Abstract

A comprehensive analysis of the production and detection of circularly polarized VUV light using reflection optics is presented. Experimental results using gold reflectors are given. The necessary measurements to determine all Stokes parameters of an arbitrary VUV light beam are discussed.

© 1985 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. A. R. Samson, Techniques of VUV Spectroscopy (Wiley, New York, 1967).
  2. J. W. McConkey, T. Crouch, J. Tomc, “Sensitivity Response of Channel Electron Multipliers and Channel Plates to the Polarization of VUV Radiation,” Appl. Opt. 21, 1643 (1982).
    [CrossRef] [PubMed]
  3. J. Tomc, P. Zetner, W. B. Westerveld, J. W. McConkey, “Variations in the Polarization Sensitivity of MicroChannel Plates with Photon Incidence Angle and Wavelength in the VUV,” Appl. Opt. 23, 656 (1984).
    [CrossRef] [PubMed]
  4. P. Zetner, A. Pradhan, W. B. Westerveld, J. W. McConkey, “Polarization Analysis Techniques in the VUV,” Appl. Opt. 22, 2210 (1983).
    [CrossRef] [PubMed]
  5. P. Zetner, K. Becker, W. B. Westerveld, J. W. McConkey, “Detection of Polarized Light in the Vacuum UV,” Appl. Opt. 23, 3184 (1984).
    [CrossRef] [PubMed]
  6. J. F. Williams, “Symmetry Properties of Electron-Photon Angular Correlations,” Abstract, ThirteenthICPEAC, Berlin (1983), p. 132.
  7. J. Slevin, “Coherence in Inelastic Low-Energy Electron Scattering,” Rep. Prog. Phys.47, 461 (1984).
    [CrossRef]
  8. K. H. Tan, J. Fryar, P. S. Farago, J. W. McConkey, “Coincidence Studies of He (11S – 21P) Excitation by Electron Impact,” J. Phys. B 10, 1073 (1977).
    [CrossRef]
  9. H. Metcalf, J. C. Baird, “Circular Polarization of VUV Light by Piezobirefringence,” Appl. Opt. 5, 1407 (1966).
    [CrossRef] [PubMed]
  10. K. Lambrecht, “Retarders and Rotators,” Technical Report, KLC Corp. (1979).
  11. T. J. McDrath, “Circular Polarizer for Lyman-Alpha Flux,” J. Opt. Soc. Am. 58, 506 (1968).
    [CrossRef]
  12. W. B. Westerveld, “Analysis of Optical Systems,” Unpublished Report, Atomic Collisions Laboratory, North Carolina State U., (1984).
  13. L. R. Canfield, G. Hass, W. Hunter, “The Optical Properties of Evaporated Gold in the VUV from 300 A to 2000 A,” J. Phys. (Paris) 25, 124 (1964).
    [CrossRef]

1984 (2)

1983 (1)

1982 (1)

1977 (1)

K. H. Tan, J. Fryar, P. S. Farago, J. W. McConkey, “Coincidence Studies of He (11S – 21P) Excitation by Electron Impact,” J. Phys. B 10, 1073 (1977).
[CrossRef]

1968 (1)

1966 (1)

1964 (1)

L. R. Canfield, G. Hass, W. Hunter, “The Optical Properties of Evaporated Gold in the VUV from 300 A to 2000 A,” J. Phys. (Paris) 25, 124 (1964).
[CrossRef]

Baird, J. C.

Becker, K.

Canfield, L. R.

L. R. Canfield, G. Hass, W. Hunter, “The Optical Properties of Evaporated Gold in the VUV from 300 A to 2000 A,” J. Phys. (Paris) 25, 124 (1964).
[CrossRef]

Crouch, T.

Farago, P. S.

K. H. Tan, J. Fryar, P. S. Farago, J. W. McConkey, “Coincidence Studies of He (11S – 21P) Excitation by Electron Impact,” J. Phys. B 10, 1073 (1977).
[CrossRef]

Fryar, J.

