Abstract

The paramagnetic optical Faraday rotation is the averaged property of all the energy states of the paramagnetic ion. Therefore, any perturbation of the population distribution of the energy states caused by the microwave power absorption would manifest itself as the interaction between the optical Faraday rotation and the microwave radiation. A general calculation of this effect, plus some experimental results, are presented in this paper. An attempt is made to analyze the behavior and to evaluate the applications as optical modulators, detectors, and relaxation measuring devices.

© 1962 Optical Society of America

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References

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  1. J. Becquerel, W. J. DeHaas, J. Van Den Handel, Physica 5, 753 (1938).
    [CrossRef]
  2. J. H. Van Vleck, M. H. Hebb, Phys. Rev. 46, 17 (1934).
    [CrossRef]
  3. L. Rosenfeld, Z. Physik 57, 835 (1929).
    [CrossRef]
  4. H. A. Kramers, Proc. Acad. Sci. Amsterdam 33, 959 (1930).
  5. A. Kastler, Compt. rend. 232, 953 (1951).
  6. W. Opechowski, Revs. Modern Phys. 25, 264 (1953).
    [CrossRef]
  7. J. M. Daniels, H. Wesemeyer, Can. J. Phys. 36, 405 (1958).
    [CrossRef]
  8. J. M. Daniels, K. E. Reickhoff, Can. J. Phys. 38, 604 (1960).
    [CrossRef]
  9. N. Bloembergen, P. S. Pershan, L. R. Wilcox, Phys. Rev. 120, 2014 (1960).
    [CrossRef]
  10. N. Bloembergen, Phys. Rev. 104, sec. 2, 324 (1956).
    [CrossRef]
  11. R. C. Tolman, Statistical Mechanics (Oxford Univ. Press, 1938).
  12. J. H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities (Clarendon Press, Oxford, 1932).
  13. W. S. C. Chang, The Ohio State University Research Foundation Technical Report 1040-2 (1961).
  14. B. Bleaney, K. W. H. Stevens, Repts. Progr. in Phys. 16, 108 (1953).
    [CrossRef]
  15. K. D. Bowers, J. Owen, Repts. Progr. in Phys. 18, 304 (1955).
    [CrossRef]
  16. A. G. Redfield, Phys. Rev. 98, 1787 (1955).
    [CrossRef]
  17. A. Abragam, W. Proctor, Compt. rend. 245, 1048 (1957).
  18. P. N. Butcher, Stanford Univ., Tech. Report 155-1 (1957).
  19. W. W. Anderson, Stanford Univ., Tech. Report 211-1 (1959).
  20. J. Weber, Revs. Modern Phys. 31, 681 (1959).
    [CrossRef]

1960 (2)

J. M. Daniels, K. E. Reickhoff, Can. J. Phys. 38, 604 (1960).
[CrossRef]

N. Bloembergen, P. S. Pershan, L. R. Wilcox, Phys. Rev. 120, 2014 (1960).
[CrossRef]

1959 (1)

J. Weber, Revs. Modern Phys. 31, 681 (1959).
[CrossRef]

1958 (1)

J. M. Daniels, H. Wesemeyer, Can. J. Phys. 36, 405 (1958).
[CrossRef]

1957 (1)

A. Abragam, W. Proctor, Compt. rend. 245, 1048 (1957).

1956 (1)

N. Bloembergen, Phys. Rev. 104, sec. 2, 324 (1956).
[CrossRef]

1955 (2)

K. D. Bowers, J. Owen, Repts. Progr. in Phys. 18, 304 (1955).
[CrossRef]

A. G. Redfield, Phys. Rev. 98, 1787 (1955).
[CrossRef]

1953 (2)

W. Opechowski, Revs. Modern Phys. 25, 264 (1953).
[CrossRef]

B. Bleaney, K. W. H. Stevens, Repts. Progr. in Phys. 16, 108 (1953).
[CrossRef]

1951 (1)

A. Kastler, Compt. rend. 232, 953 (1951).

1938 (1)

J. Becquerel, W. J. DeHaas, J. Van Den Handel, Physica 5, 753 (1938).
[CrossRef]

1934 (1)

J. H. Van Vleck, M. H. Hebb, Phys. Rev. 46, 17 (1934).
[CrossRef]

1930 (1)

H. A. Kramers, Proc. Acad. Sci. Amsterdam 33, 959 (1930).

1929 (1)

L. Rosenfeld, Z. Physik 57, 835 (1929).
[CrossRef]

Abragam, A.

