Abstract

Certain experiments had indicated that the polarization of emitted radiation was much more prevalent than had been expected. This paper is intended to present some of the background required to understand the phenomenon of emission polarization, which is not as well-known as it should be. The explanation that the phenomenon involves refraction of all the emitted radiation, advanced by Millikan in 1895, is still accepted today. More recent work, substantiating Millikan’s explanation, is cited.

© 1965 Optical Society of America

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References

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  1. T. Limperis, private communication.The work was done by T. Limperis, J. Mudar, D. Anding.
  2. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 43.
  3. F. Arago, Ann. Chem. et Phys. (2) 27, 89 (1824).
  4. R. A. Millikan, Phys. Rev. 3, 81, 177 (1895).
  5. H. H. Skilling, Fundamentals of Electric Waves (Wiley, New York, 1948), 2nd ed.
  6. A. R. Von Hippel, Dielectrics and Waves (Wiley, New York, 1954).
  7. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  8. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), 3rd ed., pp. 513, 514, 519.
  9. F. A. Jenkins, D. H. Menzel, Fundamental Formulas of Physics (Dover, New York, 1960), Vol. II, pp. 419, 420.
  10. V. Keussler, P. M. Manogg, Optik 17, 602 (1960).
  11. R. W. Ditchburn, Light (Interscience, New York, 1953), pp. 434–438.
  12. F. Goos, H. Hänchen, Ann. Physik [6], 1, 333 (1947).
    [CrossRef]
  13. C. Feldman, M. Hacskaylo, J. Opt. Soc. Am. 53, 636 (1963).
    [CrossRef]
  14. A. G. Worthing, J. Opt. Soc. Am. 13, 635 (1926).
    [CrossRef]
  15. Y. Ohman, Nature 192, 254 (1961).
    [CrossRef]
  16. A. F. Gorton, Phys. Rev. 7, 66 (1916).
    [CrossRef]
  17. W. A. Shurcliff, Polarized Light (Harvard Univ. Press, Cambridge, 1962), p. 161.
  18. P. P. Feofilov, The Physical Basis of Polarized Emission (Consultants Bureau, New York, 1961).
  19. H. H. Blau, J. L. Miles, L. E. Ashman, “The Thermal Radiation Characteristics of Solid Materials—A Review”, AFCRC-TN-58-132, Sci. Rept. No. 1 under Contract AF 19(604)-2639 (31March1958).
  20. H. H. Blau, E. Chaffee, J. R. Jasperse, W. S. Martin, “High Temperature Thermal Properties of Solid Materials”, AFCRC-TN-60-165, Sci. Rept. No. 2 under Contract AF 19(604)-2639 (31March1960).
  21. W. S. Martin, H. H. Blau, “Optical Constants at High Temperature”, AFCRL-13, Final Rept. C-60929 under Contract AF 19(604)-2639 (January1961).
  22. W. S. Martin, E. M. Duchane, H. H. Blau, “Measurement of Optical Constants at High Temperature”, AFCRL-63-547, Final Rept. under Contract No. AF 19(604)-7485 (10December1963).
  23. J. H. Brunton, Appl. Opt. 3, 1241 (1964).
    [CrossRef]

1964 (1)

1963 (1)

1961 (1)

Y. Ohman, Nature 192, 254 (1961).
[CrossRef]

1960 (1)

V. Keussler, P. M. Manogg, Optik 17, 602 (1960).

1947 (1)

F. Goos, H. Hänchen, Ann. Physik [6], 1, 333 (1947).
[CrossRef]

1926 (1)

1916 (1)

A. F. Gorton, Phys. Rev. 7, 66 (1916).
[CrossRef]

1895 (1)

R. A. Millikan, Phys. Rev. 3, 81, 177 (1895).

1824 (1)

F. Arago, Ann. Chem. et Phys. (2) 27, 89 (1824).

Arago, F.

F. Arago, Ann. Chem. et Phys. (2) 27, 89 (1824).

Ashman, L. E.

H. H. Blau, J. L. Miles, L. E. Ashman, “The Thermal Radiation Characteristics of Solid Materials—A Review”, AFCRC-TN-58-132, Sci. Rept. No. 1 under Contract AF 19(604)-2639 (31March1958).

Blau, H. H.

H. H. Blau, J. L. Miles, L. E. Ashman, “The Thermal Radiation Characteristics of Solid Materials—A Review”, AFCRC-TN-58-132, Sci. Rept. No. 1 under Contract AF 19(604)-2639 (31March1958).

W. S. Martin, E. M. Duchane, H. H. Blau, “Measurement of Optical Constants at High Temperature”, AFCRL-63-547, Final Rept. under Contract No. AF 19(604)-7485 (10December1963).

