Abstract

Two-dimensional (crossed) diffraction gratings with sinusoidal or truncated pyramidal (trapezoidal) profiles are proposed to have diffraction efficiency almost independent of the incident polarization inside the optical communication spectral window 1.51.6μm. The gratings are characterized by different periods in the two orthogonal directions, chosen to support only one dispersive diffraction order in addition to the zeroth (specular) one.

© 2008 Optical Society of America

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References

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    [CrossRef] [PubMed]
  11. J. Hoose, “Optical diffraction grating structure with reduced polarization sensitivity,” U.S. patent 6,487,019 (26 November 2002).
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  13. E. Popov, J. Hoose, B. Frankel, C. Keast, M. Fritze, T. Y. Fan, D. Yost, and S. Rabe, “Low polarization dependent diffraction grating for wavelength demultiplexing,” Opt. Express 12, 269-275 (2004).
    [CrossRef] [PubMed]
  14. J. Chandezon, M. T. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72, 839-846 (1982).
    [CrossRef]
  15. E. Popov and L. Mashev, “Convergence of Rayleigh Fourier method and rigorous differential method for relief diffraction gratings,” Opt. Acta 33, 593-605 (1986).
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2006 (3)

2005 (2)

2004 (1)

2001 (1)

1997 (1)

E. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

1996 (1)

1993 (1)

M. Sabeva, E. Popov, and L. Tsonev, “Reflection gratings in the visible region: efficiency in non-polarized light,” Opt. Commun. 100, 39-42 (1993).
[CrossRef]

1992 (1)

J.-P. Laude, Le multiplexage de Longueurs d'Onde (Masson, 1992).

1986 (1)

E. Popov and L. Mashev, “Convergence of Rayleigh Fourier method and rigorous differential method for relief diffraction gratings,” Opt. Acta 33, 593-605 (1986).
[CrossRef]

1984 (1)

1982 (1)

Adibi, A.

Askari, M.

Baba, T.

Bozhkov, B.

Capmany, J.

Chandezon, J.

Cornet, G.

Dupuis, M. T.

Fan, T. Y.

Frankel, B.

Frankel, R.

J. Hoose, R. Frankel, and E. Popov, “Diffractive structure for high-dispersion WDM applications,” U.S. patent 6,496,622(17 December 2002).

Fritze, M.

Fujita, Sh.

Hao, Y.

Hoose, J.

J. Hoose, “Optical diffraction grating structure with reduced polarization sensitivity,” U.S. patent 6,487,019 (26 November 2002).

E. Popov, J. Hoose, B. Frankel, C. Keast, M. Fritze, T. Y. Fan, D. Yost, and S. Rabe, “Low polarization dependent diffraction grating for wavelength demultiplexing,” Opt. Express 12, 269-275 (2004).
[CrossRef] [PubMed]

J. Hoose, R. Frankel, and E. Popov, “Diffractive structure for high-dispersion WDM applications,” U.S. patent 6,496,622(17 December 2002).

Huang, J.

Jiang, X.

Keast, C.

Laude, J.-P.

J.-P. Laude, Le multiplexage de Longueurs d'Onde (Masson, 1992).

Li, L.

Loewen, E.

E. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

Mashev, L.

E. Popov and L. Mashev, “Convergence of Rayleigh Fourier method and rigorous differential method for relief diffraction gratings,” Opt. Acta 33, 593-605 (1986).
[CrossRef]

Matsumoto, T.

Maystre, D.

Mohammadi, S.

Momeni, B.

Muñoz, P.

Nevière, M.

Pastor, D.

Popov, E.

E. Popov, J. Hoose, B. Frankel, C. Keast, M. Fritze, T. Y. Fan, D. Yost, and S. Rabe, “Low polarization dependent diffraction grating for wavelength demultiplexing,” Opt. Express 12, 269-275 (2004).
[CrossRef] [PubMed]

E. Popov, B. Bozhkov, and M. Nevière, “Almost perfect blazing by photonic crystal rod grating,” Appl. Opt. 40, 2417-2422(2001).
[CrossRef]

E. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

M. Sabeva, E. Popov, and L. Tsonev, “Reflection gratings in the visible region: efficiency in non-polarized light,” Opt. Commun. 100, 39-42 (1993).
[CrossRef]

E. Popov and L. Mashev, “Convergence of Rayleigh Fourier method and rigorous differential method for relief diffraction gratings,” Opt. Acta 33, 593-605 (1986).
[CrossRef]

J. Hoose, R. Frankel, and E. Popov, “Diffractive structure for high-dispersion WDM applications,” U.S. patent 6,496,622(17 December 2002).

