Abstract

Here we show, analytically and numerically, that in a TiO2 double-groove grating with two different groove widths per period attached on the SiO2 substrate, the normally incident light couples to the +1st-order transmission with 96.9% efficiency and with a 50° diffraction angle that is larger than the SiO2–air interface critical angle. Modal anal ysis reveals that three propagating modes for the +1st diffraction order reach the grating back end in phase, while the corresponding propagating modes for the 1st and zeroth orders are added destructively at the grating end. Four optical devices based on this grating characteristic are numerically demonstrated.

© 2010 Optical Society of America

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2010 (4)

M. Oliva, D. Michaelis, T. Benkenstein, J. Dunkel, T. Harzendorf, A. Matthes, and U. D. Zeitner, Opt. Lett. 35, 2774 (2010).
[CrossRef] [PubMed]

H. Iizuka, N. Engheta, H. Fujikawa, and K. Sato, Micro. Opt. Tech. Lett. 52, 1362 (2010).
[CrossRef]

H. Iizuka, N. Engheta, H. Fujikawa, K. Sato, and Y. Takeda, Appl. Phys. Lett. 97, 053108 (2010).
[CrossRef]

S. H. Lim, M. S. M. Saifullah, H. Hussain, W. W. Loh, and H. Y. Low, Nanotechnology 21, 285303 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (4)

2007 (1)

2006 (1)

2005 (1)

2004 (1)

2001 (1)

2000 (2)

1999 (3)

1998 (2)

1996 (1)

1993 (1)

1992 (1)

1982 (1)

P. Sheng, R. S. Stepleman, and P. N. Sanda, Phys. Rev. B 26, 2907 (1982).
[CrossRef]

Astilean, S.

Astratov, V. N.

Benkenstein, T.

Borghi, R.

Cambril, E.

Chavel, P.

Clausnitzer, T.

Culshaw, I. S.

De La Rue, R. M.

Dunkel, J.

Engheta, N.

H. Iizuka, N. Engheta, H. Fujikawa, K. Sato, and Y. Takeda, Appl. Phys. Lett. 97, 053108 (2010).
[CrossRef]

H. Iizuka, N. Engheta, H. Fujikawa, and K. Sato, Micro. Opt. Tech. Lett. 52, 1362 (2010).
[CrossRef]

Farn, M. W.

Feng, J.

J. Feng, C. Zhou, J. Zheng, and B. Wang, Opt. Commun. 281, 5298 (2008).
[CrossRef]

J. Feng and Z. Zhou, Opt. Lett. 32, 1662 (2007).
[CrossRef] [PubMed]

Frezza, F.

Fujikawa, H.

H. Iizuka, N. Engheta, H. Fujikawa, and K. Sato, Micro. Opt. Tech. Lett. 52, 1362 (2010).
[CrossRef]

H. Iizuka, N. Engheta, H. Fujikawa, K. Sato, and Y. Takeda, Appl. Phys. Lett. 97, 053108 (2010).
[CrossRef]

Haidner, H.

Harzendorf, T.

Hugonin, J. P.

Huo, T.

Hussain, H.

S. H. Lim, M. S. M. Saifullah, H. Hussain, W. W. Loh, and H. Y. Low, Nanotechnology 21, 285303 (2010).
[CrossRef] [PubMed]

Iizuka, H.

H. Iizuka, N. Engheta, H. Fujikawa, K. Sato, and Y. Takeda, Appl. Phys. Lett. 97, 053108 (2010).
[CrossRef]

H. Iizuka, N. Engheta, H. Fujikawa, and K. Sato, Micro. Opt. Tech. Lett. 52, 1362 (2010).
[CrossRef]

Jin, C.

Kampfe, T.

Kley, E.-B.

Krauss, T. F.

Kuang, D.

Lalanne, P.

Launois, H.

Lee, M. S. L.

Li, L.

Lim, S. H.

S. H. Lim, M. S. M. Saifullah, H. Hussain, W. W. Loh, and H. Y. Low, Nanotechnology 21, 285303 (2010).
[CrossRef] [PubMed]

Lin, H.

Loh, W. W.

S. H. Lim, M. S. M. Saifullah, H. Hussain, W. W. Loh, and H. Y. Low, Nanotechnology 21, 285303 (2010).
[CrossRef] [PubMed]

Low, H. Y.

S. H. Lim, M. S. M. Saifullah, H. Hussain, W. W. Loh, and H. Y. Low, Nanotechnology 21, 285303 (2010).
[CrossRef] [PubMed]

Lu, N.

Matthes, A.

Michaelis, D.

Mu, G.

Oliva, M.

Pajewski, L.

Parriaux, O.

Peschel, U.

Pietarinen, J.

Rodier, J. C.

Saifullah, M. S. M.

S. H. Lim, M. S. M. Saifullah, H. Hussain, W. W. Loh, and H. Y. Low, Nanotechnology 21, 285303 (2010).
[CrossRef] [PubMed]

Sanda, P. N.

P. Sheng, R. S. Stepleman, and P. N. Sanda, Phys. Rev. B 26, 2907 (1982).
[CrossRef]

Santarsiero, M.

