Topological Spaser

We theoretically introduce a topological spaser, which consists of a hexagonal array of plasmonic metal nanoshells containing an achiral gain medium in their cores. Such a spaser can generate two mutually time-reversed chiral surface plasmon modes in the $\mathbf{K}$ and ${\mathbf{K}}^{\prime }$ valleys, which carry the opposite topological charges, $\pm 1$, and are described by a two-dimensional $E^{\prime }$ representation of the $D_{3h}$ point symmetry group. Due to the mode competition, this spaser exhibits a bistability: only one of these two modes generates, which is a spontaneous symmetry breaking. Such a spaser can be used for an ultrafast all-optical memory and information processing, and biomedical detection and sensing with chirality resolution.

Figure 1

Honeycomb array of metal nanoparticles built of two inequivalent sublattices: $A$ and $B$. Sublattice $A$ consists of plasmonic metal nanoshells with the inner radius of 8 nm and the outer radius of 14 nm while sublattice $B$ consists of similar nanoshells with the inner radius of 8 nm and the outer radius of 16 nm. The gain medium is placed inside the nanoshells. The lattice bond length is set as 50 nm. The primitive unit cell of the honeycomb crystal structure is shown by the red parallelogram. The supercell, which describes the periodicity of the SPs at both the $\mathbf{K}$ and ${\mathbf{K}}^{\prime }$ points, see Eqs. (9)–(12), is marked by the yellow parallelogram.

Figure 2

(a) Band structure of honeycomb array of metal nanoshells. Due to the broken inversion symmetry, there are band gaps at the $\mathbf{K}$ and ${\mathbf{K}}^{\prime }$ points. The spasing SP modes at the $\mathbf{K}$ and ${\mathbf{K}}^{\prime }$ points are indicated by open circles; the arrows indicate the direction of the rotation of the local modal fields for the corresponding valleys. (b) Snapshot of profile of an SP electric field at the valence band in the $\mathbf{K}$ valley at a certain instance of time. Only the SPs at sublattice $A$ are excited. The color bar to the right codes the modal field amplitude.

Figure 3

(a)–(d) The valence band SPs in the $\mathbf{K}$ and ${\mathbf{K}}^{\prime }$ valleys. For both the valleys, only the SPs at the sublattice $A$ are excited. For the $\mathbf{K}$ valley, these are the SPs with $m=1$, while for the ${\mathbf{K}}^{\prime }$ valley, the SP with $m=-1$ are generated. Their phase shifts from site to site are $\pm 2\pi /3$, respectively. The SP local fields rotate in the directions shown by the red arrows. (e) Schematic of the gain medium and metal array. The SPs at the $\mathbf{K}$ and ${\mathbf{K}}^{\prime }$ points compete for the same gain.

Figure 4

Dynamics of SP population per unit supercell. (a) Temporal dynamics of the SP population. Initially the SPs in both the valleys are present, which is case (iii)—see the text. The pumping rate is $g={10}^{13}{\mathrm{s}}^{-1}$. (b) The stationary number of SPs in both valleys as a function of pumping rate.

Figure 5

Dynamics of $\mathbf{K}$-valley SP eigenmode. (a)–(d) The distributions of the local field modulus are plotted for the unit cell in the real space. The phases of the spaser oscillations are indicated. The color-coded scale of the local fields is given at the left-hand side for one SP quantum per the unit supercell. The local fields rotate in time in the direction of the black arrow, i.e., clockwise. (e) Edge fields for $\mathbf{K}$-valley mode. The instantaneous dipole vectors are indicated by the green arrows; the direction of the field rotation is depicted by the curved black arrows; crystal momentum $\mathbf{k}$ of the mode is shown by the straight black arrow. Each such a rotating dipole generates a current that is normal to this dipole.