K. H. Tan, J. Fryar, P. S. Farago, J. W. McConkey, “Coincidence Studies of He (11S – 21P) Excitation by Electron Impact,” J. Phys. B 10, 1073 (1977).
[CrossRef]

Hass, G.

L. R. Canfield, G. Hass, W. Hunter, “The Optical Properties of Evaporated Gold in the VUV from 300 A to 2000 A,” J. Phys. (Paris) 25, 124 (1964).
[CrossRef]

Hunter, W.

L. R. Canfield, G. Hass, W. Hunter, “The Optical Properties of Evaporated Gold in the VUV from 300 A to 2000 A,” J. Phys. (Paris) 25, 124 (1964).
[CrossRef]

Lambrecht, K.

K. Lambrecht, “Retarders and Rotators,” Technical Report, KLC Corp. (1979).

McConkey, J. W.

McDrath, T. J.

Metcalf, H.

Pradhan, A.

Samson, J. A. R.

J. A. R. Samson, Techniques of VUV Spectroscopy (Wiley, New York, 1967).

Slevin, J.

J. Slevin, “Coherence in Inelastic Low-Energy Electron Scattering,” Rep. Prog. Phys.47, 461 (1984).
[CrossRef]

Tan, K. H.

K. H. Tan, J. Fryar, P. S. Farago, J. W. McConkey, “Coincidence Studies of He (11S – 21P) Excitation by Electron Impact,” J. Phys. B 10, 1073 (1977).
[CrossRef]

Tomc, J.

Westerveld, W. B.

Williams, J. F.

J. F. Williams, “Symmetry Properties of Electron-Photon Angular Correlations,” Abstract, ThirteenthICPEAC, Berlin (1983), p. 132.

Zetner, P.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

J. Phys. (Paris) (1)

L. R. Canfield, G. Hass, W. Hunter, “The Optical Properties of Evaporated Gold in the VUV from 300 A to 2000 A,” J. Phys. (Paris) 25, 124 (1964).
[CrossRef]

J. Phys. B (1)

K. H. Tan, J. Fryar, P. S. Farago, J. W. McConkey, “Coincidence Studies of He (11S – 21P) Excitation by Electron Impact,” J. Phys. B 10, 1073 (1977).
[CrossRef]

Other (5)

K. Lambrecht, “Retarders and Rotators,” Technical Report, KLC Corp. (1979).

W. B. Westerveld, “Analysis of Optical Systems,” Unpublished Report, Atomic Collisions Laboratory, North Carolina State U., (1984).

J. A. R. Samson, Techniques of VUV Spectroscopy (Wiley, New York, 1967).

J. F. Williams, “Symmetry Properties of Electron-Photon Angular Correlations,” Abstract, ThirteenthICPEAC, Berlin (1983), p. 132.

J. Slevin, “Coherence in Inelastic Low-Energy Electron Scattering,” Rep. Prog. Phys.47, 461 (1984).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Reflection coordinate systems. Incident linearly polarized light with electric field vector Ei is shown propagating along the zi axis. For suitably chosen values of the incident angle θ = θi and rotation angle ϕ a right-handed circularly polarized beam is produced by reflection from the mirror. See text for further details.

Fig. 2
Fig. 2

Schematic diagram of the experimental setup. An essentially 100% linearly polarized beam provided by the TRP is converted to a circularly polarized beam by M1 and analyzed by M2 as discussed in the text. For some experiments, the CEM detector associated with M2 was replaced by a second analyzer system M3 (shown in dashed box).

Fig. 3
Fig. 3

Incident angle θ, which produces a phase shift Δr, Eq. (8a), of π/2 for a gold surface as a function of wavelength. Little variation in θ occurs over wavelength intervals of 50 nm or more, as indicated by the dashed lines. Note that the phase shift varies from π at normal to zero at grazing incidence.

