Plasmonic resonances of slender nanometallic rings

Abstract

We develop an approximate quasistatic theory describing the low-frequency plasmonic resonances of slender nanometallic rings and configurations thereof. First, we use asymptotic arguments to reduce the plasmonic eigenvalue problem governing the geometric (material-and frequency-independent) modes of a given ring structure to a one-dimensional periodic integrodifferential problem in which the eigenfunctions are represented by azimuthal voltage and polarization-charge profiles associated with each ring. Second, we obtain closed-form solutions to the reduced eigenvalue problem for azimuthally invariant rings (including torus-shaped rings but also allowing for noncircular cross-sectional shapes), as well as coaxial dimers and chains of such rings. For more general geometries, involving azimuthally nonuniform rings and noncoaxial structures, we solve the reduced eigenvalue problem using a semianalytical scheme based on Fourier expansions of the reduced eigenfunctions. Third, we used the asymptotically approximated modes, in conjunction with the quasistatic spectral theory of plasmonic resonance, to study and interpret the frequency response of a wide range of nanometallic slender-ring structures under plane-wave illumination.

Theory of Hot-Carrier Generation in Bimetallic Plasmonic Catalysts

“…In the above, Γ if is given by normalΓ i f ( ω ) = 2 π ℏ | ⟨ f | normalΦ̂ tot ( ω ) false| i false⟩ | 2 δ ( E f − E i − ℏ ω ; γ ) f ( E i ) ( 1 − f false( E f false) ) where f ( E ) is the Fermi–Dirac distribution (for a continuous wave photocatalysis experiment, the electron occupation will not necessarily follow a Fermi–Dirac distribution; however, calculating the full nonequilibrium distribution function would require a detailed theory of relaxation effects, which goes beyond the scope of the current manuscript; Fermi’s Golden Rule was evaluated using distributions other than Fermi–Dirac in refs and ) with temperature T = 298 K, γ = 0.06 eV is a broadening parameter which reflects the line width of an electron–hole pair excitation (here we have used typical values for the broadening parameters σ and γ based on our previous work, in which the effect of electron–electron and electron–phonon interactions are studied in detail; we have verified that the calculated hot-carrier generation rates are not sensitive to the precise values of the broadening parameters) and normalΦ̂ tot ( ω ) denotes the total potential inside the nanoparticle. This potential is calculated using the quasistatic approximation. − In particular, we use the finite ...…”

A Dual-Band Guided Laser Absorber Based on Plasmonic Resonance and Fabry-Pérot Resonance

“…Take the metamaterial absorber as an example; the main principle behind its effective absorption at a certain wavelength is plasmonic resonance (typically excited by incident waves in an MIM 'sandwich' structure [19]). The shape, size, and period of micro-and nano-structures can significantly influence the plasmonic resonance [20]. Based on this feature, resonant characteristics can be designed by adjusting the geometry, size, and distribution of the structural units.…”