Abstract

In this work, a single-layer, multiple-channel guided mode resonance (GMR) Brewster filter with controllable spectral separation is proposed using the plane waveguide method and rigorous coupled-wave analysis. Based on the normalized eigenvalue equation, the controllability of the spectral separation is analyzed when the fill ratio of the grating layer is changed while its effective index is identical to that of the substrate. The location and the separation between resonances can be specifically controlled by modifying the fill ratio of the grating layer. In contrast to the ordinary GMR filter, where the location of the resonances is material dependent, it is demonstrated that the spectral separation for the first and second resonances can be linearly controlled by altering the fill ratio of the grating layer. In addition, the maximal shift of the second resonance is up to 5% of the first resonant wavelength using the single-layer Brewster filter.

© 2014 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. A. Sharon, D. Rosenblatt, and A. A. Friesem, “Resonant grating–waveguide structures for visible and near-infrared radiation,” J. Opt. Soc. Am. A 14, 2985–2993 (1997).
    [CrossRef]
  3. W. Suh and S. Fan, “All-pass transmission or flattop reflection filters using a single photonic crystal slab,” Appl. Phys. Lett. 84, 4905–4907 (2004).
    [CrossRef]
  4. 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. Antennas Propag. 42, 567–569 (1994).
    [CrossRef]
  5. 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]
  6. 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]
  7. D. Wawro, S. Tibuleac, R. Magnusson, and H. Liu, “Optical fiber endface biosensor based on resonances in dielectric waveguide gratings,” Proc. SPIE 3911, 86–94 (2000).
    [CrossRef]
  8. M. Cooper, “Optical biosensors in drug discovery,” Nat. Rev. Drug Discov. 1, 515–528 (2002).
    [CrossRef]
  9. B. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators B 81, 316–328 (2002).
    [CrossRef]
  10. R. Magnusson, D. Shin, and Z. S. Liu, “Guided-mode resonance Brewster filter,” Opt. Lett. 23, 612–614 (1998).
    [CrossRef]
  11. D. Shin, Z. S. Liu, and R. Magnusson, “Resonant Brewster filters with absentee layers,” Opt. Lett. 27, 1288–1290 (2002).
    [CrossRef]
  12. Z. Wang, T. Sang, L. Wang, J. Zhu, and Y. Wu, “Guided-mode resonance Brewster filters with multiple channels,” Appl. Phys. Lett. 88, 251115 (2006).
    [CrossRef]
  13. T. Sang, Z. Wang, J. Zhu, L. Wang, Y. Wu, and L. Chen, “Linewidth properties of double-layer surface relief resonant Brewster filters with equal refractive index,” Opt. Express 15, 9659–9665 (2007).
    [CrossRef]
  14. J.-Y. Ma, S.-J. Liu, D.-W. Zhang, J.-K. Yao, C. Xu, Y.-X. Jin, J.-D. Shao, and Z.-X. Fan, “Surface relief resonant Brewster filters with multiple channels,” Chin. Phys. B 17, 3704 (2008).
    [CrossRef]
  15. T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
    [CrossRef]
  16. S. S. Wang and R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995).
    [CrossRef]
  17. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

2008 (1)

J.-Y. Ma, S.-J. Liu, D.-W. Zhang, J.-K. Yao, C. Xu, Y.-X. Jin, J.-D. Shao, and Z.-X. Fan, “Surface relief resonant Brewster filters with multiple channels,” Chin. Phys. B 17, 3704 (2008).
[CrossRef]

2007 (1)

2006 (1)

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

2005 (1)

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]

2004 (1)

W. Suh and S. Fan, “All-pass transmission or flattop reflection filters using a single photonic crystal slab,” Appl. Phys. Lett. 84, 4905–4907 (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, 3248–3250 (2003).
[CrossRef]

2002 (3)

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

M. Cooper, “Optical biosensors in drug discovery,” Nat. Rev. Drug Discov. 1, 515–528 (2002).
[CrossRef]

B. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators B 81, 316–328 (2002).
[CrossRef]

2000 (1)

D. Wawro, S. Tibuleac, R. Magnusson, and H. Liu, “Optical fiber endface biosensor based on resonances in dielectric waveguide gratings,” Proc. SPIE 3911, 86–94 (2000).
[CrossRef]

1998 (1)

1997 (1)

1995 (1)

1994 (1)

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. Antennas Propag. 42, 567–569 (1994).
[CrossRef]

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).

