Frequency manipulation of topological surface states by Weyl phase transitions

Abstract

By creating a synthetic frequency dimension with dynamic modulation in a 2D honeycomb waveguide array, we construct both Type-I and Type-II Weyl semimetals (WSMs) and utilize the WSM phase transition to control the frequency evolutions of topological surface states. We show that Type-I WSMs and Type-II WSMs manifest opposite and same band slopes for the two surface states, which give rise to the bidirectional and unidirectional frequency shifts, respectively. Moreover, by cascading Type-I Weyl lattices and Type-II Weyl lattices together, we also achieve the time-reversed evolution of frequency, such as frequency negative refraction, bandwidth expansion-compression, and perfect imaging. The Letter may find applications in robust signal transmission and processing with synthesized topological states.

Direct Determination of Photonic Stopband Topological Character: A Framework Based on Dispersion Measurements

“…[12][13][14][15][16][17][18] In recent years, PTIs have been realized with a variety of structural templates, including electromagnetic (EM) composites such as photonic crystals (PhCs) and metamaterials, [19][20][21][22][23][24][25][26] and engineered artificial lattices. [27][28][29][30][31][32][33] In all these cases, the nontrivial band topology of PTIs and the resulting topological properties of bandgaps are characterized by quantized topological invariants whose determination constitutes a crucial step in understanding the attributes of PTIs. For example, in one of their simplest renditions as 1D topological PhC, the geometric Zak phase [34,35] is recognized as the relevant topological invariant that can be determined by keeping track of singularities of Bloch eigenfunction across the Brillouin zone.…”

“…[ 35–49 ] Specifically, in 1D PhCs, determination of stopband topological identity requires accessing the dynamic phase response associated to the scattering parameters. [ 5–53 ] This necessitates interferometric setups and a reliance on relative measurements. Although some of the complexities can be relieved by resorting to the bulk‐boundary correspondence principle where interferometric setups are not required, and at least the equivalence/inequivalence of bandgaps’ topological characters can be stated from reflectance measurement alone (by locating a midgap state), its experimental implementation in bosonic systems is inexpedient as it requires concatenation of bandgaps.…”