Directional excitation of surface plasmons by dielectric resonators

An important aim of current research on plasmonics is to develop compact components to manipulate surface plasmon polaritons (SPPs) and specifically to develop efficient SPP couplers. The commonly used metallic resonators are inefficient to couple free-space waves to SPPs and metallic gratings require oblique incidence for achieving unidirectional propagation. In this article, we propose to use nanoscale nonuniform arrays of dielectric resonator antennas (DRAs) to realize unidirectional launching of SPPs. DRAs are made of low-loss high-permittivity nanostructures operating on a metal surface. The applications of metallodielectric nanostructures can produce resonances mainly in the low-loss dielectric parts and hence the power dissipated through oscillating current in metal can be reduced. Similar to metallic resonators, DRAs operating near resonance can provide phase control when coupling incident waves into SPPs, adding degrees of freedom in controlling propagation direction. The theoretical analysis in this article, with numerical validation, shows efficient SPPs launching by nonuniform array of cylindrical DRAs into a predesigned direction. Furthermore, with proper patterning, optimal launching can be achieved by avoiding power leakage via deflection into free space. The SPP launching condition and the influence of propagation loss are also mathematically analyzed from the viewpoint of antenna array theory. The SPPs launchers based on DRAs have a potential for applications in highly efficient integrated optics and optical waveguides.

Figure 1

(a) A 3D illustration shows a cylindrical dielectric resonator (DR) on a metal surface. (b) The illustration of electric field distribution in the $xz$-plane cross-section. (c) Illustration of typical $E$-field distribution of SPPs along the dielectric-conductor interface.

Figure 2

DRA array for SPP excitation: (a) Schematic of DRAs for SPP unidirectional launching. (b) SPP directional launching lines for an infinite ideal array of DRAs. Here $v$ denotes the diffraction order while $L$ and $R$ denote left (solid line) and right (dashed line) directions.

Figure 3

DRA array in reflectarray configuration: (a) Schematic of DRAs for reflectarray beam deflection. (b) Deflection zone and nondeflection zone. The blue dotted lines and red dashed lines denote the first- and second-order deflections tangential to the surface (${\theta }_r=\pm {90}^{\circ }$), respectively.

Figure 4

SPP launching condition: (a) Normal incidence with $k_{\mathrm{spp}}=1.033k_0$ (SPP wavenumber calculated on silver-air interface at 633 nm). The blue dots 1, 2, and 3 correspond to design and simulation cases 1, 2, and 3, respectively, in Sec. 4. The reflectarray realized in Ref. [34] is also labeled as dot 4. (b) Oblique incidence at ${30}^{\circ }$ with increased $k_{\mathrm{spp}}=1.25k_0$ for illustration purposes.

Figure 5

Concept of a $N$-DRA array with progressive phase. The observation points $L$ and $R$ are set at left and right sides of the array.

Figure 6

Normalized SPP amplitude toward the left-hand side of finite arrays ($N=10$) with different $d$ and $\Delta \varphi$.

Figure 7

Difference of normalized power launched to the left (positive) and right (negative) for values (a) $N$ = 10 and (b) $N$ = 100.

Figure 8

Launched SPPs $E$-field amplitude for lossy (red) and lossless (blue) conditions, calculated at silver-air interface at 633 nm. Each resonator is assumed to have SPP amplitude of 1 V/m.

Figure 9

The designed SPP launcher. (a) Illustration for Cases 1 and 2 with a difference in the interelement spacing $d$ and resonator sizes. (b) Illustration for Case 3 as a bidirectional coupler.

Figure 10

Numerically calculated phase responses (a) and reflection magnitudes (b) of unit cells corresponding to simulations of marked dots 1, 2, and 3 in Fig. 4.

Figure 11

Simulated $E$-field component perpendicular to the silver surface for the four cases indicated in Fig. 4. All cases share the same amplitude and geometry scale. The black dashed boxes indicate a single subarray. (a) Case 1: Leftward SPP launcher in the nondeflection zone. 34% of the incident power is reflected while 66% is accepted, including power coupled into SPPs and dissipated inside materials. (b) Case 2: Rightward SPP launcher in the deflection zone. 54% of the incident power is reflected while 46% is accepted. A deflection wavefront is visible at ${48}^{\circ }$ from the normal. (c) Case 3: A clear standing waves is observed on this structure with 67% of the incident power being reflected while 33% is absorbed. (d) Case 4: The reflectarray in Ref. [34] is reproduced without further optimization. A clear deflection is observed at $19.9^{\circ }$ off normal. 47% of the incident power is accepted mainly dissipated inside materials while 53% is reflected.