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. Antennas Propag. 42, 567–569 (1994).
[CrossRef]

Chen, L.

Cooper, M.

M. Cooper, “Optical biosensors in drug discovery,” Nat. Rev. Drug Discov. 1, 515–528 (2002).
[CrossRef]

Cunningham, B.

B. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators B 81, 316–328 (2002).
[CrossRef]

Fan, S.

W. Suh and S. Fan, “All-pass transmission or flattop reflection filters using a single photonic crystal slab,” Appl. Phys. Lett. 84, 4905–4907 (2004).
[CrossRef]

Fan, Z.-X.

J.-Y. Ma, S.-J. Liu, D.-W. Zhang, J.-K. Yao, C. Xu, Y.-X. Jin, J.-D. Shao, and Z.-X. Fan, “Surface relief resonant Brewster filters with multiple channels,” Chin. Phys. B 17, 3704 (2008).
[CrossRef]

Friesem, A. A.

Gaylord, T. K.

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

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, 151106 (2005).
[CrossRef]

Jin, Y.-X.

J.-Y. Ma, S.-J. Liu, D.-W. Zhang, J.-K. Yao, C. Xu, Y.-X. Jin, J.-D. Shao, and Z.-X. Fan, “Surface relief resonant Brewster filters with multiple channels,” Chin. Phys. B 17, 3704 (2008).
[CrossRef]

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, 151106 (2005).
[CrossRef]

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]

Li, P.

B. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators B 81, 316–328 (2002).
[CrossRef]

Lin, B.

B. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators B 81, 316–328 (2002).
[CrossRef]

Liu, H.

D. Wawro, S. Tibuleac, R. Magnusson, and H. Liu, “Optical fiber endface biosensor based on resonances in dielectric waveguide gratings,” Proc. SPIE 3911, 86–94 (2000).
[CrossRef]

Liu, S.-J.

J.-Y. Ma, S.-J. Liu, D.-W. Zhang, J.-K. Yao, C. Xu, Y.-X. Jin, J.-D. Shao, and Z.-X. Fan, “Surface relief resonant Brewster filters with multiple channels,” Chin. Phys. B 17, 3704 (2008).
[CrossRef]

Liu, Z. S.

Ma, J.-Y.

J.-Y. Ma, S.-J. Liu, D.-W. Zhang, J.-K. Yao, C. Xu, Y.-X. Jin, J.-D. Shao, and Z.-X. Fan, “Surface relief resonant Brewster filters with multiple channels,” Chin. Phys. B 17, 3704 (2008).
[CrossRef]

Magnusson, R.

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]

D. Wawro, S. Tibuleac, R. Magnusson, and H. Liu, “Optical fiber endface biosensor based on resonances in dielectric waveguide gratings,” Proc. SPIE 3911, 86–94 (2000).
[CrossRef]

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

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

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. Antennas Propag. 42, 567–569 (1994).
[CrossRef]

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]

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]

Pepper, J.

B. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators B 81, 316–328 (2002).
[CrossRef]

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.

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

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

Shao, J.-D.

J.-Y. Ma, S.-J. Liu, D.-W. Zhang, J.-K. Yao, C. Xu, Y.-X. Jin, J.-D. Shao, and Z.-X. Fan, “Surface relief resonant Brewster filters with multiple channels,” Chin. Phys. B 17, 3704 (2008).
[CrossRef]

Sharon, A.

Shin, D.

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. Antennas Propag. 42, 567–569 (1994).
[CrossRef]

Suh, W.

W. Suh and S. Fan, “All-pass transmission or flattop reflection filters using a single photonic crystal slab,” Appl. Phys. Lett. 84, 4905–4907 (2004).
[CrossRef]

Tibuleac, S.

D. Wawro, S. Tibuleac, R. Magnusson, and H. Liu, “Optical fiber endface biosensor based on resonances in dielectric waveguide gratings,” Proc. SPIE 3911, 86–94 (2000).
[CrossRef]

Wang, L.

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

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

Wang, S. S.

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

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. Antennas Propag. 42, 567–569 (1994).
[CrossRef]

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

Wang, Z.

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

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

Wawro, D.

D. Wawro, S. Tibuleac, R. Magnusson, and H. Liu, “Optical fiber endface biosensor based on resonances in dielectric waveguide gratings,” Proc. SPIE 3911, 86–94 (2000).
[CrossRef]

Wu, Y.

