A bird's-eye view of nonlinear-optical processes: unification through scale invariance

Abstract

The Schrödinger equation has the property that when changing the length scale by $\vec{r}\to \epsilon \vec{r}$ and the energy scale by $E\to E/{\epsilon }^2$, the shape of the wavefunction remains unchanged. The same re-scaling leaves the intrinsic hyperpolarizability (as well as higher-order hyperpolarizabilities) unchanged. As such, the intrinsic hyperpolarizability is the best quantity for comparing molecules since it re-normalizes for trivial differences that are due to molecular size and energy gap. Similarly, the intrinsic hyperpolarizability is invariant to changes in the number of electrons. In this paper, we review the concept of scale invariance and how it can be applied to better understand the nonlinear optical response, which can be used to develop new paradigms for it's optimization.

16 pages, three figures

References in corpus (5)

• Reply to "the Comment on `Gauge Invariance and kT-Factorization of Exclusive Processes'"
• 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
• Monte Carlo Studies of the Fundamental Limits of the Intrinsic Hyperpolarizability

Cited by in corpus (5)

• The critical role of the energy spectrum in determining the nonlinear-optical response of a quantum system
• Monte Carlo Studies of the Intrinsic Second Hyperpolarizability
• Geometry-Controlled Nonlinear Optical Response of Quantum Graphs
• Optimum topology of quasi-one dimensional nonlinear optical quantum systems
• Scaling and universality in nonlinear optical quantum graphs containing star motifs