Comment on "Pushing the hyperpolarizability to the limit"

Wiggers, Greg; Petschek, Rolfe G.

doi:10.1364/ol.32.000942

Cited by 6 publications

(11 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1(b)(ii)]. Such a change is expected a priori from previous work [16] to make no significant difference to γ int as it is far from the region where ψ 0 and ψ 1 are large. For this well-like potential, we performed a maximization, adjusting A 2 , x 1 , and x 2 while fixing the outer walls to have a large slope (A 3 = 100).…”

Section: Resultsmentioning

confidence: 77%

Optimizing the second hyperpolarizability with minimally parametrized potentials

et al. 2013

View full text Add to dashboard Cite

The dimensionless zero-frequency intrinsic second hyperpolarizability γint = γ/4E −5 10 m −2 (e ) 4 was optimized for a single electron in a 1D well by adjusting the shape of the potential. Optimized potentials were found to have hyperpolarizabilities in the range −0.15 γint 0.60; potentials optimizing gamma were arbitrarily close to the lower bound and were within ∼ 0.5% of the upper bound. All optimal potentials posses parity symmetry. Analysis of the Hessian of γint around the maximum reveals that effectively only a single parameter, one of those chosen in the piecewise linear representation adopted, is important to obtaining an extremum. Prospects for designing new chromophores based on the design principle here elucidated are discussed.

show abstract

Section: Resultsmentioning

confidence: 77%

Optimizing the second hyperpolarizability with minimally parametrized potentials

et al. 2013

View full text Add to dashboard Cite

show abstract

“…those near the Fermi surface. This is justified by previous studies [15] that have shown the addition of small rapidly varying perturbations to the potential doesn't affect the hyperpolarizabilities. The ansatz potentials studied in this work, with delta functions and changes in slope at isolated points, all satisfy this criterion.…”

Section: Appendix A: Approximate Analysismentioning

confidence: 63%

“…perpolarizabilities can be completely reconstructed from the ground state wavefunction [15]. Extending this to the N > 1 case, it is easy to see that the hyperpolarizablities can be constructed for this problem as appropriate integrals of the occupied single particle wavefunctions alone.…”

Section: Discussionmentioning

confidence: 99%

Maximizing the hyperpolarizability of 1D potentials with multiple electrons

et al. 2016

Self Cite

View full text Add to dashboard Cite

We optimize the first and second intrinsic hyperpolarizabilities for a 1D piecewise linear potential dressed with Dirac delta functions for N non-interacting electrons. The optimized values fall rapidly for N > 1, but approach constant values of βint = 0.40, γ + int = 0.16 and γ − int = −0.061 above N 8. These apparent bounds are achieved with only 2 parameters with more general potentials achieving no better value. In contrast to previous studies, analysis of the hessian matrices of βint and γint taken with respect to these parameters shows that the eigenvectors are well aligned with the basis vectors of the parameter space, indicating that the parametrization was well-chosen. The physical significance of the important parameters is also discussed.

show abstract

“…Moreover, since the hyperpolarizability has been shown to depend only on dipole matrix elements and may be derived entirely as a multiple integral of the ground state wavefunction [8], changes in the potential where the ground state wavefunction is large are also irrelevant if they tend not to alter the wavefunction. For example, rapid variations in the potential which approximately average to zero will not significantly affect the hyperpolarizability.…”

Section: Introductionmentioning

confidence: 99%

Maximizing the hyperpolarizability poorly determines the potential

et al. 2012

View full text Add to dashboard Cite

We have optimized the zero frequency first hyperpolarizability β of a one-dimensional piecewise linear potential well containing a single electron by adjusting the shape of that potential. With increasing numbers of parameters in the potential, the maximized hyperpolarizability converges quickly to 0.708951 of the proven upper bound. The Hessian of β at the maximum has in each case only two large eigenvalues; the other eigenvalues diminish seemingly exponentially quickly, demonstrating a very wide range of nearby nearly optimal potentials, and that there are only two important parameters for optimizing β. The shape of the optimized wavefunctions converges with more parameters while the associated potentials remain substantially different, suggesting that the ground state wavefunction provides a superior physical description to the potential for the conditions that optimize the hyperpolarizability. Prospects for characterizing the two important parameters for near-optimum potentials are discussed.

show abstract

Comment on "Pushing the hyperpolarizability to the limit"

Cited by 6 publications

References 3 publications

Optimizing the second hyperpolarizability with minimally parametrized potentials

Optimizing the second hyperpolarizability with minimally parametrized potentials

Maximizing the hyperpolarizability of 1D potentials with multiple electrons

Maximizing the hyperpolarizability poorly determines the potential

Contact Info

Product

Resources

About