Abstract

The real and imaginary parts of the complex index of refraction have been measured in the R1 line of optically pumped ruby. The experiments, which employed a temperature-controlled, single-mode ruby laser as a variable-frequency monochromatic source, were performed near liquid-nitrogen temperature, where the R1 doublet structure is well resolved. R1 absorption profiles were measured for several optical-pumping conditions, ranging from zero up to a pump power that excited a population in the 2E state equal to about 60% of the population of the 4A2 ground state. For each pumping condition, the anomalous-dispersion curve was measured interferometrically. The spectral profiles of the absorption coefficient and the anomalous dispersion display a dependence on the optical-pumping conditions that is more complicated than simple saturation of the R1 transitions, but for given pumping conditions the two quantities are correlated as predicted by the Kramers–Kronig relations.

© 1973 Optical Society of America

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References

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  1. A. Kastler, Ann. Phys. (Leipz.) 7, 57 (1962).
  2. W. R. Bennett, Phys. Rev. 126, 580 (1962).
    [Crossref]
  3. A. Javan and P. L. Kelley, IEEE J. Quantum Electron. 2, 470 (1966).
    [Crossref]
  4. R. W. Minck, R. W. Terhune, and C. C. Wang, Proc. IEEE 54, 1357 (1966).
    [Crossref]
  5. J. Hilgevoord, Dispersion Relations and Causal Description (North–Holland, Amsterdam, 1962).
  6. H. C. Bolton and G. J. Troup, Philos. Mag. 19, 477 (1969).
    [Crossref]
  7. J. R. Izatt, B. L. Bean, and H. A. Daw, J. Appl. Phys. 44, 837 (1973).
    [Crossref]
  8. See, for example, R. Ladenburg, Rev. Mod. Phys. 5, 243 (1933).
    [Crossref]
  9. I. S. Gorban and G. L. Kononchuk, Opt. Spektrosk. 17, 88 (1964) [Opt. Spectrosc. 17, 478 (1964)].
  10. N. K. Bel’skii and D. A. Mukhamedova, Dokl. Akad. Nauk SSSR 2, 317 (1964) [Sov. Phys.-Dokl. 9, 798 (1965)].
  11. N. K. Bel’skii and A. M. Leontovich, Zh. Eksp. Teor. Fiz. 48, 752 (1965) [Sov. Phys.-JETP 21, 497 (1965)].
  12. A more-detailed description of the experiment is given in B. L. Bean, Dissertation, New Mexico State University, Las Ciuces (1972) (Univeisity Microfilms, Ann Arbor, Mich., order No. 72-24712).
  13. D. Milam, Dissertation, New Mexico State University, Las Cruces (1969) (University Microfilms, Ann Arbor, Mich., order No. 70-16359).
  14. S. Tolansky, Multiple Beam Interferometry (Oxford, London, 1949).
  15. M. Born and E. Wolf, Principles of Optics, 3d. ed. (Pergamon, London, 1965), p. 329.
  16. D. F. Nelson and M. D. Sturge, Phys. Rev. A 137, 1117 (1965).
  17. M. Birnbaum and T. L. Stocker, J. Appl. Phys. 36, 396 (1965).
    [Crossref]
  18. D. C. Cronemeyer, J. Opt. Soc. Am. 56, 1703 (1966).
    [Crossref]
  19. D. E. McCumber and M. D. Sturge, J. Appl. Phys. 34, 1682 (1963).
    [Crossref]
  20. The computer program is described by P. Schnebly, Thesis, New Mexico State University, Las Cruces (1969).
  21. See, for example, T. Kushida, IEEE J. Quantum Electron. 2, 524 (1966).
    [Crossref]

1973 (1)

J. R. Izatt, B. L. Bean, and H. A. Daw, J. Appl. Phys. 44, 837 (1973).
[Crossref]

1969 (1)

H. C. Bolton and G. J. Troup, Philos. Mag. 19, 477 (1969).
[Crossref]

1966 (4)

See, for example, T. Kushida, IEEE J. Quantum Electron. 2, 524 (1966).
[Crossref]

D. C. Cronemeyer, J. Opt. Soc. Am. 56, 1703 (1966).
[Crossref]

A. Javan and P. L. Kelley, IEEE J. Quantum Electron. 2, 470 (1966).
[Crossref]

R. W. Minck, R. W. Terhune, and C. C. Wang, Proc. IEEE 54, 1357 (1966).
[Crossref]

1965 (3)

