The influence of geometry and topology of quantum graphs on their nonlinear-optical properties

TL;DR

This paper investigates how the geometry and topology of quantum graphs influence their nonlinear optical properties, revealing that topological changes can cause significant shifts in nonlinear susceptibilities, with implications for designing advanced optical materials.

Contribution

It demonstrates that topology and geometry critically affect nonlinear susceptibilities in quantum graphs, introducing a new approach to optimize nonlinear optical responses.

Findings

Topology changes cause discontinuities in nonlinear susceptibilities.

Geometry variations lead to smooth changes in nonlinearities.

Quantum graph models exhibit universal behavior in nonlinear optics.

Abstract

We analyze the nonlinear optics of quasi one-dimensional quantum graphs and manipulate their topology and geometry to generate for the first time nonlinearities in a simple system approaching the fundamental limits of the first and second hyperpolarizabilities. Changes in geometry result in smooth variations of the nonlinearities. Topological changes between geometrically-similar systems cause profound changes in the nonlinear susceptibilities that include a discontinuity due to abrupt changes in the boundary conditions. This work may inform the design of new molecules or nano- scale structures for nonlinear optics and hints at the same universal behavior for quantum graph models in nonlinear optics that is observed in other systems.