Influence of geometry and topology of quantum graphs on their nonlinear optical properties

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Abstract
We analyze the nonlinear optics of quasi-one-dimensional quantum graphs and manipulate their topology and geometry to generate nonlinearities in a simple system approaching the fundamental limits of the first and second hyperpolarizabilities. We explore a huge configuration space in order to determine whether the fundamental limits may be approached for specific topologies, independent of molecular details, when the geometry is manipulated to maximize the intrinsic response. 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. We demonstrate the same universal scaling behavior for quantum graphs that is predicted for general quantum nonlinear optical systems near their fundamental limits, indicating that our results for quantum graphs may reflect general structure-property relationships for globally optimized nonlinear optical systems.
Funding Information
  • National Science Foundation

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