N. K. Bel’skii and A. M. Leontovich, Zh. Eksp. Teor. Fiz. 48, 752 (1965) [Sov. Phys.-JETP 21, 497 (1965)].

D. F. Nelson and M. D. Sturge, Phys. Rev. A 137, 1117 (1965).

M. Birnbaum and T. L. Stocker, J. Appl. Phys. 36, 396 (1965).
[Crossref]

1964 (2)

I. S. Gorban and G. L. Kononchuk, Opt. Spektrosk. 17, 88 (1964) [Opt. Spectrosc. 17, 478 (1964)].

N. K. Bel’skii and D. A. Mukhamedova, Dokl. Akad. Nauk SSSR 2, 317 (1964) [Sov. Phys.-Dokl. 9, 798 (1965)].

1963 (1)

D. E. McCumber and M. D. Sturge, J. Appl. Phys. 34, 1682 (1963).
[Crossref]

1962 (2)

A. Kastler, Ann. Phys. (Leipz.) 7, 57 (1962).

W. R. Bennett, Phys. Rev. 126, 580 (1962).
[Crossref]

1933 (1)

See, for example, R. Ladenburg, Rev. Mod. Phys. 5, 243 (1933).
[Crossref]

Bean, B. L.

J. R. Izatt, B. L. Bean, and H. A. Daw, J. Appl. Phys. 44, 837 (1973).
[Crossref]

A more-detailed description of the experiment is given in B. L. Bean, Dissertation, New Mexico State University, Las Ciuces (1972) (Univeisity Microfilms, Ann Arbor, Mich., order No. 72-24712).

Bel’skii, N. K.

N. K. Bel’skii and A. M. Leontovich, Zh. Eksp. Teor. Fiz. 48, 752 (1965) [Sov. Phys.-JETP 21, 497 (1965)].

N. K. Bel’skii and D. A. Mukhamedova, Dokl. Akad. Nauk SSSR 2, 317 (1964) [Sov. Phys.-Dokl. 9, 798 (1965)].

Bennett, W. R.

W. R. Bennett, Phys. Rev. 126, 580 (1962).
[Crossref]

Birnbaum, M.

M. Birnbaum and T. L. Stocker, J. Appl. Phys. 36, 396 (1965).
[Crossref]

Bolton, H. C.

H. C. Bolton and G. J. Troup, Philos. Mag. 19, 477 (1969).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 3d. ed. (Pergamon, London, 1965), p. 329.

Cronemeyer, D. C.

Daw, H. A.

J. R. Izatt, B. L. Bean, and H. A. Daw, J. Appl. Phys. 44, 837 (1973).
[Crossref]

Gorban, I. S.

I. S. Gorban and G. L. Kononchuk, Opt. Spektrosk. 17, 88 (1964) [Opt. Spectrosc. 17, 478 (1964)].

Hilgevoord, J.

J. Hilgevoord, Dispersion Relations and Causal Description (North–Holland, Amsterdam, 1962).

Izatt, J. R.

J. R. Izatt, B. L. Bean, and H. A. Daw, J. Appl. Phys. 44, 837 (1973).
[Crossref]

Javan, A.

A. Javan and P. L. Kelley, IEEE J. Quantum Electron. 2, 470 (1966).
[Crossref]

Kastler, A.

A. Kastler, Ann. Phys. (Leipz.) 7, 57 (1962).

Kelley, P. L.

A. Javan and P. L. Kelley, IEEE J. Quantum Electron. 2, 470 (1966).
[Crossref]

Kononchuk, G. L.

I. S. Gorban and G. L. Kononchuk, Opt. Spektrosk. 17, 88 (1964) [Opt. Spectrosc. 17, 478 (1964)].

Kushida, T.

See, for example, T. Kushida, IEEE J. Quantum Electron. 2, 524 (1966).
[Crossref]

Ladenburg, R.

See, for example, R. Ladenburg, Rev. Mod. Phys. 5, 243 (1933).
[Crossref]

Leontovich, A. M.

N. K. Bel’skii and A. M. Leontovich, Zh. Eksp. Teor. Fiz. 48, 752 (1965) [Sov. Phys.-JETP 21, 497 (1965)].

McCumber, D. E.

D. E. McCumber and M. D. Sturge, J. Appl. Phys. 34, 1682 (1963).
[Crossref]

Milam, D.

D. Milam, Dissertation, New Mexico State University, Las Cruces (1969) (University Microfilms, Ann Arbor, Mich., order No. 70-16359).

