Document Type
Article
Publication Date
12-13-2012
Abstract
The dimensionless zero-frequency electronic first hyperpolarizability 3−1/4βE7/210m3/2(eℏ)−3 of an electron in one dimension was maximized by adjusting the shape of a piecewise linear potential. Careful maximizations converged quickly to 0.708951 with increasing numbers of parameters. The Hessian shows that β is strongly sensitive to only two parameters in the potential: sensitivity to additional parameters decreases rapidly. With more than two parameters, a wide range of potentials and an apparently narrower range of wavefunctions have nearly optimal hyperpolarizability. Modulations of the potential to which the unique maximum is insensitive were characterized. Prospects for concise description of the two important constraints on near-optimum potentials are discussed.
Keywords
materials, nonlinear optic materials, nonlinear optics
Publication Title
Journal of the Optical Society of America B
Rights
© 2012 Optical Society of America. Atherton, T.J., Lesnefsky, J., Wiggers, G.A., Petschek R.G., Journal of the Optical Society of America B 29:3, 2012. This paper was published in Journal of the Optical Society of America B and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/josab/abstract.cfm?uri=josab-29-3-513. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.
Recommended Citation
T. J. Atherton, J. Lesnefsky, G. A. Wiggers, and R. G. Petschek, "Maximizing the hyperpolarizability poorly determines the potential," J. Opt. Soc. Am. B 29, 513-520 (2012)