Abstract

Bandpass filters based on guided-mode resonance effects in waveguide-grating structures are obtained by use of a genetic algorithm search-and-optimization routine. Calculated examples show that narrow linewidths, high peaks, and low sideband transmittances can be achieved in thin-film diffractive devices with few layers. A filter with a linewidth of 0.2  nm at a central wavelength of 0.55 μm is demonstrated in a two-layer–two-grating structure. At 10.6μm wavelength, a filter consisting of a single binary grating is obtained that has a linewidth of 12.7  nm and extended, low sideband transmittance. A three-layer device with a surface relief Si grating and two underlying homogeneous layers of SiO2 and Si yields a high-efficiency filter centered at 1.55 μm with a linewidth of 0.1  nm.

© 2001 Optical Society of America

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2000

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, IEEE Trans. Microwave Theory Tech. 48, 553 (2000).
[CrossRef]

D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, and J. M. Bendickson, J. Opt. Soc. Am. A 17, 1221 (2000).
[CrossRef]

1998

C. Zuffada, T. Cwik, and C. Ditchman, IEEE Trans. Antennas Propag. 46, 657 (1998).
[CrossRef]

D. Shin, S. Tibuleac, T. A. Maldonado, and R. Magnusson, Opt. Eng. 37, 2634 (1998).
[CrossRef]

R. Magnusson, D. Shin, and Z. S. Liu, Opt. Lett. 23, 612 (1998).
[CrossRef]

Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, and R. Magnusson, Opt. Lett. 23, 1556 (1998).
[CrossRef]

1997

1996

A. Sharon, D. Rosenblatt, and A. A. Friesem, Appl. Phys. Lett. 69, 4154 (1996).
[CrossRef]

1995

1992

R. Magnusson and S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
[CrossRef]

1985

T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Abushagur, M. A. G.

Bendickson, J. M.

Brundrett, D. L.

Cwik, T.

C. Zuffada, T. Cwik, and C. Ditchman, IEEE Trans. Antennas Propag. 46, 657 (1998).
[CrossRef]

Ditchman, C.

C. Zuffada, T. Cwik, and C. Ditchman, IEEE Trans. Antennas Propag. 46, 657 (1998).
[CrossRef]

Friesem, A. A.

A. Sharon, D. Rosenblatt, and A. A. Friesem, Appl. Phys. Lett. 69, 4154 (1996).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Goldberg, D.

D. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

Holzheimer, T. R.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, IEEE Trans. Microwave Theory Tech. 48, 553 (2000).
[CrossRef]

Johnson, E. G.

Levine, D.

C. Zuffada, D. Levine, and S. Tibuleac, “Designing dielectric grating filters with PGAPACK,” in Electromagnetic System Design Using Evolutionary Optimization: Genetic Algorithms, Y. Rahmat-Samii and E. Michielssen, eds. (Wiley, New York, 1999).

Liu, Z. S.

Magnusson, R.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, IEEE Trans. Microwave Theory Tech. 48, 553 (2000).
[CrossRef]

Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, and R. Magnusson, Opt. Lett. 23, 1556 (1998).
[CrossRef]

R. Magnusson, D. Shin, and Z. S. Liu, Opt. Lett. 23, 612 (1998).
[CrossRef]

D. Shin, S. Tibuleac, T. A. Maldonado, and R. Magnusson, Opt. Eng. 37, 2634 (1998).
[CrossRef]

S. Tibuleac and R. Magnusson, J. Opt. Soc. Am. A 14, 1617 (1997).
[CrossRef]

R. Magnusson and S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
[CrossRef]

Maldonado, T. A.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, IEEE Trans. Microwave Theory Tech. 48, 553 (2000).
[CrossRef]

D. Shin, S. Tibuleac, T. A. Maldonado, and R. Magnusson, Opt. Eng. 37, 2634 (1998).
[CrossRef]

Moharam, M. G.

T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Morris, G. M.

S. Peng and G. M. Morris, in Diffractive Optics and Microoptics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 257.

Peng, S.

S. Peng and G. M. Morris, in Diffractive Optics and Microoptics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 257.

Rosenblatt, D.

A. Sharon, D. Rosenblatt, and A. A. Friesem, Appl. Phys. Lett. 69, 4154 (1996).
[CrossRef]

Sharon, A.

A. Sharon, D. Rosenblatt, and A. A. Friesem, Appl. Phys. Lett. 69, 4154 (1996).
[CrossRef]

Shin, D.

Tibuleac, S.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, IEEE Trans. Microwave Theory Tech. 48, 553 (2000).
[CrossRef]

D. Shin, S. Tibuleac, T. A. Maldonado, and R. Magnusson, Opt. Eng. 37, 2634 (1998).
[CrossRef]

Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, and R. Magnusson, Opt. Lett. 23, 1556 (1998).
[CrossRef]

S. Tibuleac and R. Magnusson, J. Opt. Soc. Am. A 14, 1617 (1997).
[CrossRef]

C. Zuffada, D. Levine, and S. Tibuleac, “Designing dielectric grating filters with PGAPACK,” in Electromagnetic System Design Using Evolutionary Optimization: Genetic Algorithms, Y. Rahmat-Samii and E. Michielssen, eds. (Wiley, New York, 1999).

