Abstract

A triple-layer guided-mode resonance Brewster filter consisting of a homogeneous layer and two identical gratings with their refractive indices equal to that of the homogeneous layer is presented. The spectral properties of this filter are analyzed based on the coupling modulation of two identical binary gratings at Brewster angle for a TM-polarized wave. The grating layer between substrate and homogeneous layers can significantly change the linewidth and resonant mode position, which are due to the asymmetric field distribution inside the grating layers. The tunability of the resonance can be altered on different resonant channels and a practical filter can be obtained in TM2 waveguide mode. Variation of filling factor can alter the field localization in the grating structure and significantly adjust the linewidth of the filter.

© 2011 OSA

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    [CrossRef]
  8. A. K. Kodali, M. Schulmerich, J. Ip, G. Yen, B. T. Cunningham, and R. Bhargava, “Narrowband midinfrared reflectance filters using guided mode resonance,” Anal. Chem. 82(13), 5697–5706 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2010 (2)

A. K. Kodali, M. Schulmerich, J. Ip, G. Yen, B. T. Cunningham, and R. Bhargava, “Narrowband midinfrared reflectance filters using guided mode resonance,” Anal. Chem. 82(13), 5697–5706 (2010).
[CrossRef] [PubMed]

Q. Wang, D. W. Zhang, Y. S. Huang, Z. J. Ni, J. B. Chen, Y. W. Zhong, and S. L. Zhuang, “Type of tunable guided-mode resonance filter based on electro-optic characteristic of polymer-dispersed liquid crystal,” Opt. Lett. 35(8), 1236–1238 (2010).
[CrossRef] [PubMed]

2009 (2)

2008 (1)

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

2007 (1)

2006 (3)

Z. S. Wang, T. Sang, L. Wang, J. T. Zhu, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 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(24), 241119 (2006).
[CrossRef]

R. Magnusson and Y. Ding, “MENS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006).
[CrossRef]

2005 (2)

T. Kobayashi, Y. Kanamori, and K. Hane, “Surface laser emission from solid polymer dye in a guided mode resonant grating filter structure,” Appl. Phys. Lett. 87(15), 151106 (2005).
[CrossRef]

N. Kaiser, T. Feigl, O. Stenzel, U. Schulz, and M. Yang, “Optical coatings: trends and challenges,” Opt. Precis. Eng. 13(4), 389–396 (2005).

2004 (2)

W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004).
[CrossRef]

C. Kappel, A. Selle, M. A. Bader, and G. Marowsky, “Resonant double-grating waveguide structure as inverted Fabry-Perot interferometers,” J. Opt. Soc. Am. B 21(6), 1127–1136 (2004).
[CrossRef]

2003 (1)

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83(16), 3248–3250 (2003).
[CrossRef]

2002 (1)

2000 (2)

1998 (1)

1997 (2)

1996 (1)

1994 (3)

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

1901 (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. Phys. Soc. Lond. 18(1), 269–275 (1901).

Bader, M. A.

Bendickson, J. M.

Bhargava, R.

A. K. Kodali, M. Schulmerich, J. Ip, G. Yen, B. T. Cunningham, and R. Bhargava, “Narrowband midinfrared reflectance filters using guided mode resonance,” Anal. Chem. 82(13), 5697–5706 (2010).
[CrossRef] [PubMed]

Black, T. D.

R. Magnusson, S. S. Wang, T. D. Black, and A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antenn. Propag. 42(4), 567–569 (1994).
[CrossRef]

Britton, B.

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Brundrett, D. L.

Chateau, N.

Chen, J. B.

Chen, L. Y.

T. Sang, Z. S. Wang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Linewidth properties of double-layer surface-relief resonant Brewster filters with equal refractive index,” Opt. Express 15(15), 9659–9665 (2007).
[CrossRef] [PubMed]

Z. S. Wang, T. Sang, L. Wang, J. T. Zhu, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 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(24), 241119 (2006).
[CrossRef]

Cunningham, B. T.

A. K. Kodali, M. Schulmerich, J. Ip, G. Yen, B. T. Cunningham, and R. Bhargava, “Narrowband midinfrared reflectance filters using guided mode resonance,” Anal. Chem. 82(13), 5697–5706 (2010).
[CrossRef] [PubMed]

Ding, Y.

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

R. Magnusson and Y. Ding, “MENS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006).
[CrossRef]

Donkor, E.

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Fainman, Y.

W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004).
[CrossRef]

Feigl, T.