Fig. 4
Fig. 4

Calculated - - - and measured ○ variation of the polarization P′ measured by M2 (Fig. 2) as a function of the polarization direction ϕ of the linearly polarized beam incident on M1. When P′ = 0, the beam reflected from M1 is circularly polarized.

Fig. 5
Fig. 5

Polar diagram showing the intensity of the light detected by the M2-CEM (Figs. 2 and 6) combination as a function of the orientation α of M2. The circular patterns obtained for H2, N2, and He in the source region indicate that the light incident on M2 was completely circularly polarized independent of wavelength used.

Fig. 6
Fig. 6

Light emitted from the scattering plane is reflected by R1, then by R2, and subsequently detected by the CEM. p ̂ and s ̂ ( q ̂ and r ̂) are the principal axes of reflector R1 (R2). The plane P1, perpendicular to the propagation vector, indicates the angle α which gives the relative orientation of the ( p ̂, s ̂) and ( q ̂, r ̂) axes. The projections of these axes into the mirrors are also indicated. Incident angles θ are adjusted to give cosΔr = 0 (see text).

Equations (58)

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

( E p ( z , t ) E s ( z , t ) ) = ( E p 0 exp [ i ω ( t z n / c ) + i ϕ p ] E s 0 exp [ i ω ( t z n / c ) + i ϕ s ] ) ,
( E p E s ) = J · ( E p E s ) .
e ̂ p = ( 1 , 0 , 0 ) ,
e ̂ s = ( 0 , 1 , 0 ) ,
e ̂ π / 4 = ( e ̂ p + e ̂ s ) / 2 ,
e ̂ 3 π / 4 = ( e ̂ p e ̂ s ) / 2 ,
e ̂ r . h . = ( e ̂ p + i e ̂ s ) / 2 ,
e ̂ l . h . = ( e ̂ p i e ̂ s ) / 2 ,
S 0 = I ( e ̂ p ) + I ( e ̂ s ) total intensity ,
S 1 = I ( e ̂ p ) I ( e ̂ s ) S 2 = I ( e ̂ π / 4 ) I ( e ̂ 3 π / 4 ) } linear polarization ,
S 3 = I ( e ̂ r . h . ) I ( e ̂ l . h . ) circular polarization ,
S 0 = [ ( E p 0 ) 2 + ( E s 0 ) 2 ] / 2 ,
S 1 = [ ( E p 0 ) 2 ( E s 0 ) 2 ] / 2 ,
S 2 = E p 0 E s 0 cos ( ϕ p ϕ s ) ,
S 3 = E p 0 E s 0 sin ( ϕ p ϕ s ) .
J = ( r p 0 0 r s ) ,
r p = r p · exp ( i δ p ) , r s = r s · exp ( i δ s ) ,
S 0 = ½ ( r p 2 + r s 2 ) S 0 + ½ ( r p 2 r s 2 ) S 1 ,
S 1 = ½ ( r p 2 r s 2 ) S 0 + ½ ( r p 2 + r s 2 ) S 1 ,
S 2 = r p r s cos ( δ p δ s ) S 2 + r p r s sin ( δ p δ s ) S 3 ,
S 3 = r p r s sin ( δ p δ s ) S 2 + r p r s cos ( δ p δ s ) S 3 ,
