Studies on optimizing potential energy functions for maximal intrinsic hyperpolarizability

Abstract

We use numerical optimization to study the properties of (1) the class of one-dimensional potential energy functions and (2) systems of point charges in two-dimensions that yield the largest hyperpolarizabilities, which we find to be within 30% of the fundamental limit. We investigate the character of the potential energy functions and resulting wavefunctions and find that a broad range of potentials yield the same intrinsic hyperpolarizability ceiling of 0.709.

9 pages, 9 figures

References in corpus (5)

• Compact Sum-Over-States Expression without Dipolar Terms for Calculating Nonlinear Susceptibilities
• Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability
• Pushing the hyperpolarizability to the limit
• The Effects of Geometry on the Hyperpolarizability
• Truncated Sum Rules and their use in Calculating Fundamental Limits of Nonlinear Susceptibilities

Cited by in corpus (27)

• A new dipole-free sum-over-states expression for the second hyperpolarizability
• Monte Carlo Studies of the Fundamental Limits of the Intrinsic Hyperpolarizability
• The influence of geometry and topology of quantum graphs on their nonlinear-optical properties
• The critical role of the energy spectrum in determining the nonlinear-optical response of a quantum system
• Monte Carlo Studies of the Intrinsic Second Hyperpolarizability
• Geometry-Controlled Nonlinear Optical Response of Quantum Graphs
• The paradox of the many-state catastrophe of fundamental limits and the three-state conjecture
• Optimizing the second hyperpolarizability with minimally-parametrized potentials
• Exact fundamental limits of the first and second hyperpolarizabilities
• Physics of the fundamental limits of nonlinear optics: A theoretical perspective
• Dressed quantum graphs with optical nonlinearities approaching the fundamental limit
• The effect of extreme confinement on the nonlinear-optical response of quantum wires
• A classical model of the upper bounds of the cascading contribution to the second hyperpolarizability
• A quantum mechanical model of the upper bounds of the cascading contribution to the second hyperpolarizability
• Applying universal scaling laws to identify the best molecular design paradigms for third-order nonlinear optics
• A bird's-eye view of nonlinear-optical processes: unification through scale invariance
• Lowest-order relativistic corrections to the fundamental limits of nonlinear-optical coefficients
• Optimization of eigenstates and spectra for quasi-linear nonlinear optical systems
• Optimum topology of quasi-one dimensional nonlinear optical quantum systems
• Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability
• Applying universal scaling laws to identify the best molecular design paradigms for second-order nonlinear optics
• Maximizing the hyperpolarizability of one-dimensional systems
• A Heuristic Approach for Treating Pathologies of Truncated Sum Rules in Limit Theory of Nonlinear Susceptibilities
• Scaling and universality in nonlinear optical quantum graphs containing star motifs
• Polynomial potentials determined from the energy spectrum and transition dipole moments that give the largest hyperpolarizabilities
• Maximizing the hyperpolarizability of 1D potentials with multiple electrons
• Three-state interactions determine the second-order nonlinear optical response