Abstract

Experimental diffraction characteristics of dielectric transmission gratings on planar optical waveguides are compared to theoretical results from the rigorous coupled-wave analysis. The deep-grooved square gratings are shown to have high diffraction efficiency (>90%). In particular, the effects of higher orders of diffraction on the diffraction efficiency, at fixed wavelength, are presented in this paper for both TE and TM polarizations. The rigorous coupled-wave analysis is shown to produce excellent general agreement with the measured diffraction characteristics.

© 1985 Optical Society of America

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References

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  1. W. R. Klein, B. D. Cook, “Unified Approach to Ultrasonic Light Diffraction,” IEEE Trans. Sonic Ultrason., SU-14123 (1967).
    [CrossRef]
  2. M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg Regime Diffraction by Phase Gratings,” J. Opt. Commun. 32, 14 (1980).
    [CrossRef]
  3. M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Raman-Nath Diffraction by Phase Gratings,” J. Opt. Commun. 32, 19, (1980).
    [CrossRef]
  4. H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909 (1969).
  5. M. G. Moharam, T. K. Gaylord, “Rigorous Coupled Wave Analysis of Planar Grating Diffraction,” J. Opt. Soc. Am. 71, 811 (1981).
    [CrossRef]
  6. J-M. P. Delavaux, W. S. C. Chang, “Design and Fabrication of Efficient Diffraction Gratings on Planar Optical Waveguides,” Appl. Opt. 23, 3004 (1984).
    [CrossRef] [PubMed]
  7. M. G. Moharam, T. K. Gaylord, “Diffraction Analysis of Dielectric Surface-relief Gratings,” J. Opt. Soc. Am. 72, 1385 (1982).
    [CrossRef]

1984 (1)

1982 (1)

1981 (1)

1980 (2)

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg Regime Diffraction by Phase Gratings,” J. Opt. Commun. 32, 14 (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Raman-Nath Diffraction by Phase Gratings,” J. Opt. Commun. 32, 19, (1980).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909 (1969).

1967 (1)

W. R. Klein, B. D. Cook, “Unified Approach to Ultrasonic Light Diffraction,” IEEE Trans. Sonic Ultrason., SU-14123 (1967).
[CrossRef]

Chang, W. S. C.

Cook, B. D.

W. R. Klein, B. D. Cook, “Unified Approach to Ultrasonic Light Diffraction,” IEEE Trans. Sonic Ultrason., SU-14123 (1967).
[CrossRef]

Delavaux, J-M. P.

Gaylord, T. K.

M. G. Moharam, T. K. Gaylord, “Diffraction Analysis of Dielectric Surface-relief Gratings,” J. Opt. Soc. Am. 72, 1385 (1982).
[CrossRef]

M. G. Moharam, T. K. Gaylord, “Rigorous Coupled Wave Analysis of Planar Grating Diffraction,” J. Opt. Soc. Am. 71, 811 (1981).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Raman-Nath Diffraction by Phase Gratings,” J. Opt. Commun. 32, 19, (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg Regime Diffraction by Phase Gratings,” J. Opt. Commun. 32, 14 (1980).
[CrossRef]

Klein, W. R.

W. R. Klein, B. D. Cook, “Unified Approach to Ultrasonic Light Diffraction,” IEEE Trans. Sonic Ultrason., SU-14123 (1967).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909 (1969).

Magnusson, R.

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Raman-Nath Diffraction by Phase Gratings,” J. Opt. Commun. 32, 19, (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg Regime Diffraction by Phase Gratings,” J. Opt. Commun. 32, 14 (1980).
[CrossRef]

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, “Diffraction Analysis of Dielectric Surface-relief Gratings,” J. Opt. Soc. Am. 72, 1385 (1982).
[CrossRef]

M. G. Moharam, T. K. Gaylord, “Rigorous Coupled Wave Analysis of Planar Grating Diffraction,” J. Opt. Soc. Am. 71, 811 (1981).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg Regime Diffraction by Phase Gratings,” J. Opt. Commun. 32, 14 (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Raman-Nath Diffraction by Phase Gratings,” J. Opt. Commun. 32, 19, (1980).
[CrossRef]

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled Wave Theory for Thick Hologram Gratings,” Bell Syst. Tech. J. 48, 2909 (1969).

