Abstract

A dielectric-slab polarizing beam splitter (PBS) is described that generates two parallel beams of orthogonal p and s linear polarizations in reflection and functions as a diattenuator in transmission. The plane-parallel slab, which is set at Brewster's angle, is uncoated on one side and has an s-polarization antireflection coating (s-ARC) on the other side. Analytical results are presented for a PBS that uses a high-index slab coated with a low-index single-layer s-ARC, which is particularly suited for the IR. A novel multistage photopolarimeter that uses two such PBSs in series is described as being capable of sequential and simultaneous measurement of all four Stokes parameters of light.

© 2007 Optical Society of America

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References

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  1. H. E. Bennett and J. M. Bennett, "Polarization," in Handbook of Optics, W.G.Driscoll and W.Vaughan, eds. (McGraw-Hill, 1978), Chap. 10.
  2. J. A. Dobrowolski, "Optical properties of films and coatings," in Handbook of Optics, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe, eds. (McGraw-Hill, 1995), Chap. 42.
  3. R. M. A. Azzam, "Recent developments of division-of-amplitude photopolarimeters," in Polarization Analysis and Applications to Device Technology, T.Yoshizawa and H.Yokota, eds., Proc. SPIE 2873, pp. 1-4 (1996).
  4. R. M. A. Azzam, "Division-of-wavefront polarizing beam splitter and half-shade device using dielectric thin film on dielectric substrate," Appl. Opt. 23, 1296-1298 (1984).
    [CrossRef] [PubMed]
  5. R. M. A. Azzam, "Binary polarization modulator: a simple device for switching light polarization between orthogonal states," Opt. Lett. 13, 701-703 (1988).
    [CrossRef] [PubMed]
  6. M. E. Pedinoff, M. Braunstein, and O. M. Stafsudd, "Refractive indices of IR materials: 10.6 μm ellipsometer measurements," Appl. Opt. 16, 2849-2857 (1977).
    [CrossRef] [PubMed]
  7. J. J. Tuma, Engineering Mathematics Handbook, 3rd ed. (McGraw-Hill, 1987).
  8. E. Palik, Handbook of Optical Constants of Solids (Academic, 1985), pp. 566-567.
  9. E. Palik, Handbook of Optical Constants of Solids (Academic, 1985), p. 459.
  10. II-VI Inc., Saxonburg, PA 16056.
  11. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987), Chap. 2.

1988 (1)

1984 (1)

1977 (1)

Azzam, R. M. A.

R. M. A. Azzam, "Binary polarization modulator: a simple device for switching light polarization between orthogonal states," Opt. Lett. 13, 701-703 (1988).
[CrossRef] [PubMed]

R. M. A. Azzam, "Division-of-wavefront polarizing beam splitter and half-shade device using dielectric thin film on dielectric substrate," Appl. Opt. 23, 1296-1298 (1984).
[CrossRef] [PubMed]

R. M. A. Azzam, "Recent developments of division-of-amplitude photopolarimeters," in Polarization Analysis and Applications to Device Technology, T.Yoshizawa and H.Yokota, eds., Proc. SPIE 2873, pp. 1-4 (1996).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987), Chap. 2.

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987), Chap. 2.

Bennett, H. E.

H. E. Bennett and J. M. Bennett, "Polarization," in Handbook of Optics, W.G.Driscoll and W.Vaughan, eds. (McGraw-Hill, 1978), Chap. 10.

Bennett, J. M.

H. E. Bennett and J. M. Bennett, "Polarization," in Handbook of Optics, W.G.Driscoll and W.Vaughan, eds. (McGraw-Hill, 1978), Chap. 10.

Braunstein, M.

Dobrowolski, J. A.

J. A. Dobrowolski, "Optical properties of films and coatings," in Handbook of Optics, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe, eds. (McGraw-Hill, 1995), Chap. 42.

Palik, E.

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985), pp. 566-567.

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985), p. 459.

Pedinoff, M. E.

Stafsudd, O. M.

Tuma, J. J.

