Abstract

We consider ruby as a linear, uniaxial, maxwellian medium, which, in its absorbing state, has axially dependent material constants. It is made active by pumping with electric fields, in the region of shorter-wavelength absorption bands, which, by means of an energy transfer, induce source-type electric fields having constant amplitudes in the R1 and R2 regions, and make possible absorption, spontaneous emission, and stimulated emission. Experiments indicate that the absorption, fluorescence, and laser action are all maximum for electric fields perpendicular to the optic axis, and minimum when the electric field is parallel to the optic axis; the relative irradiances and shapes of the R1 and R2 bands in all cases depend upon the orientation of the plane of polarization of the emerging radiant flux relative to the optic axis. Attempts are made to compute the spectral distributions in the R1 and R2 bands for the ordinary and extraordinary waves, neglecting all boundary-value problems. Agreement was found to be possible only in the region below the threshold of laser action.

© 1969 Optical Society of America

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References

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  1. A. I. Mahan, J. Opt. Soc. Am. 55, 1611 (1965).
    [CrossRef]
  2. M. Born, Optik (Julius Springer, Berlin, 1933), p. 218.
    [CrossRef]
  3. H. Geiger and K. Scheel in Handbuch der Physik, V. 20 (Julius Springer-Verlag, Berlin, 1928), pp. 184, 194.
  4. It should be clear that for the study of some substances it would be necessary to consider pumping with magnetic fields, but this will be reserved for magnetic-absorption processes.
  5. C. E. Mendenhall and R. W. Wood, Phil Mag. 30, 316 (1914); P. Pringsheim, Fluorescence and Phosphorescence (Interscience Publishers, Inc., John Wiley & Sons, New York, 1949), p. 643; I. Wieder, Rev. Sci. Instr. 30, 995 (1959); E. E. Bukke and Z. L. Morgenshtern, Opt. Spectry. 14, 362 (1963).
    [CrossRef]
  6. T. H. Maiman, Nature 187, 493 (1960); T. H. Maiman, R. H. Hoskins, I. J. D’Haenens, C. K. Asawa, and V. Evtuhov, Phys. Rev. 123, 1151 (1961).
    [CrossRef]
  7. H. P. Kallmann and G. M. Spruch, Luminescence of Organic and Inorganic Materials (J. Wiley & Sons, Inc., New York, 1962), p. 659.
  8. A. Einstein, Verh. Deut. Ges. 18, 318 (1916).
  9. In the initial stages of development of the theory, we must consider fixed differences of phase ψ, before we can consider the more practical problem of random phase.
  10. P. Pringsheim, Fluorescence and Phosphorescence (Interscience Publishers, Inc., John Wiley & Sons, New York, 1949), p. 306.
  11. C. Schaefer, Einführung in die theoretische Physik (Walter DeGruyter & Co., Berlin, 1949), Vol. 3, p. 771.
  12. H. DuBois and G. J. Elias, Ann. Physik,  35, 618 (1911); O. Deutschbein, Ann. Physik. 14, 712 (1932); S. F. Jacobs, The Johns Hopkins University, Ph.D. thesis (1956); S. Sugano and I. Tsuijikawa, J. Phys. Soc. Japan 13, 899 (1958).
    [CrossRef]
  13. The interference effects in the six-inch-long ruby rod used in these experiments are too small to be resolved by the spectrograph, even with a perfectly plane parallel homogeneous crystal.
  14. A. Kastler, Appl. Opt. 1, 17 (1962).
    [CrossRef]
  15. International Critical Tables, E. W. Washburn, Ed. (McGraw–Hill Book Co., New York, 1930) Vol. VII, p. 2.
  16. D. M. Dodd, D. L. Wood, and R. L. Barns, J. Appl. Phys. 35, 1183 (1964).
    [CrossRef]
  17. The method used for measuring the refractive indices was described at 1967 Annual Meeting of the Optical Society, [M. J. Dodge, I. H. Malitson, and A. I. Mahan, J. Opt. Soc. Am. 57, 1429A (1967)], Detroit, Michigan.
  18. E. S. Dorman, The Johns Hopkins University, Ph.D. thesis (1965).
  19. F. S. Woods, Advanced Calculus (Ginn and Co., New York, 1926), p. 139.
  20. T. H. Maiman, Phys. Rev. 123, 1145 (1961).
    [CrossRef]

1967 (1)

The method used for measuring the refractive indices was described at 1967 Annual Meeting of the Optical Society, [M. J. Dodge, I. H. Malitson, and A. I. Mahan, J. Opt. Soc. Am. 57, 1429A (1967)], Detroit, Michigan.

