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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 29, Iss. 3 — Mar. 1, 2012
  • pp: 513–520

Maximizing the hyperpolarizability poorly determines the potential

T. J. Atherton, J. Lesnefsky, G. A. Wiggers, and R. G. Petschek  »View Author Affiliations

JOSA B, Vol. 29, Issue 3, pp. 513-520 (2012)

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The dimensionless zero-frequency electronic first hyperpolarizability 31/4βE107/2m3/2(e)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.

© 2012 Optical Society of America

OCIS Codes
(160.0160) Materials : Materials
(160.4330) Materials : Nonlinear optical materials
(190.0190) Nonlinear optics : Nonlinear optics

ToC Category:
Nonlinear Optical Materials

Original Manuscript: August 2, 2011
Revised Manuscript: December 8, 2011
Manuscript Accepted: December 12, 2011
Published: March 1, 2012

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)

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