Abstract

Narrowband high-reflection filters with the structure sub|H(LH)m1αL(HL)m2CrβM|air are proposed. The effects of the Cr layer and the matching stack consisting of dielectric multilayer on the reflection characteristics of the filters are analyzed. The distribution of the internal electric field and the optical absorption is also calculated. The analysis indicates that the improvement of the sidebands could be reached by applying the matching stack without impairing the maximal reflectance and half-width of the reflection band. Wide and flat reflection sidebands could be realized by applying a relatively thicker metal layer. However, lowering the sideband reflection could only be achieved by adding appropriate matching stacks. Large m1m2 could increase the maximal reflectance, while large m2 or nH/nL would reduce the width of the reflection band. In the Cr layer, the least average intense electric field occurred at the central wavelength, the relatively high electric field intensity exists at the wavelengths outside the central wavelength region. The optical absorption of the filter depends strongly on the electric field intensity inside the Cr layer.

© 2008 Optical Society of America

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References

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2007 (1)

2006 (2)

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88, 251115 (2006).
[CrossRef]

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Double-layer resonant Brewster filters consisting of a homogeneous layer and a grating with equal refractive index,” Appl. Phys. Lett. 89, 241119 (2006).
[CrossRef]

1998 (1)

1997 (1)

1995 (1)

1994 (1)

1992 (1)

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61 (9), 1022-1024 (1992).
[CrossRef]

1990 (1)

S. S. Wang, R. Magnusson, J. S. Bagby, and M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470-1474 (1990).
[CrossRef]

1989 (1)

1983 (1)

S. Y. Zheng and J. W. Y. Lit, “Design of a narrow-band reflection IR multilayer,” Can. J. Phys. 61, 361-368 (1983).
[CrossRef]

1978 (1)

A. Thetford, “Absorbing multilayers and reflection interference filters,” J. Mod. Opt. 25, 945-961 (1978).
[CrossRef]

1976 (1)

Z. Knittl, Optics of Thin Films (Wiley, 1976), pp. 300-320.

1971 (1)

Bagby, J. S.

S. S. Wang, R. Magnusson, J. S. Bagby, and M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470-1474 (1990).
[CrossRef]

Chen, L. Y.

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88, 251115 (2006).
[CrossRef]

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Double-layer resonant Brewster filters consisting of a homogeneous layer and a grating with equal refractive index,” Appl. Phys. Lett. 89, 241119 (2006).
[CrossRef]

Gamble, R.

Gu, P. F.

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, 1976), pp. 300-320.

Lin, Y.

Lissberger, P. H.

Lit, J. W. Y.

S. Y. Zheng and J. W. Y. Lit, “Design of a narrow-band reflection IR multilayer,” Can. J. Phys. 61, 361-368 (1983).
[CrossRef]

Liu, Z. S.

Magnusson, R.

Moharam, M. G.

S. S. Wang, R. Magnusson, J. S. Bagby, and M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470-1474 (1990).
[CrossRef]

Sang, T.

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88, 251115 (2006).
[CrossRef]

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Double-layer resonant Brewster filters consisting of a homogeneous layer and a grating with equal refractive index,” Appl. Phys. Lett. 89, 241119 (2006).
[CrossRef]

Shin, D.

Sun, X. Z.

Tan, M.

Thelen, A.

Thetford, A.

A. Thetford, “Absorbing multilayers and reflection interference filters,” J. Mod. Opt. 25, 945-961 (1978).
[CrossRef]

Tibuleac, S.

Wang, L.

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88, 251115 (2006).
[CrossRef]

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Double-layer resonant Brewster filters consisting of a homogeneous layer and a grating with equal refractive index,” Appl. Phys. Lett. 89, 241119 (2006).
[CrossRef]

Wang, S. S.

S. S. Wang and R. Magnusson, “Multilayer waveguide grating filters,” Appl. Opt. 34, 2414-2420 (1995).
[CrossRef] [PubMed]

S. S. Wang and R. Magnusson, “Design of waveguide grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919-921 (1994).
[CrossRef] [PubMed]

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61 (9), 1022-1024 (1992).
[CrossRef]

S. S. Wang, R. Magnusson, J. S. Bagby, and M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470-1474 (1990).
[CrossRef]

Wang, Z. S.

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Double-layer resonant Brewster filters consisting of a homogeneous layer and a grating with equal refractive index,” Appl. Phys. Lett. 89, 241119 (2006).
[CrossRef]

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88, 251115 (2006).
[CrossRef]

Wu, Y. G.

