Abstract: Photonic crystals have become a very common and powerful concept in optics since its introduction in the 1980s by Eli Yablonovitch and Sajeev John. It is in fact a concept borrowed from condensed matter physics. The discussion of photonic bands and bandgaps allows us to manipulate light on an optical chip, along a photonic crystal fiber and even in the quantum optics regime. Now, we are witnessing another round of concept translation again from condensed matter physics to optics about topology. Describing photonic bands by using their topology in the reciprocal space gives us a new tool to understand wave propagation and to design optical components. Topology is also an important aspect in light-matter interaction in the field of metamaterials and 2D materials.
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Out of many possible impacts of topology in optics, the one-way edge states existing on an interface between two topologically distinct media has drawn a lot of attention. These guiding modes flow in only one direction and can be scattering-immune to defects, allowing very recent demonstrations such as topological lasers with robust operation [1–3]. We expect this to be just the beginning of topological optical devices in giving either unconventional or robust configuration. To achieve these exciting possibilities, current works seek to realize the photonic analogs of different exotic topological states of matter in condensed matter physics and to explore unique connections of topological invariants, e.g. Chern numbers, to optical properties at the same time. It is worth mentioning that one huge advantage in employing topology in optics is that the required complex structures and material responses can be easily tailor-made by artificial materials such as photonic crystals and metamaterials. There also exist many open questions whether photons which are integer spin bosonic particles can show fundamental topological behavior similar to electrons which are half-integer spin fermionic particles.
It is the aim of this Feature Issue of Optics Express to present some of the research lines that have been recently devoted to topological photonics and materials.
An optical system can have symmetry-protected states, e.g. a Dirac cone in the band structure, and become gapped by breaking that symmetry while the bands above and below become topologically non-trivial. One-way edge states can exist within such a photonic band gap. On the other hand, some topologically gapless systems, such as those contain Weyl points, can support other topological states. Lu et.al . systematically reviews these approaches to generate one-way edge states. Different kinds of symmetry considerations are also discussed in order to give topological non-trivialness. The edge states can then be used to construct useful devices. Hang et.al. demonstrates a resonating cavity as an example .
One usual way to generate a topologically non-trivial system is by breaking time-reversal symmetry. It generates a pseudo magnetic field, which is intimately connected to nontrivial topology. Wang et. al.  applies dynamic modulation to break such symmetry with controllable parameter. It allows a phase transition from type-I to type-II Weyl points. In practice, dynamic modulation in time can be mimicked by a spatial modulation of waveguides in the propagation direction .
There is also an intuitive way to generate topological systems. We can build up two dimensional systems from the Su-Schrieffer–Heeger model, a chain of alternating structures or couplings, which has non-trivial topology in one dimension already. Lieb, Kagome or honeycomb lattices are some of the candidates, which can be used also to generate flat bands for slow light or localized orbital manipulations. Lu et.al. investigates the coexistence of edge states and flat bands . Schomerus extends the discussion of topology of these lattices to the nonlinear regime, in which saturable gain and loss can be added and is useful in considering lasering action . Non-hermiticity can also be exploited in these waveguides to pick up the desired mode for lasing 
A pseudo magnetic field in many topological systems can be generated by breaking time-reversal symmetry. It can also be generated by spin-orbit coupling. In this issue, we also incorporate several articles in using spin-orbit coupling for applications. These can give some insight for future topological applications. Jacob et. al. uses it to generate spin-dependent optical force for a particle on a non-reciprocal waveguide . Arakawa and Fong et.al., couple the orbital angular momentum of thelight to the spin angular momentum in the electronic degrees of freedom . Cai et.al. investigates how orbital angular momentum of light can be transmitted through a random medium with turbulence .
Last but not least, we are looking forward to more optical properties that can be regarded as direct consequences of topology. An actual topological insulator, e.g. Bi2Te3. can be used as an efficient saturable absorber for Q-switching . A jump in Goos-Hänchen shift can be used to reveal a corresponding transition of topological invariant .
In summary, topology is emerging as a powerful way to understand optics or to design optical components. The articles presented in this Feature Issue may serve not only a current summary of different approaches in this research field, but may also encourages future works on both theory and optical applications.
We also would like to thank all the authors who have contributed to this issue and would like to thank Andrew Weiner, John Long and Carmelita Washington in Optical Express for putting up this Feature Issue.
1. M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, and M. Khajavikhan, “Topological insulator laser: Experiments,” Science 359, 6381 (2018).
2. M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, and M. Khajavikhan, “Edge-mode lasing in 1D topological active arrays,” Phys. Rev. Lett. 120(11), 113901 (2018). [CrossRef] [PubMed]
4. B. Y. Xie, H. F. Wang, X. Y. Zhu, M. H. Lu, Z. D. Wang, and Y. F. Chen, “Photonics meets topology,” Opt. Express 26(19), 24531–24550 (2018). [CrossRef]
7. J. Chen, “Parity-time symmetry in periodically curved optical waveguides,” (2018).
8. X. Y. Zhu, S. K. Gupta, X. C. Sun, C. He, G. X. Li, J. H. Jiang, X.-P. Liu, M.-H. Lu, and Y.-F. Chen, “Z 2 topological edge state in honeycomb lattice of coupled resonant optical waveguides with a flat band,” Opt. Express 26(19), 24307–24317 (2018). [CrossRef]
9. S. Malzard, E. Cancellieri, and H. Schomerus, “Topological dynamics and excitations in lasers and condensates with saturable gain or loss,” Opt. Express 26(17), 22506–22518 (2018). [CrossRef] [PubMed]
10. Yao “Single-Transverse-Mode Broadband InAs Quantum Dot Superluminescent Light Emitting Diodes by Parity-time Symmetry,” (2018).
11. S. Pendharker, F. Kalhor, T. Van Mechelen, S. Jahani, N. Nazemifard, T. Thundat, and Z. Jacob, “Spin photonic forces in non-reciprocal waveguides,” Opt. Express 26(18), 23898–23910 (2018). [CrossRef] [PubMed]
12. C. F. Fong, Y. Ota, S. Iwamoto, and Y. Arakawa, “Scheme for media conversion between electronic spin and photonic orbital angular momentum based on photonic nanocavity,” (2018), arXiv preprint arXiv:1806.00223.
13. Y. Yuan, D. Liu, Z. Zhou, H. Xu, J. Qu, and Y. Cai, “Optimization of the probability of orbital angular momentum for Laguerre-Gaussian beam in Kolmogorov and non-Kolmogorov turbulence,” Opt. Express 26(17), 21861–21871 (2018). [CrossRef] [PubMed]
14. J. Yang, K. Tian, Y. Li, X. Dou, Y. Ma, W. Han, H. Xu, and J. Liu, “Few-layer Bi2Te3: an effective 2D saturable absorber for passive Q-switching of compact solid-state lasers in the 1-μm region,” Opt. Express 26(17), 21379–21389 (2018). [CrossRef] [PubMed]
15. W. Wu, W. Zhang, S. Chen, X. Ling, W. Shu, H. Luo, S. Wen, and X. Yin, “Transitional Goos-Hänchen effect due to the topological phase transitions,” Opt. Express 26(18), 23705–23713 (2018). [CrossRef] [PubMed]