OP: Collaborative Research: Landau levels and Dirac points in Continuous Photonic Systems

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The science describing the interaction between light and matter has produced a wide variety of technologically important applications that our society has come to rely on (for example, fiber optics that form the backbone of the internet, lasers used in industries ranging from telecommunications to manufacturing, solar cells used for sustainable energy, and many others). For decades, researchers have been trying to increase the strength of coupling between light and matter by engineering artificial dielectric structures (like silicon or glass) to be in resonance with incoming light. Nearly all such structures have been patterns that are periodically repeating in space: a kind of microscopic scaffolding. One of the principal goals of this project is to show that certain non-periodic structures with no repeating units can facilitate stronger light-matter coupling than periodic designs. This could open a new design principle for light-matter interaction and lead to applications like more efficient lighting, solar cells, or even components for optical quantum computers. The principal investigators will engineer photonic structures (both waveguide arrays in silica and photonic crystals in silicon) to have Dirac points in their band structure. These structures will be "strained" (either imparting physical strain or by fabricating artificially-strained structures) in such a way that they become aperiodic and experience a "pseudomagnetic field." This pseudomagnetic field causes the eigenvalue spectrum to become highly degenerate, leading to a large density-of-states, which in turn causes stronger light-matter coupling (Purcell enhancement). This project is a cross-disciplinary endeavor of an engineer, whose contribution is through fabrication and characterization of optical media (Kevin Chen, University of Pittsburgh), a physicist (Mikael Rechtsman, Penn State), who will perform optical experiments and modeling and an applied mathematician (Michael Weinstein, Columbia), who will co-develop mathematical PDE / discrete models and analyze these in collaboration with Rechtsman and Chen. Each of their expertise will be essential for the project's success.