Abstract

A simplified modal method (SMM) is presented that offers a clear physical image for subwavelength slanted grating. The diffraction characteristic of the slanted grating under Littrow configuration is revealed by the SMM as an equivalent rectangular grating, which is in good agreement with rigorous coupled-wave analysis. Based on the equivalence, we obtained an effective analytic solution for simplifying the design and optimization of a slanted grating. It offers a new approach for design of the slanted grating, e.g., a 1×2 beam splitter can be easily designed. This method should be helpful for designing various new slanted grating devices.

© 2014 Optical Society of America

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References

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2013 (2)

2012 (1)

J. Kimmel and T. Levola, J. Photon. Energy 2, 024501 (2012).
[CrossRef]

2011 (1)

2008 (2)

2007 (2)

2005 (3)

1997 (2)

1995 (2)

M. G. Moharam, E. B. Grann, D. A. Pommetand, and T. K. Gaylord, J. Opt. Soc. Am. A. 12, 1068 (1995).

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A. 12, 1077 (1995).
[CrossRef]

1981 (1)

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

Abushagur, M. A. G.

Adams, J. L.

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

Andrewartha, J. R.

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

Bi, Q.

Botten, L. C.

S. Campbell, L. C. Botten, R. C. Mchedran, and C. Martijn de Sterke, J. Opt. Soc. Am. A 25, 2415 (2008).
[CrossRef]

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

Bouzid, A.

Cambril, E.

Campbell, S.

Cao, H.

Chavel, P.

Clausnitzer, T.

Craig, M. S.

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

de beaucoudrey, N.

Feng, J.

Friesem, A. A.

Gaylord, T. K.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A. 12, 1077 (1995).
[CrossRef]

M. G. Moharam, E. B. Grann, D. A. Pommetand, and T. K. Gaylord, J. Opt. Soc. Am. A. 12, 1068 (1995).

Golub, M. A.

Grann, E. B.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A. 12, 1077 (1995).
[CrossRef]

M. G. Moharam, E. B. Grann, D. A. Pommetand, and T. K. Gaylord, J. Opt. Soc. Am. A. 12, 1068 (1995).

Hu, A.

Jia, W.

Kämpfe, T.

Kimmel, J.

J. Kimmel and T. Levola, J. Photon. Energy 2, 024501 (2012).
[CrossRef]

Kley, E.-B.

Laakonen, P.

Levola, T.

J. Kimmel and T. Levola, J. Photon. Energy 2, 024501 (2012).
[CrossRef]

T. Levola and P. Laakonen, Opt. Express 15, 2067 (2007).
[CrossRef]

Lin, Z.

Lv, P.

Martijn de Sterke, C.

Mchedran, R. C.

McPhedran, R. C.

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

Miller, J. M.

Moharam, M. G.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A. 12, 1077 (1995).
[CrossRef]

M. G. Moharam, E. B. Grann, D. A. Pommetand, and T. K. Gaylord, J. Opt. Soc. Am. A. 12, 1068 (1995).

Parriaux, O.

Peschel, U.

Pommet, D. A.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A. 12, 1077 (1995).
[CrossRef]

Pommetand, D. A.

M. G. Moharam, E. B. Grann, D. A. Pommetand, and T. K. Gaylord, J. Opt. Soc. Am. A. 12, 1068 (1995).

Sun, M.

Sun, W.

Tishchenko, A.

Tishchenko, A. V.

Tünnermann, A.

Turunen, J.

Wang, B.

Wang, S.

Wu, J.

Xie, X.

Yang, X.

Zheng, J.

Zhou, C.

Appl. Opt. (3)

Chin. Opt. Lett. (2)

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. A. (2)

M. G. Moharam, E. B. Grann, D. A. Pommetand, and T. K. Gaylord, J. Opt. Soc. Am. A. 12, 1068 (1995).

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A. 12, 1077 (1995).
[CrossRef]

J. Photon. Energy (1)

J. Kimmel and T. Levola, J. Photon. Energy 2, 024501 (2012).
[CrossRef]

Opt. Acta (1)

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

Opt. Express (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

A. V. Tishchenko, Opt. Quantum Electron. 37, 309 (2005).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Configuration of a slanted grating.

Fig. 2.
Fig. 2.

Comparison of diffraction efficiencies between equivalent rectangular grating (R) and slanted grating (S). Diffraction efficiencies of the transmission orders are obtained by using RCWA. + stands for the SMM for equivalence rectangular grating. Slanted angle φs: 15 degree. Period d: 1216 nm. f=0.5. Refractive indices of the top substrate and bottom substrate are ne. nr=1.44462. ng=1.

Fig. 3.
Fig. 3.

Diffraction efficiencies of the transmission orders are obtained by using RCWA.

Tables (1)

Tables Icon

Table 1. Corresponding Parameters of the Equivalence of Slanted Grating and Rectangular Grating

Equations (7)

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U(x1,y1)=τ×t×{c1reik02εrβ2x1+c2reik02εrβ2x1nd1x1b1+nd1c1geik02εgβ2x1+c2geik02εgβ2x1b1+nd1x1d1+nd.
cos[kg(d1b1)]cos(krb1)(kr2+kg2)(2krkg)sin[kg(d1b1)]sin(krb1)=1,
η1=sin2(Δφ/2),
η0=cos2(Δφ/2),
n1sinθin=λ/2dtanφs[ne2/(1+tan2φs)(λ2d)2]1/2.
Δφ=(n0effn1eff)=(2m1)π/2.
h1=λ/[4(n0effn1eff)].

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