Minck, R. W.

R. W. Minck, R. W. Terhune, and C. C. Wang, Proc. IEEE 54, 1357 (1966).
[Crossref]

Mukhamedova, D. A.

N. K. Bel’skii and D. A. Mukhamedova, Dokl. Akad. Nauk SSSR 2, 317 (1964) [Sov. Phys.-Dokl. 9, 798 (1965)].

Nelson, D. F.

D. F. Nelson and M. D. Sturge, Phys. Rev. A 137, 1117 (1965).

Schnebly, P.

The computer program is described by P. Schnebly, Thesis, New Mexico State University, Las Cruces (1969).

Stocker, T. L.

M. Birnbaum and T. L. Stocker, J. Appl. Phys. 36, 396 (1965).
[Crossref]

Sturge, M. D.

D. F. Nelson and M. D. Sturge, Phys. Rev. A 137, 1117 (1965).

D. E. McCumber and M. D. Sturge, J. Appl. Phys. 34, 1682 (1963).
[Crossref]

Terhune, R. W.

R. W. Minck, R. W. Terhune, and C. C. Wang, Proc. IEEE 54, 1357 (1966).
[Crossref]

Tolansky, S.

S. Tolansky, Multiple Beam Interferometry (Oxford, London, 1949).

Troup, G. J.

H. C. Bolton and G. J. Troup, Philos. Mag. 19, 477 (1969).
[Crossref]

Wang, C. C.

R. W. Minck, R. W. Terhune, and C. C. Wang, Proc. IEEE 54, 1357 (1966).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 3d. ed. (Pergamon, London, 1965), p. 329.

Ann. Phys. (Leipz.) (1)

A. Kastler, Ann. Phys. (Leipz.) 7, 57 (1962).

Dokl. Akad. Nauk SSSR (1)

N. K. Bel’skii and D. A. Mukhamedova, Dokl. Akad. Nauk SSSR 2, 317 (1964) [Sov. Phys.-Dokl. 9, 798 (1965)].

IEEE J. Quantum Electron. (2)

A. Javan and P. L. Kelley, IEEE J. Quantum Electron. 2, 470 (1966).
[Crossref]

See, for example, T. Kushida, IEEE J. Quantum Electron. 2, 524 (1966).
[Crossref]

J. Appl. Phys. (3)

J. R. Izatt, B. L. Bean, and H. A. Daw, J. Appl. Phys. 44, 837 (1973).
[Crossref]

M. Birnbaum and T. L. Stocker, J. Appl. Phys. 36, 396 (1965).
[Crossref]

D. E. McCumber and M. D. Sturge, J. Appl. Phys. 34, 1682 (1963).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Spektrosk. (1)

I. S. Gorban and G. L. Kononchuk, Opt. Spektrosk. 17, 88 (1964) [Opt. Spectrosc. 17, 478 (1964)].

Philos. Mag. (1)

H. C. Bolton and G. J. Troup, Philos. Mag. 19, 477 (1969).
[Crossref]

Phys. Rev. (1)

W. R. Bennett, Phys. Rev. 126, 580 (1962).
[Crossref]

Phys. Rev. A (1)

D. F. Nelson and M. D. Sturge, Phys. Rev. A 137, 1117 (1965).

Proc. IEEE (1)

R. W. Minck, R. W. Terhune, and C. C. Wang, Proc. IEEE 54, 1357 (1966).
[Crossref]

Rev. Mod. Phys. (1)

See, for example, R. Ladenburg, Rev. Mod. Phys. 5, 243 (1933).
[Crossref]

Zh. Eksp. Teor. Fiz. (1)

N. K. Bel’skii and A. M. Leontovich, Zh. Eksp. Teor. Fiz. 48, 752 (1965) [Sov. Phys.-JETP 21, 497 (1965)].

Other (6)

A more-detailed description of the experiment is given in B. L. Bean, Dissertation, New Mexico State University, Las Ciuces (1972) (Univeisity Microfilms, Ann Arbor, Mich., order No. 72-24712).

D. Milam, Dissertation, New Mexico State University, Las Cruces (1969) (University Microfilms, Ann Arbor, Mich., order No. 70-16359).

S. Tolansky, Multiple Beam Interferometry (Oxford, London, 1949).

M. Born and E. Wolf, Principles of Optics, 3d. ed. (Pergamon, London, 1965), p. 329.

The computer program is described by P. Schnebly, Thesis, New Mexico State University, Las Cruces (1969).