H. H. Blau, E. Chaffee, J. R. Jasperse, W. S. Martin, “High Temperature Thermal Properties of Solid Materials”, AFCRC-TN-60-165, Sci. Rept. No. 2 under Contract AF 19(604)-2639 (31March1960).

W. S. Martin, H. H. Blau, “Optical Constants at High Temperature”, AFCRL-13, Final Rept. C-60929 under Contract AF 19(604)-2639 (January1961).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 43.

Brunton, J. H.

Chaffee, E.

H. H. Blau, E. Chaffee, J. R. Jasperse, W. S. Martin, “High Temperature Thermal Properties of Solid Materials”, AFCRC-TN-60-165, Sci. Rept. No. 2 under Contract AF 19(604)-2639 (31March1960).

Ditchburn, R. W.

R. W. Ditchburn, Light (Interscience, New York, 1953), pp. 434–438.

Duchane, E. M.

W. S. Martin, E. M. Duchane, H. H. Blau, “Measurement of Optical Constants at High Temperature”, AFCRL-63-547, Final Rept. under Contract No. AF 19(604)-7485 (10December1963).

Feldman, C.

Feofilov, P. P.

P. P. Feofilov, The Physical Basis of Polarized Emission (Consultants Bureau, New York, 1961).

Goos, F.

F. Goos, H. Hänchen, Ann. Physik [6], 1, 333 (1947).
[CrossRef]

Gorton, A. F.

A. F. Gorton, Phys. Rev. 7, 66 (1916).
[CrossRef]

Hacskaylo, M.

Hänchen, H.

F. Goos, H. Hänchen, Ann. Physik [6], 1, 333 (1947).
[CrossRef]

Jasperse, J. R.

H. H. Blau, E. Chaffee, J. R. Jasperse, W. S. Martin, “High Temperature Thermal Properties of Solid Materials”, AFCRC-TN-60-165, Sci. Rept. No. 2 under Contract AF 19(604)-2639 (31March1960).

Jenkins, F. A.

F. A. Jenkins, D. H. Menzel, Fundamental Formulas of Physics (Dover, New York, 1960), Vol. II, pp. 419, 420.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), 3rd ed., pp. 513, 514, 519.

Keussler, V.

V. Keussler, P. M. Manogg, Optik 17, 602 (1960).

Limperis, T.

T. Limperis, private communication.The work was done by T. Limperis, J. Mudar, D. Anding.

Manogg, P. M.

V. Keussler, P. M. Manogg, Optik 17, 602 (1960).

Martin, W. S.

H. H. Blau, E. Chaffee, J. R. Jasperse, W. S. Martin, “High Temperature Thermal Properties of Solid Materials”, AFCRC-TN-60-165, Sci. Rept. No. 2 under Contract AF 19(604)-2639 (31March1960).

W. S. Martin, H. H. Blau, “Optical Constants at High Temperature”, AFCRL-13, Final Rept. C-60929 under Contract AF 19(604)-2639 (January1961).

W. S. Martin, E. M. Duchane, H. H. Blau, “Measurement of Optical Constants at High Temperature”, AFCRL-63-547, Final Rept. under Contract No. AF 19(604)-7485 (10December1963).

Menzel, D. H.

F. A. Jenkins, D. H. Menzel, Fundamental Formulas of Physics (Dover, New York, 1960), Vol. II, pp. 419, 420.

Miles, J. L.

H. H. Blau, J. L. Miles, L. E. Ashman, “The Thermal Radiation Characteristics of Solid Materials—A Review”, AFCRC-TN-58-132, Sci. Rept. No. 1 under Contract AF 19(604)-2639 (31March1958).

Millikan, R. A.

R. A. Millikan, Phys. Rev. 3, 81, 177 (1895).

Ohman, Y.

Y. Ohman, Nature 192, 254 (1961).
[CrossRef]

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard Univ. Press, Cambridge, 1962), p. 161.

Skilling, H. H.

H. H. Skilling, Fundamentals of Electric Waves (Wiley, New York, 1948), 2nd ed.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

Von Hippel, A. R.

A. R. Von Hippel, Dielectrics and Waves (Wiley, New York, 1954).

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), 3rd ed., pp. 513, 514, 519.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 43.

Worthing, A. G.

