Abstract

We describe a new structure of guided-mode resonant grating (GMRG) filters with low sideband reflectance. This GMRG filter consists of a high-index thin film on an antireflective structured surface called “moth-eye structure.” Since the high-index film undulates along the surface structure, the film acts as a modulated optical waveguide. An incident light wave satisfying a resonant condition is reflected by the GMRG filter, and nonresonant light waves pass through the filter. This GMRG filter is valid for reducing reflection of nonresonant light waves in a wide spectral range. The resonant reflection of this new filter was investigated by numerical calculation based on an electromagnetic grating analysis. In the case of a triangular antireflective surface structure whose thickness is 2× greater than its period, the sideband reflectance for nonresonant light waves was lower than 0.5% for TM-polarized light in a wide range of wavelengths.

© 2002 Optical Society of America

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  1. R. Magnusson, S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61, 1022–1024 (1992).
    [CrossRef]
  2. L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
    [CrossRef]
  3. Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett. 23, 1556–1558 (1998).
    [CrossRef]
  4. R. Magnusson, S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Opt. 34, 8106–8109 (1995).
    [CrossRef] [PubMed]
  5. S. S. Wang, R. Magnusson, “Design of waveguide-grating filters with symmetrical line shapes and low sidebands,” Opt. Lett. 19, 919–921 (1994).
    [CrossRef] [PubMed]
  6. D. Shin, S. Tibuleac, T. A. Maldonado, R. Magnusson, “Thin-film multilayer optical filters containing diffractive elements and waveguides,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 273–286 (1997).
    [CrossRef]
  7. R. Magnusson, D. Shin, Z. S. Liu, “Guided-mode resonance Brewster filter,” Opt. Lett. 23, 612–614 (1998).
    [CrossRef]
  8. S. S. Wang, R. Magnusson, “Multilayer waveguide-grating filters,” Appl. Opt. 34, 2414–2420 (1995).
    [CrossRef] [PubMed]
  9. See, for example, E. Hecht, “Antireflection coatings” in Optics, 3rd ed. (Addison Wesley, Boston, Mass., 1998)
  10. Z. Hegedus, R. Netterfield, “Low sideband guided-mode resonant filter,” Appl. Opt. 39, 1469–1473 (2000).
    [CrossRef]
  11. M. Auslender, D. Levy, S. Hava, “One-dimensional antireflection gratings in (100) silicon: a numerical study,” Appl. Opt. 37, 369–373 (1998).
    [CrossRef]
  12. S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth-eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
    [CrossRef]
  13. T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity homogeneous layers and high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
    [CrossRef]
  14. E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
    [CrossRef] [PubMed]
  15. D. H. Raguin, G. M. Morris, “Antireflection structured surface for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
    [CrossRef] [PubMed]
  16. D. H. Raguin, G. M. Morris, “Analysis of antireflection-structured surfaces with continuous one-dimensional surface profiles,” Appl. Opt. 32, 2582–2598 (1993).
    [CrossRef] [PubMed]
  17. M. E. Motamedi, W. H. Southwell, W. J. Gunning, “Antireflection surfaces in silicon using binary optics technology,” Appl. Opt. 31, 4371–4376 (1992).
    [CrossRef] [PubMed]
  18. H. Toyota, K. Takahara, M. Okano, T. Yotsuya, H. Kikuta, “Fabrication of micro-cone array for antireflection structured surface using metal dotted pattern,” Jpn. J. Appl. Phys. 40, Part 2, 7B, L747–L749 (2001).
    [CrossRef]
  19. D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, “Homogeneous layer models for high-spatial-frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33, 2695–2706 (1994).
    [CrossRef] [PubMed]
  20. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
    [CrossRef]
  21. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
    [CrossRef]
  22. P. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structure,” J. Mod. Opt. 43, 2063–2085 (1996).
    [CrossRef]

2001

H. Toyota, K. Takahara, M. Okano, T. Yotsuya, H. Kikuta, “Fabrication of micro-cone array for antireflection structured surface using metal dotted pattern,” Jpn. J. Appl. Phys. 40, Part 2, 7B, L747–L749 (2001).
[CrossRef]

2000

1998

1996

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
[CrossRef]

P. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structure,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

1995

1994

1993

1992

1986

1985

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

1982

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth-eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
[CrossRef]

Auslender, M.

