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. [41] 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.

Table 1. Categorization of Select, Recent Studies of Fano Resonant Plasmonic Nanostructures According to Source and Type of Description