Polarization-Orthogonal Nondegenerate Plasmonic Higher-Order Topological States

Photonic topological states, providing light-manipulation approaches in robust manners, have attracted intense attention. Connecting photonic topological states with far-field degrees of freedom (d.o.f.) has given rise to fruitful phenomena. Recently emerged higher-order topological insulators (HOTIs), hosting boundary states two or more dimensions lower than those of bulk, offer new paradigms to localize or transport light topologically in extended dimensionalities. However, photonic HOTIs have not been related to d.o.f. of radiation fields yet. Here, we report the observation of polarization-orthogonal second-order topological corner states at different frequencies on a designer-plasmonic kagome metasurface in the far field. Such phenomenon stands on two mechanisms, i.e., projecting the far-field polarizations to the intrinsic parity d.o.f. of lattice modes and the parity splitting of the plasmonic corner states in spectra. We theoretically and numerically show that the parity splitting originates from the underlying interorbital coupling. Both near-field and far-field experiments verify the polarization-orthogonal nondegenerate second-order topological corner states. These results promise applications in robust optical single photon emitters and multiplexed photonic devices.

Figure 1

The schematic of polarization-orthogonal nondegenerate SOTCS on a plasmonic kagome metasurface. The blue (red) waves with vertical (horizontal) polarizations (${\mathrm{E}}_{\perp }/{\mathrm{E}}_{//}$) correspond to the lower (higher) frequency, respectively. The parities of SOTCS are shown in the insets.

Figure 2

Parity splitting of plasmonic SOTCS. (a) A two-dimensional plasmonic HOTI. $r$, $d_1$ and $d_2$ represent cavities radius and distances, respectively. (b) Eigenfrequencies of the HOTI. The red (black) dots represent SOTCS with even (odd) parity. The gray dashed line marks the zero frequency. (c)–(d) Field patterns of SOTCS. (e) The black dashed line denotes near-field transmission spectrum of a single cavity. The red, green, and blue solid lines are Lorentzian fittings. The “$S(P)$” mark the position of source (probe). (f) The parity-dependent trimer supermodes, and their corresponding eigenfrequencies. The black dashed line represents the zero frequency. The red (blue) dashed lines represent the average frequency $\overline{\omega }=({\omega }_{-}+{\omega }_{+})/2$ of even(odd) modes. (g) The schematic of the IOC-induced effective LRC. (h) The tight-binding model of the HOTI in (a). The ${\kappa }_1$, ${\kappa }_2$, and ${\kappa }_3$ are the intracell, intercell couplings, and effective LRC, respectively. (i) The calculated eigenspectrum of the model in (h). The red (black) line denotes the eigenfrequencies of even (odd) SOTCS. The dashed line corresponds to the HOTI in (b).

Figure 3

Demonstrating parity splitting of SOTCS on a designer-plasmonic metasurface. (a) The photograph for the sample, with $d_1=29$, and $d_2=26\mathrm{mm}$. We probe even(odd) SOTCS at “$A(B)$”. (b) The transmission of a meta-trimer shown in the inset. “$S(P)$” denotes the source(probe). (c) The field patterns at ${\omega }_{2;\mathrm{odd}}$ (${\omega }_{2;\mathrm{even}}$). The patterns on the middle metaatom are the superpositions of quadrupole, and octupole. (d) The calculated eigenfrequencies of the metasurface, and measured LDOS at $A(B)$ in (a). The red (blue) corresponds to even (odd). (e)–(f) The experimentally captured near-field patterns of SOTCS.

Figure 4

Observing polarization-orthogonal nondegenerate SOTCS. (a) The schematic of far-field experiment setup. The sample is normally illuminated with linearly-polarized beams. (b) The measured spectra at $A(B)$ in (a) corresponds to $x(y)$-polarized incidence. The gray line represents the spectrum without sample. (c)–(d) Measured patterns on the top corner resonator at peak frequencies in (b). (e)–(f) The polarization-parity correspondence. Dipolar compound of the hexapole on the corner resonator corresponding to the odd (e) and even (f) SOTCS.