Baird, W. E.

Brundrett, D. L.

Gaylord, T. K.

Glytsis, E. N.

Gunning, W. J.

Hava, S.

Hecht, E.

See, for example, E. Hecht, “Antireflection coatings” in Optics, 3rd ed. (Addison Wesley, Boston, Mass., 1998)

Hegedus, Z.

Hutley, M. C.

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth-eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

Kikuta, H.

H. Toyota, K. Takahara, M. Okano, T. Yotsuya, H. Kikuta, “Fabrication of micro-cone array for antireflection structured surface using metal dotted pattern,” Jpn. J. Appl. Phys. 40, Part 2, 7B, L747–L749 (2001).
[CrossRef]

Lalanne, P.

P. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structure,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

Lemercier-Lalanne, D.

P. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structure,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

Levy, D.

Li, L.

Liu, Z. S.

Magnusson, R.

Maldonado, T. A.

D. Shin, S. Tibuleac, T. A. Maldonado, R. Magnusson, “Thin-film multilayer optical filters containing diffractive elements and waveguides,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 273–286 (1997).
[CrossRef]

Mashev, L.

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

Moharam, M. G.

Morris, G. M.

Motamedi, M. E.

Netterfield, R.

Okano, M.

H. Toyota, K. Takahara, M. Okano, T. Yotsuya, H. Kikuta, “Fabrication of micro-cone array for antireflection structured surface using metal dotted pattern,” Jpn. J. Appl. Phys. 40, Part 2, 7B, L747–L749 (2001).
[CrossRef]

Popov, E.

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

Raguin, D. H.

Shin, D.

Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett. 23, 1556–1558 (1998).
[CrossRef]

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

D. Shin, S. Tibuleac, T. A. Maldonado, R. Magnusson, “Thin-film multilayer optical filters containing diffractive elements and waveguides,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 273–286 (1997).
[CrossRef]

Southwell, W. H.

Takahara, K.

H. Toyota, K. Takahara, M. Okano, T. Yotsuya, H. Kikuta, “Fabrication of micro-cone array for antireflection structured surface using metal dotted pattern,” Jpn. J. Appl. Phys. 40, Part 2, 7B, L747–L749 (2001).
[CrossRef]

Tibuleac, S.

Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, R. Magnusson, “High-efficiency guided-mode resonance filter,” Opt. Lett. 23, 1556–1558 (1998).
[CrossRef]

D. Shin, S. Tibuleac, T. A. Maldonado, R. Magnusson, “Thin-film multilayer optical filters containing diffractive elements and waveguides,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 273–286 (1997).
[CrossRef]

Toyota, H.

H. Toyota, K. Takahara, M. Okano, T. Yotsuya, H. Kikuta, “Fabrication of micro-cone array for antireflection structured surface using metal dotted pattern,” Jpn. J. Appl. Phys. 40, Part 2, 7B, L747–L749 (2001).
[CrossRef]

Wang, S. S.

Wilson, S. J.

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth-eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

Yotsuya, T.

H. Toyota, K. Takahara, M. Okano, T. Yotsuya, H. Kikuta, “Fabrication of micro-cone array for antireflection structured surface using metal dotted pattern,” Jpn. J. Appl. Phys. 40, Part 2, 7B, L747–L749 (2001).
[CrossRef]

Young, P. P.

Appl. Opt.

