Abstract

Based on the theory of photonic crystals and the framework of a single-channel reflection filter that we presented before, structures of reflection filters with multiple channels are proposed. These structures can overcome some drawbacks of conventional multichannel transmission filters and are much easier to fabricate. We have practically fabricated the reflection filters with two and three channels, and the tested results show approximate agreement with theoretical simulation. Moreover, the superprism effect is also simulated in the single-channel reflection filter, the superiorities to transmission filters are discussed, and these analyses may shed some light on new applications of reflection filters in optical communication and other systems.

© 2008 Optical Society of America

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  1. E. Pelletier and H. A. Macleod, "Interference filters with multiple peaks," J. Opt. Soc. Am. 72, 683-687 (1982).
    [CrossRef]
  2. P. Gu, Y. Yang, H. Chen, Z. Zheng, and Y. Zhang, "Interference filters with multiple transmittance peaks used for wavelength division multiplexing systems," Acta Photonica Sin. 32, 837-839 (2003).
  3. Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
    [CrossRef]
  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. 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]
  6. X. Sun, P. Gu, W. Shen, X. Liu, Y. Wang, and Y. Zhang, "Design and fabrication of a novel reflection filter," Appl. Opt. 46, 2899-2902 (2007).
    [CrossRef] [PubMed]
  7. H. A. Macleod, Thin-film Optical Filters, 2nd ed. (Adam Hilger Ltd., 1986).
    [CrossRef]
  8. E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, "Tight-binding parametrization for photonic band gap materials," Phys. Rev. Lett. 81, 1405-1408 (1998).
    [CrossRef]
  9. B. E. Nelson, M. Gerken, D. A. B. Miller, and R. Piestun, "Use of a dielectric stack as a one-dimensional photonic crystal for wavelength demultiplexing by beam shifting," Opt. Lett. 25, 1502-1504 (2000).
    [CrossRef]
  10. X. Sun, P. Gu, M. Li, X. Liu, D. Wang, and J. Zhang, "Tunable spatial demultiplexer based on the Fabry-Perot filter," Opt. Express 14, 8470-8475 (2006).
    [CrossRef] [PubMed]
  11. C.-F. Li, "Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects," Phys. Rev. Lett. 91, 133903 (2003).
    [CrossRef] [PubMed]

2007 (1)

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

2006 (1)

2003 (3)

C.-F. Li, "Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects," Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef] [PubMed]

P. Gu, Y. Yang, H. Chen, Z. Zheng, and Y. Zhang, "Interference filters with multiple transmittance peaks used for wavelength division multiplexing systems," Acta Photonica Sin. 32, 837-839 (2003).

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

2000 (1)

B. E. Nelson, M. Gerken, D. A. B. Miller, and R. Piestun, "Use of a dielectric stack as a one-dimensional photonic crystal for wavelength demultiplexing by beam shifting," Opt. Lett. 25, 1502-1504 (2000).
[CrossRef]

1998 (1)

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, "Tight-binding parametrization for photonic band gap materials," Phys. Rev. Lett. 81, 1405-1408 (1998).
[CrossRef]

1997 (1)

1992 (1)

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]

1986 (1)

H. A. Macleod, Thin-film Optical Filters, 2nd ed. (Adam Hilger Ltd., 1986).
[CrossRef]

1982 (1)

Chen, H.

P. Gu, Y. Yang, H. Chen, Z. Zheng, and Y. Zhang, "Interference filters with multiple transmittance peaks used for wavelength division multiplexing systems," Acta Photonica Sin. 32, 837-839 (2003).

Economou, E. N.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, "Tight-binding parametrization for photonic band gap materials," Phys. Rev. Lett. 81, 1405-1408 (1998).
[CrossRef]

Gerken, M.

B. E. Nelson, M. Gerken, D. A. B. Miller, and R. Piestun, "Use of a dielectric stack as a one-dimensional photonic crystal for wavelength demultiplexing by beam shifting," Opt. Lett. 25, 1502-1504 (2000).
[CrossRef]

Gu, P.