Sato, K.

H. Iizuka, N. Engheta, H. Fujikawa, K. Sato, and Y. Takeda, Appl. Phys. Lett. 97, 053108 (2010).
[CrossRef]

H. Iizuka, N. Engheta, H. Fujikawa, and K. Sato, Micro. Opt. Tech. Lett. 52, 1362 (2010).
[CrossRef]

Sauvan, C.

Schettini, G.

Sheng, P.

P. Sheng, R. S. Stepleman, and P. N. Sanda, Phys. Rev. B 26, 2907 (1982).
[CrossRef]

Sheridan, J. T.

Skolnick, M. S.

Stepleman, R. S.

P. Sheng, R. S. Stepleman, and P. N. Sanda, Phys. Rev. B 26, 2907 (1982).
[CrossRef]

Stevenson, R. M.

Streibl, N.

Takeda, Y.

H. Iizuka, N. Engheta, H. Fujikawa, K. Sato, and Y. Takeda, Appl. Phys. Lett. 97, 053108 (2010).
[CrossRef]

Tishchenko, A. V.

Tunnermann, A.

Turunen, J.

Vallius, T.

Wang, B.

J. Feng, C. Zhou, J. Zheng, and B. Wang, Opt. Commun. 281, 5298 (2008).
[CrossRef]

Whittaker, D. M.

Zeitner, U. D.

Zhang, L.

Zheng, J.

J. Feng, C. Zhou, J. Zheng, and B. Wang, Opt. Commun. 281, 5298 (2008).
[CrossRef]

Zhou, C.

J. Feng, C. Zhou, J. Zheng, and B. Wang, Opt. Commun. 281, 5298 (2008).
[CrossRef]

Zhou, H.

Zhou, Z.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

H. Iizuka, N. Engheta, H. Fujikawa, K. Sato, and Y. Takeda, Appl. Phys. Lett. 97, 053108 (2010).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. A (4)

Micro. Opt. Tech. Lett. (1)

H. Iizuka, N. Engheta, H. Fujikawa, and K. Sato, Micro. Opt. Tech. Lett. 52, 1362 (2010).
[CrossRef]

Nanotechnology (1)

S. H. Lim, M. S. M. Saifullah, H. Hussain, W. W. Loh, and H. Y. Low, Nanotechnology 21, 285303 (2010).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. Feng, C. Zhou, J. Zheng, and B. Wang, Opt. Commun. 281, 5298 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (8)

Phys. Rev. B (1)

P. Sheng, R. S. Stepleman, and P. N. Sanda, Phys. Rev. B 26, 2907 (1982).
[CrossRef]

Other (1)

CST Microwave Studio 2009, http://www.cst.com.

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Figures (3)

Fig. 1
Fig. 1

(a) Configuration of the double-groove grating (dimensions: p = 540 nm , w 1 = 35 nm , w 2 = 130 nm , d = 170 nm , h g = 280 nm ; refractive index: n a = 1 , n s = 1.45 , n g = 2.38 ; + 1 st/ 1 st-order diffraction angle: θ t , + 1 = θ t , 1 = 50 ° at 600 nm operating wavelength). (b) Snapshot of electric field distribution at 600 nm obtained by the CST Microwave Studio simulation.

Fig. 2
Fig. 2

(a) Equivalent circuit and coupling coefficients for (b) n = + 1 , (c) n = 0 , and (d) n = 1 obtained from the modal analysis.

Fig. 3
Fig. 3

Simulation results for the electric field amplitude distributions at 600 nm for (a) coupler, (b) parallel beam splitter, (c) reflector, and (d) delay device. A 5-μm-wide incident light source is located at h a = 3 μm away from the input grating. Transmission efficiencies with 7-μm-wide ports at h a = 3 μm away from output gratings are 72%, 74.4%, and 36.7% for three devices (a), (b), and (d), respectively. Each grating has a 13 period length (other dimensions: h s = 6 μm and l i o = 23 μm ).

Tables (1)

Tables Icon

Table 1 Scattering Parameters at 600 nm When the Grating Is Regarded As a Four-Port Device

Equations (2)

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C 1 C 2 C 3 C 4 ( C 1 S 2 C 3 S 4 + S 1 C 2 S 3 C 4 ) + ( 1 / 2 ) { [ ( α t β ) / ( β t α ) ] 2 + [ ( β t α ) / ( α t β ) ] 2 } S 1 S 2 S 3 S 4 ( 1 / 2 ) [ ( α t β ) / ( β t α ) + ( β t α ) / ( α t β ) ] ( C 1 C 2 S 3 S 4 + S 1 S 2 C 3 C 4 + C 1 S 2 S 3 C 4 + S 1 C 2 C 3 S 4 ) = cos ( k 0 n a p sin ( θ in ) ) ,
T n = m C m , n = exp { j k 0 [ n s 2 ( n λ 0 / p ) 2 ] 1 / 2 h g } × m ( 1 / p ) 0 p X m ( x ) exp [ j k 0 ( n λ 0 / p ) x ] d x [ A m exp ( j Λ m h g ) + B m exp ( j Λ m h g ) ] ,

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