Maximizing the hyperpolarizability of 1D potentials with multiple electrons

Abstract

We optimize the first and second intrinsic hyperpolarizabilities for a 1D piecewise linear potential dressed with Dirac delta functions for N non-interacting electrons. The optimized values fall rapidly for N > 1, but approach constant values of βint = 0.40, γ + int = 0.16 and γ − int = −0.061 above N 8. These apparent bounds are achieved with only 2 parameters with more general potentials achieving no better value. In contrast to previous studies, analysis of the hessian matrices of βint and γint taken with respect to these parameters shows that the eigenvectors are well aligned with the basis vectors of the parameter space, indicating that the parametrization was well-chosen. The physical significance of the important parameters is also discussed.

Physics of the fundamental limits of nonlinear optics: a theoretical perspective [Invited]

“…A multi-electron version of the quantum graph model was developed to confirm that graphs with N electrons could still achieve a sizable fraction of the Hamiltonian limits [84]. The limits were similar to those recently reported by Burke et al [88]. In each model, the electrons TABLE II.…”

“…Recently, the piecewise potential optimization approach was applied to maximize the hyperpolarizability in one dimension of a multiple electron system [88]. The potential models included a δ potential, a sort of triangular potential, and the piecewise potential used in the authors' earlier studies [86,87].…”

Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability

“…A study on the optimal many-electron nonlinear response can be found in [44]. There is no reason to doubt that the excited state response can be enhanced in the excited state over the ground state configuration for particular systems given that the calculations of the excited state limits as quantified by Equation 28 applies to the manyelectron case and works even when there are interactions between the electrons.…”

“…Here we consider multiple noninteracting electrons in an analysis similar to that of Burke and Atherton. [44] The fact that pre-excitation can enhance the intrinsic polarizability has interesting consequences on such multielectron systems. To illustrate, consider a single-particle energy spectrum associated with an external potential.…”