The off-resonant hyperpolarizability is calculated by using the dipole-free sum-over-states expression from a randomly chosen set of energies and transition dipole moments that are forced to be consistent with the sum rules. The process is repeated so that the distribution of hyperpolarizabilities can be determined. We find this distribution to be a cycloidlike function. In contrast to variational techniques that when applied to the potential energy function yield an intrinsic hyperpolarizability less than 0.71, our Monte Carlo method yields values that approach unity. While many transition dipole moments are large when the calculated hyperpolarizability is near the fundamental limit, only two excited states dominate the hyperpolarizability—consistent with the three-level ansatz. We speculate on the character of the Hamiltonian that is needed to optimize the intrinsic hyperpolarizability.
© 2008 Optical Society of America
Atomic and Molecular Physics
Original Manuscript: August 21, 2007
Revised Manuscript: October 27, 2007
Manuscript Accepted: November 2, 2007
Published: December 21, 2007
Mark C. Kuzyk and Mark G. Kuzyk, "Monte Carlo studies of the fundamental limits of the intrinsic hyperpolarizability," J. Opt. Soc. Am. B 25, 103-110 (2008)