Exciting Pseudospin-Dependent Edge States in Plasmonic Metasurfaces

Abstract

We study a plasmonic metasurface that supports pseudospin dependent edge states confined at a subwavelength scale, considering full electrodynamic interactions including retardation and radiative effects. The spatial symmetry of the lattice of plasmonic nanoparticles gives rise to edge states with properties reminiscent of the quantum spin Hall effect in topological insulators. However, unlike the spin-momentum locking characteristic of topological insulators, these modes are not purely unidirectional and their propagation properties can be understood by analysing the spin angular momentum of the electromagnetic field, which is inhomogenous in the plane of the lattice. The local 1 sign of the spin angular momentum determines the propagation direction of the mode under a near-field excitation source. We also study the optical response under far-field excitation and discuss in detail the effects of radiation and retardation. dospin Topological insulators are materials which are insulating in the bulk but which have conduction surface states protected against disorder (1). The remarkable properties of these states in electronic systems has inspired the search for photonic topological insulators (PTIs), which aim to guide and manipulate photons with the same level of control and efficiency (2-6). Systems which possess these effects whilst preserving time reversal symmetry are appealing as they do not require complicated experimental setups such as strong magnetic fields or bianisotropic coupling. Motivated by this, a proposal to emulate the quantum spin Hall (QSH) effect in photonic crystals was presented by Wu and Hu in Ref. 7. Effects reminiscent of the QSH phase such as a band inversion between dipolar and quadrupolarmodes, and pseudospin dependent edge states are realised but, rather than relying on the time reversal symmetric pairs characteristic of electronic systems, they instead rely on the spatial symmetry of the lattice structure. As a result, the edge states have a reduction in backscattering over trivial ones (8,9). The method has since been applied to a variety of bosonic systems (10-14), and has recently experimentally been demonstrated in the visible regime (15).The combination of topological effects with plasmonics offers the possibility of precisely controlling light on the the nanoscale. The strong enhancement and localisation of electric fields due to localised surface plasmon (LSP) resonances (16) is a widely employed platform for light confinement on the nanoscale (17,18). Plasmonic metasurfaces can be formed by arranging plasmonic nanoparticles in two-dimensional (2D) lattices, where the LSPs become

Manipulating topological valley modes in plasmonic metasurfaces

“…To prevent the mode reflecting off the hard boundary with the vacuum, we gradually increase the losses towards these boundaries. Since the topologically non-trivial edge states possess a chirality, a circularly polarised magnetic dipole source external to the lattice could also be used to excite unidirectional modes, where the direction is determined by the spin angular momentum at the source position [16].…”

“…Exploiting the radiative coupling regime between the NPs [7], whose interactions are mediated by diffractive modes in the plane of the array (surface lattice resonances), has enabled the experimental demonstration of lasing [8,9] and Bose-Einstein condensation [10] in plasmonic lattices, due to their dramatic quality factor enhancement. On the other hand, the near field coupling regime, where the distance between the NPs is very subwavelength, is currently regaining interest due to the possibility of realising topological phases of light confined at nanoscale dimensions using metal NPs as well as other nanoresonators such as dielectric NPs [11][12][13][14][15][16][17][18][19]. This has been sparked by the potential of topological protection to provide robust light propagation immune to certain kinds of disorder and imperfections in samples; in analogy to the effects present * matthew.proctor12@imperial.ac.uk in topological insulators, materials which are insulating in the bulk and possess protected conduction states along their edge [20].…”

Near- and Far-Field Excitation of Topological Plasmonic Metasurfaces

“…A direct analogy of the QSHE would produce purely unidirectional edge states, in the absence of spin-mixing impurities. However, as we showed in a previous work [15], the edge mode directionality for near-field sources is source-position-dependent and is determined by the spin angular momentum of the modes: it is the local handedness of the elliptical field polarisation which determines the propagation direction of the edge modes, rather than an absolute pseudospin quantity as in the QSHE [15]. This result is true for any bosonic breathing honeycomb lattice [16], since it is rooted in time-reversal symmetry and the absence of Kramer's degeneracy for bosons as opposed to fermions.…”

“…As a result, it couples very strongly with the light line and exhibits a polariton-like splitting. We note that the ordering in this plasmonic metasurface is opposite to the photonic crystal due to the metallic nature of the NPs [15]. A band inversion occurs around Γ between the shrunken and expanded phases, causing the dipolar and quadrupolar bands to flip.…”

“…The larger unit cell (compared to the rhombic Wigner-Seitz unit cell) folds the Brillouin zone and results in a double Dirac cone at Γ (as shown in Appendix A, Figure A1). We note that the Dirac cone lies below the localised surface plasmon frequency ω lsp due to chiral symmetry breaking and long-range interactions [15]. By perturbing the nearest neighbour separation with a scale factor s, such that R = sR 0 , a band gap is opened at Γ.…”