Surface plasmon dispersion on a single-sheeted hyperboloid

Becker, R. S.; Anderson, V. E.; Birkhoff, R.D.; Ferrell, T. L.; Ritchie, R.H.

doi:10.1139/p81-067

Cited by 10 publications

(4 citation statements)

References 2 publications

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“…These functions which also enter integral transforms such as those of Kontorovich-Lebedev, and Mehler-Fock as kernels [3] find important applications in boundary value problems of electrostatics and elasticity [4]. These applications typically entail modeling material domains [5][6][7] or voids in material domains [8] with the appropriate continuous surfaces generated by fixing one of the coordinates in the chosen coordinate system [9].…”

Section: Introductionmentioning

confidence: 99%

On the orthogonality of the MacDonald's functions

Passian

Simpson

Kouchekian

et al. 2009

Journal of Mathematical Analysis and Applications

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Section: Introductionmentioning

confidence: 99%

On the orthogonality of the MacDonald's functions

Passian

Simpson

Kouchekian

et al. 2009

Journal of Mathematical Analysis and Applications

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“…Becker et al studied the resonant surface modes for a hyperboloidal void to model a submicron hole in a dielectric material under the assumption of a local dielectric function for the medium. 2 Similarly, Ferrell calculated the nonretarded surface plasmon dispersion relations for several cases related to scanning probe microscopy where the material domains were modeled as hyperboloids of revolution. 3,4 Here we consider the case of a hyperboloidal dielectric tip immersed in a homogeneous field set up by a uniform surface charge density residing on a plane bounded semi-infinite dielectric medium.…”

Section: Introductionmentioning

confidence: 99%

Potential distribution and field intensity for a hyperboloidal probe in a uniform field

Passian

Wig

Mériaudeau

et al. 2002

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

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The scalar potential and electric field distributions in the gap region of a probe-substrate system are calculated. The probe, modeled as a dielectric medium with the geometry of a one sheeted hyperboloid of revolution, is located above a charged substrate surface which is modeled as a dielectric half space interfaced with a uniform surface charge density. The potential and field distributions are then calculated as functions of the dielectric constant of the medium filling the space between the tip and the surface, and as functions of the hyperboloidal shape parameter. Comparisons are made with the case of a dielectric spheroidal body. The analytical results attained can be used to study other related quantities such as energy density or Coulomb interaction in the neighborhood of the nanometer sized apex region without resorting to numerical methods. This investigation allows for tip shape related field variation in various dielectric media to be studied. Application of this approach to modeling probe tip-sample (probe tip-substrate) interaction in scanning probe microscopy, or to modeling dielectric breakdown processes, are examples of the potential use of the method.

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“…[12][13][14][15][16] For example, the probe tip of an atomic force microscope can be gold coated in order to locally enhance the Raman signal during spectroscopy. 17 However, the dynamics of collective electronic behavior in the involved metallic or dielectric particulates, [18][19][20] voids, 21,22 and thin films 15,16 can be greatly modified by geometric effects, in particular, as the dimensions of the system are reduced. Regularly patterned surfaces such as metal gratings, 23,24 or randomly distributed inhomogeneities such as surface roughness, 25 can be mentioned in this regard.…”

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confidence: 99%