Science - USA (2022-06-03)

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ACKNOWLEDGMENTS

We thank C. Otto for preparing the high-quality fused silica samples

that were used for the inscription of all photonic structures used

in this work.Funding:Deutsche Forschungsgemeinschaft

grants SCHE 612/6-1 (A.S.), SZ 276/12-1 (A.S.), BL 574/13-1 (A.S.),

SZ 276/15-1 (A.S.), SZ 276/20-1 (A.S.), and SFB 1477“Light-

matter interactions at interfaces,”project number 441234705

(A.S. and M.H.); the Krupp von-Bohlen-and-Halbach Foundation

Biesenthalet al., Science 376 , 1114–1119 (2022) 3 June 2022 5of6

Fig. 4. Edge-state spectroscopy and velocity in topological fractals.
(A) Broad-beam excitations in planar“straw”arrays appended to a corner of
the driven Sierpinski gasket serve to synthesize wave packets with a narrow
k-space spectrum, allowing for specific quasi-energies to be addressed by
selecting an appropriate wavefront tilt (for details, see figs. S5 and S6).
(B) Measured edge-state occupation ratio at the end of the 150-mm-long
sample. (C) Quasi-energies outside the topological gap allow light to diffract
deep into the lattice. (D) By contrast, excitations within the gap yield a
pronounced population of the topological edge state near the resonant angle
of excitation. A certain leakage into the lattice interior occurs because of
the presence of internal topological edge states with similar quasi-energies.
(E to H) Applying the same excitation conditions to the honeycomb shows that,
whereas mismatched excitations primarily populate the bulk of the lattice (G), a

substantial fraction of the injected light is deposited into the topological edge

state (H). In (C), (D), (G), and (H), the lattice outlines, excluding the straws,

are indicated by semitransparent overlays as a guide to the eye, and the

sites that were evaluated for the edge occupation ratio are outlined in white.

In (B) and (F), the width of the respective resonances was measured as full

width at half maximum of a Gaussian fit in the quasi-energy (dashed red lines;

see fig. S7 for the plot with a linear energy scale). (I andJ) A direct comparison

for equivalent excitation conditions shows that the Sierpinski edge state

systematically outpaces its conventional counterpart. (K)Aseriesof

measurements with varying placement of the broad Gaussian excitation,

indicated by its initial central positionnXwithin the straw, shows that the fractal

topological edge transport is about 11% faster than it is in the honeycomb lattice.

More details on these measurements are provided in figs. S8 and S9.

RESEARCH | REPORT