Abstract

Arrays of transparent dielectric nanorods are shown to produce very large local field enhancements at specific resonant conditions. These structures would lead to enhancement of molecular fluorescence signals without quenching. The resonant angular width and field enhancements are analytically derived as a function of wavelength, grating period, rod radius, and dielectric constant.

© 2007 Optical Society of America

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References

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2007

S. Gerber, F. Reil, U. Hohenester, T. Schlagenheufen, J. R. Krenn, and A. Leitner, Phys. Rev. B 75, 073404 (2007).
[CrossRef]

2006

R. Carminati, C. Henkel, J.-J. Greffet, and J. M. Vigoureux, Opt. Commun. 261, 368 (2006).
[CrossRef]

P. Nager, P. Bharadwaj, and L. Novotny, Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef]

S. Kühn, U. Hakenson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

R. Gómez-Medina, M. Laroche, and J. J. Sáenz, Opt. Express 14, 3730 (2006).
[CrossRef] [PubMed]

M. Laroche, S. Albaladejo, R. Gómez-Medina, and J. J. Sáenz, Phys. Rev. B 74, 245422 (2006).
[CrossRef]

L. Qin, S. Zou, C. Xue, A. Atkinson, G. C. Schatz, and C. A. Mirkin, Proc. Natl. Acad. Sci. U.S.A. 103, 13300 (2006).
[CrossRef] [PubMed]

2005

J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

2004

2000

A. N. Shipway, E. Katz, and I. Willner, ChemPhysChem 1, 18 (2000).
[CrossRef]

J. Azoulay, A. Débarre, A. Richard, and P. Tchénio, Europhys. Lett. 51, 374 (2000).
[CrossRef]

1999

1997

D. Rosenblatt, A. Sharon, and A. A. Friesem, IEEE J. Quantum Electron. 33, 2038 (1997).
[CrossRef]

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

S. Nie and S. R. Emory, Science 275, 1102 (1997).
[CrossRef] [PubMed]

1988

B. T. Draine, Astrophys. J. 333, 848 (1988).
[CrossRef]

1978

R. R. Chance, A. Prock, and R. Sylbey, Adv. Chem. Phys. 37, 1 (1978).
[CrossRef]

1951

Adv. Chem. Phys.

R. R. Chance, A. Prock, and R. Sylbey, Adv. Chem. Phys. 37, 1 (1978).
[CrossRef]

Appl. Phys. Lett.

M. Thomas, J.-J. Greffet, R. Carminati, and J. R. Arias-Gonzalez, Appl. Phys. Lett. 85, 3863 (2004).
[CrossRef]

Appl. Spectrosc.

Astrophys. J.

B. T. Draine, Astrophys. J. 333, 848 (1988).
[CrossRef]

ChemPhysChem

A. N. Shipway, E. Katz, and I. Willner, ChemPhysChem 1, 18 (2000).
[CrossRef]

Europhys. Lett.

J. Azoulay, A. Débarre, A. Richard, and P. Tchénio, Europhys. Lett. 51, 374 (2000).
[CrossRef]

IEEE J. Quantum Electron.

D. Rosenblatt, A. Sharon, and A. A. Friesem, IEEE J. Quantum Electron. 33, 2038 (1997).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

R. Carminati, C. Henkel, J.-J. Greffet, and J. M. Vigoureux, Opt. Commun. 261, 368 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

M. Laroche, S. Albaladejo, R. Gómez-Medina, and J. J. Sáenz, Phys. Rev. B 74, 245422 (2006).
[CrossRef]

S. Gerber, F. Reil, U. Hohenester, T. Schlagenheufen, J. R. Krenn, and A. Leitner, Phys. Rev. B 75, 073404 (2007).
[CrossRef]

Phys. Rev. Lett.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

P. Nager, P. Bharadwaj, and L. Novotny, Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef]

S. Kühn, U. Hakenson, L. Rogobete, and V. Sandoghdar, Phys. Rev. Lett. 97, 017402 (2006).
[CrossRef] [PubMed]

J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, Phys. Rev. Lett. 95, 017402 (2005).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A.

L. Qin, S. Zou, C. Xue, A. Atkinson, G. C. Schatz, and C. A. Mirkin, Proc. Natl. Acad. Sci. U.S.A. 103, 13300 (2006).
[CrossRef] [PubMed]

Science

S. Nie and S. R. Emory, Science 275, 1102 (1997).
[CrossRef] [PubMed]

Other

M. Neviere, Electromagnetic Theory of Gratings, R.Petit, ed. (Springer-Verlag, 1980), Chap. 5.

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Figures (3)

Fig. 1
Fig. 1

(a) Sketch of the nanorod structure and relevant field directions. TE- or s-polarized waves are characterized by an electrical field vector orthogonal to the plane of incidence (i.e., along the cylinder axis), while the electric field is in plane for TM- or p-polarized waves. (b) Normalized total field intensity (FE) map at resonance in an array of Ti O 2 nanorods with radius a = 40 nm ( λ = 800 nm , d = 783.6 nm , and normal incidence θ = 0 ).

Fig. 2
Fig. 2

(s polarization) FE factor in a period d λ versus in-plane wavenumber ( d λ ) sin ( θ ) map calculated at fixed λ = 800 nm for the Ti O 2 nanorod array in Fig. 1. Inset: FE versus the period at normal incidence (both on the surface and in the center between rods).

Fig. 3
Fig. 3

Calculated FE versus the incident angle θ for both s and p polarizations for the system sketched in Fig. 1 (with λ = 800 nm and d = 468 nm ).

Equations (11)

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E ( ρ ) = E 0 ( ρ ) + j k 2 G 0 ( ρ , ρ j ) { α E in ( ρ j ) } = E 0 ( ρ ) + E in ( ρ 0 ) m F m e i Q m x e i q m z ,
E in ( ρ 0 ) = E 0 ( ρ 0 ) + k 2 j 0 G 0 ( ρ 0 , ρ j ) α E in ( ρ j ) = E 0 ( ρ 0 ) + k 2 G b α E in ( ρ 0 ) ,
k 2 G b , z z = k 2 G b , k 2 G b , x x = y 2 G b , k 2 G b , y y = x 2 G b .
E i in 2 = E i 0 2 M i 1 + M i ( Re { 1 k 2 α i i G b , i i } ) 2 ,
M z = 2 d q 0 k 2 α z z 2 , M y = 2 d q 0 Q 0 2 α y y 2 , M x = 2 d q 0 q 0 2 α y y 2 .
Re { k 2 G b } Re { x 2 G b } k 2 2 d q 1 ,
E i in E i 0 2 M i { 1 + M i ( 1 θ R θ 0 θ R θ ) 2 } 1 ,
θ 0 θ R 1 2 cos θ R k 2 α i i 4 π d λ 2 .
M max ( s ) = E z in + E z scatt 2 E 0 2 M z 1 + i k 2 α z z 4 H 0 ( k a ) 2 .
M z = 4 π d λ k 2 α z z 2 cos 2 θ 0 1 ( ϵ 1 ) 2 ( a λ ) 4
Δ θ ( s ) 2 cos θ R ( M z ) 3 2 ( ϵ 1 ) 3 ( a λ ) 6 .

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