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Register a new userHigher-order topological phases in tunable $C_3$-symmetric photonic crystals
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We demonstrate that multiple higher-order topological transitions can be triggered via the continuous change of the geometry in kagome photonic crystals composed of three dielectric rods. By tuning a single geometry parameter, the photonic corner and edge states emerge or disappear with the higher-order topological transitions. Two distinct higher-order topological insulator phases and a normal insulator phase are revealed. Their topological indices are obtained from symmetry representations. A photonic analog of fractional corner charge is introduced to distinguish the two higher-order topological insulator phases. Our predictions can be readily realized and verified in configurable dielectric photonic crystals.
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The studies of topological phases of matter have been extended from condensed matter physics to photonic systems, resulting in fascinating designs of robust photonic devices. Recently, higher-order topological insulators (HOTIs) have been investigated as a novel topological phase of matter beyond the conventional bulk-boundary correspondence. Previous studies of HOTIs have been mainly focused on the topological multipole systems with negative coupling between lattice sites. Here we experimentally demonstrate that second-order topological insulating phases without negative coupling can be realized in two-dimensional dielectric photonic crystals (PCs). We visualize both one-dimensional topological edge states and zero-dimensional topological corner states by using near-field scanning technique. To characterize the topological properties of PCs, we define a novel topological invariant based on the bulk polarizations. Our findings open new research frontiers for searching HOTIs in dielectric PCs and provide a new mechanism for light-manipulating in a hierarchical way.
Photonic topological states have revolutionized our understanding on the propagation and scattering of light. Recent discovery of higher-order photonic topological insulators opens an emergent horizon for zero-dimensional topological corner states. However, the previous realizations of higher-order photonic topological insulators suffer from either a limited operational frequency range due to the lumped components involved or a bulky structure with a large footprint, which are unfavorable for future integrated photonics. To overcome these limitations, we hereby experimentally demonstrate a planar surface-wave photonic crystal realization of two-dimensional higher-order topological insulators. The surface-wave photonic crystals exhibit a very large bulk bandgap (a bandwidth of 28%) due to multiple Bragg scatterings and host one-dimensional gapped edge states described by massive Dirac equations. The topology of those higher-dimensional photonic bands leads to the emergence of zero-dimensional corner states, which provide a route toward robust cavity modes for scalable, integrated photonic chips and an interface for the control of light-matter interaction.
Here, the frequency degree of freedom is introduced into valley photonic crystals with dual band gaps. Based on the high-order plane wave expansion model, we derive an effective Hamiltonian which characterizes dual band gaps. Metallic valley photonic crystals are demonstrated as examples in which all four topological phases are found. At the domain walls between topologically distinct valley photonic crystals, frequency-dependent edge states are demonstrated and a broadband photonic detouring is proposed. Our findings provide the guidance for designing the frequency-dependent property of topological structures and show its potential applications in wavelength division multiplexers.
Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to continuum theories for realistic materials require the identification of quantized invariants describing the bulk quadrupole order. Here we identify the analog of quadrupole order in Maxwells equations for a photonic crystal (PhC) and identify quadrupole topological photonic crystals formed through a band inversion process. Unlike prior studies relying on threaded flux, our quadrupole moment is quantized purely by crystalline symmetries, which we confirm using three independent methods: analysis of symmetry eigenvalues, numerical calculations of the nested Wannier bands, and the expectation value of the quadrupole operator. Furthermore, through the bulk-edge correspondence of Wannier bands, we reveal the boundary manifestations of nontrivial quadrupole phases as quantized polarizations at edges and bound states at corners. Finally, we relate the nontrivial corner states to the emergent phenomena of quantized fractional corner charges and a filling anomaly as first predicted in electronic systems. Our work paves the way to further explore higher-order topological phases in nanophotonic systems and our method of inducing quadrupole phase transitions is also applicable to other wave systems, such as electrons, phonons and polaritons.
In this paper, the photonic quantum spin Hall effect (PQSHE) is realized in dielectric two-dimensional (2D) honeycomb lattice photonic crystal (PC) by stretching and shrinking the honeycomb unit cell. Combining two honeycomb lattice PCs with a common photonic band gap (PBG) but different band topologies can generate a topologically protected edge state at the combined junction. The topological edge states and their unidirectional transmission as the scatterers with triangular, pentagonal, and heptagonal shapes are researched. Meanwhile, the unidirectional transmission in an inverted {Omega}-shaped waveguide with large bending angle is realized, and verifies the characteristics of the topological protection by adding different kind of defects. Moreover, the frequency varies significantly when changing the scatterers shape, which shows that the PC with various scatterers shape can tune the frequency range of the topological edge state significantly. In other words, it can adjust the frequency of unidirectional transmission and increase the adjustability of the topological edge state.
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