Figure 1

Top view, scanning electron micrograph of the ML-Au sample (scale bar $=$ 10 μm). Inset top: this ML in a side view (scale bar $=$ 1 μm). Inset bottom: schematic representation of waveguiding in the hybrid ML of spheres. Numbers show the dimensions of structural elements. The incidence light intensity (I) is distributed between the reflected (R), transmitted (T), and guided light. The guided light is transported by index-guided modes (GM), SPP modes, and Fabry–Perot modes (FP). Dashed arrows show light losses.Reuse & Permissions

Figure 2

Transmission (curves 1, 3) and reflectance (2, 4) spectra of (a) ML-glass sample and (b) ML-Au-glass hybrid at $\theta =6^{\circ }$ in $pp$-polarized light. Curve 5 represents the transmission of 30-nm Au film. Calculated transmission (6, 10) and reflectance (7, 11) spectra of (c) 50L-glass and (d) 50L-Au-glass samples at $\theta =0^{\circ }$. Calculated spectra of forward (8, 12) and backward (9, 13) scattered light of (c) sphere on a glass substrate and (d) sphere on Au-coated glass substrate at $\theta =0^{\circ }$.Reuse & Permissions

Figure 3

Refractive index profiles of (a) 50L-glass and (d) 50L-Au-glass model structures. The complex index of gold is displayed as a grey bar. Eigenmodes of (c), (d) 50L-glass and (e), (f) 50L-Au-glass structures are shown for (c), (e) $s$- and (d), (f) $p$-polarized light, numbered consecutively. Dotted lines show the light line in air. Empty circles and squares mark the points at which the Poynting vector profiles have been calculated. Modes ${\mathrm{SPP}}_{\mathrm{ML}}$ and ${\mathrm{SPP}}_{\mathrm{sub}}$ in panel (f) are the SPP modes located at 50L and glass interfaces of the Au film, respectively.Reuse & Permissions

Figure 4

Distributions of electromagnetic flux across the 50L-glass and 50L-Au-glass structures calculated for characteristic points at dispersion curves shown in Fig. 3. Dashed lines show the refractive index profile as in Fig. 3d. The grey bar indicates the Au film.Reuse & Permissions

Figure 5

(a), (b) Transmission maps of 50L-glass model. (c), (d) Reflectance and (e), (f) transmission maps of 50L-Au-glass multilayers in $s$- (left column) and $p$- (right column) polarized light.Reuse & Permissions

Figure 6

(a) Reciprocal lattice of a 2D hexagonal array of spheres. Numbers indicate the lattice sites. Dashed line is the projection of the Ewald sphere. Thin arrows show the diffraction orders of the incident wave. (b), (c) Sketches of in-plane diffraction orders with transverse and longitudinal orientation of the electric field for $s$- and $p$-polarized guided modes, respectively. ${\mathbf{E}}_{s,p}^{\mathrm{t},\mathrm{l}}$ is the vector of the electric field, indices $s$ and $p$ indicate the polarization of the incident light, and indices $t$ and $l$ distinguish between transverse and longitudinal orientation of this vector, respectively. $\Gamma$ is the center of the Brillouin zone. ${\mathbf{G}}^{i,k}$ are vectors of the reciprocal lattice. ${\mathbf{k}}_{}^{\mathrm{inc}}$ and ${\mathbf{k}}_{\mathrm{GM}}^{i,k}$ are the in-plane projection of the wavevector of incident light and the wavevector of diffracted light, respectively.Reuse & Permissions

Figure 7

Calculated maps of (a), (b) backward- and (c), (d) forward-scattered light intensity in $ss$- (left column) and $pp$- (right column) polarized light for the 1063-nm PS sphere on the glass substrate coated with 30-nm Au film.Reuse & Permissions

Figure 8

Experimental maps of (a), (b) transmission of the ML-glass sample and (c), (d) reflectance and (e), (f) transmission of the ML-Au-glass hybrid. Left and right columns are for $ss$- and $pp$-polarized light, respectively. Intensities are plotted on a logarithmic scale. Thin solid and dashed lines in panel (a) show the dispersions of diffraction bands of $0_s$ and $1_s$ localized modes, respectively. Solid and dashed lines in panel (f) show the dispersions of diffraction bands of ${\mathrm{SPP}}_{\mathrm{ML}}$ and ${\mathrm{SPP}}_{\mathrm{sub}}$ modes, respectively. Thick dash-dotted lines show the Fabry–Perot modes $0_p$, $1_p$, and $2_p$ of the 50L-Au-glass structure.Reuse & Permissions