Abstract

A dielectric lamellar-grating layer-substrate structure is proposed to be capable, under some conditions, of acting as a 100% efficiency mirror when operated at fixed wavelengths and incidence angles. The design of such mirrors for 1.3 μm and near normal incidence is achieved with silicon as the grating-layer material and glass substrates of two types. The study is based on a new matrix–vector procedure for the solution of rigorous coupled-wave equations. The computations use matlab, and, in particular, its goal-attainment routine. Design parameter tolerances are also discussed.

© 1995 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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  16. K. E. Petersen, “Silicon as a mechanical material,” Proc. IEEE 70, 420–457 (1982); W. H. Kho, J. T. Suminto, G. J. Yeh, “Bonding techniques for microsensors,” in Micromachining and Micropackaging of Transducers (Elsevier, London, 1985).
    [CrossRef]

1994

1993

A. Sharon, D. Rosenblatt, Y. Noifeld, A. A. Friesem, “Resonance phenomena in a grating/waveguide structure,” Bull. Israel Phys. Soc. 39, 130 (1993).

C. W. Haggans, L. Li, T. Fujita, R. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427–5442 (1993).
[CrossRef] [PubMed]

1992

1982

K. E. Petersen, “Silicon as a mechanical material,” Proc. IEEE 70, 420–457 (1982); W. H. Kho, J. T. Suminto, G. J. Yeh, “Bonding techniques for microsensors,” in Micromachining and Micropackaging of Transducers (Elsevier, London, 1985).
[CrossRef]

1981

1978

K. Knop, “Rigorous theory for transmission phase gatings with deep rectangular grooves,” J. Opt. Soc. Am. 68, 1206–1210 (1978).
[CrossRef]

K. Knop, “Reflection grating polarizer for the infrared,” Opt. Commun. 26, 281–283 (1978); L. Li, Q. Gong, G. N. Lawrence, J. J. Burke, “Polarization properties of planar dielectric waveguide gratings,” Appl. Opt. 31, 4190–4197 (1992).
[CrossRef] [PubMed]

1973

N. Neviere, R. Petit, Cadilhac, “About theory of optical grating coupler-waveguide systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

Ailwadi, N. K.

Aspnes, D. E.

D. E. Aspnes, “Optical functions of intrinsic silicon: table of refractive index, extinction coefficient and absorption coefficient vs energy (0 to 400 eV),” in Properties of Silicon, Emis Datareviews Series No. 4 (Institution of Electrical Engineers, London, 1988), Sect. 2.6, pp. 72–79.

Auslender, M.

Bovard, B. G.

Cadilhac,

N. Neviere, R. Petit, Cadilhac, “About theory of optical grating coupler-waveguide systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

Friesem, A. A.

A. Sharon, D. Rosenblatt, Y. Noifeld, A. A. Friesem, “Resonance phenomena in a grating/waveguide structure,” Bull. Israel Phys. Soc. 39, 130 (1993).

Fujita, T.

C. W. Haggans, L. Li, T. Fujita, R. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

Gaylord, T. K.

Ghen, R. T.

Grase, A.

A. Grase, Optimization Toolbox for Use with matlab User’s Guide (MathWorks, Inc., Natick, Mass., 1992).

Haggans, C. W.

C. W. Haggans, L. Li, T. Fujita, R. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

Hava, S.

Jahns, J.

Jannson, T.

Knop, K.

K. Knop, “Reflection grating polarizer for the infrared,” Opt. Commun. 26, 281–283 (1978); L. Li, Q. Gong, G. N. Lawrence, J. J. Burke, “Polarization properties of planar dielectric waveguide gratings,” Appl. Opt. 31, 4190–4197 (1992).
[CrossRef] [PubMed]

K. Knop, “Rigorous theory for transmission phase gatings with deep rectangular grooves,” J. Opt. Soc. Am. 68, 1206–1210 (1978).
[CrossRef]

Kostuk, R.

C. W. Haggans, L. Li, T. Fujita, R. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

Li, L.

Mansfield, W. M.

Maylstre, D.

D. Maylstre, N. Neviere, R. Petit, “Experimental verification and applications of the theory,” in Electromagnetic Theory of Gratings. R. Petit, ed., Topics in Current Physics Series (Springer, New York, 1980), Chap. 6.

Moharam, M. G.

Mulgrew, P.

Neviere, N.

N. Neviere, R. Petit, Cadilhac, “About theory of optical grating coupler-waveguide systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

D. Maylstre, N. Neviere, R. Petit, “Experimental verification and applications of the theory,” in Electromagnetic Theory of Gratings. R. Petit, ed., Topics in Current Physics Series (Springer, New York, 1980), Chap. 6.

Noifeld, Y.

A. Sharon, D. Rosenblatt, Y. Noifeld, A. A. Friesem, “Resonance phenomena in a grating/waveguide structure,” Bull. Israel Phys. Soc. 39, 130 (1993).

Petersen, K. E.

K. E. Petersen, “Silicon as a mechanical material,” Proc. IEEE 70, 420–457 (1982); W. H. Kho, J. T. Suminto, G. J. Yeh, “Bonding techniques for microsensors,” in Micromachining and Micropackaging of Transducers (Elsevier, London, 1985).
[CrossRef]

Petit, R.

N. Neviere, R. Petit, Cadilhac, “About theory of optical grating coupler-waveguide systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

D. Maylstre, N. Neviere, R. Petit, “Experimental verification and applications of the theory,” in Electromagnetic Theory of Gratings. R. Petit, ed., Topics in Current Physics Series (Springer, New York, 1980), Chap. 6.

Rabinovic, D.

Rosenblatt, D.