J. J. Tuma, Engineering Mathematics Handbook, 3rd ed. (McGraw-Hill, 1987).

Appl. Opt. (2)

Opt. Lett. (1)

Other (8)

H. E. Bennett and J. M. Bennett, "Polarization," in Handbook of Optics, W.G.Driscoll and W.Vaughan, eds. (McGraw-Hill, 1978), Chap. 10.

J. A. Dobrowolski, "Optical properties of films and coatings," in Handbook of Optics, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe, eds. (McGraw-Hill, 1995), Chap. 42.

R. M. A. Azzam, "Recent developments of division-of-amplitude photopolarimeters," in Polarization Analysis and Applications to Device Technology, T.Yoshizawa and H.Yokota, eds., Proc. SPIE 2873, pp. 1-4 (1996).

J. J. Tuma, Engineering Mathematics Handbook, 3rd ed. (McGraw-Hill, 1987).

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985), pp. 566-567.

E. Palik, Handbook of Optical Constants of Solids (Academic, 1985), p. 459.

II-VI Inc., Saxonburg, PA 16056.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987), Chap. 2.

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Figures (2)

Fig. 1
Fig. 1

Dielectric-slab PBS. A light beam incident on the slab at the Brewster angle ϕ B is split into two reflected beams 1 and 2 that are purely s and p polarized, respectively, and a transmitted beam 3 that has both p- and s-polarized components. The front surface of the slab is uncoated and the back surface has an s - ARC. d 2 is the thickness of the slab, and D is the separation of the parallel reflected beams with orthogonal polarizations.

Fig. 2
Fig. 2

Photopolarimeter that employs a cascade of two parallel-slab PBSs (PBS1 and PBS2) with a 45° optical rotator OR in the middle. PBS1 generates reflected beams 1 and 2, and PBS2 produces reflected beams 3 and 4. Detection of light in dual channels 1 and 2 and in dual channels 3 and 4 determines the first and second normalized Stokes parameters, respectively. The last stage, that consists of a quarter-wave retarder (QWR) followed by a conventional PBS (PBS3), produces beams 5 and 6, whose detection enables the determination of the third normalized Stokes parameter.

Equations (27)

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D = 2 d 2 / n 2 ( n 2 2 + 1 ) 1 / 2 .
n 1 = 2 n 2 / ( n 2 2 + 1 ) 1 / 2 ,
d 1 = 0.3536 ( λ / n 1 ) ,
R fs = cos 2 ( 2 ϕ B ) = [ ( n 2 2 1 ) / ( n 2 2 + 1 ) ] 2 ,
R bp = [ R fs / ( 2 R fs ) ] 2 .
T p = 1 R bp , T s = 1 R fs .
R av = ( R fs + R bp ) / 2 .
R av = ( R fs / 2 ) ( R fs 2 R fs + 4 ) / ( R fs 2 4 R fs + 4 ) .
tan α = ( R bp / R fs ) 1 / 2 = ( n 2 4 1 ) / ( n 2 4 + 6 n 2 2 + 1 ) .
R = 2 R fs R bp / ( R fs + R bp ) ,
R 1 = ( 1 / 2 ) ( R fs 1 + R bp 1 ) ] .
ϕ B = 75.964° , D = 0.1213 d 2 ,
n 1 = 1.372 , d 1 = 0.2577 λ ,
R fs = 77.855 % , R bp = 40.627 % ,
R av = 59.241 % , R = 53.392 % ,
T s = 22.145 % , T p = 59.373 % ,
α = 35.844° .
R fs 3 4 R fs 2 + 8 R fs 4 = 0.
R fs = 0.704402.
n 2 = 3.383.
3 R fs 3 11 R fs 2 + 20 R fs 8 = 0 ,
Δ R = R fs R bp = ( x 3 5 x 2 + 4 x ) / ( 2 x ) 2 .
x 3 6 x 2 + 16 x 8 = 0.
x = R fs = 0.635344.
n 2 = 3.9844.
Δ R max = 0.373354.
s 3 = ±( 1 s 1 2 s 2 2 ) 1 / 2 .

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