Abstract

In this paper, double-layer surface-relief resonant Brewster filters consisting of a homogenous layer and a grating with equal refractive index are obtained by adjusting the grating filling factor, and linewidth properties of these types of filters are investigated. It is shown etch depth error does not change the filter linewidth, but the grating filling factor and the substrate refractive index can significantly change the filter linewidth. Moreover, the coupling strength can be appreciately affected by the homogeneous layer thickness, and one can obtain different linewidths at the same operating wavelength by selecting different homogeneous layer thickness with other physical parameters maintained.

© 2007 Optical Society of America

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  1. R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
    [CrossRef]
  2. Y. Ding and R. Magnusson, "Band gaps and leaky-wave effects in resonant photonic-crystal waveguides," Opt. Express 15, 680-694 (2007).
    [CrossRef] [PubMed]
  3. S. S. Wang and R. Magnusson, "Theory and applications of guided-mode resonance filters," Appl. Opt. 32,2606-2613 (1993).
    [CrossRef] [PubMed]
  4. Y. Ding and R. Magnusson, "Use of nondegenerate resonant leaky modes to fashion diverse optical spectra," Opt. Express 12, 1885-1891 (2004)
    [CrossRef] [PubMed]
  5. S. Tibuleac and R. Magnusson, "Reflection and transmission guided-mode resonance filter," J. Opt. Soc. Am. A 14, 1617-1626 (1997).
    [CrossRef]
  6. Y. Ding and R. Magnusson, "Doubly-resonant single-layer bandpass optical filters," Opt. Lett. 29, 1135-1137 (2004).
    [CrossRef] [PubMed]
  7. G. Niederer, W. Nakagawa, H. Herzig, and H. Thiele, "Design and characterization of a tunable polarization-independent resonant grating filter," Opt. Express 13, 2196-2200 (2005)
    [CrossRef] [PubMed]
  8. R. Magnusson and Y. Ding, "MEMS Tunable Resonant Leaky Mode Filters," IEEE Photon. Technol. Lett. 18, 1479-1481 (2006).
    [CrossRef]
  9. P. S. Priambodo, T. A. Maldonado, and R. Magnusson, "Fabrication and characterization of high-quality waveguide-mode resonant optical filters," Appl. Phys. Lett. 83, 3248-3250 (2003).
    [CrossRef]
  10. 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, 151106 (2005).
    [CrossRef]
  11. M. C. Y. Huang, Y. Zhou, and C. J . Chang- Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photonic 1,119-122 (2007).
    [CrossRef]
  12. A. -L. Fehrembach and A. Sentenac, "Unpolarized narrow-band filtering with resonant gratings," Appl. Phys. Lett. 86,121105 (2005).
    [CrossRef]
  13. A. Mizutani, H. Kikuta, and K. Iwata, "Numerical study on an asymmetric guided-mode resonant grating with a Kerr medium for optical switching," J. Opt. Soc. Am. A 22, 355-360 (2005).
    [CrossRef]
  14. T. Katchalski, G. Levy-Yurista, A. Friesem, G. Martin, R. Hierle, and J. Zyss, "Light modulation with electro-optic polymer-based resonant grating waveguide structures," Opt. Express 13, 4645-4650 (2005)
    [CrossRef] [PubMed]
  15. R. Magnusson, D. Shin, and Z. S. Liu, "Guided-mode resonance Brewster filter," Opt. Lett. 23, 612-614 (1998).
    [CrossRef]
  16. D. Shin, Z. S. Liu, and R. Magnusson, "Resonant Brewster filters with absentee layers," Opt. Lett. 27, 1288-1290 (2002).
    [CrossRef]
  17. Z. Wang, T. Sang, L. Wang, J. Zhu, Y. Wu, and L. Chen, "Guided-mode resonance Brewster filters with multiple channels," Appl. Phys. Lett. 88, 251115 (2006).
    [CrossRef]
  18. J. S. Ye, Y. Kanamori, F.-R. Hu, and K. Hane, "Rigorous reflectance performance analysis of Si3N4 self-suspended subwavelength gratings," Opt. Commun. 270,233-237 (2007).
    [CrossRef]
  19. Z. Wang, T. Sang, J. Zhu, L. Wang, Y. Wu, and L. 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]
  20. S. M. Rytov, "Electromagnetic properties of a finely stratified medium," Sov. Phys. JETP 2, 466-475 (1956).
  21. H. A. Macleod, Thin-film optical filter, 2th edition (McGraw-Hill, New York, 1989).
  22. T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
    [CrossRef]
  23. D. Rosenblatt, A. Sharon, and A. A. Friesem, "Resonant grating waveguide structures," IEEE J. Quantum Electron. 33,2038-2059 (1997).
    [CrossRef]
  24. D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, and J. M. Bendickson, "Effects of modulation strength in guided-mode resonant subwavelength gratings at normal incidence," J. Opt. Soc. Am. A 17, 1221-1230 (2000).
    [CrossRef]
  25. Z. S. Liu and R. Magnusson, "Concept of multiorder multimode resonant optical filters," IEEE Photonics Tech. Lett. 14, 1091-1093 (2002).
    [CrossRef]

