Plasmonic surface lattice resonances on arrays of different lattice symmetry

Arrays of metallic particles may exhibit optical collective excitations known as surface lattice resonances (SLRs). These SLRs occur near the diffraction edge of the array and can be sharper than the plasmon resonance associated with the isolated single particle response. We have fabricated and modeled arrays of silver nanoparticles of different geometries. We show that square, hexagonal, and honeycomb arrays show similar SLRs; no one geometry shows a clear advantage over the others in terms of resonance linewidth. We investigate the nature of the coupling between the particles by looking at rectangular arrays. Our results combine experiment and modeling based on a simple coupled-dipole model.

Figure 1

Calculated extinction cross section per particle $\left(\mu {\mathrm{m}}^2\right)$ vs wavelength (nm) of a single isolated particle and a particle in a 480 nm square lattice. The particles are silver disks (spheroids) with a diameter of 120 nm and a height of 30 nm embedded in a homogeneous medium with refractive index $n=1.515$. The electric field is in the plane of the particles.

Figure 2

Scanning electron micrographs (SEMs) of different arrays of silver disks $(d=120$ nm, $h=30$ nm). (a) Square lattice with 480 nm pitch; (b) rectangular lattice with 370 and 480 nm pitches; (c) hexagonal lattice with 555 nm nearest neighbor separation; and (d) honeycomb lattice with 320 nm nearest neighbor separation. Each of the structures has a lattice period of 480 nm.

Figure 3

(a) Measured extinction; (b) calculated extinction cross section per particle; and (c) array factor for a square array (480 nm pitch) of silver disks $(d=120$ nm, $h=30$ nm). The particles are illuminated with linearly polarized light at normal incidence with the electric field parallel to the $y$ axis of the array, see Fig. 2. The array is index matched using immersion oil with $n=1.515$, meaning that the diffraction edge is at 727 nm. Dashed lines in (a) and (b) indicate the intersection of the real parts of $1/\alpha$ and $S$.

Figure 4

(a) Measured extinction; (b) calculated extinction cross section per particle; and (c) array factor for a hexagonal array (555 nm nearest neighbor separation) of silver disks $(d=120$ nm, $h=30$ nm). The particles were illuminated with linearly polarized light at normal incidence with an electric field parallel to the $y$ axis of the array, see Fig. 2.

Figure 5

(a) Measured extinction; (b) calculated extinction cross section per particle; and (c) array factor for a honeycomb lattice (320 nm nearest neighbor separation) of silver disks $(d=120$ nm, $h=30$ nm). The particles are illuminated with linearly polarized light at normal incidence with the electric field parallel to the $y$ axis of the array, see Fig. 2.

Figure 6

(a) Measured extinction of square lattice [see Fig. 2], hexagonal lattice [see Fig. 2], and honeycomb lattice [see Fig. 2] with corresponding real parts of $1/\alpha$ and $S$ shown in (b).

Figure 7

Measured extinction vs wavelength (nm) of the three different geometries: (a) square, (b) hexagonal, and (c) honeycomb. In each case, the electric field polarization is swept in 15 deg increments from 0 deg (parallel to the $x$ axis of the arrays) to 90 deg (parallel to the $y$ axis).

Figure 8

(a) Measured extinction; (b) calculated extinction cross section per particle; and (c) array factor for a rectangular lattice (370 nm $\times$ 480 nm pitches) of silver disks $(d=120$ nm, $h=30$ nm), together with the calculated inverse polarizability of an isolated particle. The particles were illuminated with linearly polarized light at normal incidence with the electric field parallel to either the $x$ axis or $y$ axis of the array, see Fig. 2. The array is index matched using immersion oil with $n=1.515$. The two diffraction edges occur at 561 nm (red dashed line) and 727 nm (blue dashed line).

Figure 9

Measured extinction as a function of wavelength of a 370 nm $\times$ 480 nm rectangular lattice, 480 nm pitch square lattice, and 520 nm $\times$ 480 nm rectangular lattice. All the lattices consist of silver disks with a diameter of 120 nm and height of 30 nm. The top panel is with electric field parallel to the $x$ axis of the array and middle panel the $y$ axis. The diffraction edges relating to the $y$ period of the three lattices are shown as dashed lines at 561 nm (red), 727 nm (blue), and 788 nm (green).