Plasmonic photonic crystals realized through DNA-programmable assembly

Abstract

Three-dimensional dielectric photonic crystals have well-established enhanced light-matter interactions via high Q factors. Their plasmonic counterparts based on arrays of nanoparticles, however, have not been experimentally well explored owing to a lack of available synthetic routes for preparing them. However, such structures should facilitate these interactions based on the small mode volumes associated with plasmonic polarization. Herein we report strong light-plasmon interactions within 3D plasmonic photonic crystals that have lattice constants and nanoparticle diameters that can be independently controlled in the deep subwavelength size regime by using a DNA-programmable assembly technique. The strong coupling within such crystals is probed with backscattering spectra, and the mode splitting (0.10 and 0.24 eV) is defined based on dispersion diagrams. Numerical simulations predict that the crystal photonic modes (Fabry-Perot modes) can be enhanced by coating the crystals with a silver layer, achieving moderate Q factors (∼10(2)) over the visible and near-infrared spectrum.

Keywords: 3D photonic crystals; DNA-programmable assembly; deep subwavelength scale; plasmonics; strong coupling.

Fig. 1.

A polaritonic photonic crystal made by DNA-programmable assembly. (A) Three-dimensional illustration of a plasmonic PPC, in the shape of a rhombic dodecahedron, assembled from DNA-modified gold nanoparticles. Red arrows indicate light rays normal to the underlying substrate, impinging on and backscattering through a top facet of the crystal (FPMs). The blue ones represent light rays entering through the slanted side facets and leaving the PPC through the opposite side, not contributing to the FPMs (Fig. S2). The top right inset shows the top view of the crystal with two sets of arrows defining two polarization bases at the top and side facets. The bottom right inset shows an SEM image of a representative single crystal corresponding to the orientation of the top right inset. (Scale bar, 1 µm.) (B) A 2D scheme showing the geometric optics approximation of backscattering consistent with the explanation in A. The hexagon outline is a vertical cross-section through the gray area in the top right inset of A parallel to its long edge. The box enclosed by a dashed line depicts the interaction between localized surface plasmons and photonic modes (red arrows; FPMs) with a typical near-field profile around gold nanoparticles. The contribution of backscattering through the side facets (blue arrows) to FPMs is negligible. (C) Scheme of plasmon polariton formation. The localized surface plasmons (yellow bar) strongly couple to the photonic modes (red bars; FPMs).

Fig. 2.

Experimental and theoretical backscattering spectra of PPC1–3. (A) SEM image (Top) and optical bright field reflection mode image (Bottom) of PPC1 on a silicon substrate. (Scale bar, 1 µm.) (B) Measured backscattering spectrum (red solid line) of PPC1 from the center red spot in A, Bottom. Calculated backscattering spectra based on two infinite slab models with BCC crystal geometry (blue solid line) and EMT approximation (blue dashed line). FPMs are indicated by markers. (C–F) The same datasets for PPC2 and PPC3 as in A and B. PPC2 and PPC3 are on indium tin oxide (ITO)-coated glass slides. The optical images show bright spots at the center owing to backscattering from the top and bottom facets. Two vertical lines in F indicate spectral positions where FPMs are suppressed. (Scale bars, 1 µm.)

Fig. 3.

Calculated photonic mode dispersion, mode splitting, and effective mode index of PPC1–3. (A) The spectral density in the ΓN direction is presented for PPC1 (red is high, blue is low). Log10 scale is used. Red triangular markers are the FPMs in Fig. 2B (red markers). They are assigned to peak positions of the spectral densities and the mode number (N) is assigned on one FPM. (Inset) The same spectral density calculated based on the Drude model for gold (where there is no interband transition). (B and C) The same information as in A for PPC2 and PPC3. (D) The mode splitting to plasmonic mode energy ratio, $\hslash {\mathrm{\Omega }}_R/\hslash {\omega }_0$, is shown in terms of gold volume fraction. Blue dots are calculated based on EMT with the Drude model for gold. Squares are generated by a FDTD photonic crystal analysis with the Drude model for gold (red, green, and black: nanoparticle diameters 5.6, 9.0, and 20 nm; volume fraction of PPC3 indicated for 20 nm), and circles with experimentally measured gold permittivity (red and green: nanoparticle diameters 5.6 and 9.0 nm; PPC1 and PPC2). (E) EMT-based effective indices, Re[n_eff], for PPC1 (dotted line), PPC2 (dash-dot line), and PPC3 (dashed line). The index of the silica host medium (black solid line) is added as a reference. Red markers are Re[n_eff] based on the FPMs in A–C.

Fig. 4.

Prediction of backscattering spectra and Q factor of silver-coated PPC1–3. (A) Backscattering spectra of PPC1–3 (from bottom to top: PPC1, PPC2, and PPC3) based on the infinite slab model with BCC crystal geometry. The thickness of the slabs is ∼1.3 µm, and that of silver coating layer is varied from 10 to 30 nm. As the coating thickness increases the line shape becomes sharper. The spectra of PPC1 and 2 are translated for comparison. (B) Q factors of each silver-coated slab are shown at FPMs (PPC1, red; PPC2, green; and PPC3, blue). The coating thickness is 30 nm.