Correlation Effects in Disordered Metallic Photonic Crystal Slabs

We analyze the influence of correlations on the optical properties of disordered metallic photonic crystal slabs experimentally and theoretically. Different disorder models with different nearest-neighbor correlations are considered. We present a theory that allows us to quantitatively calculate the optical properties of the different samples. We find that different kinds of correlations produce characteristic spectral features such as peak reduction and inhomogeneous broadening. These features are caused by reduced excitation efficiencies and the excitation of multiple resonances.

Figure 1

(a) Metallic photonic crystal slab structure consisting of a gold grating on top of a waveguide layer. The light propagates through the sample at normal incidence. TE and TM indicate the direction of the electric field polarization. (b),(c) Schematic view of uncorrelated and correlated disorder, respectively. Dotted lines indicate the center positions of the perfect grating with period $d_0$.

Figure 2

Fourier analysis of exemplary structures with uncorrelated and correlated disorder. The disorder was increased in steps of 10%. Each structure consisted of 1000 nanowires with $d_0=400\mathrm{nm}$. The curves are shifted for clarity.

Figure 3

Transformation of exemplary Fourier peaks from $k$ space into energy space via the dispersion relations. Schematic line shape functions are added in energy space to yield ${\alpha }^{\mathrm{TE}}(E)$ and ${\alpha }^{\mathrm{TM}}(E)$.

Figure 4

Measured and simulated extinction spectra for different disordered samples in TE and TM polarization. Left panel: Results for uncorrelated disorder, $d_0=430\mathrm{nm}$. Right panel: Results for correlated disorder, $d_0=475\mathrm{nm}$. The disorder was increased in steps of 10%. The individual spectra are shifted for clarity.