Controlling the interaction between localized and delocalized surface plasmon modes: Experiment and numerical calculations

We study the fundamental optical effects originating from the resonant excitation of localized and delocalized surface plasmon modes supported by a multilayer metallic photonic crystal slab. The optimized model system consists of a periodic gold nanowire array and a spatially separated homogeneous silver film. We show that the spacer layer controlled dipole-surface interaction reveals a pronounced period dependence when an ordered nanowire arrangement is employed. Our analysis demonstrates that strong coupling gives rise to the formation of hybridized plasmon modes. Moreover, the magnetic activity of the metallic multilayer structure is theoretically analyzed. The presented effects provide interesting tools for the optimization of future plasmonic nanodevices and metal-based metamaterials.

Figure 1

(a) Schematic view of the metallic photonic crystal slab structure. The gold nanowire array and the 20-nm-thick silver film are separated by a dielectric layer of thickness $L_{sp}$. Experimentally and theoretically obtained extinction spectra are displayed in panels (b) and (c), respectively. Spectra of a pure gold grating (solid lines) and of a metallic multilayer structure ($L_{sp}=70\mathrm{nm}$, dashed lines) are compared. The spectra $(d_x=300\mathrm{nm})$ are shown for TM polarization and normal light incidence.

Figure 2

(a) Calculated extinction spectra of a multilayer photonic crystal slab for TM polarization and normal light incidence. From bottom to top, the spacer layer thickness is increased from $L_{sp}=0\mathrm{nm}$ (lowest spectrum) to $L_{sp}=210\mathrm{nm}$ (highest spectrum) in steps of $10\mathrm{nm}$. The grating period of $d_x=300\mathrm{nm}$ is kept constant. The individual spectra are shifted upwards for clarity. The spectral positions of the supported bare modes are indicated by vertical lines (dashed line: localized particle plasmon mode, dashed-dotted line: 1st Bragg resonance of the short range surface plasmon). A direct comparison between experimental and theoretical results is given in panels (b) and (c). Structures with a spacer layer thickness of $30\mathrm{nm}$, $50\mathrm{nm}$, and $70\mathrm{nm}$ are studied. Spectra in panel (c) correspond to the dashed curves in panel (a).

Figure 3

Calculated transmission (solid lines) and absorption spectra (shaded area) of a multilayer photonic crystal slab structure for TM polarization and normal light incidence. Spectra for structures with a spacer layer thickness of $20\mathrm{nm}$ are shown for $d_x=300\mathrm{nm}$ (a) and $500\mathrm{nm}$ (b). Additionally, the transmission spectrum of a pure 20-nm-thick silver film without nearby grating is plotted (dashed line) in both panels. The current distribution of the fundamental plasmon modes in two different coupled nanowire geometries (wire-wire or wire-image interaction) is pictorially displayed in panels (c) and (d). Note that the symmetric mode does not exist in case of image coupling.

Figure 4

(Color online) Calculated spatial distribution of the electric (a) and magnetic (b) fields in a metallic multilayer structure (TM polarization, $\vartheta =0°$, $d_x=300\mathrm{nm}$). The fields are shown for a photon energy of $\hslash \omega =1.41\mathrm{eV}$ [absorption maximum in Fig. 3a] and a spacer layer thickness of $L_{sp}=20\mathrm{nm}$. Solid magenta lines denote the cross-section of the sample structure. The length of the displayed cones is proportional to the field strength at the central point of each cone and the field direction is specified by their orientation. The red cones in panel (a) are scaled by a factor of 0.5. The field distributions are displayed for the moments of time when the field intensities (integrated over the displayed area) reach their maxima. The field magnitudes are normalized to their maximum absolute values $E_{\max }$ and $H_{\max }$ (specified in the panels) measured in units of the incoming field, respectively.

Figure 5

(Color online) Calculated spatial field distribution of the electric and magnetic fields for normal light incidence and TM polarization. Shown are the normalized time-averaged field intensities for a nanowire structure with a periodicity of $d_x=500\mathrm{nm}$, a spacer thickness of $L_{sp}=20\mathrm{nm}$, and a 20-nm-thick silver film. The local fields are depicted for an incoming photon energy of $\hslash \omega =1.35\mathrm{eV}$ and $\hslash \omega =1.61\mathrm{eV}$ in a plane perpendicular to the nanowires. The chosen energies correspond to the positions of the absorption maxima in Fig. 3b. The fields are normalized by the maximum electric $(\mid {\vec{E}}_{\max }{\mid }^2)$ and magnetic field $(\mid {\vec{H}}_{\max }{\mid }^2)$ intensities (specified in the panels) measured in units of the incoming field with amplitudes equal one, respectively. Black lines denote the cross section of the structure.

Figure 6

(Color online) Calculated extinction contour plots of grating-film structures in dependence of the spacer layer thickness. Results for structures with $d_x=200\mathrm{nm}$ (a), $d_x=300\mathrm{nm}$ (b), $d_x=400\mathrm{nm}$ (c), and $d_x=500\mathrm{nm}$ (d) are compared. The contour plots are drawn assuming normal light incidence and TM polarization, respectively. The spectral positions of the bare modes are indicated by horizontal lines (dashed line: localized nanowire plasmon resonance, dashed-dotted line: short-range surface plasmon mode of the silver film, dotted line: long-range surface plasmon mode of the silver film).

Figure 7

(Color online) Measured (a) and calculated (b) extinction spectra of the multilayer metallic photonic crystal ($d_x=300\mathrm{nm}$, $L_{sp}=70\mathrm{nm}$, TM polarization) in dependence of the incidence angle. The angle $\vartheta$ is increased from $0°$ to $18°$ in steps of $6°$. The individual spectra are shifted upwards for clarity. Additionally, the numerically obtained extinction contour plot of the studied structure is depicted in panel (c). The dispersion of the short-range surface plasmon mode in empty-lattice approximation (dashed line) is shown in panel (d). The experimentally obtained positions of the extinction maxima are indicated by solid circles, respectively.

Figure 8

(a) Experimentally measured extinction spectra of grating-film structures with $L_{sp}=50\mathrm{nm}$ for normal light incidence and TM polarization. Starting from a perfectly periodic structure with $d_x=400\mathrm{nm}$ $(f=0.0)$, random defects in the position of the nanowires were introduced from $f=0.0$ $(\mathrm{\Delta }{r}_{max}=0\mathrm{nm})$ to $f=1.0$ $(\mathrm{\Delta }{r}_{max}=\pm 200\mathrm{nm})$ in steps of 0.2. Additionally, the numerically obtained extinction spectra of a periodic structure without defects is plotted as a reference (dashed line). A schematic view of the grating-film structure is shown in panel (b). The dotted squares mark the cross section of the original wire positions without displacement. The parameter $\mathrm{\Delta }{r}_i$ indicates the spatial shift of the $i$th nanowire. The Fourier decompositions of the grating structures in dependence of the spatial frequency and of the weighting factor $f$ are displayed in panel (c). Note that the spectra in panels (a) and (b) are shifted upwards for clarity.