Monte Carlo Studies of the Intrinsic Second Hyperpolarizability

Abstract

The hyperpolarizability has been extensively studied to identify universal properties when it is near the fundamental limit. Here, we employ the Monte Carlo method to study the fundamental limit of the second hyperpolarizability. As was found for the hyperpolarizability, the largest values of the second hyperpolarizability approaches the calculated fundamental limit. The character of transition moments and energies of the energy eigenstates are investigated near the second hyperpolarizability's upper bounds using the missing state analysis, which assesses the role of each pair of states in their contribution. In agreement with the three-level ansatz, our results indicate that only three states (ground and two excited states) dominate when the second hyperpolarizability is near the limit.

8 pages, 7 figures

References in corpus (8)

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• Pushing the hyperpolarizability to the limit
• Studies on optimizing potential energy functions for maximal intrinsic hyperpolarizability
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• Optimizing the second hyperpolarizability with minimally-parametrized potentials
• Physics of the fundamental limits of nonlinear optics: A theoretical perspective
• A classical model of the upper bounds of the cascading contribution to the second hyperpolarizability
• Dressed quantum graphs with optical nonlinearities approaching the fundamental limit
• The effect of extreme confinement on the nonlinear-optical response of quantum wires
• Lowest-order relativistic corrections to the fundamental limits of nonlinear-optical coefficients
• 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
• Static hyperpolarizability of space-fractional quantum systems