Rabe, S.

Rakhshandehroo, M.

Sabeva, M.

M. Sabeva, E. Popov, and L. Tsonev, “Reflection gratings in the visible region: efficiency in non-polarized light,” Opt. Commun. 100, 39-42 (1993).
[CrossRef]

Soltani, M.

Tekeste, M.

Tsonev, L.

M. Sabeva, E. Popov, and L. Tsonev, “Reflection gratings in the visible region: efficiency in non-polarized light,” Opt. Commun. 100, 39-42 (1993).
[CrossRef]

Wang, M.

Wu, Y.

Yang, J.

Yarrison-Rice, J.

Yokomori, K.

Yost, D.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

E. Popov and L. Mashev, “Convergence of Rayleigh Fourier method and rigorous differential method for relief diffraction gratings,” Opt. Acta 33, 593-605 (1986).
[CrossRef]

Opt. Commun. (1)

M. Sabeva, E. Popov, and L. Tsonev, “Reflection gratings in the visible region: efficiency in non-polarized light,” Opt. Commun. 100, 39-42 (1993).
[CrossRef]

Opt. Express (6)

Other (4)

J.-P. Laude, Le multiplexage de Longueurs d'Onde (Masson, 1992).

E. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

J. Hoose, “Optical diffraction grating structure with reduced polarization sensitivity,” U.S. patent 6,487,019 (26 November 2002).

J. Hoose, R. Frankel, and E. Popov, “Diffractive structure for high-dispersion WDM applications,” U.S. patent 6,496,622(17 December 2002).

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Figures (8)

Fig. 1
Fig. 1

Efficiency in order 1 of a 1D sinusoidal gold grating. (a) Incidence 40 ° , period d = 1.2056 μm , groove depth dependence at 1.55 μm wavelength. (b) Spectral dependence for h / d = 1.128 and parameters from (a). (c) groove depth dependence for an incidence of 60 ° and period d = 0.89489 μm .

Fig. 2
Fig. 2

Schematic 2D view of the double-sinusoidal grating with profile given by Eq. (1).

Fig. 3
Fig. 3

Top view of a 2D grating made of truncated pyramids (Fig. 4).

Fig. 4
Fig. 4

Side view of a 2D grating made of truncated pyramids.

Fig. 5
Fig. 5

Diffraction efficiency of two gratings with profiles given by Eq. (1) and Fig. 2. Gold substrate, covered with a 50 nm thick layer of Si O 2 , groove parameters optimized for two different angles of incidence θ x and 3 ° off-plane: (a)  60 ° incidence, d x = 0.89489 μm , h x = 0.39 μm , d z = 1.4 μm , h z = 0.88 μm ; (b)  70 ° incidence, d x = 0.82474 μm , h x = 0.3 μm , d z = 1.4 μm , h z = 0.72 μm .

Fig. 6
Fig. 6

Diffraction efficiency of two gratings with profiles given in Figs. 3, 4. Gold as substrate and bum material, 60 ° incidence ( θ x ) and 3 ° off-plane: (a)  80 ° slope of the pyramids, d x = 0.89489 μm , d z = 1.4 μm , bump height h = 0.49 μm , bump width at half-height 0.3 μm in x, 0.54 μm in z; (b)  70 ° slope of the pyramids, d x = 0.89489 μm , d z = 1.4 μm , bump height h = 0.49 μm , bump width at half-height 0.3 μm in x, 0.68 μm in z

Fig. 7
Fig. 7

Angular dependence of 1 st order efficiency of the truncated pyramidal grating with parameters presented in Fig. 6a for two slightly different periods in the x direction: d x = 0.895 μm and d x = 0.886 μm , as indicated in the legend. Wavelength 1.55 μm .

Fig. 8
Fig. 8

Tolerance with respect to the structure dimension. The grating parameters are the same as in Fig. 6a and the wavelength is equal to 1.55 μm : (a) groove depth dependence, (b) dependence on the truncated pyramids dimensions in z direction for h = 0.49 μm .

Equations (1)

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f ( x , z ) = h x 2 sin ( K x x ) + h z 2 sin ( K z z ) ,

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