Abstract

A thin-film optical filter used as a one-dimensional spatial filter is presented, and its design is briefly examined. The filter consists of a stack of quarter-wave dielectric layers upon a right-angle prism that selectively cancel a reflected or transmitted plane-wave front for various angles of incidence. Transmittance and reflectance are low-pass functions or high-pass functions of the angle of incidence with a high degree of steepness. In combination, these filters exhibit bandpass transmittance with a variable bandwidth. Applications to detection of extrasolar planets are briefly discussed.

© 2005 Optical Society of America

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References

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2004 (4)

J. L. Codona and R. Angel, Astrophys. J. 604, L117 (2004).
[CrossRef]

I. Moreno, G. Paez, and M. Strojnik, Opt. Commun. 233, 245 (2004).
[CrossRef]

R. Rabady and I. Avrutsky, Opt. Lett. 29, 605 (2004).
[CrossRef] [PubMed]

I. Moreno, Appl. Opt. 43, 3373 (2004).
[CrossRef] [PubMed]

2003 (2)

D. Schurig and D. R. Smith, Appl. Phys. Lett. 82, 2215 (2003).
[CrossRef]

M. Strojnik and G. Paez, Appl. Opt. 42, 5897 (2003).
[CrossRef] [PubMed]

1999 (1)

1996 (1)

1984 (1)

1976 (1)

Angel, R.

J. L. Codona and R. Angel, Astrophys. J. 604, L117 (2004).
[CrossRef]

Avrutsky, I.

Chavel, P.

Codona, J. L.

J. L. Codona and R. Angel, Astrophys. J. 604, L117 (2004).
[CrossRef]

Dettwiller, L.

Huang, P. S.

Kato, J.

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (Institute of Physics, Bristol, UK, 2001).
[CrossRef]

Moreno, I.

I. Moreno, G. Paez, and M. Strojnik, Opt. Commun. 233, 245 (2004).
[CrossRef]

I. Moreno, Appl. Opt. 43, 3373 (2004).
[CrossRef] [PubMed]

Paez, G.

I. Moreno, G. Paez, and M. Strojnik, Opt. Commun. 233, 245 (2004).
[CrossRef]

M. Strojnik and G. Paez, Appl. Opt. 42, 5897 (2003).
[CrossRef] [PubMed]

Rabady, R.

Schurig, D.

D. Schurig and D. R. Smith, Appl. Phys. Lett. 82, 2215 (2003).
[CrossRef]

Smith, D. R.

D. Schurig and D. R. Smith, Appl. Phys. Lett. 82, 2215 (2003).
[CrossRef]

Strojnik, M.

I. Moreno, G. Paez, and M. Strojnik, Opt. Commun. 233, 245 (2004).
[CrossRef]

M. Strojnik and G. Paez, Appl. Opt. 42, 5897 (2003).
[CrossRef] [PubMed]

Tanaka, H.

Thelen, A.

Yamaguchi, I.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

D. Schurig and D. R. Smith, Appl. Phys. Lett. 82, 2215 (2003).
[CrossRef]

Astrophys. J. (1)

J. L. Codona and R. Angel, Astrophys. J. 604, L117 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

I. Moreno, G. Paez, and M. Strojnik, Opt. Commun. 233, 245 (2004).
[CrossRef]

Opt. Lett. (2)

Other (1)

H. A. Macleod, Thin-Film Optical Filters (Institute of Physics, Bristol, UK, 2001).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Thin-film filter for spatial frequencies assembled with a multilayer stack upon a glass prism; θ prism is the angle of the prism, n M is the index of refraction of the incident medium, and n sub is the index of the substrate medium.

Fig. 2
Fig. 2

Top, reflectance and bottom, transmittance of a multilayer design as a function of angle of incidence for n M = 1.5 , n sub = 1 (air), Δ θ C = 0.1 ° , θ prism = 45 ° (right-angle prism), and m = 2 (five layers); all the layers are one quarter-wave thick at θ = 4.938 ° ( θ 0 = 41.71 ° ) . For s polarization, n H = 2.1 , n L = 1.389 , and the design is 1.5 L H L H L air . For p polarization, n L = 1.38 , n H = 2.615 , and the design is 1.5 H L H L H air .

Fig. 3
Fig. 3

Bandpass spatial filter assembled with two edge thin-film spatial filters like the filter shown in Fig. 1. The second prism is rotated by ϕ to control bandwidth Δ θ .

Fig. 4
Fig. 4

Transmittance of the bandpass filter shown in Fig. 3. The design of the edge filters is that which was analyzed for s polarization in Fig. 2. Bandwidth Δ θ is variable with angle of prism rotation ϕ.

Equations (6)

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Y = ( n H n L ) 2 m n H 2 n sub ;
Y = ( n L n H ) 2 m n L 2 n sub ,
n L = { [ cos θ 0 ( n M n sub ) m ( 1 n M 2 n sub 2 sin 2 θ 0 ) 1 2 ( n H 2 n M 2 sin 2 θ 0 ) m ] 1 m + 1 + n M n sub sin 2 θ 0 } 1 2 ( n M n sub ) 1 2 ,
n H = ( 1 + { 1 4 n M 2 sin 2 θ 0 [ cos θ 0 n M n sub ( 1 n M 2 n sub 2 sin 2 θ 0 ) 1 2 ( n L 2 n M 2 sin 2 θ 0 n L 4 ) m ] 1 m + 1 } 1 2 2 [ ( n M n sub ) m cos θ 0 ( 1 n M 2 n sub 2 sin 2 θ 0 ) 1 2 ( n L 2 n M 2 sin 2 θ 0 n L 4 ) m ] 1 m + 1 ) 1 2 ( n M n sub ) 1 2 .
θ 0 = sin 1 ( n sub n M ) Δ θ C
Δ θ ( ϕ ) = sin 1 ( n M sin { θ prism sin 1 [ 1 n M sin ( ψ 0 + θ prism ϕ ) ] } ) ψ 0 ,

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