S = M · S ,
M = ½ ( r p 2 + r s 2 ) ( 1 cos 2 ψ r 0 0 cos 2 ψ r 1 0 0 0 0 sin 2 ψ r cos Δ r sin 2 ψ r sin Δ r 0 0 sin 2 ψ r sin Δ r sin 2 ψ r cos Δ r )
Δ r = δ p δ s ,
tan ψ r = r p / r s .
S ( s , p ) = R ( ϕ ) S ( x , y ) ,
R ( ϕ ) = [ 1 0 0 0 0 cos 2 ϕ sin 2 ϕ 0 0 sin 2 ϕ cos 2 ϕ 0 0 0 0 1 ] .
S 0 ( s , p ) = I ( intensity ) ,
S 1 ( s , p ) = I P cos 2 ϕ ,
S 2 ( s , p ) = I P sin 2 ϕ ,
S 3 ( s , p ) = 0 ( no circular polarization ) .
S 0 = ½ ( r p 2 + r s 2 ) I ( 1 P cos 2 ψ r cos 2 ϕ ) ,
S 1 = ½ ( r p 2 + r s 2 ) I ( cos 2 ψ r + P cos 2 ϕ ) ,
S 2 = ½ ( r p 2 + r s 2 ) I P sin 2 ψ r cos Δ r sin 2 ϕ ,
S 3 = ½ ( r p 2 + r s 2 ) I P sin 2 ψ r sin Δ r sin 2 ϕ .
S 1 = 0 ,
S 2 = 0 ,
| S 3 | = S 0 .
cos 2 ϕ 0 = ( 1 / P ) cos 2 ψ r ,
| P | cos 2 ψ r .
cos Δ r = 0 .
| P | = 1 ,
S 0 = I = 2 r p 2 r s 2 ( r p 2 + r s 2 ) I .
cos 2 ψ r = ( r s 2 r p 2 ) / ( r s 2 + r p 2 ) , sin 2 ψ r = 2 r s r p / ( r s 2 + r p 2 ) .
M = ρ ( 1 cos 2 ψ r 0 0 cos 2 ψ r 1 0 0 0 0 0 sin 2 ψ r 0 0 sin 2 ψ r 0 ) ,
S ( s , p ) = R ( ϕ ) S ( x , y ) ,
S ( s , p ) = ( S 0 S 1 cos 2 ϕ + S 2 sin 2 ϕ S 1 sin 2 ϕ + S 2 cos 2 ϕ S 3 ) .
S ( s , p ) = M · S ( s , p ) = ρ ( S 0 cos 2 ψ r ( S 1 cos 2 ϕ + S 2 sin 2 ϕ ) S 0 cos 2 ψ r + S 1 cos 2 ϕ + S 2 sin 2 ϕ S 3 sin 2 ψ r sin 2 ψ r ( S 1 sin 2 ϕ S 2 cos 2 ϕ ) ) .
I = q I q + r I r = η [ S 0 ( q , r ) + Q S 1 ( q , r ) ] ,
S ( q , r ) = R ( α ) S ( s , p ) .
I ( α , ϕ ) = η ρ ( S 0 cos 2 ψ r ( S 1 cos 2 ϕ + S 2 sin 2 ϕ ) + Q [ ( S 0 cos 2 ψ r + S 1 cos 2 ϕ + S 2 sin 2 ϕ ) cos 2 α + S 3 sin 2 ψ r sin 2 α ] ) .
S 1 / S 2 = [ I ( 0 , π / 2 ) I ( 0 , 0 ) ] / [ I ( 0 , π / 4 ) I ( 0 , π / 4 ) ] .
tan 2 ϕ = S 1 / S 2 .
S 3 S 0 = cot 2 ψ r I ( π / 4 , ϕ ) I ( π / 4 , ϕ ) I ( π / 4 , ϕ ) + I ( π / 4 , ϕ ) 2 I ( 0 , ϕ ) ,
a Q cos 2 ψ r = 2 I ( 0 , ϕ ) I ( π / 4 , ϕ ) + I ( π / 4 , ϕ ) .
S 1 S 0 = ( 1 Q cos 2 ψ r Q cos 2 ψ r ) · I ( 0 , 0 ) I ( 0 , π / 2 ) I ( 0 , 0 ) + I ( 0 , π / 2 ) ,
S 2 S 0 = ( 1 Q cos 2 ψ r Q cos 2 ψ r ) · I ( 0 , π / 4 ) I ( 0 , π / 4 ) I ( 0 , π / 4 ) + I ( 0 , π / 4 ) ·
S 3 S 0 = [ 1 Q sin 2 ψ r ] I ( π / 4 , ϕ ) I ( π / 4 , ϕ ) I ( π / 4 , ϕ ) + I ( π / 4 , ϕ ) ·

Metrics