Monte Carlo Studies of the Fundamental Limits of the Intrinsic Hyperpolarizability

Abstract

The off-resonant hyperpolarizability is calculated using the dipole-free sum-over-stats expression from a randomly chosen set of energies and transition dipole moments that are forced to be consistent with the sum rules. The process is repeated so that the distribution of hyperpolarizabilities can be determined. We find this distribution to be a cycloid-like function. In contrast to variational techniques that when applied to the potential energy function yield an intrinsic hyperpolarizability less than 0.71, our Monte Carlo method yields values that approach unity. While many transition dipole moments are large when the calculated hyperpolarizability is near the fundamental limit, only two excited states dominate the hyperpolarizability - consistent with the three-level ansatz.

arXiv comment7 pages, 5 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
• Studies on optimizing potential energy functions for maximal intrinsic hyperpolarizability
• The Effects of Geometry on the Hyperpolarizability

Cited by in corpus (16)

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• The paradox of the many-state catastrophe of fundamental limits and the three-state conjecture
• Experimental verification of a self-consistent theory of the first-, second-, and third-order (non)linear optical response
• Exact fundamental limits of the first and second hyperpolarizabilities
• Physics of the fundamental limits of nonlinear optics: A theoretical perspective
• The effect of extreme confinement on the nonlinear-optical response of quantum wires
• Dressed quantum graphs with optical nonlinearities approaching the fundamental limit
• 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
• 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
• Static hyperpolarizability of space-fractional quantum systems