Abstract

We describe a nonpolarizing filter design at oblique incidence and a polarizing filter design at normal incidence that use a uniaxially anisotropic layer. The phase thicknesses and the optical admittances of the layers are compensated for by the birefringent properties of a thin film at oblique incidence. This concept can be applied to the design of nonpolarizing bandpass and edge filters at oblique incidence and of polarizing beam splitters at normal incidence. Besides, the dependence of narrow-bandpass filters on normal incidence is discussed.

© 2005 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. K. Nosu, H. Ishio, K. Hashimoto, “Multireflection optical muti/demultiplexer using interference filters,” Electron. Lett. 15, 414–415 (1979).
    [CrossRef]
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    [CrossRef]
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1997 (1)

J. A. Dobrowolski, “Numerical methods for optical thin films,” Opt. Photon. News 8(6), 24–33 (1997).
[CrossRef]

1992 (1)

1989 (1)

M. Zukic, K. H. Guenther, “Design of non-polarizing beam splitters with dielectric multilayer coatings,” Opt. Eng. 28, 165–171 (1989).
[CrossRef]

1984 (1)

1982 (1)

1981 (1)

1980 (1)

1979 (1)

K. Nosu, H. Ishio, K. Hashimoto, “Multireflection optical muti/demultiplexer using interference filters,” Electron. Lett. 15, 414–415 (1979).
[CrossRef]

1976 (1)

1970 (1)

1966 (1)

1952 (1)

Ciosek, J.

J. Ciosek, “Non-polarizing beam-splitter inside a glass cube,” in Gradient Index Optics in Science and Engineering, M. Pluta, ed., Proc. SPIE2943, 179–183 (1996).
[CrossRef]

Costich, V. R.

Dobrowolski, J. A.

J. A. Dobrowolski, “Numerical methods for optical thin films,” Opt. Photon. News 8(6), 24–33 (1997).
[CrossRef]

Epstein, L.

Gilo, M.

Guenther, K. H.

M. Zukic, K. H. Guenther, “Design of non-polarizing beam splitters with dielectric multilayer coatings,” Opt. Eng. 28, 165–171 (1989).
[CrossRef]

Hashimoto, K.

K. Nosu, H. Ishio, K. Hashimoto, “Multireflection optical muti/demultiplexer using interference filters,” Electron. Lett. 15, 414–415 (1979).
[CrossRef]

Houserkova, H.

Ishio, H.

K. Nosu, H. Ishio, K. Hashimoto, “Multireflection optical muti/demultiplexer using interference filters,” Electron. Lett. 15, 414–415 (1979).
[CrossRef]

Knittl, Z.

Nosu, K.

K. Nosu, H. Ishio, K. Hashimoto, “Multireflection optical muti/demultiplexer using interference filters,” Electron. Lett. 15, 414–415 (1979).
[CrossRef]

Thelen, A.

Zukic, M.

M. Zukic, K. H. Guenther, “Design of non-polarizing beam splitters with dielectric multilayer coatings,” Opt. Eng. 28, 165–171 (1989).
[CrossRef]

Appl. Opt. (5)

Electron. Lett. (1)

K. Nosu, H. Ishio, K. Hashimoto, “Multireflection optical muti/demultiplexer using interference filters,” Electron. Lett. 15, 414–415 (1979).
[CrossRef]

J. Opt. Soc. Am. (4)

Opt. Eng. (1)

M. Zukic, K. H. Guenther, “Design of non-polarizing beam splitters with dielectric multilayer coatings,” Opt. Eng. 28, 165–171 (1989).
[CrossRef]

Opt. Photon. News (1)

J. A. Dobrowolski, “Numerical methods for optical thin films,” Opt. Photon. News 8(6), 24–33 (1997).
[CrossRef]

Other (1)

J. Ciosek, “Non-polarizing beam-splitter inside a glass cube,” in Gradient Index Optics in Science and Engineering, M. Pluta, ed., Proc. SPIE2943, 179–183 (1996).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Spectral transmittance of a nonpolarizing narrow bandpass filter for s- and p-polarized light at a wavelength of 900 nm. The design is 1.52/(HL)10 H 2L (HL)10 H L (HL)10H 2L (HL)10 H/1.0, with λr = 1000 nm for p-polarized light, where the incident angle is 45°. The refractive indices of the two materials for p and s polarization are 1.92, 1.809 and 1.46, 1.525, respectively.

Fig. 2
Fig. 2

Spectral transmittance of a nonpolarizing broad-bandpass filter for s- and p-polarized light. The design is 1.52/1.5037H 2.5875L 2.1166H 1.0280L 0.9722H 1.0141L H (HLHLHLH)4 H 0.9442L 0.8298H 0.6370L/1.0, with λr = 1000 nm for p-polarized light, where the incident angle is 45°. The refractive indices of two materials for p and s polarization are 1.92, 1.84 and 1.46, 1.54, respectively.

Fig. 3
Fig. 3

Spectral transmittances of the long-wave-pass filter for s-and p-polarized light after optimization, which results in the following design: 1.52/0.8620H 0.3698L 1.3012H 0.7343L 1.377H 0.6182L (HL)11 0.8250H 1.0547L 0.3934H 0.4887L/1.0 for s-polarized light, where the reference wavelength is 880 nm and the incident angle is 45°. The refractive indices of two materials for p and s polarization are 2.093, 1.97 and 1.4, 1.42, respectively.

Fig. 4
Fig. 4

Transmittance spectra of a polarizing beam splitter at a wavelength of 1.06 µm with the indices of H and L layers for p and s polarization: (a) 1.92, 1.46 and 2.3, 1.56, respectively, (b) 2.3, 1.56 and 1.92, 1.46, respectively.

Fig. 5
Fig. 5

Angular performance of the peak wavelength of the narrow-band-pass filter for p- and s-polarized light.

Fig. 6
Fig. 6

Dependence on angle of the FWHM of the narrow-bandpass filter for p- and s-polarized light.

Equations (9)

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[ cos δ s ( i / η s ) sin δ s i η s sin δ s cos δ s ] , [ cos δ p ( i / η p ) sin δ p i η p sin δ p cos δ p ] ,
[ B C ] = M [ 1 η g ] ,
[ B C ] = M n M n 1 M 2 M 1 [ B C ] = M [ 1 η g ] ,
R = ( η 0 B C η 0 B + C ) ( η 0 B C η 0 B + C ) * ,
T = 4 η 0 η g ( η 0 B + C ) ( η 0 B + C ) * ,
R = [ 1 ( n H / n L ) 2 m ( n H 2 / n g ) 1 + ( n H / n L ) 2 m ( n H 2 / n g ) ] 2 ,
Δ g = π 2 arcsin ( n H n L n H n L ) ,
cos θ p H + cos θ p L n s H n p H cos θ s H + n s L n p L cos θ s L ,
n p H cos θ p l n p L cos θ p H n s H cos θ s H n s L cos θ s L .

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