# Plasmon dispersion in a multilayer solid torus in terms of three-term vector recurrence relations and matrix continued fractions

## Abstract

Toroidal confinement, which has played a crucial role in magnetized plasmas and Tokamak physics, is emerging as an effective means to obtain useful electronic and optical response in solids. In particular, excitation of surface plasmons in metal nanorings by photons or electrons finds important applications due to the engendered field distribution and electromagnetic energy confinement. However, in contrast to the case of a plasma, often the solid nanorings are multilayered and/or embedded in a medium. The non-simply connected geometry of the torus results in surface modes that are not linearly independent. A three-term difference equation was recently shown to arise when seeking the nonretarded plasmon dispersion relations for a stratified solid torus (Garapati et al 2017 Phys. Rev. B 95 165422). The reported generalized plasmon dispersion relations are here investigated in terms of the involved matrix continued fractions and their convergence properties including the determinant forms of the dispersion relations obtained for computing the plasmon eigenmodes. We also present the intricacies of the derivation and properties of the Green's function employed to solve the three term amplitude equation that determines the response of the toroidal structure to arbitrary external excitations.

- Authors:

- Univ. of South Florida, Tampa, FL (United States). Dept. of Mathematics & Statistics
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of South Florida, Tampa, FL (United States)

- Sponsoring Org.:
- USDOE; ORNL Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1424498

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Physics Communications

- Additional Journal Information:
- Journal Volume: 2; Journal Issue: 1; Journal ID: ISSN 2399-6528

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; plasmon dispersion relations; plasmon three-term vector recurrence; matrix continued fraction; Green's function; infinite determinant

### Citation Formats

```
Garapati, K. V., Bagherian, M., Passian, A., and Kouchekian, S.
```*Plasmon dispersion in a multilayer solid torus in terms of three-term vector recurrence relations and matrix continued fractions*. United States: N. p., 2018.
Web. doi:10.1088/2399-6528/aaa4e3.

```
Garapati, K. V., Bagherian, M., Passian, A., & Kouchekian, S.
```*Plasmon dispersion in a multilayer solid torus in terms of three-term vector recurrence relations and matrix continued fractions*. United States. doi:10.1088/2399-6528/aaa4e3.

```
Garapati, K. V., Bagherian, M., Passian, A., and Kouchekian, S. Wed .
"Plasmon dispersion in a multilayer solid torus in terms of three-term vector recurrence relations and matrix continued fractions". United States.
doi:10.1088/2399-6528/aaa4e3. https://www.osti.gov/servlets/purl/1424498.
```

```
@article{osti_1424498,
```

title = {Plasmon dispersion in a multilayer solid torus in terms of three-term vector recurrence relations and matrix continued fractions},

author = {Garapati, K. V. and Bagherian, M. and Passian, A. and Kouchekian, S.},

abstractNote = {Toroidal confinement, which has played a crucial role in magnetized plasmas and Tokamak physics, is emerging as an effective means to obtain useful electronic and optical response in solids. In particular, excitation of surface plasmons in metal nanorings by photons or electrons finds important applications due to the engendered field distribution and electromagnetic energy confinement. However, in contrast to the case of a plasma, often the solid nanorings are multilayered and/or embedded in a medium. The non-simply connected geometry of the torus results in surface modes that are not linearly independent. A three-term difference equation was recently shown to arise when seeking the nonretarded plasmon dispersion relations for a stratified solid torus (Garapati et al 2017 Phys. Rev. B 95 165422). The reported generalized plasmon dispersion relations are here investigated in terms of the involved matrix continued fractions and their convergence properties including the determinant forms of the dispersion relations obtained for computing the plasmon eigenmodes. We also present the intricacies of the derivation and properties of the Green's function employed to solve the three term amplitude equation that determines the response of the toroidal structure to arbitrary external excitations.},

doi = {10.1088/2399-6528/aaa4e3},

journal = {Journal of Physics Communications},

number = 1,

volume = 2,

place = {United States},

year = {Wed Jan 03 00:00:00 EST 2018},

month = {Wed Jan 03 00:00:00 EST 2018}

}