Abstract

It is shown that a three-mirror device with ideal mirror reflectivities may be used in place of a halfwave plate to rotate the plane of polarization of a plane polarized beam by any angle with no loss of polarization purity. For coated mirrors, with more general reflectivities, specifications are set on the allowed reflectivity ratio and phase shift difference for the s and p components in order that polarization purity be preserved to a specified amount.

© 1988 Optical Society of America

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References

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  1. E. Hecht, A. Zajac, Optics (Addison-Wesley, Menlo Park, CA, 1979), p. 248.
  2. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 38.
  3. Ref. 2, p. 40.
  4. D. Fink, “Polarization Effects of Axicons,” Appl. Opt. 18, 581 (1979).
    [CrossRef] [PubMed]
  5. Ref. 2, p. 619.
  6. P. Beckmann, The Depolarization of Electromagnetic Waves (Golem, Boulder, CO, 1968), p. 52.
  7. W. A. Shurcliff, Polarized Light (Harvard U. P., Cambridge, MA, 1962).
  8. R. A. Chipman, “Polarization Ray Tracing,” Proc. Soc. Photo-Opt. Instrum. Eng. 766, 53 (1987). Although the second mirror in the set will have a different angle of incidence than the other two mirrors, coated mirrors can still be specified to have equal reflectivities, and ideal mirrors will also have equal reflectivities.

1987 (1)

R. A. Chipman, “Polarization Ray Tracing,” Proc. Soc. Photo-Opt. Instrum. Eng. 766, 53 (1987). Although the second mirror in the set will have a different angle of incidence than the other two mirrors, coated mirrors can still be specified to have equal reflectivities, and ideal mirrors will also have equal reflectivities.

1979 (1)

Beckmann, P.

P. Beckmann, The Depolarization of Electromagnetic Waves (Golem, Boulder, CO, 1968), p. 52.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 38.

Chipman, R. A.

R. A. Chipman, “Polarization Ray Tracing,” Proc. Soc. Photo-Opt. Instrum. Eng. 766, 53 (1987). Although the second mirror in the set will have a different angle of incidence than the other two mirrors, coated mirrors can still be specified to have equal reflectivities, and ideal mirrors will also have equal reflectivities.

Fink, D.

Hecht, E.

E. Hecht, A. Zajac, Optics (Addison-Wesley, Menlo Park, CA, 1979), p. 248.

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light (Harvard U. P., Cambridge, MA, 1962).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 38.

Zajac, A.

E. Hecht, A. Zajac, Optics (Addison-Wesley, Menlo Park, CA, 1979), p. 248.

Appl. Opt. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

R. A. Chipman, “Polarization Ray Tracing,” Proc. Soc. Photo-Opt. Instrum. Eng. 766, 53 (1987). Although the second mirror in the set will have a different angle of incidence than the other two mirrors, coated mirrors can still be specified to have equal reflectivities, and ideal mirrors will also have equal reflectivities.

Other (6)

E. Hecht, A. Zajac, Optics (Addison-Wesley, Menlo Park, CA, 1979), p. 248.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970), p. 38.

Ref. 2, p. 40.

Ref. 2, p. 619.

P. Beckmann, The Depolarization of Electromagnetic Waves (Golem, Boulder, CO, 1968), p. 52.

W. A. Shurcliff, Polarized Light (Harvard U. P., Cambridge, MA, 1962).

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Figures (6)

Fig. 1
Fig. 1

Reflective polarization rotation device.

Fig. 2
Fig. 2

Coordinate system in plane of incidence for each mirror.

Fig. 3
Fig. 3

Beam coordinate system as viewed into the beam. Here the first mirror in the set is obscured behind the mirror to the lower left.

Fig. 4
Fig. 4

Allowed ρs/ρp vs allowed δ for various amounts of polarization coupling into the orthogonal polarization for a polarization rotation of 30°.

Fig. 5
Fig. 5

Allowed ρs/ρp vs δ for polarization rotation of 60°.

Fig. 6
Fig. 6

Allowed ρs/ρp vs δ for polarization rotation of 90°.

Equations (9)

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E ˜ 0 = ( cos 2 θ sin 2 θ ) .
M ˜ = ( cos θ sin θ sin θ cos θ ) ( r p 3 0 0 r s 3 ) ( cos θ sin θ sin θ cos θ ) .
E ˜ = M ˜ E ˜ 0 = [ r p 3 cos 2 θ r s 3 sin 2 θ ( r p 3 + r s 3 2 ) sin 2 θ ] .
A = E y E x = [ 1 + B exp ( i Δ ) ] sin 2 θ 2 ( cos 2 θ B exp ( i Δ ) sin 2 θ ) ,
B ( ρ s / ρ p ) 3 , Δ 3 ( ϕ s ϕ p ) .
Δ = 3 ( 180 ° + δ ) ,
A = ( a + i b δ ) / ( c + i d δ ) ,
a = ( 1 B ) sin 2 θ , b = 3 B sin 2 θ , c = 2 ( cos 2 θ + B sin 2 θ ) , d = 6 B sin 2 θ .
δ = ± [ ( | A | 2 c 2 a 2 ) / ( b 2 | A | 2 d 2 ) ] 1 / 2 .

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