A. Abragam, W. Proctor, Compt. rend. 245, 1048 (1957).

Anderson, W. W.

W. W. Anderson, Stanford Univ., Tech. Report 211-1 (1959).

Becquerel, J.

J. Becquerel, W. J. DeHaas, J. Van Den Handel, Physica 5, 753 (1938).
[CrossRef]

Bleaney, B.

B. Bleaney, K. W. H. Stevens, Repts. Progr. in Phys. 16, 108 (1953).
[CrossRef]

Bloembergen, N.

N. Bloembergen, P. S. Pershan, L. R. Wilcox, Phys. Rev. 120, 2014 (1960).
[CrossRef]

N. Bloembergen, Phys. Rev. 104, sec. 2, 324 (1956).
[CrossRef]

Bowers, K. D.

K. D. Bowers, J. Owen, Repts. Progr. in Phys. 18, 304 (1955).
[CrossRef]

Butcher, P. N.

P. N. Butcher, Stanford Univ., Tech. Report 155-1 (1957).

Chang, W. S. C.

W. S. C. Chang, The Ohio State University Research Foundation Technical Report 1040-2 (1961).

Daniels, J. M.

J. M. Daniels, K. E. Reickhoff, Can. J. Phys. 38, 604 (1960).
[CrossRef]

J. M. Daniels, H. Wesemeyer, Can. J. Phys. 36, 405 (1958).
[CrossRef]

DeHaas, W. J.

J. Becquerel, W. J. DeHaas, J. Van Den Handel, Physica 5, 753 (1938).
[CrossRef]

Hebb, M. H.

J. H. Van Vleck, M. H. Hebb, Phys. Rev. 46, 17 (1934).
[CrossRef]

Kastler, A.

A. Kastler, Compt. rend. 232, 953 (1951).

Kramers, H. A.

H. A. Kramers, Proc. Acad. Sci. Amsterdam 33, 959 (1930).

Opechowski, W.

W. Opechowski, Revs. Modern Phys. 25, 264 (1953).
[CrossRef]

Owen, J.

K. D. Bowers, J. Owen, Repts. Progr. in Phys. 18, 304 (1955).
[CrossRef]

Pershan, P. S.

N. Bloembergen, P. S. Pershan, L. R. Wilcox, Phys. Rev. 120, 2014 (1960).
[CrossRef]

Proctor, W.

A. Abragam, W. Proctor, Compt. rend. 245, 1048 (1957).

Redfield, A. G.

A. G. Redfield, Phys. Rev. 98, 1787 (1955).
[CrossRef]

Reickhoff, K. E.

J. M. Daniels, K. E. Reickhoff, Can. J. Phys. 38, 604 (1960).
[CrossRef]

Rosenfeld, L.

L. Rosenfeld, Z. Physik 57, 835 (1929).
[CrossRef]

Stevens, K. W. H.

B. Bleaney, K. W. H. Stevens, Repts. Progr. in Phys. 16, 108 (1953).
[CrossRef]

Tolman, R. C.

R. C. Tolman, Statistical Mechanics (Oxford Univ. Press, 1938).

Van Den Handel, J.

J. Becquerel, W. J. DeHaas, J. Van Den Handel, Physica 5, 753 (1938).
[CrossRef]

Van Vleck, J. H.

J. H. Van Vleck, M. H. Hebb, Phys. Rev. 46, 17 (1934).
[CrossRef]

J. H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities (Clarendon Press, Oxford, 1932).

Weber, J.

J. Weber, Revs. Modern Phys. 31, 681 (1959).
[CrossRef]

Wesemeyer, H.

