Plasmon spectroscopy: Theoretical and numerical calculations, and optimization techniques

We present an overview of recent advances in plasmonics, mainly concerning theoretical and numerical tools required for the rigorous determination of the spectral properties of complex-shape nanoparticles exhibiting strong localized surface plasmon resonances (LSPRs). Both quasistatic approaches and full electrodynamic methods are described, providing a thorough comparison of their numerical implementations. Special attention is paid to surface integral equation formulations, giving examples of their performance in complicated nanoparticle shapes of interest for their LSPR spectra. In this regard, complex (single) nanoparticle configurations (nanocrosses and nanorods) yield a hierarchy of multiple-order LSPR s with evidence of a rich symmetric or asymmetric (Fano-like) LSPR line shapes. In addition, means to address the design of complex geometries to retrieve LSPR spectra are commented on, with special interest in biologically inspired algorithms. Thewealth of LSPRbased applications are discussed in two choice examples, single-nanoparticle surface-enhanced Raman scattering (SERS) and optical heating, and multifrequency nanoantennas for fluorescence and nonlinear optics.