Related papers: Tutorial: Computing topological invariants in two-…
Topological invariants are global properties of the ground-state wave function, typically defined as winding numbers in reciprocal space. Over the years, a number of topological markers in real space have been introduced, allowing to map…
Vortex crystals are geometric arrays of vortices found in various physics fields, owing their regular internal structure to mutual interactions within a spatially confined system. In optics, vortex crystals may form spontaneously within a…
Motivated by the recent theoretical and experimental progress in implementing topological orders with photons, we analyze photonic systems with different topologies and present a scheme to probe their topological features. Specifically, we…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
Rare-earth doped nanocrystals are emerging light sources used for many applications in nanotechnology enabled by human ability to control their various optical properties with chemistry and material science. However, one important optical…
We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations…
Designing photonic topological insulators is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely…
The application of topology in optics has led to a new paradigm in developing photonic devices with robust properties against disorder. Although significant progress on topological phenomena has been achieved in the classical domain, the…
Over the past decade, topological photonics has emerged as a vibrant field, attracting significant attention and witnessing remarkable advancements. This growth can be attributed to its fundamental appeal and the unique opportunities it…
We provide an introduction to complex photonic media, that is, composite materials with spatial inhomogeneities that are distributed over length scales comparable to or smaller than the wavelength of light. This blossoming field is firmly…
The influence of controlable parameters like temperature and wavelength on the trajectories of light in a nematic liquid crystal with topological defects is studied through a geometric model. The model incorporates phenomenological details…
We propose a method derived from the simple plane wave expansion that can easily solve the interface problem between vacuum and a semi-infinite photonic crystal. The method is designed to find the complete set of all the eigenfunctions,…
We present a characterization of topological phases in photonic lattices. Our theory relies on a formal equivalence between the singular value decomposition of the non-Hermitian coupling matrix and the diagonalization of an effective…
Based on previous results of digital topology, this paper focuses on algorithms of topological invariants of objects in 2D and 3D Digital Spaces. We specifically interest in solving hole counting of 2D objects and genus of closed surface in…
Using a semi-analytic guided-mode expansion technique, we present theory and analysis of intrinsic propagation losses for topological photonic crystal slab waveguide structures with modified honeycomb lattices of circular or triangular…
We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $\pi$-conjugated chains as representative model…
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…
Topological photonic systems, with their ability to host states protected against disorder and perturbation, allow us to do with photons what topological insulators do with electrons. Topological photonics can refer to electronic systems…
We review both theoretical and experimental advances in the recently emerged physics of modulated photonic lattices. Artificial periodic dielectric media, such as photonic crystals and photonic lattices, provide a powerful tool for the…
TopologicalNumbers.jl is an open-source Julia package designed to calculate topological invariants, mathematical quantities that characterize the properties of materials in condensed matter physics. These invariants, such as the Chern…