Abstract

We first derive the round-trip Jones matrix for double passage through a reciprocal optical medium by means of reflection off a plane mirror that could be optically anisotropic. We then show that if a medium with only linear birefringence and linear dichroism is placed between a pair of orthogonal quarter-wave plates with principal axes at 45° to that of the medium and the sandwich is placed in front of an isotropic mirror it behaves, under double passage, like an isotropic medium. We describe a simple liquid crystal device that behaves, in reflection, as an isotropic medium whose refractive index can be varied by application of an electric field, thus acting as a phase only modulator for light in any polarization state.

© 2008 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), p. 40.
  2. R. Bhandari, Phys. Lett. A 135, 240 (1989).
    [Crossref]
  3. R. Bhandari, Physica B 175, 111 (1991).
    [Crossref]
  4. It can be shown that the final results of any calculation by this method is independent of the choice of the plane of incidence.
  5. R. Bhandari, Opt. Lett. 33, 854 (2008).
    [Crossref] [PubMed]
  6. R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941).
    [Crossref]
  7. The factor r, though unimportant, should also have been present in the analysis described in .
  8. N. C. Pistoni and M. Martinelli, Opt. Lett. 16, 711 (1991).
    [Crossref] [PubMed]
  9. M. O. van Deventer, Electron. Lett. 27, 1538 (1991).
    [Crossref]
  10. V. G. Chigrinov, Liquid Crystal Devices: Physics and Application (Artech, 1999), p. 85.
  11. G. D. Love, Appl. Opt. 32, 2222 (1993).
    [Crossref] [PubMed]

2008 (1)

1993 (1)

1991 (3)

R. Bhandari, Physica B 175, 111 (1991).
[Crossref]

M. O. van Deventer, Electron. Lett. 27, 1538 (1991).
[Crossref]

N. C. Pistoni and M. Martinelli, Opt. Lett. 16, 711 (1991).
[Crossref] [PubMed]

1989 (1)

R. Bhandari, Phys. Lett. A 135, 240 (1989).
[Crossref]

1941 (1)

Bhandari, R.

R. Bhandari, Opt. Lett. 33, 854 (2008).
[Crossref] [PubMed]

R. Bhandari, Physica B 175, 111 (1991).
[Crossref]

R. Bhandari, Phys. Lett. A 135, 240 (1989).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), p. 40.

Chigrinov, V. G.

V. G. Chigrinov, Liquid Crystal Devices: Physics and Application (Artech, 1999), p. 85.

Jones, R. C.

Love, G. D.

Martinelli, M.

Pistoni, N. C.

van Deventer, M. O.

M. O. van Deventer, Electron. Lett. 27, 1538 (1991).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), p. 40.

Appl. Opt. (1)

Electron. Lett. (1)

M. O. van Deventer, Electron. Lett. 27, 1538 (1991).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Phys. Lett. A (1)

R. Bhandari, Phys. Lett. A 135, 240 (1989).
[Crossref]

Physica B (1)

R. Bhandari, Physica B 175, 111 (1991).
[Crossref]

Other (4)

It can be shown that the final results of any calculation by this method is independent of the choice of the plane of incidence.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), p. 40.

The factor r, though unimportant, should also have been present in the analysis described in .

V. G. Chigrinov, Liquid Crystal Devices: Physics and Application (Artech, 1999), p. 85.

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Figures (2)

Fig. 1
Fig. 1

(a) Double passage of a polarized light beam through a reciprocal medium by means of normal reflection off an optically anisotropic surface, (b) equivalent optical circuit consisting of a pure polarization evolution given by the Jones matrix M ¯ Z M followed by a rotation of the beam about an axis perpendicular to the plane of incidence, and (c) equivalent circuit in the fixed frame for the evolution shown in (b).

Fig. 2
Fig. 2

Sandwich consisting of a reciprocal optical medium with linear birefringence and linear dichroism along the same axis, placed between a pair of orthogonal quarter-wave plates at + 45 ° or 45 ° behaves like an isotropic medium when placed in front of an isotropic mirror. (a) Actual optical configuration, (b) equivalent optical circuit, (c) reduced circuit, and (d) equivalent reduced circuit in the fixed frame. The isotropic factors a, p, and r have been omitted for convenience.

Equations (14)

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M ¯ = ( m 11 m 21 m 12 m 22 ) for M = ( m 11 m 12 m 21 m 22 ) .
M ( rt ) = M ¯ Z M .
M ( rt ) = H 0 M ¯ Z M .
L ϕ ( δ ) = R ( ϕ ) L 0 ( δ ) R ( ϕ ) , D ϕ ( γ ) = R ( ϕ ) D 0 ( γ ) R ( ϕ ) ,
L ¯ ϕ ( δ ) = L ϕ ( δ ) , D ¯ ϕ ( γ ) = D ϕ ( γ ) ,
D ϕ ( γ ) D ϕ + 90 ° ( γ ) = L ϕ ( δ ) L ϕ + 90 ° ( δ ) = 1 ,
R ( ϕ 1 ) R ( ϕ 2 ) = R ( ϕ 1 + ϕ 2 ) , R ( ± 180 ) = 1
H ϕ = L ϕ ( π ) , Q ϕ = L ϕ ( π 2 ) , Q ϕ H ϕ Q ϕ = 1 ,
R ( ϕ ) H 0 R ( ϕ ) = H 0 ,
M = a p L 0 ( δ ) D 0 ( γ ) ,
M ( rt ) = r a 2 p 2 Q ¯ 45 D ¯ 0 ( γ ) L ¯ 0 ( δ ) Q ¯ 45 H 0 Q 45 L 0 ( δ ) D 0 ( γ ) Q 45 = r a 2 p 2 Q 45 D 0 ( γ ) L 0 ( δ ) Q 45 H 0 Q 45 L 0 ( δ ) D 0 ( γ ) Q 45 = r a 2 p 2 R ( 45 ) Q 0 R ( 45 ) D 0 ( γ ) L 0 ( δ ) R ( 45 ) Q 0 R ( 45 ) H 0 R ( 45 ) Q 0 R ( 45 ) L 0 ( δ ) D 0 ( γ ) R ( 45 ) Q 0 R ( 45 ) = r a 2 p 2 R ( 45 ) Q 0 R ( 45 ) D 0 ( γ ) L 0 ( δ ) R ( 90 ) L 0 ( δ ) D 0 ( γ ) R ( 45 ) Q 0 R ( 45 ) = r a 2 p 2 R ( 45 ) Q 0 R ( 45 ) R ( 90 ) R ( 90 ) D 0 ( γ ) L 0 ( δ ) R ( 90 ) L 0 ( δ ) D 0 ( γ ) R ( 45 ) Q 0 R ( 45 ) = r a 2 p 2 R ( 45 ) Q 0 R ( 45 ) R ( 90 ) D 90 ( γ ) L 90 ( δ ) L 0 ( δ ) D 0 ( γ ) R ( 45 ) Q 0 R ( 45 ) = r a 2 p 2 R ( 45 ) Q 0 R ( 180 ) Q 0 R ( 45 ) = r a 2 p 2 H 0 ,
M ( rt ) = H 0 M ( rt ) = r a 2 p 2 1 .
p = exp ( i ϕ iso ) with ϕ iso = ( 2 π d λ ) ( n e + n o ) 2 ,
δ = ( 2 π d λ ) ( n e n o ) .

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