Abstract

The validity and accuracy of the simplified modal method for a highly efficient transmission subwavelength triangular grating are fully and quantitatively evaluated by a comparison of diffraction efficiencies predicted from the modal method to exact results calculated by a rigorous coupled wave analysis. The larger errors are revealed in smaller periods and in lower groove depths. More importantly, with the consideration of the reflection loss of the two propagating modes, the accuracy of the simplified modal method is significantly enhanced. The calculated diffraction efficiencies are in good agreement with the results of the vector method. This enhanced simplified modal method can be effectively used in the design of a shallower subwavelength grating. It is important to note that the consideration of the modal reflection loss can be applicable to any dielectric diffraction structure, e.g., the rectangular grating, in which the accuracy of the simplified modal method could be excellently improved to more exactly design a grating.

© 2012 Optical Society of America

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References

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2010 (1)

2009 (2)

2008 (3)

2007 (1)

2005 (1)

1997 (1)

1995 (2)

1981 (1)

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

Adams, J. L.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

Andrewartha, J. R.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

Botten, I. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

Boyd, R. D.

Britten, J. A.

Bryan, S. J.

Cao, H.

Cheng, C.

Clausnitzer, T.

Craig, M. S.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

Fainman, Y.

Fan, Z.

Feng, J.

Gaylord, T. K.

Grann, E. B.

He, H.

Jin, Y.

Jing, X.

Kämpfe, T.

Kley, E. B.

Liu, S.

Lu, P.

Lv, P.

Ma, J.

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters (Institute of Physics Publishing, 2001), p. 41.

McPhedran, R. C.

I. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, and J. R. Andrewartha, Opt. Acta 28, 413 (1981).
[CrossRef]

Moharam, M. G.

Nguyen, H. T.

Parriaux, O.

Perry, M. D.

Peschel, U.

Pommet, D. A.

Scherer, A.

Shao, J.

Shore, B. W.

Sun, P.

Tishchenko, A.

Tishchenko, A. V.

Tünnermann, A.

Tyan, R.

Wang, B.

Xu, F.

Zheng, J.

Zhou, C.

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of a subwavelength transmission grating.

Fig. 2.
Fig. 2.

Comparison of diffraction efficiencies between RCWA and the simplified modal method.

Fig. 3.
Fig. 3.

Reflection of the first two propagating modes with respect to (a) the grating period and (b) the groove depth, respectively.

Fig. 4.
Fig. 4.

Enhanced accuracy of the simplified modal method with the consideration of modes reflection.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

η0T=cos2(Δφ/2),
η1T=sin2(Δφ/2),
[BC]={q=1N[cosδq(isinδq)/ηqiηqsinδqcosδq]}[1ηs],
R=(η0neffairYneffsubη0neffair+Yneffsub)(η0neffairYneffsubη0neffair+Yneffsub)*,
η0=η0T·[1(1/2)R0]·[1(1/2)R1],
η1=η1T·[1(1/2)R0]·[1(1/2)R1],

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