Abstract

Reflection and refraction of monochromatic light by an air–dielectric interface at an incidence angle below the Brewster angle can generate split beams of equal power and orthogonal polarizations under certain achievable conditions. Generation of photon streams of orthogonal polarizations, previously thought to be possible mainly by double refraction in anisotropic crystals, is achieved for an infinite set of input states that leads to a correspondingly infinite set of pairs of orthogonal output states. A bare substrate of PbTe is particularly suitable for this beam splitting function in the IR. However, use of a high-refractive-index quarter-wave layer on a low-refractive-index substrate extends the operating range of this interesting device to a much wider spectral range including the visible.

© 2006 Optical Society of America

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References

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  1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987), Sec. 4.2.
  2. R. M. A. Azzam, Opt. Lett. 10, 107 (1985).
    [CrossRef] [PubMed]
  3. R. M. A. Azzam, Opt. Lett. 10, 110 (1985).
    [CrossRef] [PubMed]
  4. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  5. D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, 1971).
  6. A. G. Lopez and H. G. Craighead, Opt. Lett. 23, 1627 (1998).
    [CrossRef]
  7. P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, J. Opt. A 1, 215 (1999).
    [CrossRef]
  8. L. Zhou and W. Liu, Opt. Lett. 30, 1434 (2005).
    [CrossRef] [PubMed]
  9. R. M. A. Azzam and A. De, J. Opt. Soc. Am. A 20, 955 (2003).
    [CrossRef]
  10. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987), p. 174.
  11. Ref. 10, pp. 273-277.
  12. Ref. 10, Sec. 1.7.
  13. Ref. 10, p. 32.
  14. R. M. A. Azzam, J. Opt. Soc. Am. 69, 1007 (1979).
    [CrossRef]
  15. R. H. Muller, Surf. Sci. 16, 14 (1969).
    [CrossRef]
  16. W. J. Tropf, M. E. Thomas, and T. J. Harris, in Handbook of Optics, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe (McGraw-Hill, 1995), Vol. II, Chap. 33.

2005

2003

1999

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, J. Opt. A 1, 215 (1999).
[CrossRef]

1998

1985

1979

1969

R. H. Muller, Surf. Sci. 16, 14 (1969).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam and A. De, J. Opt. Soc. Am. A 20, 955 (2003).
[CrossRef]

R. M. A. Azzam, Opt. Lett. 10, 107 (1985).
[CrossRef] [PubMed]

R. M. A. Azzam, Opt. Lett. 10, 110 (1985).
[CrossRef] [PubMed]

R. M. A. Azzam, J. Opt. Soc. Am. 69, 1007 (1979).
[CrossRef]

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987), Sec. 4.2.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987), p. 174.

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987), p. 174.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987), Sec. 4.2.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Cambril, E.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, J. Opt. A 1, 215 (1999).
[CrossRef]

Chavel, P.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, J. Opt. A 1, 215 (1999).
[CrossRef]

Clarke, D.

D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, 1971).

Craighead, H. G.

De, A.

Grainger, J. F.

D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, 1971).

Harris, T. J.

W. J. Tropf, M. E. Thomas, and T. J. Harris, in Handbook of Optics, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe (McGraw-Hill, 1995), Vol. II, Chap. 33.

Hazart, J.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, J. Opt. A 1, 215 (1999).
[CrossRef]

Lalanne, P.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, J. Opt. A 1, 215 (1999).
[CrossRef]

Launois, H.

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, J. Opt. A 1, 215 (1999).
[CrossRef]

Liu, W.

Lopez, A. G.

Muller, R. H.

R. H. Muller, Surf. Sci. 16, 14 (1969).
[CrossRef]

Thomas, M. E.

W. J. Tropf, M. E. Thomas, and T. J. Harris, in Handbook of Optics, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe (McGraw-Hill, 1995), Vol. II, Chap. 33.

Tropf, W. J.

W. J. Tropf, M. E. Thomas, and T. J. Harris, in Handbook of Optics, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe (McGraw-Hill, 1995), Vol. II, Chap. 33.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Zhou, L.

J. Opt. A

P. Lalanne, J. Hazart, P. Chavel, E. Cambril, and H. Launois, J. Opt. A 1, 215 (1999).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Surf. Sci.

R. H. Muller, Surf. Sci. 16, 14 (1969).
[CrossRef]

Other

W. J. Tropf, M. E. Thomas, and T. J. Harris, in Handbook of Optics, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe (McGraw-Hill, 1995), Vol. II, Chap. 33.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987), Sec. 4.2.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

D. Clarke and J. F. Grainger, Polarized Light and Optical Measurement (Pergamon, 1971).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987), p. 174.

Ref. 10, pp. 273-277.

Ref. 10, Sec. 1.7.

Ref. 10, p. 32.

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Figures (3)

Fig. 1
Fig. 1

Locus of incident polarization states in the complex plane that can produce orthogonally polarized beams in reflection and refraction by a dielectric surface.

Fig. 2
Fig. 2

Incident linearly polarized light at 45 ° azimuth is split into reflected and transmitted beams of orthogonal linear polarizations.

Fig. 3
Fig. 3

Incident right-handed circularly polarized light is split into reflected and transmitted beams of orthogonal elliptical polarizations.

Equations (23)

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R u = 0.5 .
ψ r + ψ t = π 2 .
Δ r = π , Δ t = 0 .
χ k = E ks E kp , k = i , r , t ,
E r v = r v E i v , E t v = t v E i v , v = p , s .
χ r = χ i ( tan ψ r ) , χ t = χ i ( tan ψ t ) ,
χ r χ t * = 1 .
χ i χ i * = 1 .
χ i = exp ( j 2 ϵ i ) , θ i = + 45 ° ,
χ i = exp [ j ( π 2 ϵ i ) ] , θ i = 45 ° ,
45 ° ϵ i + 45 ° .
R p + R s = 1 ,
r p 2 + r s 2 = 1 ,
r p = r s ( r s cos 2 ϕ ) ( 1 r s cos 2 ϕ )
( 1 + cos 2 2 ϕ ) r s 4 ( 4 cos 2 ϕ ) r s 3 + r s 2 + ( 2 cos 2 ϕ ) r s 1 = 0 ,
n 2 = sin 2 ϕ + ( 1 r s 1 + r s ) 2 cos 2 ϕ .
n = 5.94822 .
5 r s 4 8 r s 3 + 4 r s 2 + 4 r s 4 = 0 ,
n = 5.84879 ,
r s = 1 2 ,
n = 3 + 2 2 = 5.8284 ,
cos 2 ( ϕ 0 ϕ 1 ) = cos ( ϕ 0 + ϕ 1 ) .
d = ( λ 4 ) ( n 1 2 sin 2 ϕ ) 1 2

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