Abstract

Under the condition of first-order blooming, a parallel dielectric slab, which is inserted in the path of an obliquely incident p- or s-polarized light beam, introduces multiple discrete attenuation levels given by 1/3,4/27,4/243, in reflection and 4/9,4/81,4/729, in transmission. These attenuation levels are independent of the slab refractive index, incident p or s linear polarization, or the presence of identical transparent surface coatings at the front and back sides of the slab. Therefore, the tilted slab provides multidecade reflectance and attenuation reference values that can be used in calibrating spectrophotometers and filters, and also for testing the linearity of photodetectors. For an uncoated dielectric slab, incidence angles that cause first-order blooming are determined as functions of the slab refractive index for incident p- or s-polarized light.

© 2009 Optical Society of America

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References

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  1. J. E. Stewart, “A rotating-sector attenuator of adjustable transmittance for precise spectrophotometry,” Appl. Opt. 1, 75-77 (1962).
    [CrossRef]
  2. H. E. Bennett, “Accurate method for determining photometric linearity,” Appl. Opt. 5, 1265-1270 (1966).
    [CrossRef] [PubMed]
  3. C. L. Sanders, “A photocell linearity tester,” Appl. Opt. 1, 207-211 (1962).
    [CrossRef]
  4. W. Budde, “Multidecade linearity measurements on Si photodiodes,” Appl. Opt. 18, 1555-1558 (1979).
    [CrossRef] [PubMed]
  5. W. Budde, “Large-flux-ratio linearity measurements on Si photodiodes,” Appl. Opt. 21, 3699-3701 (1982).
    [CrossRef] [PubMed]
  6. T. Oseki and S. Saito, “A precision variable, double prism attenuator for CO2 lasers,” Appl. Opt. 10, 144-149 (1971).
    [CrossRef] [PubMed]
  7. K. Wilner and N. P. Murarka, “Design considerations and test results of an evanescent switch-attenuator,” Appl. Opt. 20, 3600-3604 (1981).
    [CrossRef] [PubMed]
  8. K. Bennett and R. L. Byer, “Computer-controllable wedged-plate variable attenuator,” Appl. Opt. 19, 2408-2412 (1980).
    [CrossRef] [PubMed]
  9. H. Lotem, A. Eyal, and R. Shuker, “Variable attenuator for intense unpolarized laser beams,” Opt. Lett. 16, 690-692(1991).
    [CrossRef] [PubMed]
  10. J. H. Lehman, D. Livigni, X. Li, C. L. Cromer, and M. L. Dowell, “Reflective attenuator for high-energy laser measurements,” Appl. Opt. 47, 3360-3363(2008).
    [CrossRef] [PubMed]
  11. A. M. El-Saba, R. M. A. Azzam, and M. A. G. Abushagur, “Parallel-slab division-of-amplitude photopolarimeter,” Opt. Lett. 21, 1709-1711 (1996).
    [CrossRef] [PubMed]
  12. R. M. A Azzam, A. M. El-Saba, and M. A. G. Abushagur, “Spectrophotopolarimeter based on multiple reflections in a coated dielectric slab,” Thin Solid Films 313/314, 53-57(1998).
    [CrossRef]
  13. R. M. A. Azzam, “Parallel-slab polarizing beam splitter and photopolarimeter,” Appl. Opt. 46, 292-294 (2007).
    [CrossRef] [PubMed]
  14. R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14-33 (1969).
    [CrossRef]
  15. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, 1987).
  16. W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, Vol. II, M.Bass, E.W.Van Stryland, D.R.Williams, and W.L.Wolfe, eds. (McGraw-Hill, 1995), Chap. 33.
  17. R. M. A. Azzam and F. F. Sudradjat, “Reflection of p- and s-polarized light by a quarter-wave layer: explicit expressions and applications to beam splitters,” Appl. Opt. 47, 1103-1108 (2008).
    [CrossRef] [PubMed]

2008 (2)

2007 (1)

1998 (1)

R. M. A Azzam, A. M. El-Saba, and M. A. G. Abushagur, “Spectrophotopolarimeter based on multiple reflections in a coated dielectric slab,” Thin Solid Films 313/314, 53-57(1998).
[CrossRef]

1996 (1)

1991 (1)

1982 (1)

1981 (1)

1980 (1)

1979 (1)

1971 (1)

1969 (1)

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14-33 (1969).
[CrossRef]

1966 (1)

1962 (2)

Abushagur, M. A. G.

R. M. A Azzam, A. M. El-Saba, and M. A. G. Abushagur, “Spectrophotopolarimeter based on multiple reflections in a coated dielectric slab,” Thin Solid Films 313/314, 53-57(1998).
[CrossRef]

A. M. El-Saba, R. M. A. Azzam, and M. A. G. Abushagur, “Parallel-slab division-of-amplitude photopolarimeter,” Opt. Lett. 21, 1709-1711 (1996).
[CrossRef] [PubMed]

Azzam, R. M. A

R. M. A Azzam, A. M. El-Saba, and M. A. G. Abushagur, “Spectrophotopolarimeter based on multiple reflections in a coated dielectric slab,” Thin Solid Films 313/314, 53-57(1998).
[CrossRef]

Azzam, R. M. A.

Bashara, N. M.

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

Bennett, H. E.

Bennett, K.

Budde, W.

Byer, R. L.

Cromer, C. L.

Dowell, M. L.

