Abstract

The measurement of optical excitation functions excited by electron impact is typically accomplished by recording atomic fluorescence emitted into a small solid angle perpendicular to the incident electron beam. This measured intensity is not proportional to the emission cross section because the fluorescence exhibits an angular distribution and polarization that varies with the energy of the exciting electrons. Typically, a polarizer is set at the “magic angle” (54.7°) with respect to the electron beam axis to remove this polarization dependence. The literature for the derivation of the magic angle value assumes the polarizing element is perfect. An expression for the angle that accounts for the use of a partial polarizer is presented.

© 2008 Optical Society of America

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References

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  1. B. L. Moiseiwitsch and S. J. Smith, “Electron impact excitation of atoms,” Rev. Mod. Phys. 40, 238-353 (1968).
    [CrossRef]
  2. A. R. Filippelli, C. C. Lin, L. W. Anderson, and J. W. McConkey, “Principles and methods for measurement of electron impact excitation cross sections for atoms and molecules by optical techniques,” Adv. At., Mol., Opt. Phys. 33, 1-62 (1994).
  3. U. Fano and J. H. Macek, “Impact excitation and polarization of the emitted light,” Rev. Mod. Phys. 45, 553-573 (1973).
    [CrossRef]
  4. P. N. Clout and D. W. O. Heddle, “Elimination of polarization corrections from optical excitation-function measurements,” J. Opt. Soc. Am. 59, 715-717 (1969).
    [CrossRef]
  5. B. L. Moiseiwitsch and S. J. Smith, “Erratum: Electron impact excitation of atoms,” Rev. Mod. Phys. 41, 574 (1969).
    [CrossRef]
  6. D. W. O. Heddle and J. W. Gallagher, “Measurements of electron impact optical excitation functions,” Rev. Mod. Phys. 61, 221-278 (1989).
    [CrossRef]
  7. L. J. Curtis, Atomic Structure and Lifetimes: a Conceptual Approach (Cambridge, 2003).
  8. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North Holland, 1989).

1994 (1)

A. R. Filippelli, C. C. Lin, L. W. Anderson, and J. W. McConkey, “Principles and methods for measurement of electron impact excitation cross sections for atoms and molecules by optical techniques,” Adv. At., Mol., Opt. Phys. 33, 1-62 (1994).

1989 (1)

D. W. O. Heddle and J. W. Gallagher, “Measurements of electron impact optical excitation functions,” Rev. Mod. Phys. 61, 221-278 (1989).
[CrossRef]

1973 (1)

U. Fano and J. H. Macek, “Impact excitation and polarization of the emitted light,” Rev. Mod. Phys. 45, 553-573 (1973).
[CrossRef]

1969 (2)

1968 (1)

B. L. Moiseiwitsch and S. J. Smith, “Electron impact excitation of atoms,” Rev. Mod. Phys. 40, 238-353 (1968).
[CrossRef]

Anderson, L. W.

A. R. Filippelli, C. C. Lin, L. W. Anderson, and J. W. McConkey, “Principles and methods for measurement of electron impact excitation cross sections for atoms and molecules by optical techniques,” Adv. At., Mol., Opt. Phys. 33, 1-62 (1994).

Azzam, R. M. A.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North Holland, 1989).

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North Holland, 1989).

Clout, P. N.

Curtis, L. J.

L. J. Curtis, Atomic Structure and Lifetimes: a Conceptual Approach (Cambridge, 2003).

Fano, U.

U. Fano and J. H. Macek, “Impact excitation and polarization of the emitted light,” Rev. Mod. Phys. 45, 553-573 (1973).
[CrossRef]

Filippelli, A. R.

A. R. Filippelli, C. C. Lin, L. W. Anderson, and J. W. McConkey, “Principles and methods for measurement of electron impact excitation cross sections for atoms and molecules by optical techniques,” Adv. At., Mol., Opt. Phys. 33, 1-62 (1994).

Gallagher, J. W.

D. W. O. Heddle and J. W. Gallagher, “Measurements of electron impact optical excitation functions,” Rev. Mod. Phys. 61, 221-278 (1989).
[CrossRef]

Heddle, D. W. O.

D. W. O. Heddle and J. W. Gallagher, “Measurements of electron impact optical excitation functions,” Rev. Mod. Phys. 61, 221-278 (1989).
[CrossRef]

P. N. Clout and D. W. O. Heddle, “Elimination of polarization corrections from optical excitation-function measurements,” J. Opt. Soc. Am. 59, 715-717 (1969).
[CrossRef]

Lin, C. C.

