Pushing the hyperpolarizability to the limit

Abstract

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.

Maximizing the hyperpolarizability poorly determines the potential

“…The wide range of parametrizations that have been explored, particularly by Kuzyk et al [3][4][5], strongly suggests that qualitatively different but substantially better potentials do not exist and that the true optimum hyperpolarizability is close to those presented here.…”

“…Kuzyk et al have studied a sub-problem of this, namely performing the optimization for the single-electron case with both one and two dimensional potentials. They suggest that implementing the qualitative (modulated) features observed in their optimized potentials might allow design of molecules with higher hyperpolarizabilities [4,5]. While these calculations have resulted in a number of potentials with large hyperpolarizabilities, they do not distinguish which features of the optimized potential are required for high β and which are artifacts of the minimization procedure or chosen parametrization.…”

Intrinsic Hyperpolarizabilities as a Figure of Merit for Electro-optic Molecules

“…Recently, it has been proposed that a better measure of the intrinsic hyperpolarizability of a molecule is the ratio of the off-resonant hyperpolarizability to the off-resonant fundamental limit of the hyperpolarizability, [27] …”

“…[27] Perhaps the twist in the molecule provides an effective kink in the potential energy function that leads to an enhancement. Figure 2 shows a plot of the intrinsic hyperpolarizability at the measurement wavelength, β int (ω, ω), and the off resonance value,…”

Lowest-order relativistic corrections to the fundamental limits of nonlinear-optical coefficients

“…[24][25][26][27][28][29][30][31][32] Another approach to breach the gap involves a systematic search for new classes of organic nonlinear optical molecules with multipolar chargedensity analysis from crystallographic data. [33][34][35] New abstract methods of calculating large nonlinear responses have also been studied for low-dimensional quantum graphs.…”