Abstract

The angular dependence of filtering properties for a novel narrowband reflection-and-transmission filter made of an ultrathin metallic film in front of a planar Fabry–Perot resonator is theoretically investigated. It is shown that the simultaneous peaks in reflection and transmission are strongly dependent on the polarization of the incident wave. The peak positions of the reflection and transmission are shifted to shorter wavelengths as the angle of incidence increases in both TM and TE polarization. Additionally, the reflection peak height is increased in TE polarization, whereas it is decreased in TM polarization. Two effective Brewster angles can be defined through the angle-dependent reflectance at the resonant wavelength for both polarizations. The first, for TE polarization, is found at 34°, and the second is 77° for TM polarization. The structure could thus be used as a polarizing device in addition to a filtering one.

© 2009 Optical Society of America

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References

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  1. S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University, 2008), www.ece.rutgers.edu/~orfanidi/ewa, Chap. 7.
  2. M. Q. Tan, Y. C. Lin, and D. Z. Zhao, “Reflection filter with high reflectivity and narrow bandwidth,” Appl. Opt. 36, 827-830 (1997).
    [CrossRef] [PubMed]
  3. X. Z. Sun, P. F. Gu, W. D. Shen, X. Liu, Y. Wang, and Y. G. Zhang, “Design and fabrication of a novel reflection filter,” Appl. Opt. 46, 2899-2902 (2007).
    [CrossRef] [PubMed]
  4. J.-S. Sheng and J.-T. Lue, “Ultraviolet narrow-band rejection filters composed of multiple metal and dielectric layers,” Appl. Opt. 31, 6117-6121 (1992).
    [CrossRef] [PubMed]
  5. T. Augustsson, “Proposal of a DMUX with a Fabry-Perot all-reflection filter-based MMIMI configuration,” IEEE Photon. Technol. Lett. 13, 215-217 (2001).
    [CrossRef]
  6. R. Gamble and P. H. Lissberger, “Reflection filter multilayers of metallic and dielectric thin films,” Appl. Opt. 28, 2838-2846 (1989).
    [CrossRef] [PubMed]
  7. W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filter in both transmission and reflection with metal/dielectric thin films,” Opt. Commun. 282, 242-246 (2009).
    [CrossRef]
  8. E. Hecht, Optics (Addison Wesley, 2002), Chap. 9.

2009 (1)

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filter in both transmission and reflection with metal/dielectric thin films,” Opt. Commun. 282, 242-246 (2009).
[CrossRef]

2007 (1)

2001 (1)

T. Augustsson, “Proposal of a DMUX with a Fabry-Perot all-reflection filter-based MMIMI configuration,” IEEE Photon. Technol. Lett. 13, 215-217 (2001).
[CrossRef]

1997 (1)

1992 (1)

1989 (1)

Augustsson, T.

T. Augustsson, “Proposal of a DMUX with a Fabry-Perot all-reflection filter-based MMIMI configuration,” IEEE Photon. Technol. Lett. 13, 215-217 (2001).
[CrossRef]

Gamble, R.

Gu, P.

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filter in both transmission and reflection with metal/dielectric thin films,” Opt. Commun. 282, 242-246 (2009).
[CrossRef]

Gu, P. F.

Hecht, E.

E. Hecht, Optics (Addison Wesley, 2002), Chap. 9.

Lin, Y. C.

Lissberger, P. H.

Liu, X.

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filter in both transmission and reflection with metal/dielectric thin films,” Opt. Commun. 282, 242-246 (2009).
[CrossRef]

X. Z. Sun, P. F. Gu, W. D. Shen, X. Liu, Y. Wang, and Y. G. Zhang, “Design and fabrication of a novel reflection filter,” Appl. Opt. 46, 2899-2902 (2007).
[CrossRef] [PubMed]

Lue, J.-T.

Luo, Z.

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filter in both transmission and reflection with metal/dielectric thin films,” Opt. Commun. 282, 242-246 (2009).
[CrossRef]

Orfanidis, S. J.

S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University, 2008), www.ece.rutgers.edu/~orfanidi/ewa, Chap. 7.

