Abstract

It is shown from numerical results deduced from a rigorous theory of diffraction that diffraction gratings made with two-dimensional dielectric photonic crystals may present blazing effects. Since these structures are lossless, efficiencies of 100% in the -1st order can be obtained in polarized light. Efficiency curves in Littrow mount are shown.

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References

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  1. R. Petit, Electromagnetic theory of gratings (Springer-Verlag, 1980).
    [CrossRef]
  2. M. C. Hutley, Diffraction gratings (Academic press, 1982)
  3. D. Maystre, Diffraction gratings (SPIE Milestones series, 1992).
  4. E.G. Loewen and E. Popov, Diffraction gratings and applications (Marcel Dekker, 1997).
  5. D. Maystre, "Rigorous vector theories of diffraction gratings" in Progress in Optics Volume XXI,E. Wolf ed.(North-Holland, Amsterdam, 1984).
    [CrossRef]
  6. D. Maystre, "General study of grating anomalies from electromagnetic surface modes," in Electromagnetic surface modes, A.D. Boardman ed.(John Wiley &sons, 1982).
  7. E. Yablonovitch, "Photonic crystals," J. of Modern Optics 41, 173-194 (1994).
    [CrossRef]
  8. C.M. Soukoulis, Photonic band gap materials (Kluwer Academic publishers, 1995).
  9. J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic crystals (Princeton university press, 1995).
  10. D. Maystre, "Electromagnetic study of photonic band gaps," Pure Appl. Opt. 3, 975-993 (1994).
    [CrossRef]
  11. R.C.McPhedran and D. Maystre, "A detailed theoretical study of the anomalies of a sinusoidal diffraction grating," Optica Acta 21, 413-421 (1994).
    [CrossRef]
  12. F. Gadot, A. Chelnokov, A. De Lustrac, P. Crozat and J.M. Lourtioz, "Experimental demonstration of complete photonic band gap in graphite structure," Appl. Phys. Lett. 71, 1780-1782 (1997).
    [CrossRef]

Other (12)

R. Petit, Electromagnetic theory of gratings (Springer-Verlag, 1980).
[CrossRef]

M. C. Hutley, Diffraction gratings (Academic press, 1982)

D. Maystre, Diffraction gratings (SPIE Milestones series, 1992).

E.G. Loewen and E. Popov, Diffraction gratings and applications (Marcel Dekker, 1997).

D. Maystre, "Rigorous vector theories of diffraction gratings" in Progress in Optics Volume XXI,E. Wolf ed.(North-Holland, Amsterdam, 1984).
[CrossRef]

D. Maystre, "General study of grating anomalies from electromagnetic surface modes," in Electromagnetic surface modes, A.D. Boardman ed.(John Wiley &sons, 1982).

E. Yablonovitch, "Photonic crystals," J. of Modern Optics 41, 173-194 (1994).
[CrossRef]

C.M. Soukoulis, Photonic band gap materials (Kluwer Academic publishers, 1995).

J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic crystals (Princeton university press, 1995).

D. Maystre, "Electromagnetic study of photonic band gaps," Pure Appl. Opt. 3, 975-993 (1994).
[CrossRef]

R.C.McPhedran and D. Maystre, "A detailed theoretical study of the anomalies of a sinusoidal diffraction grating," Optica Acta 21, 413-421 (1994).
[CrossRef]

F. Gadot, A. Chelnokov, A. De Lustrac, P. Crozat and J.M. Lourtioz, "Experimental demonstration of complete photonic band gap in graphite structure," Appl. Phys. Lett. 71, 1780-1782 (1997).
[CrossRef]

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Figures (4)

Fig.1.
Fig.1.

Structure of a photonic crystal grating. Left: grating made with dielectric rods in air, right: grating made by air galleries in a dielectric substrate (inverted contrast).

Fig.2.
Fig.2.

Efficiency of a photonic crystal grating (see the left hand side of fig.1) in a -1st order Littrow mount and s-polarization. From (a) to (f), the values of R′/d are respectively equal to 0.1, 0.125, 0.15, 0.175, 0.2, 0.25.

Fig.3.
Fig.3.

Efficiency of photonic crystal gratings with inverted contrast for h=d√3/2. From a to c, R′ is equal to 0.25, 0.325 and 0.4.

Fig. 4..
Fig. 4..

Efficiency of photonic crystal gratings with inverted contrast for h=0.41 The top grid is made of elliptic rods with a semi-axis along the vertical (parallel to the y axis) direction equal to 0.4. From a to f, the horizontal (parallel to the x axis) semi-axis is equal to 0.4, 0.5, 0.6, 0.8, 1., 1.2.

Equations (2)

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λ d g = 2 sin ( θ )
λ d = 2 M sin ( θ )

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