2007 (3)

Y. Ding and R. Magnusson, "Band gaps and leaky-wave effects in resonant photonic-crystal waveguides," Opt. Express 15, 680-694 (2007).
[CrossRef] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J . Chang- Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photonic 1,119-122 (2007).
[CrossRef]

J. S. Ye, Y. Kanamori, F.-R. Hu, and K. Hane, "Rigorous reflectance performance analysis of Si3N4 self-suspended subwavelength gratings," Opt. Commun. 270,233-237 (2007).
[CrossRef]

2006 (3)

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

R. Magnusson and Y. Ding, "MEMS Tunable Resonant Leaky Mode Filters," IEEE Photon. Technol. Lett. 18, 1479-1481 (2006).
[CrossRef]

2005 (5)

2004 (2)

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, 3248-3250 (2003).
[CrossRef]

2002 (2)

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

Z. S. Liu and R. Magnusson, "Concept of multiorder multimode resonant optical filters," IEEE Photonics Tech. Lett. 14, 1091-1093 (2002).
[CrossRef]

2000 (1)

1998 (1)

1997 (2)

S. Tibuleac and R. Magnusson, "Reflection and transmission guided-mode resonance filter," J. Opt. Soc. Am. A 14, 1617-1626 (1997).
[CrossRef]

D. Rosenblatt, A. Sharon, and A. A. Friesem, "Resonant grating waveguide structures," IEEE J. Quantum Electron. 33,2038-2059 (1997).
[CrossRef]

1993 (1)

1992 (1)

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

1985 (1)

T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
[CrossRef]

1956 (1)

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

Bendickson, J. M.

Brundrett, D. L.

Chang- Hasnain, C. J

M. C. Y. Huang, Y. Zhou, and C. J . Chang- Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photonic 1,119-122 (2007).
[CrossRef]

Chen, L.

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

Ding, Y.

Fehrembach, A. -L.

A. -L. Fehrembach and A. Sentenac, "Unpolarized narrow-band filtering with resonant gratings," Appl. Phys. Lett. 86,121105 (2005).
[CrossRef]

Friesem, A.

Friesem, A. A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, "Resonant grating waveguide structures," IEEE J. Quantum Electron. 33,2038-2059 (1997).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Hane, K.

J. S. Ye, Y. Kanamori, F.-R. Hu, and K. Hane, "Rigorous reflectance performance analysis of Si3N4 self-suspended subwavelength gratings," Opt. Commun. 270,233-237 (2007).
[CrossRef]

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, 151106 (2005).
[CrossRef]

Herzig, H.

Hierle, R.

Hu, F.-R.

J. S. Ye, Y. Kanamori, F.-R. Hu, and K. Hane, "Rigorous reflectance performance analysis of Si3N4 self-suspended subwavelength gratings," Opt. Commun. 270,233-237 (2007).
[CrossRef]

Huang, M. C. Y.

M. C. Y. Huang, Y. Zhou, and C. J . Chang- Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photonic 1,119-122 (2007).
[CrossRef]

Iwata, K.