R. Magnusson, S. S. Wang, “Transmission bandpass guided-mode resonance filters,” Appl. Opt. 34, 8106–8109 (1995).
[CrossRef] [PubMed]

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

Z. Hegedus, R. Netterfield, “Low sideband guided-mode resonant filter,” Appl. Opt. 39, 1469–1473 (2000).
[CrossRef]

M. Auslender, D. Levy, S. Hava, “One-dimensional antireflection gratings in (100) silicon: a numerical study,” Appl. Opt. 37, 369–373 (1998).
[CrossRef]

T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity homogeneous layers and high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
[CrossRef]

E. N. Glytsis, T. K. Gaylord, “High-spatial-frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 31, 4459–4470 (1992).
[CrossRef] [PubMed]

D. H. Raguin, G. M. Morris, “Antireflection structured surface for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
[CrossRef] [PubMed]

D. H. Raguin, G. M. Morris, “Analysis of antireflection-structured surfaces with continuous one-dimensional surface profiles,” Appl. Opt. 32, 2582–2598 (1993).
[CrossRef] [PubMed]

M. E. Motamedi, W. H. Southwell, W. J. Gunning, “Antireflection surfaces in silicon using binary optics technology,” Appl. Opt. 31, 4371–4376 (1992).
[CrossRef] [PubMed]

D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, “Homogeneous layer models for high-spatial-frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33, 2695–2706 (1994).
[CrossRef] [PubMed]

Appl. Phys. Lett.

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

J. Mod. Opt.

P. Lalanne, D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structure,” J. Mod. Opt. 43, 2063–2085 (1996).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

H. Toyota, K. Takahara, M. Okano, T. Yotsuya, H. Kikuta, “Fabrication of micro-cone array for antireflection structured surface using metal dotted pattern,” Jpn. J. Appl. Phys. 40, Part 2, 7B, L747–L749 (2001).
[CrossRef]

Opt. Acta

S. J. Wilson, M. C. Hutley, “The optical properties of ‘moth-eye’ antireflection surfaces,” Opt. Acta 29, 993–1009 (1982).
[CrossRef]

Opt. Commun.

L. Mashev, E. Popov, “Zero order anomaly of dielectric coated gratings,” Opt. Commun. 55, 377–380 (1985).
[CrossRef]

Opt. Lett.

Other

D. Shin, S. Tibuleac, T. A. Maldonado, R. Magnusson, “Thin-film multilayer optical filters containing diffractive elements and waveguides,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 273–286 (1997).
[CrossRef]

See, for example, E. Hecht, “Antireflection coatings” in Optics, 3rd ed. (Addison Wesley, Boston, Mass., 1998)

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Figures (5)

Fig. 1
Fig. 1

Antireflective GMRG filter. (a) A thin film of high refractive index n and thickness Δd covers an antireflective surface structure with period Λ and index ns. The refractive index of the incident space is n0. (b) The distribution of horizontal mean refractive index of TE and TM polarization has a maximum index peak that is higher than n0 and ns.

Fig. 2
Fig. 2

Calculated reflectance of antireflective GMRG filters as a function of wavelength. The light wave is normally incident on the GMRG filter. When the wavelength of the incident light is shorter than 0.875λ0, the light wave is diffracted into the substrate. (a) Film thickness, Δd=0.24λ0; other parameters, n0=1, n=2.25, ns=1.46, Λ=0.6λ0, d=2Λ. (b) Film thickness Δd=0.6λ0; other parameters, same as in (a).

Fig. 3
Fig. 3

Calculated reflectance for different aspect ratios. The grating period and the film thickness are fixed at 0.6λ0 and 0.2λ0, respectively. “Rigorous” denotes the reflectance calculated with the RCWA. “Flat” is the reflectance from the high-index film on a flat substrate, i.e., the reflectance of the zero aspect ratio. “UHF” denotes the reflectance of an ultra-high-frequency structure, i.e., Λλ0 and grating heights of d=0.6λ0, 1.2λ0, and 1.8λ0. “EMT” is the reflectance estimated by effective medium theory. All the thin-film thickness are fixed at 0.2λ0.

Fig. 4
Fig. 4

Two-layered low-sideband GMRG filter. (a) The designed GMRG filter according to Hegedus’s optimization method. (b) Calculated reflectance of the filter shown in (a) and antireflective GMRG filter with an aspect ratio of 2.

Fig. 5
Fig. 5

Reflectance with respect to the angle of incidence for the antireflective GMRG filter of aspect ratio 2 and the two-layered GMRG filter. The incident light wave has the resonant wavelength of each GMRG filter. The polarization state is TM.

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