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

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

Xu, C.

J.-Y. Ma, S.-J. Liu, D.-W. Zhang, J.-K. Yao, C. Xu, Y.-X. Jin, J.-D. Shao, and Z.-X. Fan, “Surface relief resonant Brewster filters with multiple channels,” Chin. Phys. B 17, 3704 (2008).
[CrossRef]

Yao, J.-K.

J.-Y. Ma, S.-J. Liu, D.-W. Zhang, J.-K. Yao, C. Xu, Y.-X. Jin, J.-D. Shao, and Z.-X. Fan, “Surface relief resonant Brewster filters with multiple channels,” Chin. Phys. B 17, 3704 (2008).
[CrossRef]

Zhang, D.-W.

J.-Y. Ma, S.-J. Liu, D.-W. Zhang, J.-K. Yao, C. Xu, Y.-X. Jin, J.-D. Shao, and Z.-X. Fan, “Surface relief resonant Brewster filters with multiple channels,” Chin. Phys. B 17, 3704 (2008).
[CrossRef]

Zhu, J.

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

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

Appl. Opt. (1)

Appl. Phys. Lett. (5)

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

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

W. Suh and S. Fan, “All-pass transmission or flattop reflection filters using a single photonic crystal slab,” Appl. Phys. Lett. 84, 4905–4907 (2004).
[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]

Chin. Phys. B (1)

J.-Y. Ma, S.-J. Liu, D.-W. Zhang, J.-K. Yao, C. Xu, Y.-X. Jin, J.-D. Shao, and Z.-X. Fan, “Surface relief resonant Brewster filters with multiple channels,” Chin. Phys. B 17, 3704 (2008).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

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. Antennas Propag. 42, 567–569 (1994).
[CrossRef]

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

Nat. Rev. Drug Discov. (1)

M. Cooper, “Optical biosensors in drug discovery,” Nat. Rev. Drug Discov. 1, 515–528 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

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]

Proc. SPIE (1)

D. Wawro, S. Tibuleac, R. Magnusson, and H. Liu, “Optical fiber endface biosensor based on resonances in dielectric waveguide gratings,” Proc. SPIE 3911, 86–94 (2000).
[CrossRef]

Sens. Actuators B (1)

B. Cunningham, P. Li, B. Lin, and J. Pepper, “Colorimetric resonant reflection as a direct biochemical assay technique,” Sens. Actuators B 81, 316–328 (2002).
[CrossRef]

Sov. Phys. JETP (1)

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

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Figures (6)

Fig. 1.
Fig. 1.

Structure of single-layer GMR grating under TM illumination at Brewster angle. The high and low refractive indices of the grating structure are labeled as nh and nl, respectively. The refractive indices of cover and substrate are denoted to be nc and ns, respectively. The depth of the grating structure is expressed as d.

Fig. 2.
Fig. 2.

Resonance curves with respect to the normalized wavelength and thickness (d). The calculations are based on the normalized eigenfunction of a single-layer homogenous grating, and the refractive index of the substrate stays the same as that of the grating layer; other parameters are nh=2.48, nl=1.46, and nc=1. (a) f=0.1, (b) f=0.3, (c) f=0.5, (d) f=0.7, and (e) f=0.9.

Fig. 3.
Fig. 3.

Normalized wavelength gap of the first two resonant wavelengths with respect to the fill ratio; the parameters are the same as those in Fig. 2.

Fig. 4.
Fig. 4.

Controllability of the wavelength gap with regard to the first resonance wavelength; the parameters are the same as those in Fig. 2.

Fig. 5.
Fig. 5.

(a)–(d) Spectral responses of the Brewster GMR filters for the different fill ratio; the calculation parameters are listed in Table 1.

Fig. 6.
Fig. 6.

Spectral distribution of the Brewster GMR filter under variation of the Brewster angle; the calculation parameters are f=0.5, d=1612nm, and T=578nm.

Tables (1)

Tables Icon

Table 1. Parameters for Multiple Channel Filters with Different Fill Ratios

Equations (4)

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

tan(kd)=k(γ+δ)k2γδ,
βv/k0|m|λ/T,
tan(2πdTλTkm,v)km,v(γm,v+δm,v)km,v2γm,vδm,v=0.
neff={nh2nl2/[fnl2+(1f)nh2]}1/2.

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