Geometry-Controlled Nonlinear Optical Response of Quantum Graphs

Abstract

We study for the first time the effect of the geometry of quantum wire networks on their nonlinear optical properties and show that for some geometries, the first hyperpolarizability is largely enhanced and the second hyperpolarizability is always negative or zero. We use a one-electron model with tight transverse confinement. In the limit of infinite transverse confinement, the transverse wavefunctions drop out of the hyperpolarizabilities, but their residual effects are essential to include in the sum rules. The effects of geometry are manifested in the projections of the transition moments of each wire segment onto the 2-D lab frame. Numerical optimization of the geometry of a loop leads to hyperpolarizabilities that rival the best chromophores. We suggest that a combination of geometry and quantum-confinement effects can lead to systems with ultralarge nonlinear response.

arXiv commentTo appear in J. Opt. Society of America B

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Cited by in corpus (11)

• The influence of geometry and topology of quantum graphs on their nonlinear-optical properties
• Physics of the fundamental limits of nonlinear optics: A theoretical perspective
• Dressed quantum graphs with optical nonlinearities approaching the fundamental limit
• Lowest-order relativistic corrections to the fundamental limits of nonlinear-optical coefficients
• Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability
• Optimum topology of quasi-one dimensional nonlinear optical quantum systems
• Optimization of eigenstates and spectra for quasi-linear nonlinear optical systems
• A Heuristic Approach for Treating Pathologies of Truncated Sum Rules in Limit Theory of Nonlinear Susceptibilities
• Polynomial potentials determined from the energy spectrum and transition dipole moments that give the largest hyperpolarizabilities
• Scaling and universality in nonlinear optical quantum graphs containing star motifs
• General solution to nonlinear optical quantum graphs using Dalgarno-Lewis summation techniques