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88, 251115 (2006).
[CrossRef]

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Double-layer resonant Brewster filters consisting of a homogeneous layer and a grating with equal refractive index,” Appl. Phys. Lett. 89, 241119 (2006).
[CrossRef]

Young, P. P.

Zhao, D.

Zheng, S. Y.

S. Y. Zheng and J. W. Y. Lit, “Design of a narrow-band reflection IR multilayer,” Can. J. Phys. 61, 361-368 (1983).
[CrossRef]

Zhu, J. T.

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88, 251115 (2006).
[CrossRef]

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Double-layer resonant Brewster filters consisting of a homogeneous layer and a grating with equal refractive index,” Appl. Phys. Lett. 89, 241119 (2006).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (3)

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61 (9), 1022-1024 (1992).
[CrossRef]

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88, 251115 (2006).
[CrossRef]

Z. S. Wang, T. Sang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Double-layer resonant Brewster filters consisting of a homogeneous layer and a grating with equal refractive index,” Appl. Phys. Lett. 89, 241119 (2006).
[CrossRef]

Can. J. Phys. (1)

S. Y. Zheng and J. W. Y. Lit, “Design of a narrow-band reflection IR multilayer,” Can. J. Phys. 61, 361-368 (1983).
[CrossRef]

J. Mod. Opt. (1)

A. Thetford, “Absorbing multilayers and reflection interference filters,” J. Mod. Opt. 25, 945-961 (1978).
[CrossRef]

J. Opt. Soc. Am. (1)

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

S. S. Wang, R. Magnusson, J. S. Bagby, and M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A 8, 1470-1474 (1990).
[CrossRef]

Opt. Lett. (2)

Other (2)

http://semrock.com/Catalog/Raman_edgevsnotch.htm

Z. Knittl, Optics of Thin Films (Wiley, 1976), pp. 300-320.

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Figures (12)

Fig. 1
Fig. 1

(a) Reflection and (b) absorption spectra of the film structure sub | H ( L H ) 15 2 L ( H L ) 3 Cr β | air with various β.

Fig. 2
Fig. 2

Equivalent admittance of the film stack sub | H ( L H ) 15 2 L ( H L ) 3 Cr β , where (a)  β = 3 nm , (b)  β = 8 nm , (c)  β = 13 nm , and (d)  β = 18 nm . λ 0 = 632.8 nm .

Fig. 3
Fig. 3

Equivalent admittances of the film stacks (a)  sub | H ( L H ) 15 2 L ( H L ) 3 , (b)  sub | H ( L H ) 15 2 L ( H L ) 3 Cr 12.8 , and (c)  sub | H ( L H ) 15 2 L ( H L ) 3 Cr 12.8 0.84 H . The insets in the figures are the enlarged sections around λ 0 = 632.8 nm .

Fig. 4
Fig. 4

Reflection spectra of the structures sub | H ( L H ) 15 2 L ( H L ) 3 Cr 12.8 0.84 H | air and sub | H ( L H ) 15 2 L ( H L ) 3 Cr 12.8 0.813 H 0.91 L 1.588 H 0.779 L | air .

Fig. 5
Fig. 5

Performance of the structure sub | H ( L H ) 15 2 L ( H L ) 3 Cr 9.4 0.49 H 0.61 L | air .

Fig. 6
Fig. 6

(a) Reflection spectra of the structure sub | H ( L H ) m 1 2 L ( H L ) 5 Cr 9.4 0.49 H 0.61 L | air corresponding to different m 1 . (b) Enlargement of the reflection spectra around the central wavelength.

Fig. 7
Fig. 7

(a) Reflection spectra of the structure sub | H ( L H ) 15 2 L ( H L ) m 2 Cr 9.4 0.49 H 0.61 L | air with various m 2 , (b) Magnification of the spectra around the central wavelength.

Fig. 8
Fig. 8

Position of the reflection band with regard to the thickness of the spacer layer for the structure sub | H ( L H ) 15 α L ( H L ) 5 Cr 9.4 0.49 H 0.61 L | air .

Fig. 9
Fig. 9

Reflection spectra of the structure sub | H ( L H ) 15 2 L ( H L ) 5 Cr 9.4 0.49 H 0.61 L | air , where the curves correspond to various n and k of the Cr layer. The reflection curve corresponding to n and k obtained directly from Table 1 is also displayed.

Fig. 10
Fig. 10

Reflection spectra of the structure sub | H ( L H ) 15 2 L ( H L ) 5 Cr β 0.49 H 0.61 L | air with various thickness of the Cr layer.

