Metallodielectric photonic crystal superlattices: Influence of periodic defects on transmission properties

We experimentally and theoretically investigate the influence of periodic defects on the transmission properties of one-dimensional metallodielectric photonic crystal slabs. The spectral positions and the excitation efficiencies of the quasiguided waveguide modes in the slab are determined by the reciprocal lattice vector and the structure factor of the supercells, respectively. We show that by introducing periodic defects in the wire position, the structure factor of the supercells can be strongly modified. For a polarization of the light perpendicular to the wires, the coupling of higher order Bragg resonances of the lattice structure to localized nanowire plasmon resonances can be sensitively controlled by the structure of the supercell. All experimental results show a good agreement with the theory.

Figure 1

Schematic view of the sample geometry. The gold nanowires are deposited on top of a dielectric slab waveguide made of ITO. The superperiod is marked by $d_{x1}$ and the subcell period by $d_{x2}$. For some experiments, the number of nanowires $n$ in the supercell was changed.

Figure 2

(a) Schematic views of the sample geometries for design $A$. While the superperiod $d_{x1}=2640\mathrm{nm}$ and the subcell period $d_{x2}=440\mathrm{nm}$ have been retained unchanged in this series, the number of missing nanowires per supercell is increased stepwise from 0 to 5. Dispersion relations of TE guided modes obtained by the empty-lattice approximation are shown in (b). The modes are folded into the first Brillouin zone of a lattice with periods $d_x=440\mathrm{nm}$ (dotted line) and $d_x=2640\mathrm{nm}$ (solid line). The numbers indicate the order of the Bragg resonance at the zone center for the period of $d_x=2640\mathrm{nm}$. In (c) the Fourier decompositions of the grating structures are presented in dependence on the spatial frequency. The number in brackets denotes the sample in this series.

Figure 3

Measured (a), (c) and calculated (b), (d) extinction spectra of the sample design $A$ of metallodielectric superlattice structures for normal light incidence and both polarization directions. The number in brackets denotes the sample in this series. The individual spectra are shifted upward for clarity in each panel. While the periods $d_{x1}=2640\mathrm{nm}$ and $d_{x2}=440\mathrm{nm}$ have been retained unchanged, the number of missing nanowires per supercell is increased stepwise from 0 to 5. The arrows mark the eighth Bragg resonance. For better visibility of the peaks, the experimentally obtained spectra (4) and (5) in panels (a) and (c) are multiplied by a factor of 2 and 5, respectively.

Figure 4

(a) Schematic views of the sample geometries for design $B$. The number in brackets denotes the sample in this series. While the subcell period $d_{x2}=475\mathrm{nm}$ and the number of nanowires $(n=10)$ have been kept constant for all samples in this series, the superperiod $d_{x1}$ is increased from $4750\mathrm{nm}$ (0) to $5550\mathrm{nm}$ (8) in steps of $100\mathrm{nm}$. In (b), the Fourier decompositions of the grating structures are shown in dependence on the spatial frequency and the superperiod $d_{x1}$.

Figure 5

Measured (a), (c) and calculated (b), (d) extinction spectra of the sample design $B$ of metallodielectric superlattice structures for normal light incidence and both polarization directions. The individual spectra are shifted upward for clarity in each panel. Again, the number in brackets denotes the sample. While the subcell period of $475\mathrm{nm}$ and the number of nanowires $(n=10)$ per supercell have been kept constant for all samples with this design, the superperiod $d_{x1}$ is increased from $4750\mathrm{nm}$ (0) to $5550\mathrm{nm}$ (8) in steps of $100\mathrm{nm}$. The numbers in panel (b) denote the order of the Bragg resonances.

Figure 6

Schematic view of the sample geometry for design $C$. While all fundamental periods have been kept constant in this series, a small random displacement $\mathrm{\Delta }r$ in the positions of the nanowires was introduced. The dotted squares mark the cross section of original positions of the nanowires without displacement. The individual wires in each supercell are labeled by the numbers 1 to 6. Notice that the same randomization was used in each supercell within the structure, i.e., all wires “1” have the same displacement $\mathrm{\Delta }r$.

Figure 7

Fourier decompositions of the grating structures (design $C$) in dependence on the spatial frequency and the strength $f$ of the displacement. The individual Fourier spectra are shifted upward for clarity.

Figure 8

Measured (a), (c) and calculated (b), (d) extinction spectra of the sample design $C$ of metallodielectric superlattice structures for normal light incidence and both polarization directions. The individual spectra are shifted upward for clarity in each panel. While the subcell period of $475\mathrm{nm}$, the number of nanowires $(n=6)$, and the superperiod of $3325\mathrm{nm}$ have been kept constant for all samples with this design, periodic defects in the position of the nanowires were introduced from $f=0$ (no defects, $\mathrm{\Delta }{r}_{\max }=0$) to $f=1.0$ $(\mathrm{\Delta }{r}_{\max }=\pm 135\mathrm{nm})$ in steps of 0.1. The numbers in panel (b) denote the order of the Bragg resonance. All extinction values in panel (a) are multiplied by a factor of 2 for better visibility of the peaks.