Abstract

We have proposed a novel transmission slanted grating at the central wavelength of 1550 nm, which can be used in optical communication. We have presented an approximate analytical expression that provides an insightful physical description of the simplified modal method for the slanted grating. The odd grating mode, which only exists in the asymmetric structure under normal incidence, plays the positive role of enhancing the 1st order diffraction efficiency. The analytic expressions of mode conversion and coupling can be obtained to explain the asymmetric field distribution, which cannot occur in the rectangular grating region. Numerical results achieved by the rigorous wave analysis verify the validity of the simplified modal method. We expect that the theoretical modal method set forth in this work will be helpful for the tremendous potential application of the slanted grating.

© 2014 Optical Society of America

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S. Li, C. Zhou, H. Cao, and J. Wu, Opt. Lett 39, 781 (2014).
[CrossRef]

2013

2012

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, J. Opt. 14, 055705 (2012).
[CrossRef]

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, Appl. Opt. 51, 4902 (2012).
[CrossRef]

2011

2008

2007

2005

2004

2001

B. Chernov, M. Neviere, and E. Popov, Opt. Commun. 194, 289 (2001).
[CrossRef]

1997

1996

1995

1984

1983

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

1981

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]

Bi, Q.

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]

Botten, L. C.

Cambril, E.

Campbell, S.

Cao, H.

S. Li, C. Zhou, H. Cao, and J. Wu, Opt. Lett 39, 781 (2014).
[CrossRef]

J. Wu, C. Zhou, H. Cao, A. Hu, W. Sun, and W. Jia, Chin. Opt. Lett. 11, 060501 (2013).
[CrossRef]

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, J. Opt. 14, 055705 (2012).
[CrossRef]

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, Appl. Opt. 51, 4902 (2012).
[CrossRef]

Chavel, P.

Chernov, B.

B. Chernov, M. Neviere, and E. Popov, Opt. Commun. 194, 289 (2001).
[CrossRef]

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]

de Beaucoudrey, N.

de Sterke, C. M.

Feng, J.

Gaylord, T. K.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Granet, G.

Grann, E. B.

Guizal, B.

Hu, A.

Jia, W.

Käpfe, T.

Kikuta, H.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Kley, E. B.

Laakonen, P.

Lalanne, P.

Levola, T.

Li, L.

Li, S.

S. Li, C. Zhou, H. Cao, and J. Wu, Opt. Lett 39, 781 (2014).
[CrossRef]

Lin, Z.

Loewen, E. G.

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997), Chap. 5.

Lv, P.

Maikisch, J. S.

McHedran, R. C.

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]

Miller, J. M.

Moharam, M. G.

Morris, G. M.

Neviere, M.

B. Chernov, M. Neviere, and E. Popov, Opt. Commun. 194, 289 (2001).
[CrossRef]

Okanno, M.

Parriaux, O.

Peschel, U.

Pommet, D. A.

Popov, E.

B. Chernov, M. Neviere, and E. Popov, Opt. Commun. 194, 289 (2001).
[CrossRef]

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997), Chap. 5.

Sun, M.-Z.

Sun, W.

Tishchenko, A. V.

Tünermann, A.

Turunen, J.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Wang, B.

Wang, S.

Wu, J.

Xie, X.

Yamamoto, K.

Yang, X.

Yokomori, K.

Yotsuya, T.

Yu, J.

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, Appl. Opt. 51, 4902 (2012).
[CrossRef]

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, J. Opt. 14, 055705 (2012).
[CrossRef]

Zheng, J.

Zhou, C.

Appl. Opt.

Chin. Opt. Lett.

J. Opt.

A. Hu, C. Zhou, H. Cao, J. Wu, J. Yu, and W. Jia, J. Opt. 14, 055705 (2012).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Acta

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

Opt. Commun.

B. Chernov, M. Neviere, and E. Popov, Opt. Commun. 194, 289 (2001).
[CrossRef]

Opt. Express

Opt. Lett

S. Li, C. Zhou, H. Cao, and J. Wu, Opt. Lett 39, 781 (2014).
[CrossRef]

Opt. Lett.

Science

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 671 (1983).
[CrossRef]

Other

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997), Chap. 5.

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of a slanted grating under normal incidence.

Fig. 2.
Fig. 2.

Mode profiles of the three grating propagating modes for TE polarization.

Fig. 3.
Fig. 3.

Schematic of one period for the two adjacent lamellar gratings, one offset from the other by Δx. 0, 1, 2, stand for modes 0, 1, and 2, respectively. In the first layer, only modes 0 and 1 can be excited. In the other layers, mode 2 can also be excited.

Fig. 4.
Fig. 4.

Comparison of diffraction efficiencies between RCWA (R) and the simplified modal method (SMM).

Tables (1)

Tables Icon

Table 1. Coupling Energy Coefficients of Odd and Even Grating Modes for Three Diffractive Waves Obtained by Simplified Modal Method

Equations (20)

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

Eyin=a0u0(x)+a1u1(x).
a=(a0,a1,0)T.
u2m(xΔx)=u1m(x).
u1m(x)=u2m(x)u2m(x)Δx.
Tinter=I+MΔx,
M(i,j)=0du2i(x)u2j*(x)dx.
Tpad=NTinterN,
N=diag[e(iβmΔz/2)],
Tpad=I+KΔz,
Δz=Δx/tanθ,
K=idiag(βm)+Mtanθ.
T=limn(I+KΔz)n=limn(I+Kh/n)n=ehK.
Eyout(x,h)=E1eikxx+E0+E1eikxx=02am(h)um(x),
a(h)=Ta(0).
E0=1d0d02am(h)um(x)dx,
E1=1d0d02am(h)um(x)eikxxdx,
E1=1d0d02am(h)um(x)eikxxdx.
E1=1d0da2(h)u2(x)eikxxdx+1d[0da1(h)u1(x)eikxxdx+0da0(h)u0(x)eikxxdx]=E1odd+E1even.
E0=E0odd+E0even,
E1=E1odd+E1even.

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