Source: http://aoot.osa.org/prj/abstract.cfm?uri=prj-2-1-15
Timestamp: 2019-04-19 12:18:57+00:00

Document:
Fano resonances between plasmons and diffracted light offer tunable energies and locales, but attribution of Fano resonance features to geometry and physicochemistry of metal nanostructures and adjacent dielectrics has been confounded by complexity and computational expense. This work shows predictable modal shifts of Fano resonance in square lattices of plasmonic nanostructures can be attributed directly to changes in medium wavenumber, particle size, and lattice constant that alter plasmon polarizability and diffractive interference. For 45 to 80 nm radius particles, a window of lattice constants that support Fano resonances is identified in a range from 500 to 900 nm. Lattice constants that support high intensity resonances are determined by individual particle polarizability and medium wavenumber. Fano resonance wavelengths redshift from diffracted photon energies as local refractive index (RI) changes due to coupling with particle polarizability in the window. Redshift sensitivities for quadrupole, dipole, and Fano resonances are 150, 348, and 541 nm, respectively, per RI unit. Fano resonance intensity may be enhanced more than tenfold by selecting nanoparticle sizes and lattice constants. The quantitative effects of such parametric changes are rapidly and intuitively distinguished using a semi-analytic approach, consisting of an exact expression for particle polarizability, a trigonometric description of diffraction, and a semi-analytical coupled dipole approximation.
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Fig. 1. Schematic of the square lattice of nanoparticles (hollow circles) identifying diffraction modes (solid lines) that constitute unique particle chains. Inset depicts wavelength contraction of a plane wave moving from a smaller to a larger index of refraction medium and its effects on nanoparticle polarizability. Incident energy that excites resonance at η1 must be reduced to excite resonance at η2>η1.
Fig. 2. Phase overlap (dashed line) onto a center particle was calculated using Ref.  for a lattice constant of 600 nm and RI values of 1.00 (black; peak ∼600 nm), 1.17 (blue; ∼700 nm), and 1.33 (red; ∼800 and 575 nm). Extinction spectra (solid line) were calculated by rsa-CDA for corresponding infinite arrays of 70 nm radius Au particles with lattice constant 600 nm. The inset expands the 1.17 RI array to show that constructive interference from lattice scattering supports extinction peaks.
Fig. 3. Imaginary component of particle polarizability [Eq. (1)] is shown as the color gradient for RI values of 1.00 and 1.33 over a range of particle sizes and incident vacuum wavelength values.
Fig. 4. Comparison of single particle extinction spectra calculated for 70 nm radius spherical particles using the exact Mie theory (dotted) and the dynamic dipole polarizability (solid lines) with the quadrupole extension. The homogeneous RI surrounding each particle is shown in the legend.
Fig. 5. Extinction spectra for a square lattice of 70 nm radius particles spaced at 600 nm with RI values of 1.00, 1.17, and 1.33 using the rsa-CDA. Inset shows spectral results for a 5×5 array of 70 nm Au particles with a lattice constant of 600 nm using the finite CDA. The value of extinction efficiency at the RI and wavelength shown appears as a color gradient.
Fig. 6. Sensitivity shown by wavelength shift of Fano resonance peak wavelength per RI unit (RIU) for a given geometric combination of lattice constant and particle radius. RI change for the calculation was from 1.00 to 1.10.
Fig. 7. Array geometries that yield extraordinary Fano resonance through constructive interference of scattered light. The color gradient shows the maximum extinction of the Fano resonance as a function of lattice constant and particle radius.

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