Abstract

Computer optimization shows that the first-order diffraction efficiency of a lossless-transmission surface-relief grating with a rectangular surface profile can be made very large (∼95%) simultaneously for light of TE and TM polarizations incident near the Bragg angle by the proper choice of the fill factor. The case for visible light incident close to the Bragg angle on unslanted gratings with periodicities corresponding to Bragg angles of 30°, 37.5°, and 45° is presented. The refractive index of the grating material was chosen in the range between 1.2 and 2.

© 1998 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  5. H. J. Gerritsen, “Diffractive daylighting: ways to obtain wide angular range, large efficiency, and near chromatic operation,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XIIC. M. Lampert, ed., Proc. SPIE2017, 377–388 (1993).
    [Crossref]
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1997 (1)

1993 (1)

1991 (1)

1984 (1)

1983 (1)

1982 (1)

Bolton, S. R.

Boyd, R. D.

Britten, J. A.

Bryan, S. J.

Case, S. K.

Enger, R. C.

Gaylord, T. K.

Gerritsen, H. J.

H. J. Gerritsen, D. K. Thornton, S. R. Bolton, “Application of Kogelnik’s two-wave theory to deep, slanted, highly efficient, relief transmission gratings,” Appl. Opt. 30, 807–814 (1991).
[Crossref] [PubMed]

H. J. Gerritsen, “Diffractive daylighting: ways to obtain wide angular range, large efficiency, and near chromatic operation,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XIIC. M. Lampert, ed., Proc. SPIE2017, 377–388 (1993).
[Crossref]

Gupta, M. C.

Moharam, M. G.

Nguyen, H. T.

Peng, S. T.

Perry, M. D.

Shore, B. W.

Sincerbox, G. T.

Thornton, D. K.

Werlich, H.

Yung, B.

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

Opt. Lett. (1)

Other (2)

R. Kingslake, eds., Light: Its Generation and Modification, Vol. 1 of the Applied Optics and Optical Engineering Series (Academic, New York, 1965), pp. 156–157, 183.

H. J. Gerritsen, “Diffractive daylighting: ways to obtain wide angular range, large efficiency, and near chromatic operation,” in Optical Materials Technology for Energy Efficiency and Solar Energy Conversion XIIC. M. Lampert, ed., Proc. SPIE2017, 377–388 (1993).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

Diffraction efficiency for first-order diffracted light with the following parameters: λ = Λ = 0.55 μm, θ B = 30°, and n = 1.58. Curves: ⋯⋯ the (TE + 1) order transmitted; ------- the (TM + 1) order transmitted; ——— the average or unpolarized diffracted light. (a) Fill factor of f = 0.50. (b) Fill factor of f = 0.56.

Fig. 2
Fig. 2

Diffraction efficiency for first-order diffracted light with the same parameters as for Fig. 1 except that n = 1.85. Curves: ⋯⋯ the (TE + 1) order transmitted; ------- the (TM + 1) order transmitted; ——— the average or unpolarized diffracted light. (a) Fill factor of f = 0.50. (b) Fill factor of f = 0.42.

Fig. 3
Fig. 3

For λ = Λ = 0.55 μm and θ B = 30°: (a) Matching fill factor f m , for which the maxima of the diffraction efficiencies for TE and TM light occur at the same depth d m , as a function of the refractive index. (b) Depth d m as a function of the refractive index. (c) First-order diffraction efficiencies as a function of the refractive index n.

Fig. 4
Fig. 4

For three grating spacings (λ = 0.55 μm) of Λ = 0.55 μm (θ B = 30°), Λ = 0.4517 μm B = 37.5°), and Λ = 0.3889 μm (θ B = 45°): (a)Matching fill factor f m for which the maxima of the diffraction efficiency for TE and TM light occur at the same depth as a function of the refractive index. (b) Depth d m as a function of refractive index. (c) First-order diffraction efficiencies as a function of the refractive index n for unpolarized light.

Fig. 5
Fig. 5

(a) First-order diffraction efficiencies for a grating with λ = 0.55 μm, Λ = 0.3889 μm, θ B = 45°, n = 1.50, and f = 0.50. (b) First-order diffraction efficiencies for a grating with λ = 0.55 μm, Λ = 0.3889 μm, θ B = 45°, n = 1.50, and f = 0.80.

Fig. 6
Fig. 6

Angular dependence of the efficiency of the first-order diffracted light of a wavelength of λ = 0.55 μm for a grating with a periodicity of Λ = 0.55 μm, a refractive index of n = 1.50, a fill factor of f = 0.60, and a depth of d m = 1.16 μm. Curves: Dotted curve, the (TE + 1) order; dashed curve, the (TM + 1) order; and solid curve, the average diffracted efficiency.

Fig. 7
Fig. 7

Angular dependence of the efficiency of the first-order diffracted light of a wavelength of λ = 0.65 μm on a grating with periodicity Λ = 0.55 μm, refractive index n = 1.50, a fill factor of f = 0.60, and a depth of d m = 1.16 μm. Curves: Dotted curve, the (TE + 1) order; dashed curve, the (TM + 1) order; solid curve, the average diffracted efficiency; and curve with black circles, the average transmitted efficiency.

Fig. 8
Fig. 8

Angular dependence of the efficiency of the first-order diffracted light of a wavelength of λ = 0.45 μm on a grating with a periodicity of Λ = 0.55 μm, a refractive index of n = 1.50, a fill factor of f = 0.60, and a depth of d m = 1.16 μm. Curves: Dotted curve, the (TE + 1) order; dashed curve, the (TM + 1) order; solid curve, the average first-order diffracted efficiency; and curve with black triangles, the second-order diffraction efficiency.

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