Abstract

Plasmons, which are excited by an evanescent wave and localized in a narrow slit between two metallic cylinders overlying a dielectric substrate, are found by numerical solution of Maxwell equations. The simulation is carried out by a modified boundary elements method with the Green function for layered medium. For the wave incident from a dielectric to its border near the angle of total internal reflection, the amplitude of plasmon resonance is shown to change sharply with the incidence angle. The effect allows one to tune up the field enhancement factor. The control over plasmons is promising for applications in “smart” adaptive plasmonic optical elements.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. G. H. Golub and C. F. van Loan, Matrix Computations (John Hopkins University, 1996).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013 (1)

2012 (2)

V. E. Babicheva, S. S. Vergeles, P. E. Vorobev, and S. Burger, “Localized surface plasmon modes in a system of two interacting metallic cylinders,” J. Opt. Soc. Am. B 29, 1263–1269 (2012).
[CrossRef]

O. V. Belai, L. L. Frumin, S. V. Perminov, and D. A. Shapiro, “Scattering of evanescent wave by two cylinders near a flat boundary,” Europhys. Lett. 97, 10007 (2012).
[CrossRef]

2011 (4)

O. V. Belai, L. L. Frumin, S. V. Perminov, and D. A. Shapiro, “Scattering of evanescent electromagnetic waves by cylinder near flat boundary: the Green function and fast numerical method,” Opt. Lett. 36, 954–956 (2011).
[CrossRef]

M. I. Stockman, “Nanoplasmonics: the physics behind the applications,” Phys. Today 64(2), 39–44 (2011).
[CrossRef]

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
[CrossRef]

2010 (2)

M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components at subwavelength scale,” Opt. Express 18, 11728–11736 (2010).
[CrossRef]

P. E. Vorobev, “Electric field enhancement between two parallel cylinders due to plasmonic resonance,” J. Exp. Theor. Phys. 110, 193–198 (2010).
[CrossRef]

2009 (1)

2007 (2)

2006 (1)

S. V. Zymovetz and P. I. Geshev, “Boundary integral equation method for analysis of light scattering by 2D nanoparticles,” Tech. Phys. 51, 291–296 (2006).
[CrossRef]

2005 (1)

1998 (1)

O. J. F. Martin and N. B. Piller, “Electromagnetic scattering in polarizable backgrounds,” Phys. Rev. E 58, 3909–3915 (1998).
[CrossRef]

Babicheva, V. E.

Belai, O. V.

O. V. Belai, L. L. Frumin, S. V. Perminov, and D. A. Shapiro, “Scattering of evanescent wave by two cylinders near a flat boundary,” Europhys. Lett. 97, 10007 (2012).
[CrossRef]

O. V. Belai, L. L. Frumin, S. V. Perminov, and D. A. Shapiro, “Scattering of evanescent electromagnetic waves by cylinder near flat boundary: the Green function and fast numerical method,” Opt. Lett. 36, 954–956 (2011).
[CrossRef]

Boisvert, R. F.

F. W. J. Ovler, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

Born, M.

M. Born and E. Wolf, Principles of Optics; Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1965).

Burger, S.

Cai, W.

Chettiar, U. K.

Chou, S. Y.

Clark, C. W.

F. W. J. Ovler, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

Drachev, V. P.

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953).

Frumin, L. L.

O. V. Belai, L. L. Frumin, S. V. Perminov, and D. A. Shapiro, “Scattering of evanescent wave by two cylinders near a flat boundary,” Europhys. Lett. 97, 10007 (2012).
[CrossRef]

O. V. Belai, L. L. Frumin, S. V. Perminov, and D. A. Shapiro, “Scattering of evanescent electromagnetic waves by cylinder near flat boundary: the Green function and fast numerical method,” Opt. Lett. 36, 954–956 (2011).
[CrossRef]

Geshev, P. I.

S. V. Zymovetz and P. I. Geshev, “Boundary integral equation method for analysis of light scattering by 2D nanoparticles,” Tech. Phys. 51, 291–296 (2006).
[CrossRef]

Golub, G. H.