N. Kaiser, T. Feigl, O. Stenzel, U. Schulz, and M. Yang, “Optical coatings: trends and challenges,” Opt. Precis. Eng. 13(4), 389–396 (2005).

Friesem, A. A.

Gaylord, T. K.

Glytsis, E. N.

Hane, K.

T. Kobayashi, Y. Kanamori, and K. Hane, “Surface laser emission from solid polymer dye in a guided mode resonant grating filter structure,” Appl. Phys. Lett. 87(15), 151106 (2005).
[CrossRef]

Huang, Y. S.

Hugonin, J. P.

Ip, J.

A. K. Kodali, M. Schulmerich, J. Ip, G. Yen, B. T. Cunningham, and R. Bhargava, “Narrowband midinfrared reflectance filters using guided mode resonance,” Anal. Chem. 82(13), 5697–5706 (2010).
[CrossRef] [PubMed]

Kaiser, N.

N. Kaiser, T. Feigl, O. Stenzel, U. Schulz, and M. Yang, “Optical coatings: trends and challenges,” Opt. Precis. Eng. 13(4), 389–396 (2005).

Kanamori, Y.

T. Kobayashi, Y. Kanamori, and K. Hane, “Surface laser emission from solid polymer dye in a guided mode resonant grating filter structure,” Appl. Phys. Lett. 87(15), 151106 (2005).
[CrossRef]

Kappel, C.

Kim, S.

Kobayashi, T.

T. Kobayashi, Y. Kanamori, and K. Hane, “Surface laser emission from solid polymer dye in a guided mode resonant grating filter structure,” Appl. Phys. Lett. 87(15), 151106 (2005).
[CrossRef]

Kodali, A. K.

A. K. Kodali, M. Schulmerich, J. Ip, G. Yen, B. T. Cunningham, and R. Bhargava, “Narrowband midinfrared reflectance filters using guided mode resonance,” Anal. Chem. 82(13), 5697–5706 (2010).
[CrossRef] [PubMed]

LaComb, R.

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Lee, K. J.

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Li, L.

Liu, Z. S.

Magnusson, R.

H. Y. Song, S. Kim, and R. Magnusson, “Tunable guided-mode resonances in coupled gratings,” Opt. Express 17(26), 23544–23555 (2009).
[CrossRef]

Q. M. Ngo, S. Kim, S. H. Song, and R. Magnusson, “Optical bistable devices based on guided-mode resonance in slab waveguide gratings,” Opt. Express 17(26), 23459–23467 (2009).
[CrossRef]

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

R. Magnusson and Y. Ding, “MENS tunable resonant leaky mode filters,” IEEE Photon. Technol. Lett. 18(14), 1479–1481 (2006).
[CrossRef]

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83(16), 3248–3250 (2003).
[CrossRef]

D. Shin, Z. S. Liu, and R. Magnusson, “Resonant Brewster filters with absentee layers,” Opt. Lett. 27(15), 1288–1290 (2002).
[CrossRef]

R. Magnusson, D. Shin, and Z. S. Liu, “Guided-mode resonance Brewster filter,” Opt. Lett. 23(8), 612–614 (1998).
[CrossRef]

S. Tibuleac and R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14(7), 1617–1626 (1997).
[CrossRef]

S. S. Wang and R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19(12), 919–921 (1994).
[CrossRef] [PubMed]

R. Magnusson, S. S. Wang, T. D. Black, and A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antenn. Propag. 42(4), 567–569 (1994).
[CrossRef]

Maldonado, T. A.

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83(16), 3248–3250 (2003).
[CrossRef]

Marowsky, G.

Nakagawa, W.

W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004).
[CrossRef]

Nevière, M.

Ngo, Q. M.

Ni, Z. J.

Popov, E.

Priambodo, P. S.

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83(16), 3248–3250 (2003).
[CrossRef]

Rosenblatt, D.

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Sang, T.

T. Sang, Z. S. Wang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Linewidth properties of double-layer surface-relief resonant Brewster filters with equal refractive index,” Opt. Express 15(15), 9659–9665 (2007).
[CrossRef] [PubMed]

Z. S. Wang, T. Sang, L. Wang, J. T. Zhu, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 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(24), 241119 (2006).
[CrossRef]

Schulmerich, M.

A. K. Kodali, M. Schulmerich, J. Ip, G. Yen, B. T. Cunningham, and R. Bhargava, “Narrowband midinfrared reflectance filters using guided mode resonance,” Anal. Chem. 82(13), 5697–5706 (2010).
[CrossRef] [PubMed]

Schulz, U.