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

X. Sun, P. Gu, M. Li, X. Liu, D. Wang, and J. Zhang, "Tunable spatial demultiplexer based on the Fabry-Perot filter," Opt. Express 14, 8470-8475 (2006).
[CrossRef] [PubMed]

P. Gu, Y. Yang, H. Chen, Z. Zheng, and Y. Zhang, "Interference filters with multiple transmittance peaks used for wavelength division multiplexing systems," Acta Photonica Sin. 32, 837-839 (2003).

Li, C.-F.

C.-F. Li, "Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects," Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef] [PubMed]

Li, M.

Lidorikis, E.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, "Tight-binding parametrization for photonic band gap materials," Phys. Rev. Lett. 81, 1405-1408 (1998).
[CrossRef]

Lin, Y. C.

Liu, X.

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

X. Sun, P. Gu, M. Li, X. Liu, D. Wang, and J. Zhang, "Tunable spatial demultiplexer based on the Fabry-Perot filter," Opt. Express 14, 8470-8475 (2006).
[CrossRef] [PubMed]

Lu, H.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

Lue, J. T.

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]

Macleod, H. A.

Miller, D. A. B.

B. E. Nelson, M. Gerken, D. A. B. Miller, and R. Piestun, "Use of a dielectric stack as a one-dimensional photonic crystal for wavelength demultiplexing by beam shifting," Opt. Lett. 25, 1502-1504 (2000).
[CrossRef]

Ming, N. B.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

Nelson, B. E.

B. E. Nelson, M. Gerken, D. A. B. Miller, and R. Piestun, "Use of a dielectric stack as a one-dimensional photonic crystal for wavelength demultiplexing by beam shifting," Opt. Lett. 25, 1502-1504 (2000).
[CrossRef]

Pelletier, E.

Piestun, R.

B. E. Nelson, M. Gerken, D. A. B. Miller, and R. Piestun, "Use of a dielectric stack as a one-dimensional photonic crystal for wavelength demultiplexing by beam shifting," Opt. Lett. 25, 1502-1504 (2000).
[CrossRef]

Qin, Q.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

Shen, W.

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

Sheng, J. S.

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]

Sigalas, M. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, "Tight-binding parametrization for photonic band gap materials," Phys. Rev. Lett. 81, 1405-1408 (1998).
[CrossRef]

Soukoulis, C. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, "Tight-binding parametrization for photonic band gap materials," Phys. Rev. Lett. 81, 1405-1408 (1998).
[CrossRef]

Sun, X.

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

X. Sun, P. Gu, M. Li, X. Liu, D. Wang, and J. Zhang, "Tunable spatial demultiplexer based on the Fabry-Perot filter," Opt. Express 14, 8470-8475 (2006).
[CrossRef] [PubMed]

Tan, M. Q.

Wang, D.

Wang, Y.

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

Yang, Y.

P. Gu, Y. Yang, H. Chen, Z. Zheng, and Y. Zhang, "Interference filters with multiple transmittance peaks used for wavelength division multiplexing systems," Acta Photonica Sin. 32, 837-839 (2003).

Yuan, C. S.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

Zhang, J.

Zhang, Y.

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

P. Gu, Y. Yang, H. Chen, Z. Zheng, and Y. Zhang, "Interference filters with multiple transmittance peaks used for wavelength division multiplexing systems," Acta Photonica Sin. 32, 837-839 (2003).

Zhao, D. Z.

Zheng, Z.

P. Gu, Y. Yang, H. Chen, Z. Zheng, and Y. Zhang, "Interference filters with multiple transmittance peaks used for wavelength division multiplexing systems," Acta Photonica Sin. 32, 837-839 (2003).

Zhu, S. N.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

Zhu, Y. Y.

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

Acta Photonica Sin. (1)

P. Gu, Y. Yang, H. Chen, Z. Zheng, and Y. Zhang, "Interference filters with multiple transmittance peaks used for wavelength division multiplexing systems," Acta Photonica Sin. 32, 837-839 (2003).

