Optimizing the second hyperpolarizability with minimally parametrized potentials

Burke, Christopher; Atherton, Timothy J.; Lesnefsky, Joseph; Petschek, Rolfe G.

doi:10.1364/josab.30.001438

Cited by 16 publications

(22 citation statements)

References 17 publications

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“…Following a similar approach to that established in our earlier papers [4,5], we optimize β int and γ int with respect to the shape of a piecewise linear potential dressed with Dirac delta functions for N electrons interacting only through Pauli exclusion. We perform this optimization for two carefully chosen potentials depicted in Fig.…”

Section: Modelmentioning

confidence: 99%

Maximizing the hyperpolarizability of 1D potentials with multiple electrons

et al. 2016

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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.

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Section: Modelmentioning

confidence: 99%

Maximizing the hyperpolarizability of 1D potentials with multiple electrons

et al. 2016

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“…The energy difference between the ground and first excited state, E 10 , sets a fundamental limit on the electric polarizability and first hyperpolarizability. These limits have been corroborated by experiment [12], potential optimization [13][14][15][16][17], and calculations on quantum graphs [18][19][20][21] though a recent Monte Carlo study utilizing filtered sampling suggests that these limits may be an overestimate by approximately 30% [22].…”

Section: Introductionmentioning

confidence: 84%

Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability

Crowell¹,

Kuzyk²

2018

J. Opt. Soc. Am. B

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We investigate the efficacy of boosting the nonlinear-optical response by using novel systems such as those in an excited state or with a degenerate ground state. By applying the Three Level Ansatz (TLA) and using the Thomas-Reiche-Kuhn (TRK) sum rules as constraints, we find the electric polarizability and first hyperpolarizability of excited state systems to be bounded, but larger than those derived for a system in the ground state. It is shown that a system with a degenerate ground state can have divergent polarizabilities and that such divergences are real and not relics of a pathology in the perturbation theory. Furthermore, we demonstrate that these divergences only occur on time scales short compared to the relaxation time of the population difference to an equilibrium value. Such systems provide a way to get ultra-large nonlinear optical response.We discuss examples of huge enhancements in molecules and double quantum dots using a double quantum well as a model. arXiv:1805.06977v2 [physics.optics]

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“…The fundamental limit to the scalar second hyperpolarizability derived from the standard Schrödinger equation with the three-level ansatz is well-established, γ max = 4e 4 gives the first transition moment relationship in Table I. All transition dipole moments for a three-level model of the space-fractional Schrödinger equation with a mechanical Hamiltonian can be expressed in terms ofX, E, and λ α (k, ℓ). These remaining transition dipole moments are given in Table I.…”

Section: Theorymentioning

confidence: 95%

The second hyperpolarizability of systems described by the space-fractional Schrödinger equation

2018

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The static second hyperpolarizability is derived from the space-fractional Schrödinger equation in the particle-centric view. The Thomas-Reiche-Kuhn sum rule matrix elements and the three-level ansatz determines the maximum second hyperpolarizability for a space-fractional quantum system. The total oscillator strength is shown to decrease as the space-fractional parameter α decreases, which reduces the optical response of a quantum system in the presence of an external field. This damped response is caused by the wavefunction dependent position and momentum commutation relation. Although the maximum response is damped, we show that the one-dimensional quantum harmonic oscillator is no longer a linear system for α = 1, where the second hyperpolarizability becomes negative before ultimately damping to zero at the lower fractional limit of α → 1/2.

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Optimizing the second hyperpolarizability with minimally parametrized potentials

Cited by 16 publications

References 17 publications

Maximizing the hyperpolarizability of 1D potentials with multiple electrons

Maximizing the hyperpolarizability of 1D potentials with multiple electrons

Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability

The second hyperpolarizability of systems described by the space-fractional Schrödinger equation

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