Abstract

A new approach for the realization of highly dispersive dielectric transmission gratings is presented, which enables the suppression of any reflection losses and, thus, 100% diffraction efficiency. By applying a simple two-mode-model a comprehensible explanation as well as a theoretical design of such a reflection-free transmission grating is presented.

© 2008 Optical Society of America

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References

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  1. M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1391 (1982).
    [CrossRef]
  2. T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, U. Peschel, A. V. Tishchenko, and O. Parriaux, "An intelligible explanation of highly-efficient diffraction in deep dielectric rectangular transmission gratings," Opt. Express 13, 10448-10456 (2005).
    [CrossRef] [PubMed]
  3. J. Turunen, "Diffraction theory of dielectric surface relief gratings," in Micro-optics, H.P. Herzig ed. (Taylor&Francis Inc., 1997).
  4. J. Nishii, K. Kintaka, and T. Nakazawa, "High-Efficiency Transmission Gratings Buried in a Fused-SiO2 Glass Plate," Appl. Opt. 43, 1327-1330 (2004).
    [CrossRef] [PubMed]
  5. L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta. 28, 413-428 (1981).
    [CrossRef]
  6. A. V. Tishchenko, "Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method," Opt. Quantum Electron. 37, 309-330 (2005).
    [CrossRef]
  7. P. Lalanne, J. P. Hugonin, and P. Chavel, "Optical properties of deep lamellar Gratings: A coupled Bloch-mode insight," J. Lightwave Technol. 24, 2442- 2449 (2006).
    [CrossRef]
  8. J. Y. Suratteau, M. Cadilhac, and R. Petit, "Sur la détermination numerique des efficacités de certains réseaux diélectriques profonds," J. Opt. 14, 273-288 (1983).
    [CrossRef]
  9. E. B. Kley, H. J. Fuchs, and K. Zöllner, "Fabrication technique for high-aspect-ratio gratings," in Micromachine Technology for Diffractive and Holographic Optics, Proc. SPIE 3879, S. H. Lee, J. A. Cox, Eds., 71-78 (1999).
  10. T. Clausnitzer, T. Kämpfe, E.-B. Kley, A. Tünnermann, A. V. Tishchenko, and O. Parriaux, "Investigation of the polarization-dependent diffraction of deep dielectric rectangular transmission gratings," Appl. Opt. 46, 819-826 (2007).
    [CrossRef] [PubMed]

2007

2006

2005

2004

1983

J. Y. Suratteau, M. Cadilhac, and R. Petit, "Sur la détermination numerique des efficacités de certains réseaux diélectriques profonds," J. Opt. 14, 273-288 (1983).
[CrossRef]

1982

1981

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta. 28, 413-428 (1981).
[CrossRef]

Appl. Opt.

J. Lightwave Technol.

J. Opt.

J. Y. Suratteau, M. Cadilhac, and R. Petit, "Sur la détermination numerique des efficacités de certains réseaux diélectriques profonds," J. Opt. 14, 273-288 (1983).
[CrossRef]

J. Opt. Soc. Am.

Opt. Acta.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta. 28, 413-428 (1981).
[CrossRef]

Opt. Express

Opt. Quantum Electron.

A. V. Tishchenko, "Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method," Opt. Quantum Electron. 37, 309-330 (2005).
[CrossRef]

Other

E. B. Kley, H. J. Fuchs, and K. Zöllner, "Fabrication technique for high-aspect-ratio gratings," in Micromachine Technology for Diffractive and Holographic Optics, Proc. SPIE 3879, S. H. Lee, J. A. Cox, Eds., 71-78 (1999).

J. Turunen, "Diffraction theory of dielectric surface relief gratings," in Micro-optics, H.P. Herzig ed. (Taylor&Francis Inc., 1997).

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Figures (8)

Fig. 1.
Fig. 1.

Grating and illumination parameters.

Fig. 2.
Fig. 2.

Reflection of a rectangular surface relief fused silica transmission grating as a function of the grating period, and the corresponding Fresnel-reflection at a plane air-fused silica interface (wavelength 1.064µm, TE-polarized illumination).

Fig. 3.
Fig. 3.

The two-mode-diffraction model.

Fig. 4.
Fig. 4.

Effective indices of the two propagating modes against the fill factor.

Fig. 5.
Fig. 5.

Reflection of the two modes at the grating-air (blue) and the grating-substrate (green) interface.

Fig. 6.
Fig. 6.

Simulation of the reflection according to Eq. (7). The dashed white lines represent the groove depths where a complete suppression of the reflection is achieved (Eq. (6)).

Fig. 7.
Fig. 7.

(a) Simulation of the diffraction efficiency of a buried grating with a 600nm period as a function of the profile parameters, according to the two-mode-model Eq. (9) (wavelength 1064nm, Littrow-configuration). (b) Corresponding numerical calculation by rigorous Fourier modal method.

Fig. 8.
Fig. 8.

Numerical simulation of the diffraction efficiency of the corresponding surface relief grating. The maximum diffraction efficiency is 93%.

Equations (11)

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sin φ in = λ 2 p ,
λ 2 < p < 3 λ 2 n
η 1 T ( f , h ) = sin 2 ( π 2 h h max ( f ) )
η 0 T ( f , h ) = cos 2 ( π 2 h h max ( f ) ) ,
h max ( f ) = λ 2 Δ n eff ( f ) = λ 2 n eff 0 ( f ) n eff 1 ( f ) .
R m air sub ( f ) = ( n eff m ( f ) n eff air sub n eff m ( f ) + n eff air sub ) 2 ,
h R ( f ) = λ 2 n eff 1 ( f ) ,
R ( f , h ) = 1 2 · F ( f ) · sin 2 ( π h h R ( f ) ) 1 + F ( f ) · sin 2 ( π h h R ( f ) ) , where F ( f ) = 4 R 1 sub ( f ) ( 1 R 1 sub ( f ) ) 2 .
R max ( f ) = 1 1 1 + F ( f ) 2 ,
η 1 ( f , h ) = η 1 T ( f , h ) · ( 1 R ( f , h ) )
= sin 2 ( π 2 h h max ( f ) ) · 1 + 1 2 F ( f ) · sin 2 ( π h h R ( f ) ) 1 + F ( f ) · sin 2 ( π h h R ( f ) ) .

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