Ideal Unconventional Weyl Point in a Chiral Photonic Metamaterial

Unconventional Weyl points (WPs), carrying topological charge 2 or higher, possess interesting properties different from ordinary charge-1 WPs, including multiple Fermi arcs that stretch over a large portion of the Brillouin zone. Thus far, such WPs have been observed in chiral materials and acoustic metamaterials, but there has been no clean demonstration in photonics in which the unconventional photonic WPs are separated from trivial bands. We experimentally realize an ideal symmetry-protected photonic charge-2 WP in a three-dimensional topological chiral microwave metamaterial. We use field mapping to directly observe the projected bulk dispersion, as well as the two long surface arcs that form a noncontractible loop wrapping around the surface Brillouin zone. The surface states span a record-wide frequency window of around 22.7% relative bandwidth. We demonstrate that the surface states exhibit a novel topological self-collimation property and are robust against disorder. This work provides an ideal photonic platform for exploring fundamental physics and applications of unconventional WPs.

Figure 1

Ideal UWP in a 3D topological chiral metamaterial. (a)–(b) Fabricated sample and unit cell of the 3D topological chiral metamaterial. (c) 3D first Brillouin zone (BZ). (d) Band structure of the chiral metamaterial. The red dot denotes the UWP at $\mathrm{\Gamma }$, which has topological charge $+2$. The green dot represents the UWP at $A$, which has topological charge $-2$. (e)–(f) Perspective view of the 2D band structures in the vicinity of the UWP at $\mathrm{\Gamma }$ in the $k_x{k}_y$ plane (e) and $k_y{k}_z$ plane (f).

Figure 2

Observation of the UWP. (a) Experimental setup. Field patterns in the middle $xz$ plane of the sample are measured data. (b) Schematic of the projected 2D surface BZ. (c) Measured projected bulk band structure along the high-symmetry line $\overline{X^{\prime }}\overline{X}$. The colormap measures the energy density. (d) Numerically calculated projected bulk band structure along the high-symmetry line $\overline{X^{\prime }}\overline{X}$.

Figure 3

Observed surface states of the ideal UWP, whose isofrequency contours form noncontractible loops wrapping around the BZ. (a) Experimental setup. The electric field distribution is mapped on the sample surface, with a source placed at the edge of the bottom surface (010). The inset image shows measurement data at 9.0 GHz, revealing a self-collimated beam of surface waves propagating from the source. (b) Schematic of the BZ projection onto the 2D measurement plane. The UWPs at $\mathrm{\Gamma }$ and $A$ are projected onto $\overline{\mathrm{\Gamma }}$ and $\overline{Y}$, respectively. The right inset shows measurement results obtained by Fourier transforming the complex field pattern measured in (a). (c)–(d) Measured and numerically calculated surface state dispersion along the high-symmetry line $\overline{\mathrm{\Gamma }}\overline{Y}$. The blue, red, and dotted black lines in (d) represent bulk dispersion, surface dispersion, and light line, respectively. (e)–(f) Measured and numerically calculated 2D isofrequency contours of the surface states as a function of frequency. The blue and red lines in (f) denote bulk and surface isofrequency contours, respectively. The circles in (a) near the BZ center are the air isofrequency contours. The color bar below (b) indicates the energy intensity.

Figure 4

Robust topological surfaces state. (a) The disordered chiral metamaterial. (b) Spatial distribution of $g$ in the $xy$ plane for the disordered sample. For each in-plane lattice site, $g$ is drawn randomly from 0.25 to 2.75 mm, and is independent of $z$. (c) Frequencies of the UWPs versus the gap shift parameter $g$. The red and green lines represent the UWPs at $\mathrm{\Gamma }$ and $A$, respectively. (d) Measured field distributions on the sample surfaces (010) and (100) at 9.3 GHz. The blue star denotes the location of a pointlike source. (e) Energy maps obtained by 2D spatial Fourier transforming the measured field distributions on the sample surface (010).