G. H. Golub and C. F. van Loan, Matrix Computations (John Hopkins University, 1996).

Han, Z.

Harrington, R. F.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (Wiley, 2001).

Hassani, A.

Kabashin, A.

Kern, A. M.

Kildishev, A. V.

Lacroix, S.

Lozier, D. W.

F. W. J. Ovler, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

Martin, O. J. F.

A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A 26, 732–740 (2009).
[CrossRef]

O. J. F. Martin and N. B. Piller, “Electromagnetic scattering in polarizable backgrounds,” Phys. Rev. E 58, 3909–3915 (1998).
[CrossRef]

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953).

Novotny, L.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
[CrossRef]

Ovler, F. W. J.

F. W. J. Ovler, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

Perminov, S. V.

O. V. Belai, L. L. Frumin, S. V. Perminov, and D. A. Shapiro, “Scattering of evanescent wave by two cylinders near a flat boundary,” Europhys. Lett. 97, 10007 (2012).
[CrossRef]

O. V. Belai, L. L. Frumin, S. V. Perminov, and D. A. Shapiro, “Scattering of evanescent electromagnetic waves by cylinder near flat boundary: the Green function and fast numerical method,” Opt. Lett. 36, 954–956 (2011).
[CrossRef]

Piller, N. B.

O. J. F. Martin and N. B. Piller, “Electromagnetic scattering in polarizable backgrounds,” Phys. Rev. E 58, 3909–3915 (1998).
[CrossRef]

Pone, E.

Sarychev, A. K.

Shalaev, V. M.

Shapiro, D. A.

O. V. Belai, L. L. Frumin, S. V. Perminov, and D. A. Shapiro, “Scattering of evanescent wave by two cylinders near a flat boundary,” Europhys. Lett. 97, 10007 (2012).
[CrossRef]

O. V. Belai, L. L. Frumin, S. V. Perminov, and D. A. Shapiro, “Scattering of evanescent electromagnetic waves by cylinder near flat boundary: the Green function and fast numerical method,” Opt. Lett. 36, 954–956 (2011).
[CrossRef]

Skorobogatiy, M.

Soukoulis, C. M.

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

Stockman, M. I.

M. I. Stockman, “Nanoplasmonics: the physics behind the applications,” Phys. Today 64(2), 39–44 (2011).
[CrossRef]

Van, V.

Van Duyne, R. P.

K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58, 267–297 (2007).
[CrossRef]

van Hulst, N.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
[CrossRef]

van Loan, C. F.

G. H. Golub and C. F. van Loan, Matrix Computations (John Hopkins University, 1996).

Vergeles, S. S.

Vorobev, P. E.

V. E. Babicheva, S. S. Vergeles, P. E. Vorobev, and S. Burger, “Localized surface plasmon modes in a system of two interacting metallic cylinders,” J. Opt. Soc. Am. B 29, 1263–1269 (2012).
[CrossRef]

P. E. Vorobev, “Electric field enhancement between two parallel cylinders due to plasmonic resonance,” J. Exp. Theor. Phys. 110, 193–198 (2010).
[CrossRef]

Wegener, M.

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

Wei, D.

Willets, K. A.

K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58, 267–297 (2007).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics; Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1965).

Wu, M.

Yuan, H.-K.

Zymovetz, S. V.

S. V. Zymovetz and P. I. Geshev, “Boundary integral equation method for analysis of light scattering by 2D nanoparticles,” Tech. Phys. 51, 291–296 (2006).
[CrossRef]

Annu. Rev. Phys. Chem. (1)

K. A. Willets and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Annu. Rev. Phys. Chem. 58, 267–297 (2007).
[CrossRef]

Europhys. Lett. (1)

O. V. Belai, L. L. Frumin, S. V. Perminov, and D. A. Shapiro, “Scattering of evanescent wave by two cylinders near a flat boundary,” Europhys. Lett. 97, 10007 (2012).
[CrossRef]

