (Chapman and Hall Ltd., London, 1962), p. 441.

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Figures (7)

Fig. 1
Fig. 1

Schematic drawing of the experimental arrangement.

Fig. 2
Fig. 2

Transmissivity at 6328 Å vs optical path length change for a 0.54-cm thick flux-grown ruby5 with as-grown reflector surfaces. A theoretical curve due to Dufour and Picca15 has been fitted to the experimental points.

Fig. 3
Fig. 3

Transmissivity at 6328 Å vs optical path length change for the ruby of Fig. 2 with multiple layer zinc sulfide–cryolite reflectors on the feedback surfaces (R1 = R2 = 0.875). Theoretical points from the Dufour–Picca model are plotted on the experimental curve.

Fig. 4
Fig. 4

Transmissivity at 6328 Å vs optical path length change for both polarizations for a 90° orientation coated (R1 = 0.891, R2 = 0.884) ruby trumpet.8,22

Fig. 5
Fig. 5

Transmissivity at 6328 Å vs optical path length change for a 0° orientation coated (R1 = 0.895, R2 = 0.940) ruby trumpet.22

Fig. 6
Fig. 6

Transmissivity at 6328 Å vs optical path length change for a 7.5-cm long, 0.05 wt % Cr2O3, 60° orientation, coated (R1 = 0.933, R2 = 0.936) ruby rod for EC. Theoretical points from the plane wave model [Eq. (1)] are shown for a loss per pass of β = 0.022.

Fig. 7
Fig. 7

Schematic drawing of an optical pumping arrangement for continuous operation of ruby trumpet-shaped crystals. The inset shows how the crystal is held flush with the dewar window without bending the crystal. The dewar must be made of Pyrex in order to filter out harmful uv wavelengths. Threshold power to the lamp is about 800 W.

Equations (13)

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I ( φ ) / I 0 = τ / [ 1 + ( C - 1 ) sin 2 φ / 2 ] ,
τ = ( T 1 T 2 exp - α l ) / [ 1 - R 1 R 2 ) ½ exp - α l ] 2 ,
C = 1 + { 4 ( R 1 R 2 ) ½ exp - α l / [ 1 - ( R 1 R 2 ) ½ exp - α l ] 2 } ,
φ = 4 π n l / λ .
F = π 2 sin - 1 { [ 1 - ( R 1 R 2 ) ½ exp - α l ] / [ 2 ( R 1 R 2 ) ¼ exp - α l / 2 } .
f = 1 + h - [ ( 1 + h ) 2 - 1 ] ½ ,
h = 2 sin 2 ( π / 2 F ) ,
= 2 / ( C - 1 ) ,
= T 1 T 2 / 2 ( R 1 R 2 ) ½ τ .
β = ln [ ( R 1 R 2 ) ½ / f ] - α g l .
I ( φ ) I 0 = τ δ φ M C ½ [ tan - 1 ( C ½ tan φ + δ φ M 2 ) - tan - 1 ( C ½ tan φ - δ φ M 2 ) ] ,
I ( 0 ) I 0 = 2 τ tan - 1 ( C ½ tan δ φ M / 2 ) δ φ M C ½ ,
I ( π ) / I 0 = τ C { 1 + [ ( C - 1 ) / 12 C ] δ φ M 2 + } .

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