1965 (1)

1964 (1)

D. M. Dodd, D. L. Wood, and R. L. Barns, J. Appl. Phys. 35, 1183 (1964).
[CrossRef]

1962 (1)

1961 (1)

T. H. Maiman, Phys. Rev. 123, 1145 (1961).
[CrossRef]

1960 (1)

T. H. Maiman, Nature 187, 493 (1960); T. H. Maiman, R. H. Hoskins, I. J. D’Haenens, C. K. Asawa, and V. Evtuhov, Phys. Rev. 123, 1151 (1961).
[CrossRef]

1916 (1)

A. Einstein, Verh. Deut. Ges. 18, 318 (1916).

1914 (1)

C. E. Mendenhall and R. W. Wood, Phil Mag. 30, 316 (1914); P. Pringsheim, Fluorescence and Phosphorescence (Interscience Publishers, Inc., John Wiley & Sons, New York, 1949), p. 643; I. Wieder, Rev. Sci. Instr. 30, 995 (1959); E. E. Bukke and Z. L. Morgenshtern, Opt. Spectry. 14, 362 (1963).
[CrossRef]

1911 (1)

H. DuBois and G. J. Elias, Ann. Physik,  35, 618 (1911); O. Deutschbein, Ann. Physik. 14, 712 (1932); S. F. Jacobs, The Johns Hopkins University, Ph.D. thesis (1956); S. Sugano and I. Tsuijikawa, J. Phys. Soc. Japan 13, 899 (1958).
[CrossRef]

Barns, R. L.

D. M. Dodd, D. L. Wood, and R. L. Barns, J. Appl. Phys. 35, 1183 (1964).
[CrossRef]

Born, M.

M. Born, Optik (Julius Springer, Berlin, 1933), p. 218.
[CrossRef]

Dodd, D. M.

D. M. Dodd, D. L. Wood, and R. L. Barns, J. Appl. Phys. 35, 1183 (1964).
[CrossRef]

Dodge, M. J.

The method used for measuring the refractive indices was described at 1967 Annual Meeting of the Optical Society, [M. J. Dodge, I. H. Malitson, and A. I. Mahan, J. Opt. Soc. Am. 57, 1429A (1967)], Detroit, Michigan.

Dorman, E. S.

E. S. Dorman, The Johns Hopkins University, Ph.D. thesis (1965).

DuBois, H.

H. DuBois and G. J. Elias, Ann. Physik,  35, 618 (1911); O. Deutschbein, Ann. Physik. 14, 712 (1932); S. F. Jacobs, The Johns Hopkins University, Ph.D. thesis (1956); S. Sugano and I. Tsuijikawa, J. Phys. Soc. Japan 13, 899 (1958).
[CrossRef]

Einstein, A.

A. Einstein, Verh. Deut. Ges. 18, 318 (1916).

Elias, G. J.

H. DuBois and G. J. Elias, Ann. Physik,  35, 618 (1911); O. Deutschbein, Ann. Physik. 14, 712 (1932); S. F. Jacobs, The Johns Hopkins University, Ph.D. thesis (1956); S. Sugano and I. Tsuijikawa, J. Phys. Soc. Japan 13, 899 (1958).
[CrossRef]

Geiger, H.

H. Geiger and K. Scheel in Handbuch der Physik, V. 20 (Julius Springer-Verlag, Berlin, 1928), pp. 184, 194.

Kallmann, H. P.

H. P. Kallmann and G. M. Spruch, Luminescence of Organic and Inorganic Materials (J. Wiley & Sons, Inc., New York, 1962), p. 659.

Kastler, A.

Mahan, A. I.

The method used for measuring the refractive indices was described at 1967 Annual Meeting of the Optical Society, [M. J. Dodge, I. H. Malitson, and A. I. Mahan, J. Opt. Soc. Am. 57, 1429A (1967)], Detroit, Michigan.