Ann. Chem. et Phys. (1)

F. Arago, Ann. Chem. et Phys. (2) 27, 89 (1824).

Ann. Physik (1)

F. Goos, H. Hänchen, Ann. Physik [6], 1, 333 (1947).
[CrossRef]

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

Nature (1)

Y. Ohman, Nature 192, 254 (1961).
[CrossRef]

Optik (1)

V. Keussler, P. M. Manogg, Optik 17, 602 (1960).

Phys. Rev. (2)

R. A. Millikan, Phys. Rev. 3, 81, 177 (1895).

A. F. Gorton, Phys. Rev. 7, 66 (1916).
[CrossRef]

Other (14)

W. A. Shurcliff, Polarized Light (Harvard Univ. Press, Cambridge, 1962), p. 161.

P. P. Feofilov, The Physical Basis of Polarized Emission (Consultants Bureau, New York, 1961).

H. H. Blau, J. L. Miles, L. E. Ashman, “The Thermal Radiation Characteristics of Solid Materials—A Review”, AFCRC-TN-58-132, Sci. Rept. No. 1 under Contract AF 19(604)-2639 (31March1958).

H. H. Blau, E. Chaffee, J. R. Jasperse, W. S. Martin, “High Temperature Thermal Properties of Solid Materials”, AFCRC-TN-60-165, Sci. Rept. No. 2 under Contract AF 19(604)-2639 (31March1960).

W. S. Martin, H. H. Blau, “Optical Constants at High Temperature”, AFCRL-13, Final Rept. C-60929 under Contract AF 19(604)-2639 (January1961).

W. S. Martin, E. M. Duchane, H. H. Blau, “Measurement of Optical Constants at High Temperature”, AFCRL-63-547, Final Rept. under Contract No. AF 19(604)-7485 (10December1963).

H. H. Skilling, Fundamentals of Electric Waves (Wiley, New York, 1948), 2nd ed.

A. R. Von Hippel, Dielectrics and Waves (Wiley, New York, 1954).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957), 3rd ed., pp. 513, 514, 519.

F. A. Jenkins, D. H. Menzel, Fundamental Formulas of Physics (Dover, New York, 1960), Vol. II, pp. 419, 420.

R. W. Ditchburn, Light (Interscience, New York, 1953), pp. 434–438.

T. Limperis, private communication.The work was done by T. Limperis, J. Mudar, D. Anding.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), p. 43.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram depicting incident, reflected, and transmitted waves. Wave crests shown perpendicular to directions of propagation. (After Skilling,5 p. 56.)

Fig. 2
Fig. 2

Schematic diagram depicting incident, reflected, and transmitted waves. Case I—Ē normal and H ¯ parallel to the plane of incidence. Only H ¯ p , 1 shown resolved into parallel and normal components with reference to the surface separating medium 1 from medium 2. The other two H ¯ p vectors are assumed similarly resolved.

Fig. 3
Fig. 3

Reflection of optical and microwaves from water surface. (After Von Hippel,6 p. 53.)

Fig. 4
Fig. 4

Intensity curves for internal reflection. n12 = 1.54. (After Jenkins and White,8 p. 513.)

Fig. 5
Fig. 5

Schematic representation of total internal reflection and nontransverse transmission propagation. (After Goos and Hänschen.12)

Fig. 6
Fig. 6

Relative brightness for the principal polarized light components B and B and the natural light B + B, and the polarization of the natural light P emitted by tungsten at incandescence as functions of the angle of emission. (After Worthing.14)

Tables (3)

Tables Icon

Table I Emission Polarization of Various Substancesa

Tables Icon

Table II Comparison of Experimental and Calculated Results for the Polarization of Uranium Glass Fluorescencea

Tables Icon

Table III Comparison of Experimental and Calculated Results for the Polarization of Platinum and Silvera

Equations (64)

