Three-dimensional metamaterial nanotips

We investigate the optical properties of a three-dimensional metamaterial nanotip that has a pyramidal shape. The nanotip itself is made of a large number of densely packed metallic nanospheres. In analogy to the emergence of a continuous energy band in a crystal, the strong coupling among neighboring nanospheres forces them to act collectively and allows the observation of a broad plasmonic band. The largely increased degrees of freedom within the metamaterial nanotip allow to sustain a great variety of different localized eigenmodes. In this contribution, we systematically reveal their peculiar polarization state and show that they allow for light localization in various well-defined spatial domains.

Figure 1

(Color online) Composition of the 3D nanotip made of periodically arranged, identical nanospheres with diameter $d=2a$ and period $\Lambda$. The small rectangle depicts the interval where the electric field is integrated later on.

Figure 2

(Color online) Extinction cross section as a function of the free-space wavelength for several numbers of nanotip layers ($d=4\text{nm}$, $\Lambda =4.8\text{nm}$). Vertical bars indicate the wavelengths where field distributions are investigated in detail; see Figs. 3, 4, 5 and Fig. 7.

Figure 3

(Color online) Electric field amplitude in a nanotip ($d=4\text{nm}$, $\Lambda =4.8\text{nm}$) containing 10 layers at the resonance wavelengths $\lambda =370\text{nm}$ (left panel) and $\lambda =380\text{nm}$ (right panel). Colored arrows depict essential spatial domains where the mutual coupling of nanospheres can be explained by looking at the field distribution.

Figure 4

(Color online) Electric field amplitude in a nanotip ($d=4\text{nm}$, $\Lambda =4.8\text{nm}$) containing 10 layers at the resonance wavelengths $\lambda =445\text{nm}$ (left panel) and $\lambda =454\text{nm}$ (right panel).

Figure 5

(Color online) Electric field amplitude in a nanotip ($d=4\text{nm}$, $\Lambda =4.8\text{nm}$) containing 10 layers at the resonance wavelength $\lambda =462\text{nm}$.

Figure 6

(Color online) Magnitude of the dipole coefficient $a_{10}$ as a function of the wavelength and the respective plane. The coefficients $a_{10}^j$ of every single nanosphere are averaged over all nanospheres in a particular plane (1 indicates the apex and 10 the base of the nanotip) and normalized to the respective coefficient of the incident field. The left and the right panel apply to a pyramid analogous to Fig. 1 ($d=4\text{nm}$, $\Lambda =4.8\text{nm}$) and a pyramid with identical parameters where only the shell contains nanospheres, respectively.

Figure 7

(Color online) Electric field amplitude in a nanotip ($d=4\text{nm}$, $\Lambda =4.8\text{nm}$) containing 10 layers at the resonance wavelength $\lambda =395\text{nm}$.

Figure 8

(Color online) Effective permittivities (blue graph: real part, green graph: imaginary part) as a function of the wavelength for two different MMs (see text). (a), (b): closely packed spheres as mentioned in Fig. 1; (c), (d): spheres on a square lattice.

Figure 9

(Color online) Effective permeabilities [(a): real part, (b): imaginary part] as a function of the wavelength for two different MMs (see text). The dashed graph depict a structure as mentioned in Fig. 1 and the solid graph is related to a square lattice.

Figure 10

(Color online) Integrated electric field as a function of the wavelength in a three-dimensional interval at the apex of the nanotip (see Fig. 1). All graphs are normalized to the incident field in the interval.