A. I. Mahan, J. Opt. Soc. Am. 55, 1611 (1965).
[CrossRef]

Maiman, T. H.

T. H. Maiman, Phys. Rev. 123, 1145 (1961).
[CrossRef]

T. H. Maiman, Nature 187, 493 (1960); T. H. Maiman, R. H. Hoskins, I. J. D’Haenens, C. K. Asawa, and V. Evtuhov, Phys. Rev. 123, 1151 (1961).
[CrossRef]

Malitson, I. H.

The method used for measuring the refractive indices was described at 1967 Annual Meeting of the Optical Society, [M. J. Dodge, I. H. Malitson, and A. I. Mahan, J. Opt. Soc. Am. 57, 1429A (1967)], Detroit, Michigan.

Mendenhall, C. E.

C. E. Mendenhall and R. W. Wood, Phil Mag. 30, 316 (1914); P. Pringsheim, Fluorescence and Phosphorescence (Interscience Publishers, Inc., John Wiley & Sons, New York, 1949), p. 643; I. Wieder, Rev. Sci. Instr. 30, 995 (1959); E. E. Bukke and Z. L. Morgenshtern, Opt. Spectry. 14, 362 (1963).
[CrossRef]

Pringsheim, P.

P. Pringsheim, Fluorescence and Phosphorescence (Interscience Publishers, Inc., John Wiley & Sons, New York, 1949), p. 306.

Schaefer, C.

C. Schaefer, Einführung in die theoretische Physik (Walter DeGruyter & Co., Berlin, 1949), Vol. 3, p. 771.

Scheel, K.

H. Geiger and K. Scheel in Handbuch der Physik, V. 20 (Julius Springer-Verlag, Berlin, 1928), pp. 184, 194.

Spruch, G. M.

H. P. Kallmann and G. M. Spruch, Luminescence of Organic and Inorganic Materials (J. Wiley & Sons, Inc., New York, 1962), p. 659.

Wood, D. L.

D. M. Dodd, D. L. Wood, and R. L. Barns, J. Appl. Phys. 35, 1183 (1964).
[CrossRef]

Wood, R. W.

C. E. Mendenhall and R. W. Wood, Phil Mag. 30, 316 (1914); P. Pringsheim, Fluorescence and Phosphorescence (Interscience Publishers, Inc., John Wiley & Sons, New York, 1949), p. 643; I. Wieder, Rev. Sci. Instr. 30, 995 (1959); E. E. Bukke and Z. L. Morgenshtern, Opt. Spectry. 14, 362 (1963).
[CrossRef]

Woods, F. S.

F. S. Woods, Advanced Calculus (Ginn and Co., New York, 1926), p. 139.

Ann. Physik (1)

H. DuBois and G. J. Elias, Ann. Physik,  35, 618 (1911); O. Deutschbein, Ann. Physik. 14, 712 (1932); S. F. Jacobs, The Johns Hopkins University, Ph.D. thesis (1956); S. Sugano and I. Tsuijikawa, J. Phys. Soc. Japan 13, 899 (1958).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (1)

D. M. Dodd, D. L. Wood, and R. L. Barns, J. Appl. Phys. 35, 1183 (1964).
[CrossRef]

J. Opt. Soc. Am. (2)

The method used for measuring the refractive indices was described at 1967 Annual Meeting of the Optical Society, [M. J. Dodge, I. H. Malitson, and A. I. Mahan, J. Opt. Soc. Am. 57, 1429A (1967)], Detroit, Michigan.

A. I. Mahan, J. Opt. Soc. Am. 55, 1611 (1965).
[CrossRef]

Nature (1)

T. H. Maiman, Nature 187, 493 (1960); T. H. Maiman, R. H. Hoskins, I. J. D’Haenens, C. K. Asawa, and V. Evtuhov, Phys. Rev. 123, 1151 (1961).
[CrossRef]

Phil Mag. (1)

C. E. Mendenhall and R. W. Wood, Phil Mag. 30, 316 (1914); P. Pringsheim, Fluorescence and Phosphorescence (Interscience Publishers, Inc., John Wiley & Sons, New York, 1949), p. 643; I. Wieder, Rev. Sci. Instr. 30, 995 (1959); E. E. Bukke and Z. L. Morgenshtern, Opt. Spectry. 14, 362 (1963).
[CrossRef]

Phys. Rev. (1)

T. H. Maiman, Phys. Rev. 123, 1145 (1961).
[CrossRef]

Verh. Deut. Ges. (1)

A. Einstein, Verh. Deut. Ges. 18, 318 (1916).

Other (11)

In the initial stages of development of the theory, we must consider fixed differences of phase ψ, before we can consider the more practical problem of random phase.

