Nonlinear optics of quantum graphs

Quantum graphs are graphical networks comprised of edges supporting Hamiltonian dynamics and vertices conserving probability flux. Lateral confinement of particle motion on every edge results in a quasi one-dimensional quantum-confined system for which nonlinear optical effects may be calculated. Our ongoing research program is the first to investigate the nonlinear optical properties of quantum graphs. We seek to discover configurations with intrinsic first and second hyperpolarizabilities approaching their respective fundamental limits, to explore the NLO variation with the geometry and topology of the graphs, and to develop scaling laws for more complex graphs with self-similar properties. This paper describes a new methodology for calculating the hyperpolarizabilities of a class of graphs comprised of sequentially-connected edges. Such graphs include closed-loop topologies and their geometrically-similar but topologically-different open loop cousins, as well as other bent wire graphs and their combinations.