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× Ē = B ¯ t = μ * H ¯ t ,
× H ¯ = D ¯ t = * Ē t ,
Ē = 0 ,
H ¯ = 0 ,
D ¯ = * Ē ,
B ¯ = μ * H ¯ ,
* = j ,
μ * = μ j μ ,
κ * = * 0 = 0 j 0 = κ j κ ,
κ * μ = μ * μ 0 = μ μ 0 j μ μ 0 = κ μ j κ μ ,
2 Ē = * μ * 2 Ē t 2 ,
2 H ¯ = * μ * 2 H ¯ t 2 .
E x = E 0 , x e j ω t γ z ,
H y = H 0 , y e j ω t γ z ,
ω = 2 π ν ,
γ = j ω ( μ * * ) ½ = α + j β ,
E x = E 0 , x e j ω t + γ z ,
H y = H 0 , y e j ω t + γ z .
× E x , 1 = E x , 1 z = γ 1 E 0 , x , 1 e j ω t γ 1 z = μ 1 * H y , 1 t .
H y , 1 = γ 1 j ω μ 1 * E x , 1 .
× H y , 1 = H y , 1 z γ 1 H 0 , y , 1 e j ω t γ 1 z = 1 * E x , 1 t ,
E x , 1 = γ 1 j ω 1 * H y , 1 .
Z 1 = γ 1 j ω 1 * = j ω μ 1 * γ 1 = μ 1 * 1 * ,
E x , 1 = Z 1 H y , 1 .
E x , 1 = Z 1 H y , 1 ,
E x , 2 = Z 2 H y , 2 .
a b = λ = λ 1 sin θ 1 = λ 1 sin θ 1 = λ 2 sin θ 2 .
sin θ 1 = sin θ 1 and θ 1 = θ 1 ,
sin θ 1 sin θ 2 = λ 1 λ 2 = υ 1 υ 2 = μ 2 * 2 * μ 1 * 1 * = n 2 * n 1 * = γ 2 γ 1 = Z 1 μ 2 * Z 2 μ 1 * ,
E n , 1 + E n , 1 = E n , 2 ,
H P , 1 + H P , 1 = H P , 2 .
H P , 1 = E n , 1 Z 1 cos θ 1 , H P , 1 = E n , 1 Z 1 cos θ 1 , H P , 2 = E n , 2 Z 2 cos θ 2 .
E n , 1 Z 1 cos θ 1 E n , 1 Z 1 cos θ 1 = E n , 2 Z 2 cos θ 2 .
r E n = E n , 1 E n , 1 , r H p = H p , 1 H p , 1 , t E n = E n , 2 E n , 1 , t H p = H p , 2 H p , 1 .
r E n = Z 2 cos θ 1 Z 1 cos θ 2 Z 2 cos θ 1 + Z 1 cos θ 2 = r H p ,
t E n = 2 Z 2 cos θ 1 Z 2 cos θ 1 + Z 1 cos θ 2 = Z 2 Z 1 t H P .
H n , 1 + H n , 1 = H n , 2 , E P , 1 + E P , 1 = E P , 2 .
Z 1 H n , 1 cos θ 1 Z 1 H n , 1 cos θ 1 = Z 2 H n , 2 cos θ 2 .
r E p = E p , 1 E p , 1 , r H n = H n , 1 H n , 1 , t E p = E p , 2 E p , 1 , t H n = H n , 2 H n , 1 .
r E p = Z 2 cos θ 2 Z 1 cos θ 1 Z 2 cos θ 2 + Z 1 cos θ 1 = r H n ,
t E p = 2 Z 2 cos θ 1 Z 2 cos θ 2 + Z 1 cos θ 1 = Z 2 Z 1 t H n .
r E n = r H p = sin ( θ 1 θ 2 ) sin ( θ 1 + θ 2 ) ,
r E p = r H n = tan ( θ 1 θ 2 ) tan ( θ 1 + θ 2 ) ,
t E n = sin θ 2 sin θ 1 t H p = 2 sin θ 2 cos θ 1 sin ( θ 1 + θ 2 ) ,
t E p = sin θ 2 sin θ 1 t H n = 2 sin θ 2 cos θ 1 sin ( θ 1 + θ 2 ) cos ( θ 1 θ 2 ) .
sin θ 2 = cos θ 1 ,
tan θ 1 = n 21 .
sin θ 1 = n 21 = 1 n 12 .
R E n = | r E n | 2 = sin 2 ( θ 1 θ 2 ) sin 2 ( θ 1 + θ 2 ) ,
R E p = | r E p | 2 = tan 2 ( θ 1 θ 2 ) tan 2 ( θ 1 + θ 2 ) ,
T E n = | t E n | 2 Z 1 cos θ 2 Z 2 cos θ 1 = sin 2 θ 1 sin 2 θ 2 sin 2 ( θ 1 + θ 2 ) ,
T E p = | t E p | 2 Z 1 cos θ 2 Z 2 cos θ 1 = sin 2 θ 1 sin 2 θ 2 sin 2 ( θ 1 + θ 2 ) cos 2 ( θ 1 θ 2 ) .
R E n + T E n = 1 , R E p + T E p = 1 .
P R = | R E p R E n R E p + R E n | , P T = | T E p T E n T E p + T E n | .
P T = 1 cos 2 ( θ 1 θ 2 ) 1 + cos 2 ( θ 1 θ 2 ) ,
K 2 = tan ( f 45 ° ) , K 2 = tan ( g 45 ° ) ,
cot f = cos ( e + u ) sin ( 2 arctan c θ cos α ) ,
cot g = cos ( e u ) sin ( 2 arctan cos α c θ ) ,
cot ( 2 u + e ) = cot e cos ( 2 arctan sin α θ ) ,
c 2 = sin 2 e sin ( 2 u + 2 e ) ,
sin 2 e = tan 2 A sin ( 4 H 2 e ) ,
θ = sin A sin 4 H sin ( 4 H 2 e ) .
P T = ( 1 K 2 ) ( 1 K 2 ) ( 1 K 2 ) + ( 1 K 2 ) .
D = 0.52 λ 0 λ 2 λ 1 sin 2 θ 1 n 21 2 ,

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