Relating localized nanoparticle resonances to an associated antenna problem

On an empirical basis, we indicate the possibility of conceptually unifying the description of resonances existing in some of the analytically studied metallic nanoparticles and optical nanowire antennas. To this end the nanoantenna is treated as a Fabry-Pérot-like resonator with arbitrary seminanoparticles forming the terminations. We show that the frequencies of the quasistatic dipolar resonances of the considered nanoparticles coincide with those where the round-trip phase of the complex reflection coefficient of the fundamental propagating plasmon polariton mode at the wire terminations amounts to $2\pi$. The lowest order Fabry-Pérot resonance of the optical wire antenna occurs therefore even for a negligible wire length.

Figure 1

Sketch of considered metallic nanoantenna geometries. (a) Circular cylinder and (b) cylindrical shell with a hemispherical termination; (c) elliptical cylinder with a semi-elliptical termination; (d) one-dimensional (1D) nanoantenna with a semicylindrical termination. All nanoantennas are composed of a nanowire (metallic color) and a termination (golden) while $L$ is the nanowire's length.

Figure 2

(a) Real and (b) imaginary part of the propagation constant $\beta$ of the lowest order PSPP mode as a function of frequency $\nu$ for selected values of ${\varepsilon }_d$; ${\varepsilon }_d=1$ (solid red), ${\varepsilon }_d=2.8$ (dashed blue), ${\varepsilon }_d=5.4$ (dotted magenta), ${\varepsilon }_d=9$ (dotted-dashed black). The inset shows the $H_{\phi }$-field norm for a core radius of 10 nm and ${\varepsilon }_d=1$.

Figure 3

(a) Amplitude and (b) phase of the reflection coefficient of the nanowire for selected values of ${\varepsilon }_d$; ${\varepsilon }_d=1$ (solid red), ${\varepsilon }_d=2.8$ (dashed blue), ${\varepsilon }_d=5.4$ (dotted magenta), ${\varepsilon }_d=9$ (dotted-dashed black).

Figure 4

Resonance frequency of a sphere (a) with a radius of 10 nm as a function of permittivity of surrounding medium and of a spherical core shell particle (b) as a function of the ratio between shell and core radii $b/a$. The core radius $a=10$ nm is fixed. The permittivity of both the core and the surrounding medium is ${\varepsilon }_d=1$. Dots correspond to resonance frequencies as extracted from the phase of the reflection coefficients and the solid lines correspond to the predictions from quasistatic theory.

Figure 5

Resonance frequency in (a) of an ellipsoid with $b=c=20$ nm surrounded by ${\varepsilon }_d=1$ as a function of the ratio $c/a$ between semi-axes and in (b) of a cylinder with a radius of 10 nm as a function of ${\varepsilon }_d$. In (a), solid blue (dashed red) curve corresponds to quasistatic resonance of the spheroid under illuminating polarization perpendicular (parallel) to semi-axis $a$. Circular (diamond) marks indicate frequencies at ${\phi }_r=\pi$ for polarization perpendicular (parallel) to semi-axis $a$. The polarization in the antenna simulation is selected by choosing respective wire mode as the illuminating field. In (b), the solid blue curve corresponds to quasistatic resonance while circular marks denote the frequencies at which ${\phi }_r=\pi$.

Figure 6

Normalized scattering cross section $\sigma$ (top) and total phase jump $\phi$ (bottom) for an asymmetric composite particle (inset) made up of a hemisphere (radius $=10$ nm) and a half prolate spheroid ($a=b=10$ nm, $c=20$ nm). Inset shows the 2D perspective of the proposed asymmetric composite particle.