Effect of a proximal substrate on plasmon propagation in silver nanowires

We investigate how the properties of a nearby substrate modify the excitation and propagation of plasmons in subwavelength silver wires. With decreasing nanowire-substrate separation, the in-coupling efficiency shows strongly oscillatory behavior due to coherent interference. The plasmon damping increases with decreasing separation due to an increased coupling of the nanowire plasmons to the photonic modes of the substrate.

Figure 1

(Color online) (a) Emission intensities from nanowires on layered substrates as a function of nanowire length $L$. The diameters of all nanowires were selected to be in the range $D=90–100\text{nm}$. Inset: a schematic of the experimental measurement. Incident light of wavelength 633 nm, polarized parallel to the nanowire, is directed onto one end of the nanowire. Light emitted from the other end is measured for various nanowire lengths $L$ and silica layer thicknesses $d=41$, 67, and 110 nm. When there is no observable light emission, the scattered light at the end of the nanowire is recorded and represented by hollow dots. (b) Average emission intensity for nanowires (black squares) of length $L=4–4.5\mu \text{m}$ and diameter $D=90–100\text{nm}$ as a function of the silica layer thickness $d$. The curve is the theoretical simulation (FDTD) of this geometry. (c) In-coupling coefficient $C$ as a function of silica thickness $d$. The unit for $I_{\text{Ave}}$ and $C$ in (b) and (c) is arbitrary. (d) $1/e$ damping length of SPPs as a function of $d$. The curve is the calculated $r$ divided by 1.4, discussed in the text. The refractive index of silicon is 3.882. The refractive of the oil is index matched to silica $n_{\text{s}}=1.518$.

Figure 2

(Color) (a) The field distribution $\left({\left|E\right|}^2\right)$ around the nanowire of diameter 96 nm, length $4\mu \text{m}$, and $d=100\text{nm}$ excited by a 633 nm laser with parallel polarization relative to the wire axis at the left end. (b) The plasmon-induced surface charge amplitude on the nanowire without and with adjacent Si surface $\left(d=10\text{nm}\right)$. The charge is obtained by the divergence of the electric field. The unit of charge is arbitrary from $+1$ to $-1$ corresponding to color from red to blue. (c) The intensity of the electric field confined in the wire-substrate gap in (b) on a logarithmic scale. (d) The Poynting vector/electromagnetic energy flow around the first 200 nm of the wire and the wire-substrate gap. Arrows denotes the direction of the flow; the color represents the local electric intensity.

Figure 3

(Color online) (a) The measured emission intensity from nanowires of diameters $D=90–100\text{nm}$ on different substrates as a function of the nanowire length. The excitation with the wavelength 633 nm at one of the nanowire is always polarized parallel to the nanowire. Triangular, circular, and squared dots represent the cases of nanowires on substrates of GaP, SiC, and CdTe, respectively. For cases with no observable light emission at the end of the nanowire, scattered light at the position of the nanowire end was recorded and represented by hollow dots. (b) The calculated damping length as a function of the refractive index of the substrate.