Topological optimization of nonlinear optical quantum wire networks

Spatially extended molecular structures, modeled as quantum graphs with one-dimensional electron dynamics, exhibit optical responses that can approach the fundamental limits. We present the results of a comprehensive study of the topological dependence of the nonlinearities of quantum graphs and show exactly how the first and second hyperpolarizability of a graph depend upon its topological class and how the hyperpolarizability tensors vary with graph geometry. We show how graphs with star motifs share universal scaling behavior near the maximum nonlinear responses and articulate design rules for quantum-confined, quasi-one dimensional systems that may be realized using molecular elements and nanowires.