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.

© 2001 Optical Society of America

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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]

1997 (1)

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]

1994 (3)

E. Yablonovitch, “Photonic crystals,” J. of Modern Optics 41, 173–194 (1994)
[CrossRef]

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]

Chelnokov, A.

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]

Crozat, P.

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]

De Lustrac, A.

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]

Gadot, F.

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]

Hutley, M. C.

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

Joannopoulos, J. D.

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

Loewen, E.G.

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

Lourtioz, J.M.

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]

Maystre, D.

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]

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

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

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

McPhedran, R.C.

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]

Meade, R. D.

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

Petit, R.

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

Popov, E.

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

Soukoulis, C.M.

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

Winn, J. N.

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

Yablonovitch, E.

E. Yablonovitch, “Photonic crystals,” J. of Modern Optics 41, 173–194 (1994)
[CrossRef]

Appl.Phys. Lett. (1)

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]

J. of Modern Optics (1)

E. Yablonovitch, “Photonic crystals,” J. of Modern Optics 41, 173–194 (1994)
[CrossRef]

Optica Acta (1)

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]

Pure Appl. Opt. (1)

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

Other (8)

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)

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)

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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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