P. Pringsheim, Fluorescence and Phosphorescence (Interscience Publishers, Inc., John Wiley & Sons, New York, 1949), p. 306.

C. Schaefer, Einführung in die theoretische Physik (Walter DeGruyter & Co., Berlin, 1949), Vol. 3, p. 771.

H. P. Kallmann and G. M. Spruch, Luminescence of Organic and Inorganic Materials (J. Wiley & Sons, Inc., New York, 1962), p. 659.

M. Born, Optik (Julius Springer, Berlin, 1933), p. 218.
[CrossRef]

H. Geiger and K. Scheel in Handbuch der Physik, V. 20 (Julius Springer-Verlag, Berlin, 1928), pp. 184, 194.

It should be clear that for the study of some substances it would be necessary to consider pumping with magnetic fields, but this will be reserved for magnetic-absorption processes.

The interference effects in the six-inch-long ruby rod used in these experiments are too small to be resolved by the spectrograph, even with a perfectly plane parallel homogeneous crystal.

International Critical Tables, E. W. Washburn, Ed. (McGraw–Hill Book Co., New York, 1930) Vol. VII, p. 2.

E. S. Dorman, The Johns Hopkins University, Ph.D. thesis (1965).

F. S. Woods, Advanced Calculus (Ginn and Co., New York, 1926), p. 139.

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Figures (17)

Fig. 1
Fig. 1

One-dimensional flow of radiant flux.

Fig. 2
Fig. 2

Absorption and stimulated-emission regions for f and φ values at or above the threshold for stimulated emission.

Fig. 3
Fig. 3

Absorption spectrum of ruby in plane and unpolarized light.

Fig. 4
Fig. 4

The fluorescence and laser spectra of ruby with increasing pumping electric fields when electric field is perpendicular and parallel to crystal axis.

Fig. 5
Fig. 5

Refractive indices of ruby (Cr2O3 0.062%±0.002% by weight) in directions perpendicular and parallel to optic axis.

Fig. 6
Fig. 6

Absorption coefficients of ruby (Cr2O30.062%±0.002% by weight) in directions perpendicular and parallel to optic axis.

Fig. 7
Fig. 7

Changes of refractive index of ruby at 6942.7 Å for perpendicular polarization with different amplitudes and phases for source-type electric fields.

Fig. 8
Fig. 8

Changes of absorption coefficient of ruby at 6942.7 Å for perpendicular polarization with different amplitudes and phases for source-type electric field.

Fig. 9
Fig. 9

Excess of time average of inflow or outflow of radiant flux in ruby at 6942.7 Å for perpendicular polarization with different amplitudes and phases for source-type electric field.

Fig. 10
Fig. 10

Time average of the emergent radiant flux in the R1 and R2 regions for perpendicular polarization with φ=π/2 and different amplitudes for source-type electric field.

Fig. 11
Fig. 11

Time average of the emergent radiant flux in the R1 and R2 regions for parallel polarization with φ=π/2 and different amplitudes for source-type electric field.

Fig. 12
Fig. 12

Excess of time average of inflow or outflow of radiant flux at 6942.7 Å for perpendicular polarization in modified model (F=1.0, 0.5) with different amplitudes and phases for source-type electric field.

Fig. 13
Fig. 13

Time average of the emergent radiant flux in the R1 and R2 regions for perpendicular polarization in modified model (F=1.0, 0.5) with φ=π/2 and different amplitudes far source-type electric field.

Fig. 14
Fig. 14

Time average of the emergent radiant flux in the R1 and R2 regions for parallel polarization in modified model (F=1.0, 0.5) with φ=π/2 and different amplitudes for source-type electric field.

