Scaling and universality in nonlinear optical quantum graphs containing star motifs

Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the fundamental limit. Loop topologies have modest responses, while bent wires have larger responses, even when the bent wire and loop geometries are identical. Topological enhancement of the nonlinear response of quantum graphs is even greater for star graphs, for which the first hyperpolarizability can exceed half the fundamental limit. In this paper, we investigate the nonlinear optical properties of quantum graphs with the star vertex topology, introduce motifs and develop new methods for computing the spectra of composite graphs. We show that this class of graphs consistently produces intrinsic optical nonlinearities near the limits predicted by potential optimization. All graphs of this type have universal behavior for the scaling of their spectra and transition moments as the nonlinearities approach the fundamental limit.