N. Kaiser, T. Feigl, O. Stenzel, U. Schulz, and M. Yang, “Optical coatings: trends and challenges,” Opt. Precis. Eng. 13(4), 389–396 (2005).

Selle, A.

Sharon, A.

Shin, D.

Shokooh-Saremi, M.

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Silva, H.

K. J. Lee, R. LaComb, B. Britton, M. Shokooh-Saremi, H. Silva, E. Donkor, Y. Ding, and R. Magnusson, “Silicon-layer guided-mode resonance polarizer with 40-nm bandwidth,” IEEE Photon. Technol. Lett. 20(22), 1857–1859 (2008).
[CrossRef]

Sohn, A.

R. Magnusson, S. S. Wang, T. D. Black, and A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antenn. Propag. 42(4), 567–569 (1994).
[CrossRef]

Song, H. Y.

Song, S. H.

Stenzel, O.

N. Kaiser, T. Feigl, O. Stenzel, U. Schulz, and M. Yang, “Optical coatings: trends and challenges,” Opt. Precis. Eng. 13(4), 389–396 (2005).

Tibuleac, S.

Wang, L.

T. Sang, Z. S. Wang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Linewidth properties of double-layer surface-relief resonant Brewster filters with equal refractive index,” Opt. Express 15(15), 9659–9665 (2007).
[CrossRef] [PubMed]

Z. S. Wang, T. Sang, L. Wang, J. T. Zhu, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 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(24), 241119 (2006).
[CrossRef]

Wang, Q.

Wang, S. S.

R. Magnusson, S. S. Wang, T. D. Black, and A. Sohn, “Resonance properties of dielectric waveguide gratings: theory and experiments at 4–18 GHz,” IEEE Trans. Antenn. Propag. 42(4), 567–569 (1994).
[CrossRef]

S. S. Wang and R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19(12), 919–921 (1994).
[CrossRef] [PubMed]

Wang, Z. S.

T. Sang, Z. S. Wang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Linewidth properties of double-layer surface-relief resonant Brewster filters with equal refractive index,” Opt. Express 15(15), 9659–9665 (2007).
[CrossRef] [PubMed]

Z. S. Wang, T. Sang, L. Wang, J. T. Zhu, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 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(24), 241119 (2006).
[CrossRef]

Wood, R. W.

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. Phys. Soc. Lond. 18(1), 269–275 (1901).

Wu, Y. G.

T. Sang, Z. S. Wang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Linewidth properties of double-layer surface-relief resonant Brewster filters with equal refractive index,” Opt. Express 15(15), 9659–9665 (2007).
[CrossRef] [PubMed]

Z. S. Wang, T. Sang, L. Wang, J. T. Zhu, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 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(24), 241119 (2006).
[CrossRef]

Yang, M.

N. Kaiser, T. Feigl, O. Stenzel, U. Schulz, and M. Yang, “Optical coatings: trends and challenges,” Opt. Precis. Eng. 13(4), 389–396 (2005).

Yen, G.

A. K. Kodali, M. Schulmerich, J. Ip, G. Yen, B. T. Cunningham, and R. Bhargava, “Narrowband midinfrared reflectance filters using guided mode resonance,” Anal. Chem. 82(13), 5697–5706 (2010).
[CrossRef] [PubMed]

Zhang, D. W.

Zhong, Y. W.

Zhu, J. T.

T. Sang, Z. S. Wang, J. T. Zhu, L. Wang, Y. G. Wu, and L. Y. Chen, “Linewidth properties of double-layer surface-relief resonant Brewster filters with equal refractive index,” Opt. Express 15(15), 9659–9665 (2007).
[CrossRef] [PubMed]

Z. S. Wang, T. Sang, L. Wang, J. T. Zhu, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 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(24), 241119 (2006).
[CrossRef]

Zhuang, S. L.

