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Femtosecond light pulse propagation through metallic nanohole arrays: The role of the dielectric substrate

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Abstract

We study theoretically ultrafast light propagation through a periodic array of holes in a silver film deposited on a dielectric substrate using a three-dimensional finite-difference time-domain (FDTD) simulation. We focus on studying the effects of the coherent coupling between resonant surface plasmon polariton (SPP) excitations at the top and bottom interfaces of the metal film on the transmission dynamics. In a free standing film, the SPP excitations at both interfaces are fully in resonance and pronounced temporal oscillations in the energy flow between the bottom and top interfaces give evidence for coupling between the (±1,0) SPP modes via photon tunneling through the holes. Variation of the dielectric constant of the substrate lifts the energetic degeneracy between the two modes and thus decreases the coupling and suppresses the energy oscillations. New SPP-enhanced transmission peaks appear when higher order modes at the substrate/metal interface are brought into resonance with the (±1,0) air/metal resonance and efficient mode coupling is achieved. Both temporal transmission dynamics and near-field mode profiles are reported and their implications for tailoring the optical properties of these two-dimensional plasmonic crystals are discussed.

©2004 Optical Society of America

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Supplementary Material (3)

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Figures (9)

Fig. 1.
Fig. 1. Schematic of a metal film perforated with an array of holes and deposited on a substrate with a refractive index ns . The medium above the film is air. a0 is the lattice constant, d the hole diameter and h the film thickness. (a) Cross section through x-z plane. The input wave is polarized along x and illuminates the bottom metal surface at normal incidence. (b) Top view.
Fig. 2.
Fig. 2. Photon flux density z,norm vs time in a hole channel at z = 0, (bottom interface, black) and z = h (top interface, red) for substrate refractive indices ns = 1.00 to 1.80, (a)–(e).The input pulse (green) is shown in (a).
Fig. 3
Fig. 3 Field energy density ex,norm vs time inside a hole at z = 0 (black line) and at z = h (red line) for ns = 1.00 to 1.80, (a)–(e).
Fig. 4.
Fig. 4. Spatial distribution of time-averaged squared electric field strengths (a) E x 2 ̄ , (b) E y 2 ̄ , (c) E x 2 ̄ + E y 2 ̄ in the x-y planes of the substrate/metal interface (bottom row, z = -2.5 nm) and the air/silver interface (top row, z = h + 2.5 nm) at time t = 45fs. The refractive index of the substrate is ns = 1.37 and the incident beam is polarized along the x-direction. A logarithmic color scale is used. The intensity of E y 2 ̄ at the top interface (b) is enhanced by a factor of 10.
Fig. 5.
Fig. 5. Same as Fig. 4 but squared z-component of the electric field, E ̅ z 2 at the substrate/silver interface at z = -2.5 nm (a) and at the air/silver interface at z = h + 2.5 nm (b). A logarithmic color scale is used.
Fig. 6.
Fig. 6. Time-averaged squared field strength on the substrate/silver interface (bottom row) and the air/silver interface (top row) at time t = 45fs (logarithmic color scale). (a) E x 2 ¯ , (b) E z 2 ¯ . The refractive index of the substrate is ns = 1.80. The intensity scale for E z 2 ¯ at the bottom interface is from 0.01 to 10.
Fig. 7.
Fig. 7. Movie sequences showing the time evolution of squared electric field strengths, averaged over one optical period T = 2π/ω, in the x-y-plane (logarithmic color scale) at (a) the bottom (t = 40fs) and (b) the top interface (t = 40 fs) for a freestanding metal film, ns = 1.00, and excitation with a 10fs optical pulse (3.9 MB movie).
Fig. 8.
Fig. 8. Movie sequences showing the time evolution of squared electric field strengths in the x - y -plane (logarithmic color scale) at (a) the bottom (t = 40 fs) and (b) the top interface (t = 40 fs) for ns = 1.37, and excitation with a 10fs optical pulse (3.4 MB movie).
Fig. 9.
Fig. 9. Movie sequences showing the time evolution of squared electric field strengths in the x-y-plane (logarithmic color scale) at (a) the bottom and (b) the top interface for ns = 1.80, and excitation with a 10fs optical pulse (2.8 MB movie).

Equations (5)

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

× E = μ 0 H t
× H = εε 0 E t + J
J t + γ J = ε 0 ω p 2 E ,
ε m ( ω ) = 1 ω p 2 ω 2 + iγω .
ω p q i = 2 πc p 2 + q 2 a 0 n i ε m + n i 2 ε m
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