Optical properties of planar metallic photonic crystal structures: Experiment and theory

We report on results of transmission measurements of metallic nanowire arrays deposited on top of different dielectric substrates. The appearance of grating anomalies, which critically depend on the substrate thickness, provides evidence that the optical response of these planar metallic photonic crystal structures can be strongly modified. While only Rayleigh-type anomalies are observed for thin dielectric substrates, thicker waveguiding substrates can induce strong coupling phenomena. This strong coupling results in the formation of waveguide-plasmon polaritons with a large Rabi splitting up to $250\mathrm{meV}$. We show that the coupling phenomena vary with the nanowire grating period, the angle of incidence, and also the waveguide layer thickness. A scattering-matrix-based numerical method is used to calculate the transmission properties and the near-field spatial distributions of such metallic photonic crystal structures. All experimental results are well confirmed by our theoretical calculations.

Figure 1

Schematic view of the gold nanowire array on top of an ITO layer. Samples with different ITO thicknesses are investigated ($L_z=15\mathrm{nm}$ or $L_z=140\mathrm{nm}$). Angle- and polarization-dependent transmission measurements are possible.

Figure 2

A collection of measured (a) and calculated (b) extinction spectra for nanowire gratings on top of $15\text{−}\mathrm{nm}$-thick ITO layers at normal incidence. From top to bottom, the nanowire period $d_x$ is changed from $350\mathrm{nm}\text{to}500\mathrm{nm}$ in steps of $50\mathrm{nm}$. In addition, measured (c) and calculated (d) extinction spectra for different angles of incidence and a fixed nanowire period of $450\mathrm{nm}$ are depicted. Spectra are shown for TE- (dotted lines) and TM-polarization (solid lines) (electric and magnetic field parallel to the nanowires, respectively). TE-polarized spectra in (b) and (d) are drawn to a larger scale (x10). The individual spectra are shifted upwards for clarity in each panel. Vertical arrows mark the positions of the diffractive anomalies.

Figure 3

Measured and calculated spectral positions of the observed grating anomalies. The dependency on the grating period (normal incidence: $k_{g,x}=2\pi ∕d_x$) is shown in panel (a). A period of $d_x=450\mathrm{nm}$ was chosen for the angle resolved experiments (variation of $k_x$) in panel (b). Light cones for air, quartz, and ITO are depicted as dotted lines. Additionally, the dispersion of the light cones folded into the first BZ are displayed in panel (b).

Figure 4

Calculated spectra (TM-polarization, normal incidence) for gold nanowire gratings on top of a free-standing $15\text{−}\mathrm{nm}$-thick ITO film are shown in panel (a). Panel (b) displays the calculated spectra for an identical structure, but without removing the quartz substrate below the ITO layer (the same structure as assumed for the calculations in Fig. 2). From top to bottom, the nanowire period $d_x$ is changed from $150\mathrm{nm}\text{to}800\mathrm{nm}$ in steps of $50\mathrm{nm}$. The individual spectra are shifted upwards for clarity. Inset: Fano-type resonance for a nanowire period of $600\mathrm{nm}$.

Figure 5

Measured extinction spectra of gold nanowire arrays (Period $d_x=450\mathrm{nm}$) for normal light incidence. Spectra of samples with $15\text{−}\mathrm{nm}$-thick (a) and $140\text{−}\mathrm{nm}$-thick (b) ITO layers are shown for a comparison in TE (dotted lines) and TM (solid lines) polarization.

Figure 6

Empty-lattice approximation: The lowest TE and TM polarized guided modes of a homogeneous and $140\text{−}\mathrm{nm}$-thick ITO waveguide. Their dependencies on $k_{g,x}$ are shown in panel (a). Panel (b) displays these guided modes folded into the first BZ for an assumed grating period of $d_x=450\mathrm{nm}$. The particle plasmon dispersion of noninteracting gold nanowires (dotted horizontal line) is shown too.

Figure 7

Measured (a) and calculated (b) extinction spectra of gold nanowire arrays deposited on top of $140\text{−}\mathrm{nm}$-thick ITO layers for normal light incidence and nanowire periods ranging from $375\mathrm{nm}\text{to}575\mathrm{nm}$ in steps of $25\mathrm{nm}$. Spectra for TE (dotted line) and TM (solid line) polarization are shown. The individual spectra are shifted upwards for clarity in each panel.

