Using Floquet periodicity to easily calculate dispersion curves and wave structures of homogeneous waveguides

Christopher Hakoda, Joseph Lawrence Rose, Parisa Shokouhi, Clifford Jesse Lissenden, III

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Dispersion curves are essential to any guided-wave-related project. The Semi-Analytical Finite Element (SAFE) method has become the conventional way to compute dispersion curves for homogeneous waveguides. However, only recently has a general SAFE formulation for commercial and open-source software become available, meaning that until now SAFE analyses have been variable and more time consuming than desirable. Likewise, the Floquet boundary conditions enable analysis of waveguides with periodicity and have been an integral part of the development of metamaterials. In fact, we have found the use of Floquet boundary conditions to be an extremely powerful tool for homogeneous waveguides, too. The nuances of using periodic boundary conditions for homogeneous waveguides that do not exhibit periodicity are discussed. Comparisons between this method and SAFE are made for selected homogeneous waveguide applications. The COMSOL Multiphysics software is used for the results shown, but any standard finite element software that can implement Floquet periodicity (user-defined or built-in) should suffice. Finally, we identify a number of complex waveguides for which dispersion curves can be found with relative ease by using the periodicity inherent to the Floquet boundary conditions.

Original languageEnglish (US)
Title of host publication44th Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 37
EditorsDale E. Chimenti, Leonard J. Bond
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735416444
DOIs
StatePublished - Apr 20 2018
Event44th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2017 - Provo, United States
Duration: Jul 16 2017Jul 21 2017

Publication series

NameAIP Conference Proceedings
Volume1949
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

Other44th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2017
CountryUnited States
CityProvo
Period7/16/177/21/17

Fingerprint

periodic variations
waveguides
curves
boundary conditions
computer programs
finite element method
formulations

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Hakoda, C., Rose, J. L., Shokouhi, P., & Lissenden, III, C. J. (2018). Using Floquet periodicity to easily calculate dispersion curves and wave structures of homogeneous waveguides. In D. E. Chimenti, & L. J. Bond (Eds.), 44th Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 37 [020016] (AIP Conference Proceedings; Vol. 1949). American Institute of Physics Inc.. https://doi.org/10.1063/1.5031513
Hakoda, Christopher ; Rose, Joseph Lawrence ; Shokouhi, Parisa ; Lissenden, III, Clifford Jesse. / Using Floquet periodicity to easily calculate dispersion curves and wave structures of homogeneous waveguides. 44th Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 37. editor / Dale E. Chimenti ; Leonard J. Bond. American Institute of Physics Inc., 2018. (AIP Conference Proceedings).
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abstract = "Dispersion curves are essential to any guided-wave-related project. The Semi-Analytical Finite Element (SAFE) method has become the conventional way to compute dispersion curves for homogeneous waveguides. However, only recently has a general SAFE formulation for commercial and open-source software become available, meaning that until now SAFE analyses have been variable and more time consuming than desirable. Likewise, the Floquet boundary conditions enable analysis of waveguides with periodicity and have been an integral part of the development of metamaterials. In fact, we have found the use of Floquet boundary conditions to be an extremely powerful tool for homogeneous waveguides, too. The nuances of using periodic boundary conditions for homogeneous waveguides that do not exhibit periodicity are discussed. Comparisons between this method and SAFE are made for selected homogeneous waveguide applications. The COMSOL Multiphysics software is used for the results shown, but any standard finite element software that can implement Floquet periodicity (user-defined or built-in) should suffice. Finally, we identify a number of complex waveguides for which dispersion curves can be found with relative ease by using the periodicity inherent to the Floquet boundary conditions.",
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Hakoda, C, Rose, JL, Shokouhi, P & Lissenden, III, CJ 2018, Using Floquet periodicity to easily calculate dispersion curves and wave structures of homogeneous waveguides. in DE Chimenti & LJ Bond (eds), 44th Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 37., 020016, AIP Conference Proceedings, vol. 1949, American Institute of Physics Inc., 44th Annual Review of Progress in Quantitative Nondestructive Evaluation, QNDE 2017, Provo, United States, 7/16/17. https://doi.org/10.1063/1.5031513

Using Floquet periodicity to easily calculate dispersion curves and wave structures of homogeneous waveguides. / Hakoda, Christopher; Rose, Joseph Lawrence; Shokouhi, Parisa; Lissenden, III, Clifford Jesse.

44th Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 37. ed. / Dale E. Chimenti; Leonard J. Bond. American Institute of Physics Inc., 2018. 020016 (AIP Conference Proceedings; Vol. 1949).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Hakoda C, Rose JL, Shokouhi P, Lissenden, III CJ. Using Floquet periodicity to easily calculate dispersion curves and wave structures of homogeneous waveguides. In Chimenti DE, Bond LJ, editors, 44th Annual Review of Progress in Quantitative Nondestructive Evaluation, Volume 37. American Institute of Physics Inc. 2018. 020016. (AIP Conference Proceedings). https://doi.org/10.1063/1.5031513