A. Sharon, D. Rosenblatt, Y. Noifeld, A. A. Friesem, “Resonance phenomena in a grating/waveguide structure,” Bull. Israel Phys. Soc. 39, 130 (1993).

Sharon, A.

A. Sharon, D. Rosenblatt, Y. Noifeld, A. A. Friesem, “Resonance phenomena in a grating/waveguide structure,” Bull. Israel Phys. Soc. 39, 130 (1993).

Sonek, G. J.

Sonek, R. T.

Tennant, D. M.

Walker, S. J.

Wang, M. R.

West, L. C.

Appl. Opt.

Bull. Israel Phys. Soc.

A. Sharon, D. Rosenblatt, Y. Noifeld, A. A. Friesem, “Resonance phenomena in a grating/waveguide structure,” Bull. Israel Phys. Soc. 39, 130 (1993).

J. Mod. Opt.

C. W. Haggans, L. Li, T. Fujita, R. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mod. Opt. 40, 675–686 (1993).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

K. Knop, “Reflection grating polarizer for the infrared,” Opt. Commun. 26, 281–283 (1978); L. Li, Q. Gong, G. N. Lawrence, J. J. Burke, “Polarization properties of planar dielectric waveguide gratings,” Appl. Opt. 31, 4190–4197 (1992).
[CrossRef] [PubMed]

N. Neviere, R. Petit, Cadilhac, “About theory of optical grating coupler-waveguide systems,” Opt. Commun. 8, 113–117 (1973).
[CrossRef]

Proc. IEEE

K. E. Petersen, “Silicon as a mechanical material,” Proc. IEEE 70, 420–457 (1982); W. H. Kho, J. T. Suminto, G. J. Yeh, “Bonding techniques for microsensors,” in Micromachining and Micropackaging of Transducers (Elsevier, London, 1985).
[CrossRef]

Other

matlab 4.0 User’s Guide (MathWorks, Inc., Natick, Mass., 1992).

D. R. Lide, ed., CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, Fla., 1993), pp. 10.310–10.318.

A. Grase, Optimization Toolbox for Use with matlab User’s Guide (MathWorks, Inc., Natick, Mass., 1992).

D. E. Aspnes, “Optical functions of intrinsic silicon: table of refractive index, extinction coefficient and absorption coefficient vs energy (0 to 400 eV),” in Properties of Silicon, Emis Datareviews Series No. 4 (Institution of Electrical Engineers, London, 1988), Sect. 2.6, pp. 72–79.

D. Maylstre, N. Neviere, R. Petit, “Experimental verification and applications of the theory,” in Electromagnetic Theory of Gratings. R. Petit, ed., Topics in Current Physics Series (Springer, New York, 1980), Chap. 6.

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Figures (7)

Fig. 1
Fig. 1

Lamellar zero-order grating-layer-substrate structure at planar-diffraction mounting: k r and k t are the wave vectors of reflected and transmitted waves, respectively. See text for definitions of other variables.

Fig. 2
Fig. 2

Reflectance spectra of silicon lamellar-grating layer (Corning No. 7740) glass-substrate structure with Λ = 0.6274 μm, w = 0.5Λ, h = 0.2247 μm, and d = 1.2039 μm: (a) 1.2 μm ≤ λ ≤ 1.4 μm, and (b) 1.29 μm ≤ λ ≤ 1.31 μm.

Fig. 3
Fig. 3

Angular reflectances of silicon lamellar-grating-layer (Corning No. 7740) glass substrate at λ = 1.3 μm, Λ = 0.6274 μm, w = 0.5Λ, h = 0.2247 μm, and d = 1.2039 μm.

Fig. 4
Fig. 4

TM angular reflectance of silicon lamellar-grating layer fused quartz substrate with Λ = 0.6089 μm, w = 0.5Λ, h = 0.2629 μm, and d = 1.1841 μm.

Fig. 5
Fig. 5

Groove-height dependence of reflectances for silicon lamellar-grating layer (Corning No. 7740) glass substrate at λ = 1.3 μm, Λ = 0.6274 μm, w = 0.5Λ, d = 1.2039 μm, and 0.2 μm ≤ h ≤ 1.2 μm.

Fig. 6
Fig. 6

Groove-height dependence of reflectances for silicon lamellar-grating layer (Corning No. 7740) glass substrate at λ = 1.3 μm, Λ = 0.6274 μm, w = 0.5Λ, d = 1.2039 μm, and 0.2 μm ≤ h ≤ 0.4 μm.

Fig. 7
Fig. 7

Layer-thickness dependence of reflectances for silicon lamellar-grating layer (Corning No. 7740) glass substrate at λ = 1.3 μm, Λ = 0.6274 μm, w = 0.5Λ, h = 0.2247 μm: (a) 0.5 μm ≤ d ≤ 3.0 μm; (b) 1.1 μm ≤ d ≤ 1.3 μm.

Equations (11)

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n sin θ m = sin θ i + m λ Λ ,             m = 0 , ± 1 , ± 2 , ,
k i = 2 π λ ( sin θ i , 0 , cos θ i ) .
λ Λ > n III + sin θ i ,             n III = ɛ III .
λ Λ ~ n II ± sin θ i ,             n II = ɛ II ,
λ Λ < n II - sin θ i
R TE ( Λ * , w * , h * , d * ) = 1 ,             R TM ( Λ * , w * , h * , d * ) = 1.
w = 0.5 Λ
Λ o = 0.65 ,             h o = 0.20 ,             d o = 1.30 ,
Λ * = 0.6274 ,             h * = 0.2247 ,             d * = 1.2039.
Λ * = 0.6403 ,             h * = 0.2204 ,             d * = 1.1952.
Λ * = 0.6089 ,             h * = 0.2629 ,             d * = 1.1841 ,

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