General solution to nonlinear optical quantum graphs using Dalgarno–Lewis summation techniques

Lytel, R.; Mossman, Sean; Kuzyk, Mark G.

doi:10.1364/josab.33.000e14

Cited by 2 publications

(2 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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: 83%

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

Crowell¹,

Kuzyk²

2018

J. Opt. Soc. Am. B

Self Cite

View full text Add to dashboard Cite

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]

show abstract

Section: Introductionmentioning

confidence: 83%

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

Crowell¹,

Kuzyk²

2018

J. Opt. Soc. Am. B

Self Cite

View full text Add to dashboard Cite

show abstract

“…The computation of the first and second hyperpolarizabilities can be accomplished in perturbation theory using a sum over states [4] (SOS), Dalgarno-Lewis perturbation theory [5][6][7], the method of finite fields [8], and others. Each method requires state and spectral information from a Hamiltonian.…”

mentioning

confidence: 99%

Exact Fundamental Limits of the First and Second Hyperpolarizabilities

et al. 2017

Self Cite

View full text Add to dashboard Cite

Nonlinear optical interactions of light with materials originate in the microscopic response of the molecular constituents to excitation by an optical field, and are expressed by the first (β) and second (γ) hyperpolarizabilities. Upper bounds to these quantities were derived seventeen years ago using approximate, truncated state models that violated completeness and unitarity, and far exceed those achieved by potential optimization of analytical systems. This letter determines the fundamental limits of the first and second hyperpolarizability tensors using Monte-Carlo sampling of energy spectra and transition moments constrained by the diagonal Thomas-Reiche-Kuhn (TRK) sum rules and filtered by the off-diagonal TRK sum rules. The upper bounds of β and γ are determined from these quantities by applying error-refined extrapolation to perfect compliance to the sum rules. The method yields the largest diagonal component of the hyperpolarizabilities for an arbitrary number of interacting electrons in any number of dimensions. The new method provides design insight to the synthetic chemist and nanophysicist for approaching the limits. This analysis also reveals that the special cases which lead to divergent nonlinearities in the many-state catastrophe are not physically realizable.PACS numbers: 42.65.An, 78.67.LtIntroduction-Nonlinear optics is the study of quantum systems with polarizations that are nonlinear functions of external electromagnetic fields. This letter solves the problem of determining the exact fundamental limits of nonlinear optics by delineating the first procedure for computing the first and second hyperpolarizabilities consistent with on-and off-diagonal quantum mechanical sum rules. In the process, we show that prior predictions of the limits using truncated sum rules are too high by nearly 30% for β[1, 2] and 40% for γ [2], that predictions of the many-state catastrophe [3] are spurious, and that predictions of the scaling of the hyperpolarizabilities with the strength of the ground-to-excited state transition moment are modified in a way that will direct molecular synthesists to make new design choices.The nonlinear optical response of a material is generated by the collective response of the basic elements comprising it. This letter concerns the maximum values of the nonlinear optical response of a molecular-scale structure, not a material. The nonlinear optics of an elemental structure is measured by the effect it has on the molecular polarization vector when perturbatively excited by an electric field E i , with i = x, y, z:

show abstract

General solution to nonlinear optical quantum graphs using Dalgarno–Lewis summation techniques

Cited by 2 publications

References 40 publications

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

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

Exact Fundamental Limits of the First and Second Hyperpolarizabilities

Contact Info

Product

Resources

About