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 ${\beta }_{int}=0.40$, ${\gamma }_{int}^{+}=0.16$ and ${\gamma }_{int}^{-}=-0.061$ above $N\gtrsim 8$. 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 ${\beta }_{int}$ and ${\gamma }_{int}$ 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.

14 pages, 5 figures

References in corpus (5)

• Studies on optimizing potential energy functions for maximal intrinsic hyperpolarizability
• A new dipole-free sum-over-states expression for the second hyperpolarizability
• Dressed quantum graphs with optical nonlinearities approaching the fundamental limit
• Optimum topology of quasi-one dimensional nonlinear optical quantum systems
• Optimization of eigenstates and spectra for quasi-linear nonlinear optical systems

Cited by in corpus (2)

• Physics of the fundamental limits of nonlinear optics: A theoretical perspective
• Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability