Nanoparticle arrays: From magnetic response to coupled plasmon resonances

We study optical properties of optomagnetic metamaterials consisting of regular arrays of single and double Au nanodots (nanopillars). Using a combination of data from variable angle spectroscopic ellipsometry, transmission, and reflection measurements, we identify localized plasmon resonances of gold nanodots and measure their dependence on dot size and substrate type. We demonstrate that arrays of Au nanopillars can support narrow collective plasmon resonances coupled to in-plane and out-of-plane localized plasmon resonances. The spectral positions of these plasmon modes are extracted from the angular dependence of the transmission and reflection spectra for two beam polarizations. We show that nanoarrays exhibit dramatically different optical response on conductive and nonconductive substrates and study its angular dependence. The optical response of nanoarrays is described well by coupled dipole approximation. The procedure for extracting optical constants of metamaterials based on ellipsometry is discussed and applied to our samples resulting in a calculated negative index of refraction for double-dot arrays at green light.

Figure 1

Schematic of the regular arrays of Au single and double nanoparticles on a glass substrate. Scanning electron microscopy image of the studied arrays of gold nanoparticles: (a) single nanodots; (b) double nanodots. (c) Schematic view of the regular arrays of Au double nanodots on a glass substrate and schematics for spectroscopic ellipsometry and transmission measurements. (d) Schematics representing two orientations of double nanodots for optical measurements: A and B.

Figure 2

Optical properties of the regular arrays of Au single dots on a glass substrate. (a) and (b) Angle dependence of transmission spectra for p- and s-polarized light ($d=120\mathrm{nm}$). (c) and (d) Transmission and reflection spectra for $p$-polarized light as a function of dot size ($\theta ={60}^{\circ }$). (e) and (f) Angle dependence of reflection spectra for p- and s-polarized light ($d=140\mathrm{nm}$). The insets show the unit cell of the arrays. Resonant features are marked by the dotted arrows.

Figure 3

Optical properties of the regular arrays of Au double dots on a glass substrate. (a) and (b) Angle dependence of transmission spectra for p- and s-polarized light ($d=120\mathrm{nm}$). (c) and (d) Transmission spectra for $p$- and s-polarized light as a function of dot size ($\theta ={45}^{\circ }$). (e) and (f) Angle dependence of reflection spectra for p- and s-polarized light ($d=110\mathrm{nm}$). The insets show the unit cell of the arrays. Resonant features are marked by the dotted arrows.

Figure 4

Optical properties of the regular arrays of Au single dots on a glass substrate covered by a thin Cr film. (a) and (b) Angle dependence of transmission spectra for p- and s-polarized light ($d=120\mathrm{nm}$). (c) and (d) Transmission and reflection spectra for $p$-polarized light as a function of dot size ($\theta ={60}^{\circ }$). (e) and (f) Angle dependence of reflection spectra for p- and s-polarized light ($d=120\mathrm{nm}$). The insets show the unit cell of the arrays. Resonant features are marked by the dotted arrows.

Figure 5

Optical properties of the regular arrays of Au double dots on a glass substrate covered by a thin Cr film. (a) and (b) Angle dependence of transmission spectra for p- and s-polarized light ($d=120\mathrm{nm}$). (c) and (d) Transmission spectra for $p$- and s-polarized light as a function of dot size ($\theta ={60}^{\circ }$). (e) and (f) Angle dependence of reflection spectra for p-polarized light for separated Au dots ($d=120\mathrm{nm}$) and stripe dots ($d=110\mathrm{nm}$). The insets show the unit cell of the arrays. Resonant features are marked by the dotted arrows.

Figure 6

Negative index of refraction extracted from ellipsometric measurements. (a) and (b) Ellipsometric spectra Ψ for the double-dot array measured in configurations A and B, respectively. (c) and (d) The best fit of the ellipsometric spectra Ψ for the single-dot array using the Fresnel model with effective thickness (c) $t=90\mathrm{nm}$ and (d) $t=31\mathrm{nm}$. (e) The details of the Fresnel model used in calculations. (f) The best fit of the ellipsometric parameter Ψ for the double-dot array in the spectral region of negative index of refraction. The insets show the unit cell of dot arrays used in the calculation of negative index of refraction.