Limitations on disorder and leveraging aperiodicity in topological photonics and beyond

In the quantum Hall effect in two-dimensional semiconductor layers, electrons are transported via electronic states that reside on t,he edge of the system and are completely resistant to any form of scattering by disorder or imperfections. This remarkable robustne,ss has led to measurements of the Hall conductance so precise that they have been used to redefine SI units, such as the kilogram.,The central goal of the work proposed herein is to continue my group?s research on bringing this type of robustness into the context, of photonic, as opposed to electronic, devices. Since a wide range of photonic devices are nanofabricated at the length scale of t,he wavelength of light, they are susceptible to parasitic effects due to fabrication imperfections. Our hope is that by leveraging,ideas from quantum Hall physics (also called ?topological physics?), we can bring to bear the incredible robustness of electronic tr,ansport to photonic devices. This has the potential to dramatically increase their efficiency, reduce their cost, and augment their, resistance to damage in the field. There are a wide range of relevant photonic devices that may have direct impact on naval operat,ions, including in the fields of lidar, optical computing for artificial intelligence, frequency comb generation for positioning, na,vigating, and precise timing, among others.This grant continues previous ONR-funded work (under the Young Investigator Program) in w,hich we explored a wide range of photonic devices with a particular emphasis on nonlinear operation (i.e., those that utilize high-p,eak-power laser light). For example, we helped to pioneer the new field of ?nonlinear topological photonics? which explores the non,linear optical dynamics of topological systems. Specifically, we demonstrated soliton-like wavepackets propagating on the edge of p,hotonic topological insulators composed of optical waveguide arrays. Using a similar system, we also demonstrated bulk solitons tha,t act to effectively induce a local chiral edge state. In another direction, we explored nonlinear Thouless pumps, a model system u,sed to understand quantized transport, in which we saw the propagation of solitons that were governed by both integer and fractional,ly charged quantized motion. In this grant, we will continue our work by exploring the limits of topological protection in optical,structures, not limiting ourselves to the periodic case but rather exploring the effects of aperiodicity as well. We will focus on,nonlinear topological photonic devices, exploring radiation effects of soliton transport that arise due to nonlinearity; period-doub,ling solitons in two-dimensional systems of this type; three-dimensional Weyl topological photonic crystals fabricated using advance,d two-photon lithography based techniques and the effects of disorder therein; we will explore quasicrystalline structures and the p,otential advantages that quasicrystallinity may offer to complex fibers and photonic crystal cavity modes; as well as one-dimensiona,l multilayer structures that exhibit such effects as Landau levels and mobility edges.