Abstract

The reflectance and transmittance of dielectric thin films at oblique angles of incidence have strong polarization effects. For some applications these effects are undesirable. A nonpolarizing beam splitter design concept is shown, which is based on the fact that in a quarter-wave stack at λ0 two effective indices that obey the Brewster condition affect only the spectral performance of the s state at λ0. This property is used as a design tool. The concept can be applied to a wide range of angles and transmittance values, with the use of effective quarter-wave layers of at least three different materials. A few examples are elaborated where these values are designed and optimized to give either Tp = Ts or Tp + Ts = constant, in the vicinity of λ0.

© 1992 Optical Society of America

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References

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  1. M. Banning, “Practical methods of making and using multilayer filters,” J. Opt. Soc. Am. 37, 792–797 (1947).
    [CrossRef] [PubMed]
  2. P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta 8, 105–119 (1961).
    [CrossRef]
  3. V. R. Costich, “Reduction of polarization effects in interference coatings,” Appl. Opt. 9, 866–870 (1970).
    [CrossRef] [PubMed]
  4. A. Thelen, “Nonpolarizing interference films inside a glass cube,” Appl. Opt. 15, 2983–2985 (1976).
    [CrossRef] [PubMed]
  5. Z. Knittl, H. Houserkova, “Equivalent layers in oblique incidence: the problem of unsplit admittance and depolarization of partial reflectors,” Appl. Opt. 21, 2055–2068 (1982).
    [CrossRef] [PubMed]
  6. C. M. de Sterke, C. J. van der Laan, H. J. Frankena, “Nonpolarizing beam splitter design,” Appl. Opt. 22, 595–601 (1983).
    [CrossRef] [PubMed]
  7. H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Macmillan, New York, 1986), p. 164.
  8. S. M. MacNeille, “Beam splitter,” U.S. patent2,403,731 (1946).
  9. Film* calc, FTG Software Associates, Princeton, N.J.
  10. J. A. Dobrowolski, R. A. Kemp, “Refinement of optical multilayer systems with different optimization procedures,” Appl. Opt. 29, 2876–2893 (1990).
    [CrossRef] [PubMed]

1990 (1)

1983 (1)

1982 (1)

1976 (1)

1970 (1)

1961 (1)

P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta 8, 105–119 (1961).
[CrossRef]

1947 (1)

Banning, M.

Baumeister, P.

P. Baumeister, “The transmission and degree of polarization of quarter-wave stacks at non-normal incidence,” Opt. Acta 8, 105–119 (1961).
[CrossRef]

Costich, V. R.

de Sterke, C. M.

Dobrowolski, J. A.

Frankena, H. J.

Houserkova, H.

Kemp, R. A.

Knittl, Z.

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Macmillan, New York, 1986), p. 164.

MacNeille, S. M.

S. M. MacNeille, “Beam splitter,” U.S. patent2,403,731 (1946).

Thelen, A.

van der Laan, C. J.

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Figures (7)

Fig. 1
Fig. 1

Effective indices np, and ns as a function of the index of refraction for a BK7 glass cube (n0 = 1.52) and θ0 = 45°.

Fig. 2
Fig. 2

Spectral transmittance of the initial stack of the wideband design. The design is 1.52/(1.131H, 1.33M, 1.594L, 1.33M)5/1.52, where the design wavelength is λ0 = 550 nm and θ0 = 45°, nH = 2.3, nM = 1.63, and nL = 1.38.

Fig. 3
Fig. 3

Computer optimization of the wideband design, which results in the following design: 1.52/(1.131H, 1.33M, 1.594L, 1.33M)4, 0.605H, 0.9468M, 2.668L, 1.222M/1.52, with λ0 = 550 nm, θ0 = 45°, nH = 2.3, nM = 1.63, and nL = 1.38.

Fig. 4
Fig. 4

Spectral transmittance of the initial stack of the narrow-band design. The design is 1.52/H, M)5, (L, M)5/1.52. The layers are in effective thicknesses at λ0 = 550 nm, with θ0 = 45°, nH = 2.3, nM = 1.63, and nL = 1.38.

Fig. 5
Fig. 5

Spectral transmittance of the 50% average transmittance design, with the following configuration: 1.52/H, M, (L, M)3, H, M, (L, M)2, (H. M)3/1.52. The layers are in effective thicknesses at λ0 = 550 nm, with θ0 = 45°, nH = 2.3, nM = 1.63, and nL = 1.38.

Fig. 6
Fig. 6

(a) Spectral transmittance and (b) the angle dependence of the 50% average transmittance design after optimization, which results in the following design: 1.52/1.1H, 1.3M,/(1.8L, 1.18M)3, 1.116H, 0.973M, (1.77L, 1.24M)2, (1.14H, 1.49M)3/1.52, where λ0 = 550 nm and θ0 = 45°.

Fig. 7
Fig. 7

Spectral transmittance of the noneffective quarter-wave design: 1.52/(1.33H, 1.33M, 1.33L, 1.33M)4, 1.06H, 0.908M, 2.53L, 1.2M/1.52, where λ0 = 550 nm and θ0 = 45°.

Equations (20)

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n p = n / cos θ ,
n s = n cos θ .
n p = n ( 1 - S 2 / n 2 ) 1 / 2 ,
n s = n ( 1 - S 2 / n 2 ) 1 / 2 .
n = 2 S .
n H / cos θ H = n L / cos θ L .
sin 2 θ H = n L 2 n H 2 + n L 2 .
tan 2 θ H = n L 2 / n H 2 .
R = ( n 0 - Y n 0 - Y ) 2 ,
Y = ( n H n L ) 2 m n H 2 n sub ,
n 0 / H ( L , H ) m , ( B , A ) k / n sub ,
Y = ( n H n L ) 2 m n H 2 n sub ( n A n B ) 2 K .
1.52 / ( H , M ) 5 / 1.52
1.52 / ( H , M , L , M ) 5 / 1.52.
1.52 / ( 1.131 H , 1.33 M , 1.594 L , 1.33 M ) 5 / 1.52.
1.52 / ( H , M ) 5 , ( L , M ) 5 / 1.52.
1.52 / ( H , M ) 4 , H , M L , ( M , L ) 4 , M / 1.52.
sin 2 [ ( θ A + θ B 2 - δ ] = 0 ,
1.52 / H , M , ( L , M ) 3 , H , M , ( L , M ) 2 , ( H , M ) 3 / 1.52 ,
1.52 / ( 1.33 H , 1.33 M , 1.33 L , 1.33 M ) 4 , 1.06 H , 0.908 M , 2.53 L , 1.2 M / 1.52 ,

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