J. M. Daniels, H. Wesemeyer, Can. J. Phys. 36, 405 (1958).
[CrossRef]

Wilcox, L. R.

N. Bloembergen, P. S. Pershan, L. R. Wilcox, Phys. Rev. 120, 2014 (1960).
[CrossRef]

Can. J. Phys. (2)

J. M. Daniels, H. Wesemeyer, Can. J. Phys. 36, 405 (1958).
[CrossRef]

J. M. Daniels, K. E. Reickhoff, Can. J. Phys. 38, 604 (1960).
[CrossRef]

Compt. rend. (2)

A. Kastler, Compt. rend. 232, 953 (1951).

A. Abragam, W. Proctor, Compt. rend. 245, 1048 (1957).

Phys. Rev. (4)

A. G. Redfield, Phys. Rev. 98, 1787 (1955).
[CrossRef]

N. Bloembergen, P. S. Pershan, L. R. Wilcox, Phys. Rev. 120, 2014 (1960).
[CrossRef]

N. Bloembergen, Phys. Rev. 104, sec. 2, 324 (1956).
[CrossRef]

J. H. Van Vleck, M. H. Hebb, Phys. Rev. 46, 17 (1934).
[CrossRef]

Physica (1)

J. Becquerel, W. J. DeHaas, J. Van Den Handel, Physica 5, 753 (1938).
[CrossRef]

Proc. Acad. Sci. Amsterdam (1)

H. A. Kramers, Proc. Acad. Sci. Amsterdam 33, 959 (1930).

Repts. Progr. in Phys. (2)

B. Bleaney, K. W. H. Stevens, Repts. Progr. in Phys. 16, 108 (1953).
[CrossRef]

K. D. Bowers, J. Owen, Repts. Progr. in Phys. 18, 304 (1955).
[CrossRef]

Revs. Modern Phys. (2)

W. Opechowski, Revs. Modern Phys. 25, 264 (1953).
[CrossRef]

J. Weber, Revs. Modern Phys. 31, 681 (1959).
[CrossRef]

Z. Physik (1)

L. Rosenfeld, Z. Physik 57, 835 (1929).
[CrossRef]

Other (5)

R. C. Tolman, Statistical Mechanics (Oxford Univ. Press, 1938).

J. H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities (Clarendon Press, Oxford, 1932).

W. S. C. Chang, The Ohio State University Research Foundation Technical Report 1040-2 (1961).

P. N. Butcher, Stanford Univ., Tech. Report 155-1 (1957).

W. W. Anderson, Stanford Univ., Tech. Report 211-1 (1959).

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Figures (5)

Fig. 1
Fig. 1

The detection of the Faraday rotation.

Fig. 2
Fig. 2

Faraday rotation versus dc magnetic field.

Fig. 3
Fig. 3

Faraday rotation versus c.w. microwave power.

Fig. 4
Fig. 4

Faraday modulation depth versus modulation frequency.

Fig. 5
Fig. 5

Faraday modulation distortion at fm > 1/T1. (a) Microwave modulated at 5 cps. (b) Microwave modulated at 100 cps.

Equations (12)

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

θ = A tanh μ H a k T + B H a ,
θ ~ A μ H a k T s ,
d θ θ ~ d T s T s .
n 1 ω 12 n 2 ω 21 + ( n 1 n 2 ) W ¯ = d n 2 d t ,
n 1 ω 12 + n 2 ω 21 + ( n 2 n 1 ) W ¯ = d n 1 d t ,
ω 12 = ω 21 exp [ ( E 2 E 1 ) / k T b ] ,
T s = T b W + ω 12 ω 12 .
W ¯ = P abs ( n 2 n 1 ) μ H a ,
P abs = P in 4 β ( 1 + β ) 2 .
Δ θ θ 0 = 4 β P in ω 12 ( n 2 n 1 ) μ H a ( 1 + β ) 2 .
θ = l π λ n m , n j ω p [ ( p x ) n m ( p y ) m n ( p x ) m n ( p y ) n m ] ћ [ ω p 2 ω m n 2 ] ρ m m ,
Δ θ p θ p 0 P × 10 3 ,

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