Kanamori, Y.

J. S. Ye, Y. Kanamori, F.-R. Hu, and K. Hane, "Rigorous reflectance performance analysis of Si3N4 self-suspended subwavelength gratings," Opt. Commun. 270,233-237 (2007).
[CrossRef]

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, 151106 (2005).
[CrossRef]

Katchalski, T.

Kikuta, H.

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, 151106 (2005).
[CrossRef]

Levy-Yurista, G.

Liu, Z. S.

Magnusson, R.

Y. Ding and R. Magnusson, "Band gaps and leaky-wave effects in resonant photonic-crystal waveguides," Opt. Express 15, 680-694 (2007).
[CrossRef] [PubMed]

R. Magnusson and Y. Ding, "MEMS Tunable Resonant Leaky Mode Filters," IEEE Photon. Technol. Lett. 18, 1479-1481 (2006).
[CrossRef]

Y. Ding and R. Magnusson, "Doubly-resonant single-layer bandpass optical filters," Opt. Lett. 29, 1135-1137 (2004).
[CrossRef] [PubMed]

Y. Ding and R. Magnusson, "Use of nondegenerate resonant leaky modes to fashion diverse optical spectra," Opt. Express 12, 1885-1891 (2004)
[CrossRef] [PubMed]

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

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

Z. S. Liu and R. Magnusson, "Concept of multiorder multimode resonant optical filters," IEEE Photonics Tech. Lett. 14, 1091-1093 (2002).
[CrossRef]

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

S. Tibuleac and R. Magnusson, "Reflection and transmission guided-mode resonance filter," J. Opt. Soc. Am. A 14, 1617-1626 (1997).
[CrossRef]

S. S. Wang and R. Magnusson, "Theory and applications of guided-mode resonance filters," Appl. Opt. 32,2606-2613 (1993).
[CrossRef] [PubMed]

R. Magnusson and S. S. Wang, "New principle for optical filters," Appl. Phys. Lett. 61, 1022-1024 (1992).
[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, 3248-3250 (2003).
[CrossRef]

Martin, G.

Mizutani, A.

Moharam, M. G.

T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
[CrossRef]

Nakagawa, W.

Niederer, G.

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, 3248-3250 (2003).
[CrossRef]

Rosenblatt, D.

D. Rosenblatt, A. Sharon, and A. A. Friesem, "Resonant grating waveguide structures," IEEE J. Quantum Electron. 33,2038-2059 (1997).
[CrossRef]

Rytov, S. M.

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

Sang, T.

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

Z. Wang, T. Sang, J. Zhu, L. Wang, Y. Wu, and L. 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]

Sentenac, A.

A. -L. Fehrembach and A. Sentenac, "Unpolarized narrow-band filtering with resonant gratings," Appl. Phys. Lett. 86,121105 (2005).
[CrossRef]

Sharon, A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, "Resonant grating waveguide structures," IEEE J. Quantum Electron. 33,2038-2059 (1997).
[CrossRef]

Shin, D.

Thiele, H.

Tibuleac, S.

Wang, L.

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

Z. Wang, T. Sang, J. Zhu, L. Wang, Y. Wu, and L. 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, "Theory and applications of guided-mode resonance filters," Appl. Opt. 32,2606-2613 (1993).
[CrossRef] [PubMed]

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

Wang, Z.

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

Z. Wang, T. Sang, J. Zhu, L. Wang, Y. Wu, and L. 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]

Wu, Y.

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

Z. Wang, T. Sang, J. Zhu, L. Wang, Y. Wu, and L. 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]

Ye, J. S.

J. S. Ye, Y. Kanamori, F.-R. Hu, and K. Hane, "Rigorous reflectance performance analysis of Si3N4 self-suspended subwavelength gratings," Opt. Commun. 270,233-237 (2007).
[CrossRef]

Zhou, Y.

M. C. Y. Huang, Y. Zhou, and C. J . Chang- Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photonic 1,119-122 (2007).
[CrossRef]

Zhu, J.

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

Zyss, J.

