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Register a new userChern numbers for the index surfaces of photonic crystals: conical refraction as a basis for topological materials
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The classification of bandstructures by topological invariants provides a powerful tool for understanding phenomena such as the quantum Hall effect. This classification was originally developed in the context of electrons, but can also be applied to photonic crystals. In this paper we study the topological classification of the refractive index surfaces of two-dimensional photonic crystals. We consider crystals formed from birefringent materials, in which the constitutive relation provides an optical spin-orbit coupling. We show that this coupling, in conjunction with optical activity, can lead to a gapped set of index surfaces with non-zero Chern numbers. This method for designing photonic Chern insulators exploits birefringence rather than lattice structure, and does not require band crossings originating from specific lattice geometries.
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The recent realizations of topological valley phase in photonic crystal, an analog of gapped valleytronic materials in electronic system, are limited to the valley Chern number of one. In this letter, we present a new type of valley phase that can have large valley Chern number of two or three. The valley phase transitions between the different valley Chern numbers (from one to three) are realized by changing the configuration of the unit cell. We demonstrate that these new topological phases can guide the wave propagation robustly along the domain wall of sharp bent. Our results are promising for the exploration of new topological phenomena in photonic systems.
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.
We clarify theoretically that the topological ring-cavity (TRC) modes propagating along the interface between two honeycomb-type photonic crystals distinct in topology can be exploited for achieving stable single-mode lasing, with the maximal intensity larger than a whispering-gallery-mode counterpart by order of magnitude. Especially, we show that the TRC modes located at the bulk bandgap center benefit maximally from the gain profile since they are most concentrated and uniform along the ring cavity, and that, inheriting from the Dirac-like dispersion of topological interface states, they are separated in frequency from each other and from other photonic modes, both favoring intrinsically single-mode lasing. A TRC mode running in a specific direction with desired orbital angular momentum can be stimulated selectively by injecting circularly polarized light. The TRC laser proposed in the present work can be fabricated by means of advanced semiconductor nanotechnologies, which generates chiral laser beams ideal for novel photonic functions.
In this work, a refractive index (RI) sensor with an effective integration of colorimetric detection and optical sensing capabilities has been developed. Colorimetric detection relies on the sensitivity of the structural color of photonic crystal (PC) substrates to the changes in background RI, while the optical sensing is performed by measuring the magnification abilities of the dielectric microspheres, which depends on the position of the photonic nanojet. Based on this concept, we have successfully assembled 35 {mu}m-diameter barium titanate glass microspheres, 4.9 {mu}m-diameter polystyrene and silica microsphere monolayers on 1D or 2D PC substrates to perform RI sensing in various liquids. In addition, the developed RI sensor is highly compatible with commercial optical microscopes and applicable for RI sensing in areas as small as tens of square microns.
Generating and manipulating Dirac points in artificial atomic crystals has received attention especially in photonic systems due to their ease of implementation. In this paper, we propose a two-dimensional photonic crystal made of a Kekule lattice of pure dielectrics, where the internal rotation of cylindrical pillars induces optical Dirac-degeneracy breaking. Our calculated dispersion reveals that the synchronized rotation reverses bands and switches parity as well so as to induce a topological phase transition. Our simulation demonstrates that such topologically protected edge states can achieve robust transmission in defect waveguides under deformation, and therefore provides a pragmatically tunable scheme to achieve reconfigurable topological phases.
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