Ellipsoidal harmonics and their application in electrostatics

Stén, Johan C.-E.

doi:10.1016/j.elstat.2005.11.002

Cited by 24 publications

(22 citation statements)

References 6 publications

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“…For this reason, products of the form E p n (µ)E p n (ν) are called surface ellipsoidal harmonics through this paper. It may also be noted that when ξ → ∞, E p n (ξ) ∼ c 0 ξ n and F p n (ξ) ∼ E p n (ξ)/ξ 2n+1 ∼ c 0 /ξ n+1 which corresponds to the r −(n+1) -potential term in the spherical system [19].…”

Section: Laplace Equation In Ellipsoidal Coordinatesmentioning

confidence: 99%

“…A list of normalization constants γ p n of low orders can be found in [19]. In particular, γ 1 0 = π/2 under the definition of (10).…”

Section: Laplace Equation In Ellipsoidal Coordinatesmentioning

confidence: 99%

“…For the determination of the Lamé functions, see e.g., [15], for a short list of the Lamé functions of the first kind, see e.g., [19], and for numerical computation of the Lamé functions, see e.g., [26,28,29]. In particular, Ref.…”

Section: Laplace Equation In Ellipsoidal Coordinatesmentioning

confidence: 99%

“…Furthermore, as is well known, it is often essential in solving harmonic boundary-value problems to have an expansion for the reciprocal distance (the basic potential given by the Green's function). Using the orthogonality relation (9), the expansion for the reciprocal distance in the ellipsoidal coordinates can also be constructed [19], namely,…”

Section: Laplace Equation In Ellipsoidal Coordinatesmentioning

confidence: 99%

“…In this paper, we shall further extend the quasi-harmonic three-layer dielectric model and the robust numerical method for general three-layer dielectric models from the spheroidal coordinates to one of the most general three-dimensional coordinates in which the Laplace equation is separable [15], the tri-axial ellipsoidal coordinates [16][17][18][19][20]. This extension may be needed since, for example, realistic quantum dots might be neither perfect spheres nor perfect spheroids, while it has been shown that a small change in the external shape of a QD may strongly influence the energy spectrum and other characteristics of such a semi-conductor structure [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Three-layer dielectric models for generalized Coulomb potential calculation in ellipsoidal geometry

Xue

Deng

2011

Phys. Rev. E

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This paper concerns a basic electrostatic problem: How to calculate generalized Coulomb and self-polarization potentials in heterogeneous dielectric media. In particular, with simulations of ellipsoidal semi-conductor quantum dots and elongated bio-macromolecules being its target applications, this paper extends the so-called three-layer dielectric models for generalized Coulomb and self-polarization potential calculation from the spherical and the spheroidal geometries to the tri-axial ellipsoidal geometry. Compared to the simple step-like dielectric model, these threelayer dielectric models can overcome the mathematical divergence in the self-polarization energy by employing continuous radial dielectric functions. More specifically, in this paper, the novel quasi-harmonic three-layer dielectric model for the ellipsoidal geometry is first discussed, and the explicit analytical series solutions of the corresponding electrostatic problem are obtained in terms of the ellipsoidal harmonics. Then, a robust numerical procedure working for general three-layer dielectric models is developed. The key component of the numerical method is to subdivide the transition layer of the underlying three-layer model into multiple sublayers, and then in each one of them approximate the select dielectric function of the transition layer by one of the quasi-harmonic functional form rather than simply by a constant value as one would normally do. As the result, the numerical method has no numerical divergence.

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Section: Laplace Equation In Ellipsoidal Coordinatesmentioning

confidence: 99%

“…A list of normalization constants γ p n of low orders can be found in [19]. In particular, γ 1 0 = π/2 under the definition of (10).…”

Section: Laplace Equation In Ellipsoidal Coordinatesmentioning

confidence: 99%

Section: Laplace Equation In Ellipsoidal Coordinatesmentioning

confidence: 99%

Section: Laplace Equation In Ellipsoidal Coordinatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Three-layer dielectric models for generalized Coulomb potential calculation in ellipsoidal geometry

Xue

Deng

2011

Phys. Rev. E

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References

2011

Separable Boundary‐Value Problems in Physics

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High Harmonic Generation Assisted by Metal Nanostructures and Nanoparticles

Husakou

Kim

et al. 2014

Progress in Nonlinear Nano-Optics

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We present a review of our theoretical studies of plasmonic field enhanced high harmonic generation in the vicinity of various metallic nanostructures, of rough metallic surfaces or in composites containing a mixture of a noble gas and metallic nanoparticles. First we present a semiclassical model for plasmonenhanced high-harmonic generation (HHG) taking into account both the field inhomogeneity in the hot spots and electron absorption by the metal surface. Both effects play an important role in the HHG process and lead to the generation of even harmonics and to an twofold increased cutoff. Further alternative arrangements or mechanism for field enhancement enabling higher HHG efficiencies and a lower damage threshold are studied. We simulate field enhancement and HHG spectra in the vicinity of metallic rough surfaces and predict an increased interaction volume of hot spots in the case of grazing incidence of s-polarized pump pulses with an efficiency of plateau harmonics in the range of 10 −7 . Finally, we investigate lowintensity high-harmonic generation enabled by the plasmonic electric field enhancement in a mixture of a noble gas with metal nanoparticles. In this case HHG efficiencies up to 10 −6 are predicted.

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Ellipsoidal harmonics and their application in electrostatics

Cited by 24 publications

References 6 publications

Three-layer dielectric models for generalized Coulomb potential calculation in ellipsoidal geometry

Three-layer dielectric models for generalized Coulomb potential calculation in ellipsoidal geometry

References

High Harmonic Generation Assisted by Metal Nanostructures and Nanoparticles

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