Fig. 15
Fig. 15

Time average of the emergent radiant flux in the R1 and R2 regions for perpendicular polarization in modified model (F=1.0, 0.5) with different amplitudes and purely random phases for source-type electric field.

Fig. 16
Fig. 16

Time average of the emergent radiant flux in the R1 and R2 regions for parallel polarization in modified model (F=1.0, 0.5) with different amplitudes and purely random phases for source-type electric field.

Fig. 17
Fig. 17

Fluorescence spectrum of ruby with strong pumping electric fields when electric field is perpendicular and parallel to crystal axis.

Tables (4)

Tables Icon

Table I Calculated material constants for perpendicular polarization of the 6942.7-Å line.

Tables Icon

Table II Calculated material constants for parallel polarization of the 6942.7-Å line.

Tables Icon

Table III Calculated material constants for perpendicular polarization of the 6928.5-Å line.

Tables Icon

Table IV Calculated material constants for parallel polarization of the 6928.5-Å line.

Equations (16)

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Δ E = 4 π σ μ c 2 E t + ( r - i i ) μ c 2 2 E t 2 , Δ H = 4 π σ μ c 2 H t + ( r - i i ) μ c 2 2 H t ,
Re P n · d S = c 8 π Re ( E × H * ) n d S = - 1 2 Re ( E · j * ) d τ - 1 8 π × Re [ ( E · D * t ) + ( H * · B t ) ] d τ ;
j = σ E , D = ( r - i i ) E , B = μ H .
E x 1 e = f E x 1 e i φ ,
j x = σ 1 ( 1 + f e i φ ) E x 1 ,             D x / t = i ω 1 ( r 1 - i i 1 ) ( 1 + f e i φ ) E x 1 , B y / t = i ω 1 μ 1 H y 1 ,
Re P n · d S = r 1 ω 1 8 π { f sin φ - W 1 f cos φ - W 1 } × ( E x 1 · E x 1 * ) d τ ,
W 1 = 4 π σ 1 / ( r 1 ω 1 ) + i 1 / r 1 .
E x 1 = B x exp { i [ ω 1 t - ( 2 π n n z / λ 1 ) ] }
n 1 = n 1 + i k 1 = { r 1 μ 1 ( W 1 f sin φ + f cos φ + 1 ) + i r 1 μ 1 · ( f sin φ - W 1 f cos φ - W 1 ) } 1 / 2 .
n 1 = { P 1 1 [ 1 + ( 1 + Q 1 2 P 1 2 ) 1 / 2 ] } 1 / 2 , k 1 = ± { P 1 2 [ - 1 + ( 1 + Q 1 2 P 1 2 ) 1 / 2 ] } 1 / 2 .
Re ( P z 2 - P z 1 ) d x d y = r 1 c 16 π k 1 × { f sin φ - W 1 f cos φ - W 1 } · B x 2 [ exp ( 4 π k 1 z 2 λ 1 ) - exp ( 4 π k 1 z 1 λ 1 ) ] d x d y .
F 1 A x 2 d τ = c 16 π B x 2 R 2 R 1 r 1 k 1 { f sin φ - W 1 f cos φ - W 1 } · [ exp ( 4 π k 1 ν 1 z 2 c ) - exp ( 4 π k 1 ν 1 z 1 c ) ] d x d y d ν 1 ;
f min = W 1 / ( 1 + W 1 2 ) 1 / 2 ,             φ ¯ min = π / 2 + tan - 1 W 1 .
n 1 2 - k 1 2 = r 1 μ 1 , n 1 k 1 = r 1 μ 1 W 1 / 2.
Re ( P z 2 - P z 1 ) = - r c 16 π k 1 W 1 [ exp ( 4 π k 1 λ 1 ) - 1 ] + r 1 c 16 π k 1 ( f ¯ sin φ ¯ + f ¯ F W 1 cos φ ¯ + F W 1 ) [ exp ( 4 π k ¯ 1 λ 1 ) - 1 ] - r 1 c 16 π k ¯ 0 F W 1 [ exp ( 4 π k ¯ 0 λ 1 ) - 1 ] .
f ¯ min = W 1 / ( 1 + F 2 W 2 ) 1 / 2 ,             φ ¯ min = π / 2 - tan - 1 F W 1 .