Abstract

This study shows that by using a wedge plate the incident direction of light propagation can be rotated as desired while still preserving beam polarization. This study also deduces the basic condition of this preservation of polarization. Two typical wedge plates are analyzed for numerical demonstration. Simulation results verify that a collimated beam with a +45° linear polarization can be guided to an expected direction while preserving the state of polarization with a square of the variation of the ellipse ratio of less than 0.0001%. This study also numerically shows that the wedge vertex angle is the most critical issue and that approximately 0.1° accuracy is required to preserve the polarization state.

© 2008 Optical Society of America

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References

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  1. M. L. Faupel, S. B. Bambot, T. Harrell, and A. Agrawal, “Multi-modal optical tissue diagnostic system,” U.S. patent 6,975,899 (December 13, 2005).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  7. E. J. Galvez, “Achromatic polarization-preserving beam displacer,” Opt. Lett. 26, 971-973 (2001).
    [Crossref]
  8. A.-C. Hsu, C.-F. Ho, and J.-L. Chern, “Tilting tolerance analysis of a broadband polarization-preserving beam displacer,” Appl. Opt. 41, 5956-5962 (2002).
    [Crossref] [PubMed]
  9. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 42-43 and M. Born and E. Wolf50-51.
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  11. Y.-K. Cheng, S.-N. Chung, and J.-L. Chern, “Analysis and reduction of dark zone in ultra-thin wedge plate display,” J. Soc. Inf. Disp. 14, 813-818 (2006).
    [Crossref]
  12. Y.-K. Cheng, S.-N. Chung, and J.-L. Chern, “Aberration analysis of a wedge-plate display system,” J. Opt. Soc. Am. A 24, 2357-2362 (2007).
    [Crossref]
  13. See http://lambdares.com for technical information.

2007 (1)

2006 (1)

Y.-K. Cheng, S.-N. Chung, and J.-L. Chern, “Analysis and reduction of dark zone in ultra-thin wedge plate display,” J. Soc. Inf. Disp. 14, 813-818 (2006).
[Crossref]

2002 (1)

2001 (1)

1999 (1)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 42-43 and M. Born and E. Wolf50-51.

1997 (1)

1992 (2)

E. Cojocaru, “Polarization-preserving totally reflecting prisms,” Appl. Opt. 31, 4340-4342 (1992).
[Crossref] [PubMed]

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1992), pp. 139-161.

1989 (1)

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

1982 (2)

Agrawal, A.

M. L. Faupel, S. B. Bambot, T. Harrell, and A. Agrawal, “Multi-modal optical tissue diagnostic system,” U.S. patent 6,975,899 (December 13, 2005).

Azzam, R. M.

Bambot, S. B.

M. L. Faupel, S. B. Bambot, T. Harrell, and A. Agrawal, “Multi-modal optical tissue diagnostic system,” U.S. patent 6,975,899 (December 13, 2005).

Bashara, N. M.

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

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 42-43 and M. Born and E. Wolf50-51.

Cheng, Y.-K.

Y.-K. Cheng, S.-N. Chung, and J.-L. Chern, “Aberration analysis of a wedge-plate display system,” J. Opt. Soc. Am. A 24, 2357-2362 (2007).
[Crossref]

Y.-K. Cheng, S.-N. Chung, and J.-L. Chern, “Analysis and reduction of dark zone in ultra-thin wedge plate display,” J. Soc. Inf. Disp. 14, 813-818 (2006).
[Crossref]

Chern, J.-L.

Chung, S.-N.

Y.-K. Cheng, S.-N. Chung, and J.-L. Chern, “Aberration analysis of a wedge-plate display system,” J. Opt. Soc. Am. A 24, 2357-2362 (2007).
[Crossref]

Y.-K. Cheng, S.-N. Chung, and J.-L. Chern, “Analysis and reduction of dark zone in ultra-thin wedge plate display,” J. Soc. Inf. Disp. 14, 813-818 (2006).
[Crossref]

Cojocaru, E.

Collett, E.

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1992), pp. 139-161.

Faupel, M. L.

M. L. Faupel, S. B. Bambot, T. Harrell, and A. Agrawal, “Multi-modal optical tissue diagnostic system,” U.S. patent 6,975,899 (December 13, 2005).

Galvez, E. J.

Harrell, T.

M. L. Faupel, S. B. Bambot, T. Harrell, and A. Agrawal, “Multi-modal optical tissue diagnostic system,” U.S. patent 6,975,899 (December 13, 2005).

Ho, C.-F.

Hsu, A.-C.

Huang, Z. J.

Kang, C.

Khan, M. E. R.

Ruan, S. L.

Sun, W. M.

Wang, Z. P.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 42-43 and M. Born and E. Wolf50-51.

Zhang, S. Q.

Appl. Opt. (4)

J. Opt. Soc. Am. A (1)

J. Soc. Inf. Disp. (1)

Y.-K. Cheng, S.-N. Chung, and J.-L. Chern, “Analysis and reduction of dark zone in ultra-thin wedge plate display,” J. Soc. Inf. Disp. 14, 813-818 (2006).
[Crossref]

Opt. Lett. (2)

Other (5)

See http://lambdares.com for technical information.

M. L. Faupel, S. B. Bambot, T. Harrell, and A. Agrawal, “Multi-modal optical tissue diagnostic system,” U.S. patent 6,975,899 (December 13, 2005).

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

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), pp. 42-43 and M. Born and E. Wolf50-51.

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1992), pp. 139-161.

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Figures (4)

Fig. 1
Fig. 1

Schematics of rays propagating in (a) a wedge plate, (b) a virtually folded wedge plate.

Fig. 2
Fig. 2

Polarization variations when total internal reflections happen. m=(a) 10 and (b) 20.

Fig. 3
Fig. 3

Possible ray deflection angles versus wedge vertex angle. The vertex angle θ v is picked up from 0.5 ° to 5 ° with a unit of 0.25 ° to determine the possible ray deflection angle.

Fig. 4
Fig. 4

Investigations of performance degradation that is due to (a), (b) incident surface tilt; (c), (d) vertex angle error; (e), (f) incident-beam misalignment.

Equations (8)

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R s = cos θ i n cos θ t cos θ i + n cos θ t E s , R p = n cos θ i cos θ t n cos θ i + cos θ t E p ,
T s = 2 cos θ i cos θ i + n cos θ t E s , T p = 2 cos θ i n cos θ i + cos θ t E p .
M T = sin 2 θ i sin θ t 2 ( sin Θ + cos Θ ) 2 ( cos 2 Θ + 1 cos 2 Θ 1 0 0 cos 2 Θ 1 cos 2 Θ + 1 0 0 0 0 2 cos Θ 0 0 0 0 2 cos Θ ) ,
M TIR = ( 1 0 0 0 0 1 0 0 0 0 cos Δ sin Δ 0 0 sin Δ cos Δ ) ,
Δ = 2 tan 1 ( cos θ i n 2 sin 2 θ i 1 n sin 2 θ i ) .
Δ α = m θ v ,
i = 1 m 2 tan 1 ( cos [ θ 1 + ( i 1 ) θ v ] n 2 sin 2 [ θ 1 + ( i 1 ) θ v ] 1 n sin 2 [ θ 1 + ( i 1 ) θ v ] ) = 2 π k ,
L = L m + 1 L 1 + D tan θ 1 , = D ( cot θ v + tan θ 1 ) cos θ 1 cos ( θ 1 + m θ v ) D cot θ v .

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