Appl. Opt. (2)

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]

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

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Q. Qin, H. Lu, S. N. Zhu, C. S. Yuan, Y. Y. Zhu, and N. B. Ming, "Resonance transmission modes in dual-periodical dielectric multilayer films," Appl. Phys. Lett. 82, 4654-4656 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

B. E. Nelson, M. Gerken, D. A. B. Miller, and R. Piestun, "Use of a dielectric stack as a one-dimensional photonic crystal for wavelength demultiplexing by beam shifting," Opt. Lett. 25, 1502-1504 (2000).
[CrossRef]

Opt. Express (1)

Phys. Rev. Lett. (2)

C.-F. Li, "Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects," Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef] [PubMed]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, "Tight-binding parametrization for photonic band gap materials," Phys. Rev. Lett. 81, 1405-1408 (1998).
[CrossRef]

Other (1)

H. A. Macleod, Thin-film Optical Filters, 2nd ed. (Adam Hilger Ltd., 1986).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Simulated reflectance curve of the filter Air∕Cr ( L H ) 2 ( 2 L ) 3 ( H L ) 7 H / S u b .

Fig. 2
Fig. 2

Real part Y′ (solid curve) and imaginary part Y′ (dashed curve) of the effective admittance of the stack ( L H ) 2 ( 2 L ) 3 ( H L ) 7 H / S u b .

Fig. 3
Fig. 3

Simulated reflectance curve of the filter Air∕Cr ( L H ) 2 L ( 2 H 2 L ) 3 ( H L ) 7 H / S u b .

Fig. 4
Fig. 4

Real part Y′ (solid curve) and imaginary part Y′ (dashed curve) of the effective admittance of the stack ( L H ) 2 L ( 2 H 2 L ) 3 ( H L ) 7 H / S u b .

Fig. 5
Fig. 5

Measured reflectance of the two-channel filter Air∕Cr ( L H ) 2 L ( 2 H 2 L ) 3 ( H L ) 7 H / S u b .

Fig. 6
Fig. 6

Measured reflectance of the three-channel filter Air∕Cr ( L H ) 2 ( 2 L 2 H 2 L ) 3 ( H L ) 7 H / S u b .

Fig. 7
Fig. 7

Sketch of superprism effect calculation in a multilayer thin film stack.

Fig. 8
Fig. 8

Theoretically calculated reflected energy utilization (dashed curve) and spatial dispersive shift (solid curve) for different wavelengths in (a) a reflection filter and (b) a transmission filter.

Fig. 9
Fig. 9

Theoretically calculated transmitted energy utilization (dashed curve) and spatial dispersive shift (solid curve) for different wavelengths in the transmission filter.

Tables (3)

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Table 1 Optical Constants of the Cr Layer as a Function of Wavelength

Tables Icon

Table 2 Physical Thickness of Several Optimized Layers in a Two-Channel Filter

Tables Icon

Table 3 Physical Thickness of Several Optimized Layers in a Three-Channel Filter

Equations (4)

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

R [ n 0 2 π d ( n 0 Y + 2 n c k c ) / λ Y ] 2 + ( 2 π n 0 d Y / λ Y ) 2 [ n 0 2 π d ( n 0 Y 2 n c k c ) / λ + Y ] 2 + ( 2 π n 0 d Y / λ + Y ) 2 .
R 0 ( 2 π n 0 n H d / λ 0 ) 2 + [ ( n 0 x / n H ) n H ( 4 π n c k c d x / n H λ 0 ) ] 2 ( 2 π n 0 n H d / λ 0 ) 2 + [ ( n 0 x / n H ) + n H + ( 4 π n c k c d x / n H λ 0 ) ] 2 ,
2 Δ λ 0.5 4 | A | λ 0 N π [ ( 24 π n 0 n c k c d / λ 0 ) n 0 2 ( 4 π n c k c d / λ 0 ) 2 ] 0.5 ,
s r ( t ) = d φ r ( t ) d k x ,

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