Anal. Chem. (1)

A. K. Kodali, M. Schulmerich, J. Ip, G. Yen, B. T. Cunningham, and R. Bhargava, “Narrowband midinfrared reflectance filters using guided mode resonance,” Anal. Chem. 82(13), 5697–5706 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett. (4)

T. Kobayashi, Y. Kanamori, and K. Hane, “Surface laser emission from solid polymer dye in a guided mode resonant grating filter structure,” Appl. Phys. Lett. 87(15), 151106 (2005).
[CrossRef]

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, “Fabrication and characterization of high-quality waveguide-mode resonant optical filters,” Appl. Phys. Lett. 83(16), 3248–3250 (2003).
[CrossRef]

Z. S. Wang, T. Sang, L. Wang, J. T. Zhu, Y. G. Wu, and L. Y. Chen, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88(25), 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(24), 241119 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

W. Nakagawa and Y. Fainman, “Tunable optical nanocavity based on modulation of near-field coupling between subwavelength periodic nanostructures,” IEEE J. Sel. Top. Quantum Electron. 10(3), 478–483 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

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Figures (7)

Fig. 1
Fig. 1

(Color online) Schematic diagram of the GMR Brewster filter. The high and low refractive indices of the identical gratings are nH = 2.25 and nL = 1.8, respectively. The filling factor of the grating is set to F = 0.5. The refractive indices of the cover, substrate and homogeneous layers are set to nc = 1.0, ns = 1.46 and nu = 1.99, respectively. The thickness of the triple-layer structure is d g 1 = d g 2 = 85.6 nm, du = 30 nm. The lateral alignment shift is denoted by S.

Fig. 2
Fig. 2

(Color online) (a) Angular response of a triple-layer GMR filter for a TM-polarized incident wave with the operating wavelength of 800 nm. (b) Spectral response of the triple-layer filter at the Brewster angle ( θ B = 57.13 ° ) indicated in (a). All the geometric parameters are given in Fig. 1.

Fig. 3
Fig. 3

(Color online) (a) Spectral response (solid curves) of the filter in Fig. 1 for a TM-polarized incidence at the Brewster angle (57.13°). The sum of (d g 1 + d u ) is kept constant for (dashed curves) dg1 = 65.6 nm and (dash-dotted curves) dg1 = 105.6 nm, the sum of (d u + d g 2) is kept constant for (short dashed curves) dg2 = 65.6 nm and (dash-dot-dotted curves) dg2 = 105.6 nm, respectively. Other parameters are the same as those in Fig. 2 except that (b) (dashed curve) θ B = 57.30 ° and (dash-dotted curve) θ B = 56.88 ° , (c) (short dashed curve) θ B = 57.35 ° and (dash-dot-dotted curve) θ B = 56.86 ° .

Fig. 4
Fig. 4

(Color online) Calculated reflectance as a function of thickness of the homogeneous layer at Brewster angle under TM polarization, other parameters are the same as those in Fig. 2.

Fig. 5
Fig. 5

(Color online) Calculated reflectance as a function of the lateral alignment shift S and wavelength at Brewster angle (57.13°) for (a) TM0, (b) TM1 and (c) TM2 guided-modes. (d) Calculated reflectance peak as a function of the lateral alignment shift S for TM0 (squares), TM1 (circles) and TM2 (up triangles) guided-modes. Other parameters are the same as those in Fig. 2.

Fig. 6
Fig. 6

(Color online) Reflection spectral response of the triple-layer filter for (a) TM0, (b) TM1 and (c) TM2 guided-modes under different alignment conditions: (solid curves) perfect alignment (S = 0), (dashed curves) quarter-period shifted (S = 0.25), and (dotted curves) half-period shifted (S = 0.5). Other parameters are the same as those in Fig. 2.

Fig. 7
Fig. 7

(Color online) Reflection spectral response of the triple-layer Brewster filter for (a) F = 0.1 and (b) F = 0.9 under different alignment conditions: (solid curves) perfect alignment (S = 0), (dashed curves) quarter-period shifted (S = 0.25), and (dotted curves) half-period shifted (S = 0.5). The other parameters are the same as those in Fig. 2 except the period of the grating: (a) Λ = 342.10  nm and (b) Λ = 321.71  nm .

Tables (1)

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Table 1 Key Parameters of Spectral Response in Fig. 3(a)

Equations (4)

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ε eff , TM ( 2 ) = ε eff , TM ( 0 ) + π 2 3 F 2 ( 1 F ) 2 ( 1 ε H 1 ε L ) 2 ( ε eff , TM ( 0 ) ) 3 ε eff , TE ( 0 ) ( Λ λ 0 ) 2 ,
ε eff , TE ( 0 ) = F ε H + ( 1 F ) ε L ε eff , TM ( 0 ) = ε H ε L / [ F ε L + ( 1 F ) ε H ] .
n eff , TM = { ε H ε L / [ F ε L + ( 1 F ) ε H ] } 1 / 2 .
[ H z y ] = 1 / k 2 1 [ E ˜ x ] [ E ˜ x y ] = α k 2 1 α [ H z ] [ H z ] ,

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