Wang, S. S.

R. Magnusson and S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
[CrossRef]

Young, P. P.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, IEEE Trans. Microwave Theory Tech. 48, 553 (2000).
[CrossRef]

Z. S. Liu, S. Tibuleac, D. Shin, P. P. Young, and R. Magnusson, Opt. Lett. 23, 1556 (1998).
[CrossRef]

Zuffada, C.

C. Zuffada, T. Cwik, and C. Ditchman, IEEE Trans. Antennas Propag. 46, 657 (1998).
[CrossRef]

C. Zuffada, D. Levine, and S. Tibuleac, “Designing dielectric grating filters with PGAPACK,” in Electromagnetic System Design Using Evolutionary Optimization: Genetic Algorithms, Y. Rahmat-Samii and E. Michielssen, eds. (Wiley, New York, 1999).

Appl. Phys. Lett.

R. Magnusson and S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).
[CrossRef]

A. Sharon, D. Rosenblatt, and A. A. Friesem, Appl. Phys. Lett. 69, 4154 (1996).
[CrossRef]

IEEE Trans. Antennas Propag.

C. Zuffada, T. Cwik, and C. Ditchman, IEEE Trans. Antennas Propag. 46, 657 (1998).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

S. Tibuleac, R. Magnusson, T. A. Maldonado, P. P. Young, and T. R. Holzheimer, IEEE Trans. Microwave Theory Tech. 48, 553 (2000).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

D. Shin, S. Tibuleac, T. A. Maldonado, and R. Magnusson, Opt. Eng. 37, 2634 (1998).
[CrossRef]

Opt. Lett.

Proc. IEEE

T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Other

C. Zuffada, D. Levine, and S. Tibuleac, “Designing dielectric grating filters with PGAPACK,” in Electromagnetic System Design Using Evolutionary Optimization: Genetic Algorithms, Y. Rahmat-Samii and E. Michielssen, eds. (Wiley, New York, 1999).

D. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

S. Peng and G. M. Morris, in Diffractive Optics and Microoptics, Vol. 5 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 257.

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Figures (5)

Fig. 1
Fig. 1

Two-grating–two-layer waveguide grating. The physical parameters that are varied during the optimization process are grating period Λ; thicknesses d1 and d2; coordinates of the high-refractive-index region within a grating normalized to the grating period xL,1, xH,1, xL,2, and xH,2; and refractive indices nH,1, nL,1, nH,2, and nL,2. The angle of incidence, as well as refractive indices of the cover nC and the substrate nS, is maintained constant.

Fig. 2
Fig. 2

Transmittance spectrum of a bandpass GMR filter found by GA optimization. The parameters are Λ=0.35 μm, nH,1=nH,2=2.35, nL,1=nL,2=1.65, d1=0.1934 μm, xL,1=0.0, xH,1=0.319, d2=0.3404 μm, xL,2=0.586, xH,2=0.785, nC=1.0, and nS=1.52. The transmittance of the equivalent two-layer structure (the average refractive indices of the gratings are n1=1.901 and n2=1.811) is denoted by the dashed curve.

Fig. 3
Fig. 3

Spectral response of a single-layer GMR bandpass filter centered at λC=10.6 μm (solid curve). Grating period, Λ=6.91 μm; fill factor f=0.42; thickness, d=3.7 μm; refractive indices, nH=4.0 and nL=2.65; cover and substrate refractive indices, nC=1.0 and nS=1.4, respectively. The equivalent homogeneous layer has thickness d=3.7 μm and refractive index n=3.285.

Fig. 4
Fig. 4

GMR bandpass filter characteristic with 0.1-nm linewidth obtained with the three-layer structure shown. Grating period, Λ=1.029 μm; fill factor, f=0.152; refractive indices of the grating, nH,1=3.2 (Si) and nL,1=1.0 (air); refractive indices of the homogeneous layers, n2=1.45 SiO2 and n3=3.2; thicknesses of the layers, d1=0.262 μm, d2=1.460 μm, d3=2.221 μm. The cover and the substrate media are air and silica n=1.45, respectively. The dashed curve represents the transmittance of the equivalent homogeneous structure with refractive index of the top layer, n=1.550.

Fig. 5
Fig. 5

GMR bandstop filter characteristic with 0.1-nm linewidth obtained with the three-layer structure shown. Grating period, Λ=0.8 μm; fill factor, f=0.1; refractive indices of the grating, nH,1=3.2 (Si) and nL,1=1.0 (air); refractive indices of the homogeneous layers, n2=1.45 SiO2 and n3=3.2; thicknesses of the layers, d1=0.664 μm, d2=0.450 μm, and d3=1.9163 μm. The cover and the substrate media are air and silica n=1.45, respectively. The dashed curve represents the reflectance of the equivalent homogeneous structure with refractive index of the top layer, n=1.387.

Equations (1)

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MF=1Mi=1MwiDEGA,i-DEref,in1/n,

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