Fig. 1. Skyrmions/merons and the origin of longitudinal spin due to chirality. (a) Artistic illustrations of Néel- and Bloch-type skyrmions and merons (figure fashions followed Ref. [3]). (b) For the evanescent wave in a nonchiral system with kx2+ky2=kr2>k2, the transverse spin ST∝k×n, the normal spin component Sn∝(∇×klocal)n, and the wave vector satisfies kx2+ky2+(ikz)2=k2, corresponding to a hyperboloid in the k-space. In the case that ±kz correspond to evanescent waves in the upper and lower sides of interface, the transverse spin is locked with the momentum (spin-momentum locking) and reverses its sign across the boundary. However, in a (c) chiral system, as circularly polarized light is always an eigenmode of an isotropic medium, the introduction of chirality splits the hyperboloid into two (one resides inside and the other outside the nonchiral hyperboloid): kx2+ky2−kz±2=k±2, corresponding to LCP and RCP waves, respectively. The normal spin component Sn′, thus, also is separated into S− and S+ due to the symmetry breaking [in this case Sn′=S−+S+ and spin vectors a→1·b→1=0, a→2·b→2=0 but (a→1+a→2)·(b→1+b→2)≠0]. This yields an extra spin component, which is perpendicular to Sn, i.e., the longitudinal spin SL, which is parallel to the momentum (klocal). Most importantly, this longitudinal spin does not obey the spin-momentum locking rule and will not change sign across the boundary. Its sign solely depends on the sign of material’s chirality.

Fig. 2. Calculated Bloch-type electric field skyrmion lattices. (a) Top-viewed hexagonal plasmonic coupling pattern and side-viewed typical electric field distributions in an MCM structure. (b) Field vectorial orientations for 1D and 2D chiral SPPs (at z=0), respectively. For a Bloch-type skyrmion, the in-plane field vectors are oriented as such. (c), (d) Bloch electric field skyrmion lattices (when φ1,2,...,6=0) for ξ<0 and ξ>0, respectively. Top panel insets, shown from left to right, are the in-plane component, out-of-plane component, and the skyrmion number density (μm−2) distribution of the electric field.

Fig. 3. Tailoring the skyrmion lattice by phase modulation and the formation of Bloch electric field meron lattice. A novel optical meron lattice, i.e., half-skyrmion lattice with each unit cell’s skyrmion number equal to either −1/2 or +1/2, can be generated by tuning the phase of excitation, such as setting φ2=π and the phases of the rest of the boundaries 0. (a) For an MIM structure, Néel-type electric field meron lattices can be found inside the insulator at anywhere except the center. (b), (c) Bloch electric field meron lattices for ξ<0 and ξ>0, respectively. Chirality dependent twist of meron textures can also be observed here. (d) Manipulation of meron lattices by tuning the phases of the SPPs at the boundaries.

Fig. 4. Optical Bloch-type spin skyrmion lattice. (a) Unique energy flow distribution is an MCM structure for a hexagonal plasmonic vortex lattice. (b) Calculated vectorial representation of a Bloch spin skyrmion lattice containing (c), (d) two subsets of Bloch spin skyrmion lattices. Each sub-spin skyrmion lattice consists of skyrmions with same skyrmion number N=1. The insets describe the out-of-plane component of the SAM Sz in the real space and momentum space.

Fig. 5. Optical Bloch-type meron lattice. (a) Energy flow distribution is an MCM structure for a square plasmonic vortex lattice. (b) Optical spin orientation distribution showing a meron lattice.

Fig. 6. Plane wave spectra in air (left) and a chiral medium (right). The colorful inset depicts the phase-intensity distributions of real-space wave functions for the monochromatic Bessel beam with l=1, where the brightness is proportional to the intensity, while the color indicates the phase.