A. R. Filippelli, C. C. Lin, L. W. Anderson, and J. W. McConkey, “Principles and methods for measurement of electron impact excitation cross sections for atoms and molecules by optical techniques,” Adv. At., Mol., Opt. Phys. 33, 1-62 (1994).

Macek, J. H.

U. Fano and J. H. Macek, “Impact excitation and polarization of the emitted light,” Rev. Mod. Phys. 45, 553-573 (1973).
[CrossRef]

McConkey, J. W.

A. R. Filippelli, C. C. Lin, L. W. Anderson, and J. W. McConkey, “Principles and methods for measurement of electron impact excitation cross sections for atoms and molecules by optical techniques,” Adv. At., Mol., Opt. Phys. 33, 1-62 (1994).

Moiseiwitsch, B. L.

B. L. Moiseiwitsch and S. J. Smith, “Erratum: Electron impact excitation of atoms,” Rev. Mod. Phys. 41, 574 (1969).
[CrossRef]

B. L. Moiseiwitsch and S. J. Smith, “Electron impact excitation of atoms,” Rev. Mod. Phys. 40, 238-353 (1968).
[CrossRef]

Smith, S. J.

B. L. Moiseiwitsch and S. J. Smith, “Erratum: Electron impact excitation of atoms,” Rev. Mod. Phys. 41, 574 (1969).
[CrossRef]

B. L. Moiseiwitsch and S. J. Smith, “Electron impact excitation of atoms,” Rev. Mod. Phys. 40, 238-353 (1968).
[CrossRef]

Adv. At., Mol., Opt. Phys. (1)

A. R. Filippelli, C. C. Lin, L. W. Anderson, and J. W. McConkey, “Principles and methods for measurement of electron impact excitation cross sections for atoms and molecules by optical techniques,” Adv. At., Mol., Opt. Phys. 33, 1-62 (1994).

J. Opt. Soc. Am. (1)

Rev. Mod. Phys. (4)

B. L. Moiseiwitsch and S. J. Smith, “Electron impact excitation of atoms,” Rev. Mod. Phys. 40, 238-353 (1968).
[CrossRef]

U. Fano and J. H. Macek, “Impact excitation and polarization of the emitted light,” Rev. Mod. Phys. 45, 553-573 (1973).
[CrossRef]

B. L. Moiseiwitsch and S. J. Smith, “Erratum: Electron impact excitation of atoms,” Rev. Mod. Phys. 41, 574 (1969).
[CrossRef]

D. W. O. Heddle and J. W. Gallagher, “Measurements of electron impact optical excitation functions,” Rev. Mod. Phys. 61, 221-278 (1989).
[CrossRef]

Other (2)

L. J. Curtis, Atomic Structure and Lifetimes: a Conceptual Approach (Cambridge, 2003).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North Holland, 1989).

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Figures (2)

Fig. 1
Fig. 1

Coordinate system.

Fig. 2
Fig. 2

Polarizer orientation α as given by Eq. (11) required to obtain optical excitation functions independent of target alignment.

Equations (11)

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

M 1 , j = k 1 + k 2 2 [ 1 k cos ( 2 α ) k sin ( 2 α ) 0 ] ,
k = k 1 k 2 k 1 + k 2 .
d I ( θ , α ) d Ω = k 1 + k 2 2 [ I z sin 2 ( θ ) [ 1 + k cos ( 2 α ) ] + I x y cos 2 ( θ ) [ 1 + k cos ( 2 α ) ] + I x y [ 1 k cos ( 2 α ) ] ] .
P = I z I x y I z + I x y ,
d I ( θ , α ) d Ω = ( k 1 + k 2 ) ( I z + I x y ) 2 [ 1 + P k cos ( 2 α ) P cos 2 ( θ ) [ 1 + k cos ( 2 α ) ] ] .
d I ( θ ) d Ω = d I ( θ , α ) d Ω + d I ( θ , α + π 2 ) d Ω = ( k 1 + k 2 ) ( I z + I x y ) [ 1 P cos 2 ( θ ) ] .
I = 4 π ( k 1 + k 2 ) ( I z + I x y ) ( 1 P 3 ) .
I 4 π ( k 1 + k 2 ) ( I z + I x y ) ( 1 P 3 ) = 1
d I ( θ , α ) d Ω I [ 1 + P k cos ( 2 α ) P cos 2 ( θ ) [ 1 + k cos ( 2 α ) ] 1 P 3 ] .
P 3 = P k cos ( 2 α ) P cos 2 ( θ ) [ 1 + k cos ( 2 α ) ] .
α = ± 1 2 cos 1 ( 3 cos 2 ( θ ) 1 3 k sin 2 ( θ ) ) .

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