On-Demand non-hermitian topology
Physical materials can display a topological order, i.e. a collective organization characterized by a discrete number or “topological charge”. Because the integer nature of this charge must be preserved throughout the structure, topological order is intrinsically immune to perturbations and the system is said to be topologically protected. Recently, the replication of topological protection in optics has raised the interest of the scientific community for its potential ability to overcome fundamental problems—like the influence of imperfections intrinsically present in nanoscale-fabrication processes, which currently preclude the development of multiple photonic technologies. Yet, at optical frequencies the weak response of materials often precludes a topological approach such that even careful designs can only partially deliver the expected protection. In contrast to material properties, gain and loss can be easily manipulated in optics. While the exploitation of non-hermitian systems—with non-conserved energy—recently enabled the formation of topological order in wave physics, it simultaneously questioned our theoretical understanding of topology and offered a large variety of new degrees of freedom that are yet to be explored.
Here I suggest exploiting the versatility of optical gain-loss to imprint topological order “on-demand” onto otherwise topologically trivial systems. Through non-uniform spatial distributions of optical gain and loss I intend to demonstrate theoretically the formation of topological protection in random systems and implement my predictions in existing experimental platforms. In sharp contrast with the conventional conception of topology that relies on careful and rigid designs, this project will explore the possibility to engineer topology through external control. In this way, I will trigger a paradigmatic change that will enable the development of new photonic devices, whose topology can be manipulated and reconfigured “on-demand”.