Optimum topology of quasi-one dimensional nonlinear optical quantum systems

TL;DR

This paper uses quantum graph models to identify optimal topologies for quasi-one dimensional nonlinear optical systems, revealing configurations that maximize intrinsic optical nonlinearities near fundamental limits.

Contribution

It introduces a method to determine the optimal topology of quantum graphs for nonlinear optical properties, highlighting their topological and geometrical features that enhance nonlinear responses.

Findings

Quantum graphs with star vertices optimize energy spectra for nonlinearities.

Graph topology and geometry critically influence transition moments.

Models predict structures with nonlinearities near fundamental limits.

Abstract

We determine the optimum topology of quasi-one dimensional nonlinear optical structures using generalized quantum graph models. Quantum graphs are relational graphs endowed with a metric and a multiparticle Hamiltonian acting on the edges, and have a long application history in aromatic compounds, mesoscopic and artificial materials, and quantum chaos. Quantum graphs have recently emerged as models of quasi-one dimensional electron motion for simulating quantum-confined nonlinear optical systems. This paper derives the nonlinear optical properties of quantum graphs containing the basic star vertex and compares their responses across topological and geometrical classes. We show that such graphs have exactly the right topological properties to generate energy spectra required to achieve large, intrinsic optical nonlinearities. The graphs have the exquisite geometrical sensitivity required to tune wave function overlap in a way that optimizes the transition moments. We show that this class of graphs consistently produces intrinsic optical nonlinearities near the fundamental limits. We discuss the application of the models to the prediction and development of new nonlinear optical structures.