Fig. 11
Fig. 11

Internal electric field intensity of the structure sub | H ( L H ) 15 2 L ( H L ) 5 Cr 9.4 0.49 H 0.61 L | air at 632.8 nm ; the inset is the enlarged section of the Cr layer, where the two vertical lines indicate the boundaries of the Cr layer.

Fig. 12
Fig. 12

Average electric field intensity and optical absorption in the Cr layer as a function of wavelength for the structure sub | H ( L H ) 15 2 L ( H L ) 5 Cr 9.4 0.49 H 0.61 L | air .

Tables (1)

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Table 1 Refractive Indices and Extinction Coefficients of the Cr Film

Equations (16)

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[ m 11 j m 12 j m 21 m 22 ] ,
[ B m C m ] = [ cos δ j sin δ / η j η sin δ cos δ ] = [ 1 j 2 π d / λ 4 π d n k / λ 1 ] ,
[ B m C m ] = [ 1 j p 2 p 1 1 ] .
[ B C ] = [ m 11 j m 12 j m 21 m 22 ] [ 1 j p 2 p 1 1 ] [ 1 Y r + j Y i ] = [ ( m 11 m 11 p 2 Y i m 12 Y i ) + j ( m 11 p 2 Y r + m 12 p 1 + m 12 Y r ) ( m 21 p 2 Y r + m 22 p 1 + m 22 Y r ) + j ( m 21 m 21 p 2 Y i + m 22 Y i ) ] ,
R = ( n 0 B C n 0 B + C ) ( n 0 B C n 0 B + C ) * = [ n 0 m 11 ( 1 p 2 Y i ) m 12 n 0 Y i + m 21 p 2 Y r m 22 ( p 1 + Y r ) ] 2 + [ m 11 n 0 p 2 Y r + m 12 n 0 ( p 1 + Y r ) m 21 ( 1 p 2 Y i ) m 22 Y i ] 2 [ n 0 m 11 ( 1 p 2 Y i ) m 12 n 0 Y i m 21 p 2 Y r + m 22 ( p 1 + Y r ) ] 2 + [ m 11 n 0 p 2 Y r + m 12 n 0 ( p 1 + Y r ) + m 21 ( 1 p 2 Y i ) + m 22 Y i ] 2 .
Y = Y r = n H 2 n S ( n H n L ) 2 ( m 1 m 2 ) .
x = 1 Y r = n S n H 2 ( n L n H ) 2 ( m 1 m 2 ) ,
R λ 0 = ( n 0 B C n 0 B + C ) ( n 0 B C n 0 B + C ) * = [ ( n 0 m 11 m 22 p 1 ) x + m 21 p 2 m 22 ] 2 + [ ( m 12 n 0 p 1 m 21 ) x + m 11 n 0 p 2 + m 12 n 0 ] 2 [ ( n 0 m 11 + m 22 p 1 ) x m 21 p 2 + m 22 ] 2 + [ ( m 12 n 0 p 1 + m 21 ) x + m 11 n 0 p 2 + m 12 n 0 ] 2 .
R = [ n 0 m 11 m 22 p 1 m 12 n 0 Y i ] 2 + [ m 12 n 0 p 1 m 21 m 22 Y i ] 2 [ n 0 m 11 + m 22 p 1 m 12 n 0 Y i ] 2 + [ m 12 n 0 p 1 + m 21 + m 22 Y i ] 2 .
Y i = b ± ( b 2 4 a c ) 1 / 2 2 a ,
a = [ ( m 12 n 0 ) 2 + m 22 2 ] , b = [ 2 n 0 m 11 m 12 n 0 + 6 m 22 p 1 m 12 n 0 6 m 12 n 0 p 1 m 22 + 2 m 21 m 22 ] , c = ( n 0 m 11 ) 2 + ( m 22 p 1 ) 2 + ( m 12 n 0 p 1 ) 2 + ( m 21 ) 2 6 n 0 m 11 m 22 p 1 6 m 12 n 0 p 1 m 21 .
ε = π 2 Δ λ λ 0 ,
Y i = n H n L ε ( 2 ( n H n L ) 2 m 2 + 1 1 ) .
2 Δ λ 1 / 2 = 4 λ 0 π 2 a A b ± ( b 2 4 a c ) 1 / 2 ,
A = n H n L ( 2 ( n H n L ) 2 m 2 + 1 1 ) .
R = ( η 0 B / C η 0 + B / C ) ( η 0 B / C η 0 + B / C ) * = ( η 0 Y η 0 + Y ) ( η 0 Y η 0 + Y ) * = ( η 0 Y r ) 2 + Y i 2 ( η 0 + Y r ) 2 + Y i 2 ,

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