The last 20 years have witnessed growing impacts of the topological concept on the
branches of physics, including materials, electronics, photonics, and acoustics. Topology …

For classical waves, phase matching is vital for enabling efficient energy transfer in many
scenarios, such as waveguide coupling and nonlinear optical frequency conversion. Here …

We present a mechanism of topological pumping in origami metamaterials with spatial
modulation by tuning the rotation angles. Through coupling spatially modulated origami …

Recent discoveries in twisted heterostructure materials have opened research directions in
classical wave systems. This Letter investigates a family of double-sided pillared phononic …

Topological pumping, as an efficient form of energy transfer protected by nontrivial topology,
has been intensively studied in condensed matter physics and optics. Conventional …

Synthetic magnetism has been recently realized using spatiotemporal modulation patterns,
producing non-reciprocal steering of charge-neutral particles such as photons and phonons …

Recently, acoustic valley Hall topological insulators have become a cutting-edge area of
acoustic physics, where the topological phase transition in phononic crystals shows the …

Topological pumping allows higher-dimensional topological phenomena to be explored in
low-dimensional systems using synthetic dimension with time modulation. Extensive studies …

Time modulation provides an important degree of freedom for classical wave steering in
topological manners. Rather than using the spatial dimension to mimic time, here we design …

Topological insulators have been widely studied for their unique properties, particularly their
ability to propagate energy with minimal losses in a manner that is robust to structural …