Abstract

The reflectance and transmittance of dielectric films at nonzero angle of incidence show strong polarization effects, and for many applications these effects are not wanted. Costich has recently published on the reduction of these effects in interference films. The extension of his theory to the case of a multilayer inside a glass cube is possible, but an efficient design does not result. In this paper another method using quarterwave layers only is developed.

© 1976 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Banning, J. Opt. Soc. Am. 37, 792 (1947).
    [CrossRef] [PubMed]
  2. V. R. Costich, Appl. Opt. 9, 866 (1970).
    [CrossRef] [PubMed]
  3. L. I. Epstein, J. Opt. Soc. Am. 42, 806 (1952).
    [CrossRef]
  4. A. Thelen, J. Opt. Soc. Am. 56, 1533 (1966).
    [CrossRef]
  5. P. Baumeister, Opt. Acta 8, 105 (1961).
    [CrossRef]
  6. A. Vasicek, Optics of Thin Films (North-Holland, Amsterdam, 1960), p. 187.

1970 (1)

1966 (1)

1961 (1)

P. Baumeister, Opt. Acta 8, 105 (1961).
[CrossRef]

1952 (1)

1947 (1)

Banning, M.

Baumeister, P.

P. Baumeister, Opt. Acta 8, 105 (1961).
[CrossRef]

Costich, V. R.

Epstein, L. I.

Thelen, A.

Vasicek, A.

A. Vasicek, Optics of Thin Films (North-Holland, Amsterdam, 1960), p. 187.

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

Opt. Acta (1)

P. Baumeister, Opt. Acta 8, 105 (1961).
[CrossRef]

Other (1)

A. Vasicek, Optics of Thin Films (North-Holland, Amsterdam, 1960), p. 187.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Equivalent index for the combination (H/2) L (H/2) with nH = 2.35 and nL = 1.51, nM = 1.52, and αM = 45°, as a function of λo/λ. λo is the wavelength where L has an optical thickness of one quarterwave.

Fig. 2
Fig. 2

Schematic of a multilayer cemented inside a glass cube.

Fig. 3
Fig. 3

Curve of Fig. 1 with nH = 2.35 and nL = 1.65.

Fig. 4
Fig. 4

Reflectance of design of Eq. (6).

Fig. 5
Fig. 5

Reflectance of the design 1.52|2.35, 1.68, 1.38, 1.68, 2.35, 1.68, 1.38, 1.68, 2.35, 1.68, 1.38, 1.68, 2.35, 1.68, 1.38, 1.68, 2.35|1.52; nM = 1.52 and αM = 45°, all layers one quarterwave thick at 520 nm.

Fig. 6
Fig. 6

Reflectance of the design 1.52|1.38, 1.68, 2.35, 1.68, 2.35, 1.68, 1.38, 1.68, 2.35, 1.68, 1.38, 1.68, 2.35, 1.68, 2.35, 1.68, 1.38|1.52; nM = 1.52 and αM = 45°, all layers one quarterwave thick at 520 nm.

Fig. 7
Fig. 7

Reflectance of the design 1.52|1.38, 1.66, 2.35, 1.66, 2.35, 1.66, 1.38, 1.66, 1.38, 1.66, 2.35, 1.66, 2.35, 1.66, 2.35, 1.66, 1.38, 1.66, 1.38, 1.66, 2.35, 1.66, 2.35, 1.66, 1.38|1.52; nM = 1.52 and αM = 45°, all layers one quarterwave thick at 520 nm.

Fig. 8
Fig. 8

Reflectance of the design 1.52|1.38, 1.62, 2.35, 1.62, 2.35, 1.62, 1.38, 1.62, 1.38, 1.62, 2.35, 1.62, 2.35, 1.62, 1.38, 1.62|1.52; nM = 1.52 and αM = 45°, all layers one quarterwave thick at 520 nm.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

Δ n H ( Δ n H / Δ n L ) 1 / 2 = 1 ,
Δ n = n p / n s = 1 / [ 1 - ( n M sin α M / n ) 2 ] ;
n L = ( n M sin α M ) / { 1 - [ 1 - ( n M sin α M / n H ) 2 ] 3 } 1 / 2 .
Δ n = ( Δ n M ) 1 / 2 ,
n = n M sin α M / ( 1 - cos α M ) 1 / 2 .
1.52 A [ ( 0.75 B 1.5 C 0.75 B ) ( 0.75 D 1.5 E 0.75 D ) ] m ( 0.75 B 1.5 C 0.75 B ) A 1.52 ,
T = T ( x ) = 4 / ( 2 + x 2 + x - 2 ) ,
x = ( n M / n S ) 1 / 2 ( n 2 n 4 n 6 / n 1 n 3 n 5 )
x = ( n M n S ) 1 / 2 ( n 2 n 4 n 6 / n 1 n 3 n 5 )
( n M s / n S s ) 1 / 2 ( n 2 s n 4 s / n 1 s n 3 s ) = ( n M p / n S p ) 1 / 2 ( n 2 p n 4 p / n 1 p n 3 p ) .
( Δ n M / Δ n S ) 1 / 2 Δ n 2 Δ n 4 = Δ n 1 Δ n 3 Δ n 5
( Δ n M Δ n S ) 1 / 2 Δ n 2 Δ n 4 = Δ n 1 Δ n 3 Δ n 5
Δ n M ( Δ n 2 ) 8 = ( Δ n 1 ) 5 ( Δ n 3 ) 4 ,

Metrics