Abstract

A shallow grating triple-layer guided-mode resonance (GMR) filter and its properties are presented. For this type of GMR filter, the grating layer has the equal refractive index to the waveguide layer. It is shown that the GMR filter with shallow grating has good characteristics of narrow bandwidth, symmetrical line shape, and low-reflection sideband. The spectral FWHM of the GMR filter can be controlled by varying the grating thickness. The desired FWHM at the same resonance wavelength with symmetrical line shape and low-reflection sideband can be obtained by adjusting the grating thickness and the grating period with the total thickness of the grating and waveguide layers kept unchanged.

© 2010 Optical Society of America

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M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A 12, 1077 (1995).
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J. Saarinen, E. Noponen, and J. Turunen, Opt. Eng. (Bellingham) 34, 2560 (1995).
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S. M. Rytov, Sov. Phys. JETP 2, 466 (1956).

Bae, B. -S.

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[CrossRef]

Friesem, A. A.

Fu, X.

Gaylord, T. K.

Grann, E. B.

Hane, K.

T. Kobayashi, Y. Kanamori, and K. Hane, Appl. Phys. Lett. 87, 151106 (2005).
[CrossRef]

Iwata, K.

Jin, J.

Jin, Y.

J. Ma, S. Liu, Y. Jin, C. Xu, J. Shao, and Z. Fan, Opt. Commun. 281, 3295 (2008).
[CrossRef]

Kanamori, Y.

T. Kobayashi, Y. Kanamori, and K. Hane, Appl. Phys. Lett. 87, 151106 (2005).
[CrossRef]

Kikuta, H.

Kobayashi, T.

T. Kobayashi, Y. Kanamori, and K. Hane, Appl. Phys. Lett. 87, 151106 (2005).
[CrossRef]

Lee, K. J.

Liu, S.

J. Ma, S. Liu, Y. Jin, C. Xu, J. Shao, and Z. Fan, Opt. Commun. 281, 3295 (2008).
[CrossRef]

Ma, J.

J. Ma, S. Liu, Y. Jin, C. Xu, J. Shao, and Z. Fan, Opt. Commun. 281, 3295 (2008).
[CrossRef]

Magnusson, R.

Maldonado, T. A.

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, Appl. Phys. Lett. 83, 3248 (2003).
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Michael Morris, G.

Mizutani, A.

Moharam, M. G.

Noponen, E.

J. Saarinen, E. Noponen, and J. Turunen, Opt. Eng. (Bellingham) 34, 2560 (1995).
[CrossRef]

Norton, S. M.

Pommet, D. A.

Priambodo, P. S.

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, Appl. Phys. Lett. 83, 3248 (2003).
[CrossRef]

Rosenblatt, D.

Rytov, S. M.

S. M. Rytov, Sov. Phys. JETP 2, 466 (1956).

Saarinen, J.

J. Saarinen, E. Noponen, and J. Turunen, Opt. Eng. (Bellingham) 34, 2560 (1995).
[CrossRef]

Shao, J.

X. Fu, K. Yi, J. Shao, and Z. Fan, Opt. Lett. 34, 124 (2009).
[CrossRef] [PubMed]

J. Ma, S. Liu, Y. Jin, C. Xu, J. Shao, and Z. Fan, Opt. Commun. 281, 3295 (2008).
[CrossRef]

Sharon, A.

Steingrueber, R.

Thurman, S. T.

Tibuleac, S.

Turunen, J.

J. Saarinen, E. Noponen, and J. Turunen, Opt. Eng. (Bellingham) 34, 2560 (1995).
[CrossRef]

Wang, S. S.

Weber, H. G.

Xu, C.

J. Ma, S. Liu, Y. Jin, C. Xu, J. Shao, and Z. Fan, Opt. Commun. 281, 3295 (2008).
[CrossRef]

Yi, K.

Appl. Opt.

Appl. Phys. Lett.

T. Kobayashi, Y. Kanamori, and K. Hane, Appl. Phys. Lett. 87, 151106 (2005).
[CrossRef]

P. S. Priambodo, T. A. Maldonado, and R. Magnusson, Appl. Phys. Lett. 83, 3248 (2003).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

J. Ma, S. Liu, Y. Jin, C. Xu, J. Shao, and Z. Fan, Opt. Commun. 281, 3295 (2008).
[CrossRef]

Opt. Eng. (Bellingham)

J. Saarinen, E. Noponen, and J. Turunen, Opt. Eng. (Bellingham) 34, 2560 (1995).
[CrossRef]

Opt. Lett.

Sov. Phys. JETP

S. M. Rytov, Sov. Phys. JETP 2, 466 (1956).

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Figures (4)

Fig. 1
Fig. 1

Structure of the triple-layer GMR filters. The first layer is the grating layer with high and low refractive indices of n 1 H and n 1 L ; n 2 and n 3 are the refractive indices of the second layer and third layer; d 1 , d 2 , and d 3 are the layer thicknesses; n C and n S are the refractive indices of the cover layer and the substrate; Λ is the grating period; f is the grating fill factor.

Fig. 2
Fig. 2

Reflection responses of the triple-layer GMR filter for the normal incidence TE-polarized wave. Inset shows a magnified view of the resonance response.

Fig. 3
Fig. 3

Reflection responses of the GMR filters with various thicknesses of the grating, waveguide layer, and subwaveguide layer. The remaining parameters are the same as in Fig. 2.

Fig. 4
Fig. 4

Designed GMR filter for different FWHMs.

Tables (1)

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Table 1 Normalized Grating Length Required to Achieve Nearly 100% Peak Reflection Efficiency

Equations (2)

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n 1 eff = [ f n 1 H 2 + ( 1 f ) n 1 L 2 ] 1 / 2 .
L Λ λ 0 / Δ λ FWHM .

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