Abstract

Giant field enhancement and field singularities are a natural consequence of the commonly employed local-response framework. We show that a more general nonlocal treatment of the plasmonic response leads to new and possibly fundamental limitations on field enhancement with important consequences for our understanding of surface-enhanced Raman spectroscopy (SERS). The intrinsic length scale of the electron gas serves to smear out assumed field singularities, leaving the SERS enhancement factor finite, even for geometries with infinitely sharp features. For silver nanogroove structures, mimicked by periodic arrays of half-cylinders (up to 120 nm in radius), we find no enhancement factors exceeding 10 orders of magnitude (1010).

© 2012 Optical Society of America

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2012 (2)

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, Phys. Rev. Lett. 108, 106802 (2012).
[CrossRef]

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, Opt. Express 20, 4176 (2012).
[CrossRef]

2011 (1)

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, Phys. Rev. B 84, 121412(R) (2011).
[CrossRef]

2010 (3)

T. Søndergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, Nano Lett. 10, 291 (2010).
[CrossRef]

P. Ginzburg, A. Hayat, N. Berkovitch, and M. Orenstein, Opt. Lett. 35, 1551 (2010).
[CrossRef]

Y. Luo, J. B. Pendry, and A. Aubry, Nano Lett. 10, 4186 (2010).
[CrossRef]

2008 (3)

S. Xiao, N. A. Mortensen, and A.-P. Jauho, J. Eur. Opt. Soc. Rapid Pub. 3, 08022 (2008).
[CrossRef]

F. J. García de Abajo, J. Phys. Chem. C 112, 17983 (2008).
[CrossRef]

S. G. Rodrigo, F. García-Vidal, and Martín-Moreno, Phys. Rev. B 77, 075401 (2008).
[CrossRef]

2007 (3)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007).
[CrossRef]

S. Lal, S. Link, and N. J. Halas, Nat. Photon. 1, 641 (2007).
[CrossRef]

K. Kneipp, Phys. Today 60(11), 40 (2007).
[CrossRef]

2006 (2)

2005 (1)

R. Ruppin, Phys. Lett. A 340, 299 (2005).
[CrossRef]

1996 (1)

F. García-Vidal and J. B. Pendry, Phys. Rev. Lett. 77, 1163 (1996).
[CrossRef]

1985 (1)

M. Moskovits, Rev. Mod. Phys. 57, 783 (1985).
[CrossRef]

Aizpurua, J.

Aubry, A.

Y. Luo, J. B. Pendry, and A. Aubry, Nano Lett. 10, 4186 (2010).
[CrossRef]

Beermann, J.

T. Søndergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, Nano Lett. 10, 291 (2010).
[CrossRef]

Berkovitch, N.

Bozhevolnyi, S. I.

T. Søndergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, Nano Lett. 10, 291 (2010).
[CrossRef]

E. Moreno, F. J. García-Vidal, S. G. Rodrigo, L. Martín-Moreno, and S. I. Bozhevolnyi, Opt. Lett. 31, 3447 (2006).
[CrossRef]

Bryant, G. W.

Chulkov, E. V.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007).
[CrossRef]

Devaux, E.

T. Søndergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, Nano Lett. 10, 291 (2010).
[CrossRef]

Ebbesen, T. W.

T. Søndergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, Nano Lett. 10, 291 (2010).
[CrossRef]

Echenique, P. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007).
[CrossRef]

Fernández-Domínguez, A. I.

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, Phys. Rev. Lett. 108, 106802 (2012).
[CrossRef]

García de Abajo, F. J.

García-Vidal, F.

S. G. Rodrigo, F. García-Vidal, and Martín-Moreno, Phys. Rev. B 77, 075401 (2008).
[CrossRef]

F. García-Vidal and J. B. Pendry, Phys. Rev. Lett. 77, 1163 (1996).
[CrossRef]

García-Vidal, F. J.

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, Phys. Rev. Lett. 108, 106802 (2012).
[CrossRef]

E. Moreno, F. J. García-Vidal, S. G. Rodrigo, L. Martín-Moreno, and S. I. Bozhevolnyi, Opt. Lett. 31, 3447 (2006).
[CrossRef]

Ginzburg, P.

Halas, N. J.

S. Lal, S. Link, and N. J. Halas, Nat. Photon. 1, 641 (2007).
[CrossRef]

Hayat, A.

Jauho, A.-P.

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, Opt. Express 20, 4176 (2012).
[CrossRef]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, Phys. Rev. B 84, 121412(R) (2011).
[CrossRef]

S. Xiao, N. A. Mortensen, and A.-P. Jauho, J. Eur. Opt. Soc. Rapid Pub. 3, 08022 (2008).
[CrossRef]

Kneipp, K.

K. Kneipp, Phys. Today 60(11), 40 (2007).
[CrossRef]

Lal, S.

S. Lal, S. Link, and N. J. Halas, Nat. Photon. 1, 641 (2007).
[CrossRef]

Link, S.

S. Lal, S. Link, and N. J. Halas, Nat. Photon. 1, 641 (2007).
[CrossRef]

Luo, Y.

Y. Luo, J. B. Pendry, and A. Aubry, Nano Lett. 10, 4186 (2010).
[CrossRef]

Maier, S. A.