Appl. Opt. (1)

Appl. Phys. Lett. (6)

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

A. -L. Fehrembach and A. Sentenac, "Unpolarized narrow-band filtering with resonant gratings," Appl. Phys. Lett. 86,121105 (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, 3248-3250 (2003).
[CrossRef]

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, 151106 (2005).
[CrossRef]

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

Z. Wang, T. Sang, J. Zhu, L. Wang, Y. Wu, and L. 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]

IEEE J. Quantum Electron. (1)

D. Rosenblatt, A. Sharon, and A. A. Friesem, "Resonant grating waveguide structures," IEEE J. Quantum Electron. 33,2038-2059 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

R. Magnusson and Y. Ding, "MEMS Tunable Resonant Leaky Mode Filters," IEEE Photon. Technol. Lett. 18, 1479-1481 (2006).
[CrossRef]

IEEE Photonics Tech. Lett. (1)

Z. S. Liu and R. Magnusson, "Concept of multiorder multimode resonant optical filters," IEEE Photonics Tech. Lett. 14, 1091-1093 (2002).
[CrossRef]

J. Opt. Soc. Am. A (3)

Nature Photonic (1)

M. C. Y. Huang, Y. Zhou, and C. J . Chang- Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photonic 1,119-122 (2007).
[CrossRef]

Opt. Commun. (1)

J. S. Ye, Y. Kanamori, F.-R. Hu, and K. Hane, "Rigorous reflectance performance analysis of Si3N4 self-suspended subwavelength gratings," Opt. Commun. 270,233-237 (2007).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Proc. IEEE (1)

T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894-937 (1985).
[CrossRef]

Sov. Phys. JETP (1)

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

Other (1)

H. A. Macleod, Thin-film optical filter, 2th edition (McGraw-Hill, New York, 1989).

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Figures (7)

Fig. 1.
Fig. 1.

Schematic diagram of a double layer zero-order dielectric grating under TM illumination with rectangular refractive-index profile of high (n1H) and low (n1L) index with period Λ and thickness dg, the incident angle is θ, and the grating filling factor is f. The homogeneous layer’s thickness and its refractive index are d l and n2, respectively. The refractive index of cover and substrate are nc and ns, respectively.

Fig. 2.
Fig. 2.

Response of a double-layer surface-relief resonant Brewster filter consisting of a homogeneous layer with a refractive index equal to that of the grating for an incident TM-polarized wave at 650-nm wavelength. The parameters are nc=n1L=1.0, n1H=2.05, n2=neff=1.63, ns=1.46, f=0.82, dg=100 nm, d l =99 nm, and Λ=281.51 nm.

Fig. 3.
Fig. 3.

Effects of underetching and overetching, and other parameters are the same as in Fig. 2. (a) Etch depth error on spectral response for the TM-polarized wave incident at the Brewster angle (56.72°). (b) The spectral shifts are adjusted by using angle tuning. Underetching 10 nm and 20 nm correspond to the incident angle of 56.41° and 56.09°, respectively. Overetching 10 nm and 20 nm correspond to the incident angle of 56.97° and 57.22°, respectively.

Fig. 4.
Fig. 4.

Spectral response as a function of the grating filling factor (f) at the Brewster angle (56.72°), and other parameters are the same as in Fig. 2.

Fig. 5.
Fig. 5.

Spectral response as a function of the substrate refractive index (ns) at the Brewster angle (56.72°), and other parameters are the same as in Fig. 2.

Fig. 6.
Fig. 6.

Reflectance as a function of the homogeneous layer thickness at the Brewster angle of 56.72° for an incident TM-polarized wave at 650 nm wavelength, and other parameters are the same as in Fig. 2.

Fig. 7.
Fig. 7.

Spectral response as a function of the homogenous layer thickness (d l ) at the Brewster angle (56.72°), and other parameters are the same as in Fig. 2.

Equations (2)

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

n eff = { n 1 H 2 · n 1 L 2 [ f · n 1 L 2 + ( 1 f ) · n 1 H 2 ] } 1 2
f = n 1 H 2 · ( n eff 2 n 1 L 2 ) [ n eff 2 · ( n 1 H 2 n 1 L 2 ) ]

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