# Tutorial: Computing Topological Invariants in 2D Photonic Crystals

@article{BlancodePaz2019TutorialCT, title={Tutorial: Computing Topological Invariants in 2D Photonic Crystals}, author={Mar{\'i}a Blanco de Paz and Chiara Devescovi and G{\'e}za Giedke and J J S{\'a}enz and Maia G. Vergniory and Barry Bradlyn and Dario Bercioux and Aitzol Garc'ia-Etxarri}, journal={Advanced Quantum Technologies}, year={2019}, volume={3} }

The field of topological photonics emerged as one of the most promising areas for applications in transformative technologies: possible applications are in topological lasers or quantum optics interfaces. Nevertheless, efficient and simple methods for diagnosing the topology of optical systems remain elusive for an important part of the community. Herein, a summary of numerical methods to calculate topological invariants emerging from the propagation of light in photonic crystals is provided…

## 40 Citations

### A Short Review of All-Dielectric Topological Photonic Crystals

- PhysicsFrontiers in Physics
- 2022

Topological photonics is an emergent field at the cross of photonics and topological physics which opens our eyes to novel topological phenomena and versatile photonic effects. Photonic crystals…

### Photonic Topological Insulators: A Beginner’s Introduction

- Physics
- 2021

1045-9243/21©2021IEEE IEEE ANTENNAS & PROPAGATION MAGAZINE J U N E 2 0 2 1 T he control and manipulation of electromagnetic (EM) waves has reached a new level with the recent understanding of…

### A brief review of topological photonics in one, two, and three dimensions

- PhysicsReviews in Physics
- 2022

### Robustness of topological corner modes in photonic crystals

- Physics
- 2020

We analyze the robustness of corner modes in topological photonic crystals, taking a $C_6$-symmetric breathing honeycomb photonic crystal as an example. First, we employ topological quantum chemistry…

### Photonic $\mathbb{Z}_2$ topological Anderson insulators

- Physics
- 2021

That disorder can induce nontrivial topology is a surprising discovery in topological physics. As a typical example, Chern topological Anderson insulators (TAIs) have been realized in photonic…

### Hybrid topological guiding mechanisms for photonic crystal fibers.

- PhysicsOptics express
- 2020

Finite element simulations, complemented by asymptotic techniques, demonstrate the effectiveness of the proposed designs for localising energy in finite arrays in a robust manner.

### Berry bands and pseudo-spin of topological photonic phases

- Physics
- 2020

Realising photonic analogues of the robust, unidirectional edge states of electronic topological insulators would improve our control of light on the nanoscale and revolutionise the performance of…

### Dual-polarization topological phases and phase transition in magnetic photonic crystalline insulator

- PhysicsNew Journal of Physics
- 2021

Two-dimensional topological photonic crystals have rapidly emerged as a recent and fascinating branch of photonic research. However, most of them were limited to a specific type of polarization, TE…

### Fragile topology based helical edge states in two-dimensional moon-shaped photonic crystals

- PhysicsPhysical Review B
- 2020

We study topological phases in a two-dimensional photonic crystal in a hexagonal lattice composed of an all-dielectric moon-shaped column (MSC) array, which preserves time-reversal symmetry, by…

### Theory of intrinsic propagation losses in topological edge states of planar photonic crystals

- Physics
- 2020

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…

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