El-Saba, A. M.

R. M. A Azzam, A. M. El-Saba, and M. A. G. Abushagur, “Spectrophotopolarimeter based on multiple reflections in a coated dielectric slab,” Thin Solid Films 313/314, 53-57(1998).
[CrossRef]

A. M. El-Saba, R. M. A. Azzam, and M. A. G. Abushagur, “Parallel-slab division-of-amplitude photopolarimeter,” Opt. Lett. 21, 1709-1711 (1996).
[CrossRef] [PubMed]

Eyal, A.

Harris, T. J.

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

Lehman, J. H.

Li, X.

Livigni, D.

Lotem, H.

Muller, R. H.

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14-33 (1969).
[CrossRef]

Murarka, N. P.

Oseki, T.

Saito, S.

Sanders, C. L.

Shuker, R.

Stewart, J. E.

Sudradjat, F. F.

Thomas, M. E.

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

Tropf, W. J.

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

Wilner, K.

Appl. Opt. (11)

C. L. Sanders, “A photocell linearity tester,” Appl. Opt. 1, 207-211 (1962).
[CrossRef]

H. E. Bennett, “Accurate method for determining photometric linearity,” Appl. Opt. 5, 1265-1270 (1966).
[CrossRef] [PubMed]

T. Oseki and S. Saito, “A precision variable, double prism attenuator for CO2 lasers,” Appl. Opt. 10, 144-149 (1971).
[CrossRef] [PubMed]

W. Budde, “Multidecade linearity measurements on Si photodiodes,” Appl. Opt. 18, 1555-1558 (1979).
[CrossRef] [PubMed]

K. Bennett and R. L. Byer, “Computer-controllable wedged-plate variable attenuator,” Appl. Opt. 19, 2408-2412 (1980).
[CrossRef] [PubMed]

K. Wilner and N. P. Murarka, “Design considerations and test results of an evanescent switch-attenuator,” Appl. Opt. 20, 3600-3604 (1981).
[CrossRef] [PubMed]

W. Budde, “Large-flux-ratio linearity measurements on Si photodiodes,” Appl. Opt. 21, 3699-3701 (1982).
[CrossRef] [PubMed]

R. M. A. Azzam, “Parallel-slab polarizing beam splitter and photopolarimeter,” Appl. Opt. 46, 292-294 (2007).
[CrossRef] [PubMed]

R. M. A. Azzam and F. F. Sudradjat, “Reflection of p- and s-polarized light by a quarter-wave layer: explicit expressions and applications to beam splitters,” Appl. Opt. 47, 1103-1108 (2008).
[CrossRef] [PubMed]

J. H. Lehman, D. Livigni, X. Li, C. L. Cromer, and M. L. Dowell, “Reflective attenuator for high-energy laser measurements,” Appl. Opt. 47, 3360-3363(2008).
[CrossRef] [PubMed]

J. E. Stewart, “A rotating-sector attenuator of adjustable transmittance for precise spectrophotometry,” Appl. Opt. 1, 75-77 (1962).
[CrossRef]

Opt. Lett. (2)

Surf. Sci. (1)

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14-33 (1969).
[CrossRef]

Thin Solid Films (1)

R. M. A Azzam, A. M. El-Saba, and M. A. G. Abushagur, “Spectrophotopolarimeter based on multiple reflections in a coated dielectric slab,” Thin Solid Films 313/314, 53-57(1998).
[CrossRef]

Other (2)

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

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

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Figures (2)

Fig. 1
Fig. 1

Multiple reflection and transmission (in air) of a light beam by a homogeneous optically isotropic dielectric slab of refractive index n and uniform thickness d at an angle of incidence ϕ. p and s represent the linear polarizations parallel and perpendicular to the plane of incidence, respectively.

Fig. 2
Fig. 2

Intensity I m of the mth-order beam that exits the slab of Fig. 1 plotted as a function of the front-surface reflectance R ν for different values of the order number m. ( ν = p , s represent the linear polarizations parallel and perpendicular to the plane of incidence, respectively.) Continuous and dashed lines correspond to the reflected and transmitted orders, respectively.

Equations (11)

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I m = R ν m ( 1 R ν ) 2 , ν = p , s , m 1.
I m / R ν = R ν m 1 ( 1 R ν ) [ m ( m + 2 ) R ν ] = 0.
R ν = m / ( m + 2 ) .
I m ( max ) = 4 m m ( m + 2 ) m + 2 .
r s = cos ϕ ( n 2 sin 2 ϕ ) 1 / 2 cos ϕ + ( n 2 sin 2 ϕ ) 1 / 2 .
n 2 = sin 2 ϕ + ( 1 sin 2 ϕ ) ( 1 r s 1 + r s ) 2 .
sin 2 ϕ s = ( ( 7 + 4 3 ) n 2 ( 6 + 4 3 ) ) .
n 2 + 3 .
r p = n 2 cos ϕ ( n 2 sin 2 ϕ ) 1 / 2 n 2 cos ϕ + ( n 2 sin 2 ϕ ) 1 / 2 ,
sin 2 ϕ p = ( n 2 [ n 2 ( 7 + 4 3 ) ] [ n 4 ( 7 + 4 3 ) ] ) , n 2 + 3 .
sin 2 ϕ p = ( n 2 [ n 2 ( 7 4 3 ) ] [ n 4 ( 7 4 3 ) ] ) , n 2 + 3 .

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