Shen, W.

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filter in both transmission and reflection with metal/dielectric thin films,” Opt. Commun. 282, 242-246 (2009).
[CrossRef]

Shen, W. D.

Sheng, J.-S.

Sun, X.

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filter in both transmission and reflection with metal/dielectric thin films,” Opt. Commun. 282, 242-246 (2009).
[CrossRef]

Sun, X. Z.

Tan, M. Q.

Wang, Y.

Zhang, Y.

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filter in both transmission and reflection with metal/dielectric thin films,” Opt. Commun. 282, 242-246 (2009).
[CrossRef]

Zhang, Y. G.

Zhao, D. Z.

Appl. Opt. (4)

IEEE Photon. Technol. Lett. (1)

T. Augustsson, “Proposal of a DMUX with a Fabry-Perot all-reflection filter-based MMIMI configuration,” IEEE Photon. Technol. Lett. 13, 215-217 (2001).
[CrossRef]

Opt. Commun. (1)

W. Shen, X. Sun, Y. Zhang, Z. Luo, X. Liu, and P. Gu, “Narrow band filter in both transmission and reflection with metal/dielectric thin films,” Opt. Commun. 282, 242-246 (2009).
[CrossRef]

Other (2)

E. Hecht, Optics (Addison Wesley, 2002), Chap. 9.

S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University, 2008), www.ece.rutgers.edu/~orfanidi/ewa, Chap. 7.

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Figures (4)

Fig. 1
Fig. 1

Calculated (a) wavelength-dependent reflectance, (b) transmittance, and (c) absorptance for TE polarization at angles of incidence 0°, 10°, 20°, and 30°, respectively. The resonant peaks in reflectance and transmittance and the dip in absorptance are located near 700 nm .

Fig. 2
Fig. 2

Calculated (a) wavelength-dependent reflectance, (b) transmittance, and (c) absorptance for TM polarization at angles of incidence 0°, 10°, 20°, and 30°, respectively. The resonant peaks in reflectance and transmittance and the dip in absorptance are located near 700 nm .

Fig. 3
Fig. 3

Calculated angle-dependent reflectance for TE (solid curve) and TM (dashed curve) polarization at λ 0 . The dotted curve is the degree of polarization P.

Fig. 4
Fig. 4

Calculated angle-dependent degree of polarization P at λ 0 for different numbers of periods N L = 2 , 3, 4, 5, 6. The two effective Brewster angles decrease with increasing N L .

Equations (13)

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M M = [ cos ( k 0 h M ) j sin ( k 0 h M ) Y M j Y M sin ( k 0 h M ) cos ( k 0 h M ) ] ,
Y M = η 0 1 n M cos θ M ( TE polarization ) ,
Y M = η 0 1 n M cos θ M ( TM polarization ) ,
M M = [ 1 j η 0 2 π d λ cos θ M η 0 1 4 π d λ n R n I cos θ M 1 ] ( TE polarization ) ,
M M = [ 1 j η 0 2 π d λ cos θ M η 0 1 4 π d λ cos θ M n R n I 1 ] ( TM polarization ) .
M L = [ cos ( k 0 n L d L cos θ L ) j sin ( k 0 n L d L cos θ L ) Y L j Y L sin ( k 0 n L d L cos θ L ) cos ( k 0 n L d L cos θ L ) ] ,
M H = [ cos ( k 0 n H d H cos θ H ) j sin ( k 0 n H d H cos θ H ) Y H j Y H sin ( k 0 n H d H cos θ H ) cos ( k 0 n H d H cos θ H ) ] ,
M = [ m 11 m 12 m 21 m 22 ] = M M ( M L M H ) N L M 2 L ( M H M L ) N R M H .
r = Y 0 m 11 + Y 0 Y s m 12 m 21 Y s m 22 Y 0 m 11 + Y 0 Y s m 12 + m 21 + Y s m 22 ,
t = 2 Y 0 Y 0 m 11 + Y 0 Y s m 12 + m 21 + Y s m 22 ,
R = r 2 ,
T = n sub cos θ sub n air cos θ air t 2 .
A = 1 R T .

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