While sophisticated numerical computational techniques can calculate the hyperpolarizabilities of complex molecules, it is not clear what scale invariant parameters determine a large nonlinear response. We investigate the first and second intrinsic hyperpolarizabilities of one-dimensional power-law potentials with a hybrid analytical semiclassical analysis of energy spectra and numerical calculations of eigenfunctions. By varying the exponent, we determine how key underlying properties drive the nonlinear response as the system smoothly varies from particle in a box, harmonic oscillator, point charge potential, to all multipolar Coulomb potentials. The role of the well-known pathology of the 1/x² potential is also discussed.

Date Published: 10 September 2013
PDF: 6 pages
Proc. SPIE 8827, Optical Processes in Organic Materials and Nanostructures II, 882703 (10 September 2013); doi: 10.1117/12.2024631

Published in SPIE Proceedings Vol. 8827:
Optical Processes in Organic Materials and Nanostructures II
Manfred Eich; Jean-Michel Nunzi; Rachel Jakubiak, Editor(s)