J. Hilgevoord, Dispersion Relations and Causal Description (North–Holland, Amsterdam, 1962).

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Figures (8)

Fig. 1
Fig. 1

Diagram illustrating the experimental apparatus. F denotes filters; S, beam splitters; L, lenses; M, mirrors; and PM, photomultipliers.

Fig. 2
Fig. 2

Samples of the data collected with a single-mode probe beam, polarized perpendicular to the optic axis of the sample. (a) Oscillogram snowing the ruby-laser spike pattern of the beam incident on the ruby sample. The time scale is 10 μs/cm and the gain is 0.1 V/cm. (b) Oscillogram showing the spiking pattern for the transmitted pulse. The time scale is the same but the gain is 0.01 V/cm. (c) Fringes formed by the Fabry–Perot interferometer. The full-circle fringes are produced by the He–Ne laser and the short-arc fringes by the ruby laser. (d) Fringes formed by the ruby sample as a Fabry–Perot étalon. The full-circle He–Ne fringes were masked off to improve the visibility of the short-arc ruby fringes indicated by the arrow.

Fig. 3
Fig. 3

Samples of the data collected with a multimode probe beam polarized with EC. This figure follows the same format as Fig. 2. (a) Oscillogram of the incident-beam spike pattern. The time scale is 10 μs/cm and the gain is 0.1 V/cm. (b) Oscillogram showing the transmitted pulse spike pattern. The time scale is the same but the gain is 0.003 V/cm. (c) Fringes formed by the Fabry–Perot interferometer. (d) Fabry–Perot fringes formed by the ruby étalon.

Fig. 4
Fig. 4

Number of longitudinal modes observed as a function of oscillator-filter temperature difference and pump energy. The temperature of the oscillator ruby was held constant at 85 K. The numbers indicate the number of modes found in the R 1 ( ± 3 2 ) component and the dashed line indicates the approximate threshold curve. Triangles indicate the points where laser action occurred in both R 1 ( ± 3 2 ) and R 1 ( ± 3 2 ). The longitudinal-mode separation is 0.018 Å.

Fig. 5
Fig. 5

Number of modes observed as a function of pump energy and the temperature of the laser crystal. The temperature of the filter ruby was 20 K higher than the temperature of the oscillator. The numbers indicate the number of modes observed at that coordinate point and an × indicates that laser action did not occur.

Fig. 6
Fig. 6

Absorption curve (upper) for the sample in the un-pumped state at a temperature of 95 K. ×, Δ, and ○ indicate three separate scans across the doublet. Refractive-index curve (lower) for the unpumped sample at 95 K. The background refractive index caused by strong ultraviolet absorption changes by only about 2 × 10−6 over the range shown. Near the absorption peak for the unpumped sample, it was necessary to use a probe beam with three or four longitudinal modes. The polarization of the probe beam was EC for both curves.

Fig. 7
Fig. 7

Absorption curve (upper) for the intermediate pumping case. Refractive-index curve (lower) for the intermediate pumping case. The sample temperature was 100 K for both curves and the polarization was EC.

Fig. 8
Fig. 8

Absorption curve (upper) for the strongest-pumping case. Refractive-index curve (lower) for the strongest-pumping case. The sample temperature was 100 K for both curves and the polarization was EC.

Tables (1)

Tables Icon

Table I Results for diverse optical-pumping conditions.

Equations (10)

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Δ G I = ( 2 / λ G ) Δ ( n d )
Δ R I = ( 2 / λ R ) Δ ( n d ) ( 2 n d / λ R 2 ) Δ λ ,
Δ λ = ( λ R / 2 n d ) ( λ G Δ G I λ R Δ R I ) .
Δ G E = ( 2 / λ G ) Δ ( n t ) ,
Δ R E = ( 2 / λ R ) Δ ( n t ) ( 2 n t / λ R 2 ) Δ λ .
Δ n = 1 2 l n d [ n d ( λ R Δ R E λ G Δ G E ) n t ( λ G Δ G I λ R Δ R I ) ] .
α = ( 1 / L ) ln ( I 0 / I ) α 0 .
α ( ω ) = α 0 γ 2 [ ( 1 W t s ) / ( 1 + W t s ) ] ( ω ω 0 ) 2 + γ 2 [ 1 + S α 0 ( 1 + W t s ) ] .
π χ s ( ω ) = A P χ s ( ω ) ω ω d ω ,
π χ s ( ω ) = 1 A P χ s ( ω ) ω ω d ω .