The unique features of topological photonics have led to many new applications where robustness is important. For example, the topological insulator laser (invented by our group, see Harari yet al., Science 2018, and Bandres et al., Science 2018), which includes gain (and natural loss) within the laser cavity and utilizes the topological edge states as the lasing mode. Topological insulator lasers combine the concepts of topological insulators with the fundamentals of lasers, which introduce gain, loss, and lasing action in a topological platform. Specifically, in the presence of an artificial gauge field, an optical lattice consisting of resonators exhibits topological edge states. Introducing gain on the edges of such a 2D topological lattice made of coupled resonators makes the topological edge mode lase, where all the tiny lasers act together as a single coherent high-power laser. This topological insulator laser displays high slope efficiency and single-mode lasing even high above the laser threshold. On this background, we took the concept of topological insulator lasers to the next level and demonstrated experimentally and theoretically the first topological VCSEL array (Vertical Cavity Surface Emitting Laser; see Dikopltsev et al., Science 2021). In addition, we explored a plethora of additional aspects of topological photonics related to lasers and gain media. All of these, taken together, can lead to new innovative technology of making many semiconductor laser emitters act together as a single highly coherent high power laser source.
On the conceptual side, we explored numerous ideas that are at the core of topological physics. One of them is our work on the first photonic topological insulators in synthetic dimensions (Lustig et al., Nature 2019), which was extended to the first synthetic-space photonic topological insulator in full 3D (Lustig et al., Nature 2022). Another milestone work was our theory paper presenting the concept of fractal topological insulators (Yang et al., Light: Science and Applications, 2020). This was a new foundational concept to the entire field of topological physics. The experiments on the topological insulator on a fractal lattice (Biesenthal et al., Science 2022) specifically investigated the platform of the 2D Sierpinski triangle (one of the most well-known fractals), and showed that, under proper modulation, it acts as a topological insulator - even though all sites are on an edge - either external edge or internal edge. That is, this system has no bulk whatsoever, yet if modulated properly - it acts as a topological insulator. This very fact stands in contrast to the general understanding that topological insulators rely on the bulk-edge correspondence, as one of its foundations. Evidently, topological insulators can exist on platforms that have no bulk at all, just edges.
In addition to the main achievements described above, there are many more conceptual ideas and experiments we did during this ERC AdG, as described in our published papers.
