Topological Photonics in Fractal Lattices

Evolution of topological edge states in the fractal SG(4) lattice. (Source: Z. Yang, Technion)

Topological insulators are a new phase of matter featured by their insu­lating bulk and perfectly conducting edges. They have been at the forefront of condensed matter physics for the past decade and more recently inspired the emergence of topo­logical phases in many classical-wave systems, such as photonics and acoustics. Up to date, all studies of topo­logical insulators have explored systems in integer dimen­sions (physically, 2D or 3D) with a well-defined bulk and edges. However, the physical dimen­sions do not always define the dimensions in which a system evolves: some structures have a noninteger (fractal) dimension, despite being in a 2D or 3D realm.

Now, a team of scientists, led by Mordechai Segev from Physics Depart­ment and Solid State Institute, Technion-Israel Institute of Technology, Israel, and co-workers have developed the photonic Floquet topo­logical insulator in a periodically driven fractal lattice. This lattice relies on a fractal photonic crystal [the Sier­pinski gasket (SG)] consisting of evanes­cently coupled helical waveguides, which can be realized by femto­second-laser-writing technology. They calculate the topological Floquet spectrum and show the existence of topo­logical edge states corres­ponding to real-space Chern number 1.

The simulations of the edge states show that wave­packets made up of topo­logical edge states can propagate along the outer and inner edges without pene­tration into the bulk and without back­scattering even in the presence of disorder and sharp corners. “Our results suggest a wealth of new kinds of topo­logical systems and new appli­cations, such as using topological robustness combined with the enhanced sensi­tivity of fractal systems for sensing and, in non-Hermitian settings, topo­logical insulator lasers in fractal dimensions”, the scientists forecast. (Source: LPC-CAS)

Reference: Z. Yang et al.: Photonic Floquet topological insulators in a fractal lattice, Light Sci. Appl. 9, 128 (2020); DOI: 10.1038/s41377-020-00354-z

Link: Physics Dept. and Solid State Institute (M. Segev), Technion–Israel Institute of Technology, Haifa, Israel

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