Abstract

A high-density dielectric rectangular grating is designed for color separation in a Fresnel diffraction field. The Fresnel field distribution is analyzed and the optimization conditions for color separation are given. The process of the modes propagating and energy exchanging with the diffraction orders are expressed by modal method. The color separation for different polarizations can be realized. The energy efficiency is 96.3% at the 633 nm wavelength and 86.9% at the 488 mm wavelength for both TE polarizations, while the energy efficiency is theoretically 96.3% at the 633 nm wavelength for TE polarization and 90.6% at the 488 nm wavelength for TM polarization. The field distributions are scanned by the near-field scanning optical microscopy, and the efficiency is 71.2% for the 633 nm wavelength and 67.3% for the 488 nm wavelength for both TE polarizations experimentally.

© 2012 Optical Society of America

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References

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2011 (1)

J. Wu, C. Zhou, H. Cao, A. Hu, J. Yu, W. Sun, and W. Jia, “Beam splitting of a double-groove fused-silica grating under normal incidence,” J. Opt. 13, 115703 (2011).
[CrossRef]

2010 (2)

2009 (1)

2008 (3)

2007 (2)

2006 (2)

Y. Lu, C. Zhou, S. Wang, and B. Wang, “Polarization-dependent Talbot effect,” J. Opt. Soc. Am. A 23, 2154–2160 (2006).
[CrossRef]

A. Drauschke, “Analysis of nearly depth-independent transmission of lamellar gratings in zeroth diffraction order in TM polarization,” J. Opt. 8, 511–517 (2006).
[CrossRef]

2005 (2)

2004 (1)

1998 (1)

1993 (1)

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553–573 (1993).
[CrossRef]

1981 (1)

I. 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]

1967 (1)

Adams, J. L.

I. 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]

Andreas, T.

Andrewartha, J. R.

I. 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]

Baets, R.

Botten, I. C.

I. 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]

Brixner, B.

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, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981).
[CrossRef]

Davis, C. C.

Delbeke, D.

Dong, Q.

Drauschke, A.

A. Drauschke, “Analysis of nearly depth-independent transmission of lamellar gratings in zeroth diffraction order in TM polarization,” J. Opt. 8, 511–517 (2006).
[CrossRef]

Ernst-Bernhard, K.

Feng, J.

Frank, B.

Hu, A.

J. Wu, C. Zhou, H. Cao, A. Hu, J. Yu, W. Sun, and W. Jia, “Beam splitting of a double-groove fused-silica grating under normal incidence,” J. Opt. 13, 115703 (2011).
[CrossRef]

Jia, W.

J. Wu, C. Zhou, H. Cao, A. Hu, J. Yu, W. Sun, and W. Jia, “Beam splitting of a double-groove fused-silica grating under normal incidence,” J. Opt. 13, 115703 (2011).
[CrossRef]

J. Feng, C. Zhou, B. Wang, J. Zheng, W. Jia, H. Cao, and P. Lv, “Three-port beam splitter of a binary fused-silica grating,” Appl. Opt. 47, 6638–6643 (2008).
[CrossRef]

Kämpfe, T.

Kley, E.-B.

Li, L.

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553–573 (1993).
[CrossRef]

Lu, P.

Lu, Y.

Lv, P.

Ma, J.

McPhedran, R. C.

I. 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]

Muys, P.

Offerhaus, H. L.

Parriaux, O.

Peschel, U.

Rathgen, H.

Roland, H.

Smolyaninov, I. I.

Sun, W.

J. Wu, C. Zhou, H. Cao, A. Hu, J. Yu, W. Sun, and W. Jia, “Beam splitting of a double-groove fused-silica grating under normal incidence,” J. Opt. 13, 115703 (2011).
[CrossRef]

Tan, Y.

Teng, S.

Thomas, K.

Tina, C.

Tishchenko, A.

Tishchenko, A. V.

Tünnermann, A.

Wang, B.

Wang, S.

Wu, J.

J. Wu, C. Zhou, H. Cao, A. Hu, J. Yu, W. Sun, and W. Jia, “Beam splitting of a double-groove fused-silica grating under normal incidence,” J. Opt. 13, 115703 (2011).
[CrossRef]

Yu, J.

J. Wu, C. Zhou, H. Cao, A. Hu, J. Yu, W. Sun, and W. Jia, “Beam splitting of a double-groove fused-silica grating under normal incidence,” J. Opt. 13, 115703 (2011).
[CrossRef]

Zhang, N.

Zheng, J.

Zhou, C.

Appl. Opt. (5)

J. Mod. Opt. (1)

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mod. Opt. 40, 553–573 (1993).
[CrossRef]

J. Opt. (2)

J. Wu, C. Zhou, H. Cao, A. Hu, J. Yu, W. Sun, and W. Jia, “Beam splitting of a double-groove fused-silica grating under normal incidence,” J. Opt. 13, 115703 (2011).
[CrossRef]

A. Drauschke, “Analysis of nearly depth-independent transmission of lamellar gratings in zeroth diffraction order in TM polarization,” J. Opt. 8, 511–517 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Acta (1)

I. 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 (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

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]

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the grating.

Fig. 2.
Fig. 2.

Diffraction distributions of different incident lights for (a) 633 nm, (b) 532 nm, and (c) 488 nm.

Fig. 3.
Fig. 3.

The profile of the grating modes.

Fig. 4.
Fig. 4.

Intensity distribution of the two incident lights with the 633 nm and 488 nm wavelengths at plane z=4.2μm.

Fig. 5.
Fig. 5.

Intensity distribution of the two incident lights with the 633 nm wavelength for TE polarization and 488 nm for TM polarization at plane z=4.2μm.

Fig. 6.
Fig. 6.

The configuration of the (a) experimental setup and (b) sample stage.

Fig. 7.
Fig. 7.

Experimental results scanned by NSOM at z=4.2μm: (a) the near-field grating profile scanning, (b) the field distribution with the wavelength at 633 nm, (c) the field distribution with the wavelength at 488 nm, and (d) the intensity distribution at the same cross section from 7(b) and 7(c).

Equations (10)

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I=Etot×Etot*=E02+4E0E+1cos[(β0β+1)z+(φ0φ+1)]cos(Kx)+4E+12cos2(Kx),
maxxmaxd4xmax+d4Idx,
E0=2E+1.
{(βr0βr1)z+(ϕr0ϕr1)=2mπ,mintegral(βb0βb1)z+(ϕb0ϕb1)=(n+12)π,nintegral,
F(neff2)=cos(k1fd)cos(k2(1f)d)k12+k222k1k2sin(k1fd)sin(k2(1f)d)=cos(kx,incd),
ϕe={cos(k1x)0|x|fd/2cos(k1fd/2)cos[k2(|x|fd/2)]k1k2sin(k1fd/2)sin[k2(|x|fd/2)]fd/2|x|d/2,
ϕe={1k1sin(k1x)0|x|fd/21k1sgn(x){sin(k1x/2)cos[k2(|x|fd/2)]+k1k2cos(k1fd/2)sin[k2(|x|fd/2)]fd/2|x|d/2.
tq=|Eyn(x,0)·φm(x)dx|2|Eyn(x,0)|2dx·|φm(x)|2dx.
t0φ0(x)exp(ikzneff0h)+t2φ2(x)exp(ikzneff2h)=E1eikx,difx+E0+E1eikx,difx,
F(neff2)=cos(k1fd)cos(k2(1f)d)ε12k12+ε22k222ε1ε2k1k2sin(k1fd)sin(k2(1f)d)=cos(kx,incd).

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