Surface second-harmonic generation from metallic-nanoparticle configurations: A transformation-optics approach

Abstract

We study surface second-harmonic generation (SHG) from a singular plasmonic structure consisting of touching metallic wires. We use the technique of transformation optics and relate the structure to a rather simpler geometry, a slab waveguide. This allows us to obtain an analytical solution to the problem, revealing rich physical insights. We identify various conditions that govern the SHG efficiency. Importantly, our analysis demonstrates that apart from the mode-matching condition, phase-matching condition is relevant even for this sub-wavelength structure. Furthermore, we identify a geometric factor which was not identified before. We support our analysis with numerical simulations.

Optimization of second-harmonic generation from touching plasmonic wires

“…The square of the FF electric field in (1) is symmetric, but the differentiation operator causes the source to be antisymmetric in x and y, so it excites the higher frequency asymmetric slab mode via the so-called mode matching (MM) condition (implicit in Eq. (A1), see [22]), see Fig. 1(b).…”

“…Instead, previous theoretical work has mostly been numeric, and usually addresses only the far-field properties of the SH fields [14]. In [22], we introduced a new analytic tool for this class of problems, namely, Transformation Optics (TO). This technique rose to fame in facilitating the design of the invisibility cloak [23], and was later used for the interpretation and design of a range of plasmonic structures [24][25][26][27].…”

“…1(b)), exciting a slab mode. The resulting SH source can be calculated and transformed back to the TW frame, as discussed in detail in [1,22,30]. It has the generic form J z,r (x, y) = χ…”

“…1(c). The FF modes excited in the slab frame have electric fields that are symmetric in x and y, since these are the surface plasmon waves that exist within the frequency band below the plasma resonance frequency (see [22]). The square of the FF electric field in (1) is symmetric, but the differentiation operator causes the source to be antisymmetric in x and y, so it excites the higher frequency asymmetric slab mode via the so-called mode matching (MM) condition (implicit in Eq.…”

Transformation optics for plasmonics: from metasurfaces to excitonic strong coupling

“…Using these ideas [42][43][44], a set of analytical and quasianalytical TO approaches have been devised to investigate the harvesting of light by a wide range of 2D and 3D geometries: touching nanoparticles [45,46], nanocrescents [47,48], nanorods [49], nanosphere dimers [50,51]. Moreover, other EM phenomena have been explored theoretically using TO ideas, such as spatial nonlocality in metallic junctions [52,53], electron energy loss in metal nanostructures [54], second harmonic generation in plasmonic dimers [55], near-field van der Waals interactions between nanoparticles [56,57], or plasmon hybridization in collections of several touching nanoparticles [58].…”