Abstract
Wave trapping and manipulation are at the heart of modern integrated photonics and acoustics. Grand challenges emerge on increasing the integration density and reducing the wave leakage/noises due to fabrication imperfections, especially for waveguides and cavities at subwavelength scales. The rising of robust wave dynamics based on topological mechanisms offers possible solutions. Ideally, in a three-dimensional (3D) topological integrated chip, there are coexisting robust two-dimensional (2D) interfaces, one-dimensional (1D) waveguides and zero-dimensional (0D) cavities. Here, we report the experimental discovery of such a dimensional hierarchy of the topologically-protected 2D surface states, 1D hinge states and 0D corner states in a single 3D system. Such an unprecedented phenomenon is triggered by the higher-order topology in simple-cubic sonic crystals and protected by the space group {P}_{mbar{3}m}. Our study opens up a new regime for multidimensional wave trapping and manipulation at subwavelength scales, which may inspire future technology for integrated acoustics and photonics.
Highlights
Wave trapping and manipulation are at the heart of modern integrated photonics and acoustics
We start with an undeformed structure composed of eight air cavities located at the positions 0:25að ±1; ±1; ±1Þ
In order to characterize the deformation of the SCs, we introduce the center-tocenter distance for the air cavities along the link within the unit cell, as dintra
Summary
We conduct four pump–probe measurements to detect the bulk, surface, hinge, and corner states separately (see the inset of Fig. 4b for the illustration of the positions of the source and the detection probes for the four pump–probe configurations). The acoustic pressure profiles for the hinge and surface states excited at their peak frequencies are shown in the Supplementary Note 8, separately, which give clear evidences of the observation of the surface and hinge states in the corner sample. Both frequencies are close to the frequency of the experimentally detected corner state in the unperturbed structure, which is 7.9 kHz (see Fig. 4) These results again illustrate that the topological boundary states are robust against symmetrypreserving perturbations, consistent with the physical picture of symmetry-protected topological phases
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