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, Phys. Rev. Lett. 108, 106802 (2012).
[CrossRef]

Martín-Moreno,

S. G. Rodrigo, F. García-Vidal, and Martín-Moreno, Phys. Rev. B 77, 075401 (2008).
[CrossRef]

Martín-Moreno, L.

Moreno, E.

Mortensen, N. A.

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, Opt. Express 20, 4176 (2012).
[CrossRef]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, Phys. Rev. B 84, 121412(R) (2011).
[CrossRef]

S. Xiao, N. A. Mortensen, and A.-P. Jauho, J. Eur. Opt. Soc. Rapid Pub. 3, 08022 (2008).
[CrossRef]

Moskovits, M.

M. Moskovits, Rev. Mod. Phys. 57, 783 (1985).
[CrossRef]

Novikov, S. M.

T. Søndergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, Nano Lett. 10, 291 (2010).
[CrossRef]

Orenstein, M.

Pendry, J. B.

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, Phys. Rev. Lett. 108, 106802 (2012).
[CrossRef]

Y. Luo, J. B. Pendry, and A. Aubry, Nano Lett. 10, 4186 (2010).
[CrossRef]

F. García-Vidal and J. B. Pendry, Phys. Rev. Lett. 77, 1163 (1996).
[CrossRef]

Pitarke, J. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007).
[CrossRef]

Raza, S.

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, Opt. Express 20, 4176 (2012).
[CrossRef]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, Phys. Rev. B 84, 121412(R) (2011).
[CrossRef]

Rodrigo, S. G.

Romero, I.

Ruppin, R.

R. Ruppin, Phys. Lett. A 340, 299 (2005).
[CrossRef]

Silkin, V. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007).
[CrossRef]

Søndergaard, T.

T. Søndergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, Nano Lett. 10, 291 (2010).
[CrossRef]

Toscano, G.

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, Opt. Express 20, 4176 (2012).
[CrossRef]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, Phys. Rev. B 84, 121412(R) (2011).
[CrossRef]

Wiener, A.

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, Phys. Rev. Lett. 108, 106802 (2012).
[CrossRef]

Wubs, M.

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, Opt. Express 20, 4176 (2012).
[CrossRef]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, Phys. Rev. B 84, 121412(R) (2011).
[CrossRef]

Xiao, S.

S. Xiao, N. A. Mortensen, and A.-P. Jauho, J. Eur. Opt. Soc. Rapid Pub. 3, 08022 (2008).
[CrossRef]

J. Eur. Opt. Soc. Rapid Pub. (1)

S. Xiao, N. A. Mortensen, and A.-P. Jauho, J. Eur. Opt. Soc. Rapid Pub. 3, 08022 (2008).
[CrossRef]

J. Phys. Chem. C (1)

F. J. García de Abajo, J. Phys. Chem. C 112, 17983 (2008).
[CrossRef]

Nano Lett. (2)

Y. Luo, J. B. Pendry, and A. Aubry, Nano Lett. 10, 4186 (2010).
[CrossRef]

T. Søndergaard, S. I. Bozhevolnyi, J. Beermann, S. M. Novikov, E. Devaux, and T. W. Ebbesen, Nano Lett. 10, 291 (2010).
[CrossRef]

Nat. Photon. (1)

S. Lal, S. Link, and N. J. Halas, Nat. Photon. 1, 641 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Lett. A (1)

R. Ruppin, Phys. Lett. A 340, 299 (2005).
[CrossRef]

Phys. Rev. B (2)

S. G. Rodrigo, F. García-Vidal, and Martín-Moreno, Phys. Rev. B 77, 075401 (2008).
[CrossRef]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, Phys. Rev. B 84, 121412(R) (2011).
[CrossRef]

Phys. Rev. Lett. (2)

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, Phys. Rev. Lett. 108, 106802 (2012).
[CrossRef]

F. García-Vidal and J. B. Pendry, Phys. Rev. Lett. 77, 1163 (1996).
[CrossRef]

Phys. Today (1)

K. Kneipp, Phys. Today 60(11), 40 (2007).
[CrossRef]

Rep. Prog. Phys. (1)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys. 70, 1 (2007).
[CrossRef]

Rev. Mod. Phys. (1)

M. Moskovits, Rev. Mod. Phys. 57, 783 (1985).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

(a) Groove structure formed by an infinite periodic array of half-cylindrical nanorods. (b) Cross section of the unit cell. (c) and (d) Typical electric-field intensity and charge distributions for a dipole mode.

Fig. 2.
Fig. 2.

Surface-averaged SERS enhancement factor γ for the case of R=75nm with r=0.1nm (upper curves) and r=5nm (lower curves). For comparison, the dashed curves show the results of the commonly employed LRA.

Fig. 3.
Fig. 3.

Surface-averaged SERS enhancement factor γ for the case of R=15nm and with r varying from 1 to 0 nm. The dashed curve connecting fundamental dipole resonances for different values of r serves as a guide to the eyes, clearly illustrating both a redshift and the saturation effect in the field enhancement as r0.

Fig. 4.
Fig. 4.

Near-resonance plots of the surface-averaged SERS enhancement factor γ for arbitrarily well-defined grooves without smoothening (r=0) for six cases with R varying from 30 to 120 nm. The inset shows the field-amplitude distribution |E|/|E0| for R=75nm.

Equations (1)

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εD(ω)=1+iσε0ω=1ωp2ω(ω+i/τD),

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