J. Exp. Theor. Phys. (1)

P. E. Vorobev, “Electric field enhancement between two parallel cylinders due to plasmonic resonance,” J. Exp. Theor. Phys. 110, 193–198 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nat. Photonics (2)

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83–90 (2011).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. E (1)

O. J. F. Martin and N. B. Piller, “Electromagnetic scattering in polarizable backgrounds,” Phys. Rev. E 58, 3909–3915 (1998).
[CrossRef]

Phys. Today (1)

M. I. Stockman, “Nanoplasmonics: the physics behind the applications,” Phys. Today 64(2), 39–44 (2011).
[CrossRef]

Tech. Phys. (1)

S. V. Zymovetz and P. I. Geshev, “Boundary integral equation method for analysis of light scattering by 2D nanoparticles,” Tech. Phys. 51, 291–296 (2006).
[CrossRef]

Other (6)

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953).

R. F. Harrington, Time-Harmonic Electromagnetic Fields (Wiley, 2001).

G. H. Golub and C. F. van Loan, Matrix Computations (John Hopkins University, 1996).

F. W. J. Ovler, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

E. D. Palik, ed. Handbook of Optical Constants of Solids, Vol. 1, 2 (Academic, 1998).

M. Born and E. Wolf, Principles of Optics; Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1965).

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Figures (6)

Fig. 1.
Fig. 1.

Scheme of the electromagnetic wave scattering: scattering of a running wave by (a) one cylinder and (b) two cylinders; (c) scattering of a propagating or an evanescent wave going from the substrate by two cylinders.

Fig. 2.
Fig. 2.

FEF η=|EC/E0|2 for propagating wave as a function of real part ε at a=50, δ=5nm, the analytic formula obtained in bipolar coordinates [Eq. (10)] (circles), and the calculation by BEM at λ=50 (solid line), 2 (dashed), and 1 μm (dot–dash).

Fig. 3.
Fig. 3.

Profile illustrating the distribution of |Hz(x,y)| in arbitrary units. Coordinates x,y are in micrometers.

Fig. 4.
Fig. 4.

FEF η=|EC/E0|2 as a function of real part ε for the evanescent wave at ε1=2.25, ε2=1, a=50nm, δ=5nm, λ=2μm, and different incidence angles: θ=43° (dotted), θ=44° (long dashes), 45° (dashed), 46° (dot–dash), and 49° (solid line).

Fig. 5.
Fig. 5.

(Solid line) FEF for evanescent wave as a function of angle θ in degrees, calculated by BEM. (Circles) magnified solution of Fresnel problem K|E2x/E0|2 for field intensity near the interface.

Fig. 6.
Fig. 6.

FEF η=|EC/E0|2 for evanescent wave as a function of real part ε at a=25 (solid line), 50 (dashed), 75 (dot–dash), and 100 nm (dotted).

Equations (12)

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

(Δ+k2)H=0.
H(p)=H0(p)+Γ[Gev(q)Genqu(q)]dq,
Ge(p,q)=14iH0(1)(k(xpxq)2+(ypyq)2),
H(p)=Γ[εiεeGiv(q)Ginqu(q)]dq.
u(p)2+Γ[εiεeGi(p,q)v(q)Gi(p,q)nqu(q)]dq=0,u(p)2Γ[Ge(p,q)v(q)Ge(p,q)nqu(q)]dq=H0(p).
Ex=icωεHy,Ey=icωεHx.
G1|Γ0=G2|Γ0,1ε1G1y|Γ0=1ε2G2y|Γ0.
G2(p,q)=12πG˜2(p,q)eiκ(xpxq)dκ.
G˜1(p,q)=12μ2[1+r]eμ1ypμ2yq,G˜2(p,q)=12μ2[eμ2|ypyq|+reμ2(yp+yq)],
EC=E0+E0n=08n(1)n(1ε)1ε+(1+ε)e2nξ0,
εn=cothnξ0.
E2x=2cosθε1(ε2ε1sin2θ)ε1cosθ+ε1(ε2ε1sin2θ),E2y=ε1sin2θε1cosθ+ε1(ε2ε1sin2θ).

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