A new dipole-free sum-over-states expression for the second hyperpolarizability

Abstract

The generalized Thomas-Kuhn sum rules are used to eliminate the explicit dependence on dipolar terms in the traditional sum-over-states (SOS) expression for the second hyperpolarizability to derive a new, yet equivalent, SOS expression. This new dipole-free expression may be better suited to study the second hyperpolarizability of non-dipolar systems such as quadrupolar, octupolar, and dodecapolar structures. The two expressions lead to the same fundamental limits of the off-resonance second hyperpolarizability; and when applied to a particle in a box and a clipped harmonic oscillator, have the same frequency-dependence. We propose that the new dipole-free equation, when used in conjunction with the standard SOS expression, can be used to develop a three-state model of the dispersion of the third-order susceptibility that can be applied to molecules in cases where normally many more states would have been required. Furthermore, a comparison between the two expressions can be used as a convergence test of molecular orbital calculations when applied to the second hyperpolarizability.

14 pages, 10 figures

References in corpus (3)

• Compact Sum-Over-States Expression without Dipolar Terms for Calculating Nonlinear Susceptibilities
• Fundamental Limits of the Dispersion of the Two-Photon Absorption Cross-Section
• Studies on optimizing potential energy functions for maximal intrinsic hyperpolarizability

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• Experimental verification of a self-consistent theory of the first-, second-, and third-order (non)linear optical response
• The effect of extreme confinement on the nonlinear-optical response of quantum wires
• A classical model of the upper bounds of the cascading contribution to the second hyperpolarizability
• A quantum mechanical model of the upper bounds of the cascading contribution to the second hyperpolarizability
• Lowest-order relativistic corrections to the fundamental limits of nonlinear-optical coefficients
• The Local Field Factor and Microscopic Cascading: A Self-Consistent Method Applied to Confined Systems of Molecules
• The second hyperpolarizability of systems described by the space-fractional Schrodinger equation
• Modeling off-resonant nonlinear-optical cascading in mesoscopic thin films and guest-host molecular systems
• Maximizing the hyperpolarizability of 1D potentials with multiple electrons