Figure 8

Measured (hollow circles) and calculated (solid circles) energies of the extinction spectra maxima for gold nanowire arrays deposited on top of $140\text{−}\mathrm{nm}$-thick ITO layers. The dependence on $d_x$ for normal light incidence and TM polarization is shown.

Figure 9

Measured (a),(b) and calculated (c),(d) extinction spectra of gold nanowire arrays deposited on top of $140\text{−}\mathrm{nm}$-thick ITO layers for a fixed nanowire period of $d_x=450\mathrm{nm}$. From top to bottom, the angle $\vartheta$ is increased from 0° to 20° in steps of 2° while $\phi =0°$ remains unchanged. Spectra for TE (a),(c) and TM (b),(d) polarization are depicted. The different spectra are shifted upwards for clarity in each panel.

Figure 10

Measured (solid circles) and calculated (open circles) positions of the extinction spectra maxima in TE and TM polarization for nanowire arrays on top of $140\text{−}\mathrm{nm}$-thick ITO layers. The angle $\vartheta$ is increased from 0° to 20° while $\phi =0°$ and $d_x=450\mathrm{nm}$ remain unchanged. The arrows show the 1D stopbands in TE and TM polarizations.

Figure 11

Measured (a),(b) and calculated (c),(d) extinction spectra of gold nanowire arrays deposited on top of $140\text{−}\mathrm{nm}$-thick ITO layers for a fixed nanowire period of $d_x=450\mathrm{nm}$. From top to bottom the angle $\vartheta$ is increased from 0 to 20° in steps of 2° while $\phi =90°$ remains unchanged. Spectra for TE-like (a),(c) and TM-like (b),(d) polarization are depicted. For the calculations a wire cross-section of $85\times 30{\mathrm{nm}}^2$ has been assumed to bring the calculated wire plasmon resonance to better agreement with the measured one. The individual spectra are shifted upwards for clarity in each panel.

Figure 12

Calculated extinction spectra for a fixed nanowire period of $d_x=450\mathrm{nm}$ and a fixed angle of $\vartheta =20°$. Calculations for $\phi =90°$ [panel (a)] and $\phi =88°$ [panel (b)] are compared. Spectra for TE-like (dotted lines, $p$-polarization) and TM-like polarization (solid lines, $s$-polarization) are depicted. Again, a wire cross-section of $85\times 30{\mathrm{nm}}^2$ has been assumed. The arrows in (b) correspond to the spectral positions of the extra modes.

Figure 13

(Color online) The calculated spatial distributions of the electric [blue and red cones in panels (a) and (b)] and magnetic [green cones in panels (c) and (d)] fields in a waveguiding structure with period $d_x=450\mathrm{nm}$, for normal incidence $(\vartheta =\phi =0°)$ and TM-polarized (across the wires) light. The fields are shown for an incoming photon energy of $\hslash \omega =1.74\mathrm{eV}$, corresponding to the 1st (lower energy) peak in extinction. The electric and magnetic fields are depicted at the moments of time $t$ (measured in units of light period $T=2\pi ∕\omega$ and shown in the title of each panel) when the field intensities that are integrated over the displayed cross sections ${\int }_A{\mathbf{E}}^{2}dA$ and ${\int }_A{\mathbf{H}}^{2}dA$ reach maxima (see the explanation in the text). Solid magenta lines denote the cross-section of the structure. The incoming wave arrives from vacuum (at $z<0$). Panels (b),(d) show the fields in a magnified region around the gold nanowire. Red cones in panels (a),(c) are scaled by a multiplier of 0.5 in order to exclude the cones overlap in the regions of high electric fields near the sharp edges of the gold nanowire.

Figure 14

(Color online) The calculated spatial distributions of the electric [blue and red cones in panels (a) and (b)] and magnetic [green cones in panels (c) and (d)] fields in a waveguiding structure with period $d_x=450\mathrm{nm}$, for normal incidence $(\vartheta =\phi =0)$ and TM-polarized (across the wires) light. The fields are shown for photon energy $\hslash \omega =1.9\mathrm{eV}$, corresponding to the extinction minimum. All other rules for drawing this figure are the same as in Fig. 13.