IEEE Trans. Sonic Ultrason. (1)

W. R. Klein, B. D. Cook, “Unified Approach to Ultrasonic Light Diffraction,” IEEE Trans. Sonic Ultrason., SU-14123 (1967).
[CrossRef]

J. Opt. Commun. (2)

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Bragg Regime Diffraction by Phase Gratings,” J. Opt. Commun. 32, 14 (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, R. Magnusson, “Criteria for Raman-Nath Diffraction by Phase Gratings,” J. Opt. Commun. 32, 19, (1980).
[CrossRef]

J. Opt. Soc. Am. (2)

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Figures (10)

Fig. 1
Fig. 1

Diffraction transmission grating on planar optical waveguide.

Fig. 2
Fig. 2

Diffraction efficiency of 80- and 250-μm long and 8-μm periodicity grating as a function of the mode-index change for the Bragg angle of incidence θB: for d = 80 μm, Λ = 8 μm, and Kcdπ/2, Q ≃ 3.3 and ρ = 1.05; for d = 250 μm, Λ = 8 μm, and Kcdπ/2, Q ≃ 13.25 and ρ = 3.29.

Fig. 3
Fig. 3

Diffraction efficiency of 80- and 250-μm long and 4-μm periodicity grating as a function of the mode-index change for the Bragg angle of incidence θB: for d = 80 μm, Λ = 4 μm, and Kcdπ/2, Q = 12.75 and ρ = 4.21; for d = 250 μm, Λ = 4 μm, and Kcdπ/2, Q = 41.4 and ρ = 13.25.

Fig. 4
Fig. 4

Diffraction efficiency of 80- and 250-μm long and 2-μm periodicity grating as a function of the mode-index change for the Bragg angle of incidence θB: for d = 80 μm, Λ = 2μm, and Kcdπ/2, Q = 52.9 and ρ = 16.9; for d = 250 μm, Λ = 2 μm, and Kcdπ/2, Q = 165.6 and ρ = 52.7.

Fig. 5
Fig. 5

Calculated diffraction efficiency characteristics of a grating (d = 80 μm, Λ = 8 μm) as a function of the mode-index change. The strongest diffraction orders are included for the Bragg angle of incidence.

Fig. 6
Fig. 6

Measured diffracted power in higher orders other than the zeroth and first order as a function of the mode-index change.

Fig. 7
Fig. 7

Efficiencies of the strongest orders of diffraction of an 80-μm long and 8-μm periodicity grating vs angular deviation from its Bragg angle for TE mode: (a) theoretical prediction; (b) experimental measurement.

Fig. 8
Fig. 8

Efficiencies of the strongest orders of diffraction of an 80-μm long and 8-μm periodicity grating vs angular deviation from its Bragg angle for the TM mode: (a) theoretical prediction; (b) experimental measurement.

Fig. 9
Fig. 9

Efficiencies of the strongest orders of diffraction of an 80-μm long and 4-μm periodicity grating vs angular deviation from its Bragg angle for the TE mode: (a) theoretical prediction; (b) experimental measurement.

Fig. 10
Fig. 10

Efficiencies of the strongest orders of diffraction of an 80-μm long and 4-μm periodicity grating vs angular deviation from its Bragg angle for the TM mode: (a) theoretical prediction; (b) experimental measurement.

Equations (9)

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Q = ( 2 π λ 0 d ) / ( Λ 2 n e ) ,
ρ = λ 0 2 / ( Λ 2 n e Δ n e ) ,
η = sin 2 ( K c d ) ,
K c = π n 1 / ( λ 0 cos θ B )
n 1 = ( 2 / π ) Δ n eff .
K c = 2 Δ n eff / ( λ 0 cos θ B ) .
ρ = Q / ( 2 K c d ) .
ρ = Q / π .
Δ n eff = n eff n eff .

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