The influence of geometry and topology of quantum graphs on their nonlinear-optical properties

Abstract

We analyze the nonlinear optics of quasi one-dimensional quantum graphs and manipulate their topology and geometry to generate for the first time nonlinearities in a simple system approaching the fundamental limits of the first and second hyperpolarizabilities. 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. This work may inform the design of new molecules or nano- scale structures for nonlinear optics and hints at the same universal behavior for quantum graph models in nonlinear optics that is observed in other systems.

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• Lowest-order relativistic corrections to the fundamental limits of nonlinear-optical coefficients
• Dalgarno-Lewis perturbation theory for nonlinear optics
• Optimum topology of quasi-one dimensional nonlinear optical quantum systems
• Optimization of eigenstates and spectra for quasi-linear nonlinear optical systems
• Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability
• Hybrid quantum systems for enhanced nonlinear optical susceptibilities
• Scaling and universality in nonlinear optical quantum graphs containing star motifs
• A Heuristic Approach for Treating Pathologies of Truncated Sum Rules in Limit Theory of Nonlinear Susceptibilities
• General solution to nonlinear optical quantum graphs using Dalgarno-Lewis summation techniques
• Maximizing the hyperpolarizability of 1D potentials with multiple electrons
• Static hyperpolarizability of space-fractional quantum systems