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Register a new userTopological Invariants in Point Group Symmetric Photonic Topological Insulators
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We proposed a group-theory method to calculate topological invariant in bi-isotropic photonic crystals invariant under crystallographic point group symmetries. Spin Chern number has been evaluated by the eigenvalues of rotation operators at high symmetry k-points after the pseudo-spin polarized fields are retrieved. Topological characters of photonic edge states and photonic band gaps can be well predicted by total spin Chern number. Nontrivial phase transition is found in large magnetoelectric coupling due to the jump of total spin Chern number. Light transport is also issued at the {epsilon}/{mu} mismatching boundary between air and the bi-isotropic photonic crystal. This finding presents the relationship between group symmetry and photonic topological systems, which enables the design of photonic nontrivial states in a rational manner.
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The recent realization of photonic topological insulators has brought the discovery of fundamentally new states of light and revolutionary applications such as non-reciprocal devices for photonic diodes and robust waveguides for light routing. The spatially distinguished layer pseudospin has attracted attention in two-dimensional electronic materials. Here we report layered photonic topological insulators based on all-dielectric bilayer photonic crystal slabs. The introduction of layer pseudospin offers more dispersion engineering capability, leading to the layer-polarized and layer-mixed photonic topological insulators. Their phase transition is demonstrated with a model Hamiltonian by considering the nonzero interlayer coupling. Layer-direction locking behavior is found in layer-polarized photonic topological insulators. High transmission is preserved in the bilayer domain wall between two layer-mixed photonic topological insulators, even when a large defect is introduced. Layered photonic topological insulators not only offer a route towards the observation of richer nontrivial phases, but also open a way for device applications in integrated photonics and information processing by using the additional layer pseudospin.
Topological invariants characterising filled Bloch bands attract enormous interest, underpinning electronic topological insulators and analogous artificial lattices for Bose-Einstein condensates, photons, and acoustic waves. In the latter bosonic systems there is no Fermi exclusion principle to enforce uniform band filling, which makes measurement of their bulk topological invariants challenging. Here we show how to achieve controllable filling of bosonic bands using leaky photonic lattices. Leaky photonic lattices host transitions between bound and radiative modes at a critical energy, which plays a role analogous to the electronic Fermi level. Tuning this effective Fermi level into a band gap results in disorder-robust dynamical quantization of bulk topological invariants such as the Chern number. Our findings establish leaky lattices as a novel and highly flexible platform for exploring topological and non-Hermitian wave physics.
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.
Edge modes in topological insulators are known to be robust against defects. We investigate if this also holds true when the defect is not static, but varies in time. We study the influence of defects with time-dependent coupling on the robustness of the transport along the edge in a Floquet system of helically curved waveguides. Waveguide arrays are fabricated via direct laser writing in a negative tone photoresist. We find that single dynamic defects do not destroy the chiral edge current, even when the temporal modulation is strong. Quantitative numerical simulation of the intensity in the bulk and edge waveguides confirms our observation.
We show that the bulk winding number characterizing one-dimensional topological insulators with chiral symmetry can be detected from the displacement of a single particle, observed via losses. Losses represent the effect of repeated weak measurements on one sublattice only, which interrupt the dynamics periodically. When these do not detect the particle, they realize negative measurements. Our repeated measurement scheme covers both time-independent and periodically driven (Floquet) topological insulators, with or without spatial disorder. In the limit of rapidly repeated, vanishingly weak measurements, our scheme describes non-Hermitian Hamiltonians, as the lossy Su-Schrieffer-Heeger model of Phys. Rev. Lett. 102, 065703 (2009). We find, contrary to intuition, that the time needed to detect the winding number can be made shorter by decreasing the efficiency of the measurement. We illustrate our results on a discrete-time quantum walk, and propose ways of testing them experimentally.
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