The effect of electron interactions on the universal properties of systems with optimized off-resonant intrinsic hyperpolarizability.

Because of the potentially large number of important applications of nonlinear optics, researchers have expended a great deal of effort to optimize the second-order molecular nonlinear-optical response, called the hyperpolarizability. The focus of our present studies is the intrinsic hyperpolarizability, which is a scale-invariant quantity that removes the effects of simple scaling, thus being the relevant quantity for comparing molecules of varying sizes. Past theoretical studies have focused on structural properties that optimize the intrinsic hyperpolarizability, which have characterized the structure of the quantum system based on the potential energy function, placement of nuclei, geometry, and the effects of external electric and magnetic fields.

Optimizing the hyperpolarizability tensor using external electromagnetic fields and nuclear placement.

We investigate the effects of an external electric and magnetic field on the first hyperpolarizability tensor of a quantum system, such as a molecule or nanoparticle, whose nonlinear response is well below the fundamental limit. We find that the intrinsic hyperpolarizability is optimized when the applied electric and magnetic fields are comparable to the internal molecular fields. Indeed, the nonlinear response is just as large for an electron in the presence of the external field without the nuclei as it is for an electron bound to a molecule and in the presence of the applied field.

Pushing the hyperpolarizability to the limit.

We use numerical optimization to find a one-dimensional potential energy function that yields the largest hyperpolarizability, which we find is within 30% of the fundamental limit. Our results reveal insights into the character of the potential energy functions and wave functions that lead to the largest hyperpolarizability. We suggest that donor-acceptor molecules with a conjugated bridge with many sites of reduced conjugation to impart conjugation modulation may be the best paradigm for making materials with huge hyperpolarizabilities that approach the fundamental limit.

The effects of geometry on the hyperpolarizability.

Extensive studies in the past have focused on precise calculations of the nonlinear-optical susceptibility of thousands of molecules. In this work, we use the broader approach of considering how geometry and symmetry alone play a role, irrespective of molecular constraints. We investigate the nonlinear optical response of potential energy functions that are given by a superposition of force centers (representing the nuclear charges) that lie in various planar geometrical arrangements.

A framework model based on the Smoluchowski equation in two reaction coordinates.

The general form of the Smoluchowski equation in two reaction coordinates is obtained as the diffusion limit of a random walk on an infinite square grid using transition probabilities that satisfy detailed balance at thermodynamic equilibrium. The diffusion limit is then used to construct a generalization of the single-particle model to two reaction coordinates. The state space includes a square on which diffusion takes place and an isolated empty state.