Optimizing the second hyperpolarizability with minimally-parametrized potentials

TL;DR

This paper investigates how to optimize the second hyperpolarizability of a single electron in a 1D potential well by adjusting potential shapes, revealing that only one parameter significantly influences the maximum achievable hyperpolarizability.

Contribution

It demonstrates that minimal parametrization suffices to approach the theoretical bounds of hyperpolarizability in potential design.

Findings

Optimized potentials achieve hyperpolarizabilities close to theoretical bounds.

Parity-symmetric potentials are optimal for maximizing hyperpolarizability.

Effectively only one parameter influences the extremum of hyperpolarizability.

Abstract

The dimensionless zero-frequency intrinsic second hyperpolarizability \gamma_{int}=\gamma/4E_{10}^{-5}m^{-2}(e\hbar)^{4} was optimized for a single electron in a 1D well by adjusting the shape of the potential. Optimized potentials were found to have hyperpolarizabilities in the range -0.15\lessapprox\gamma_{int}\lessapprox0.60 ; potentials optimizing gamma were arbitrarily close to the lower bound and were within \sim0.5% of the upper bound. All optimal potentials posses parity symmetry. Analysis of the Hessian of \gamma_{int} around the maximum reveals that effectively only a single parameter, one of those chosen in the piecewise linear representation adopted, is important to obtaining an extremum. Prospects for designing new chromophores based on the design principle here elucidated are discussed.