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

Abstract

We propose the scale-invariant intrinsic hyperpolarizability as a measure of the figure of merit for electro-optic molecules. By applying our analysis to the best second-order nonlinear optical molecules that are made using present paradigms, we conclude that it should be possible to make dye-doped polymers with electro-optic coefficients of several thousand pico-meters per volt.

Applying universal scaling laws to identify the best molecular design paradigms for second-order nonlinear optics

“…It can be shown rigorously that the Schrödinger Equation is invariant under transformations in which the lengths are re-scaled by a factor ǫ if the energies are simultaneously re-scaled by a factor 1/ǫ 2 . [12,25] This same re-scaling leaves the intrinsic polarizability and hyperpolarizabilities unchanged. We can expand this idea to the case of molecules and classify them in terms of their scaling behavior.…”

“…The fundamental limit defines an absolute maximum, so the ratio of the measured nonlinearity to the limit is a dimensionless parameter of magnitude less than unity. We define the intrinsic first hyperpolarizability as this ratio: [12,28] …”

“…[5][6][7][8] The performance of a molecule is evaluated by comparing its response with that of the optimal structure that uses the same number of electrons * jperezmo@skidmore.edu (the quantum limit). An analysis based on the quantum limit theory applied to experimental data allows one to determine the mechanisms that dominate the nonlinear optical response at the molecular level, [9][10][11][12][13][14][15][16][17][18] introduce new paradigms for optimization, [14,[19][20][21][22][23][24] and establish fundamental scaling laws. [25,26] In this paper we introduce a new analysis that we apply to experimental data in the literature to identify the best molecular candidates for the largest second-order nonlinear optical response.…”

Classical model of the upper bounds of the cascading contribution to the second hyperpolarizability

“…[30,36,41] While there is no analytical proof, the TLA has been shown to hold in all cases ever studied. [30,42,43] However, for systems with a nonlinear response substantially smaller than the limit, more states can contribute.…”

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

“…The oscillator strength is limited by the nonrelativistic kinetic energy of a free particle, where field interactions from a four-potential do not contribute to the maximum oscillator strength. The intrinsic values of the hyperpolarizability and second hyperpolarizability in the non-relativistic limit have been studied in great detail, [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] where there is a looming gap between the measured/calculated values and the fundamental limits in the non-relativistic regime.…”