Accurate cutoff wavenumbers of a waveguide perturbed by axially aligned inner conductors

Paul D. Smith, Elena D. Vinogradova, Yu V. Shestopalov

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionResearchpeer-review

Abstract

Time-harmonic propagating modes in a perfectly electrically conducting waveguide with constant cross-section ∂D and axis aligned with the z-axis have the form u(x,y)e -iωt-iγz where the cross-sectional function u satisfies the two-dimensional Helmholtz equation (Δ+λ)u=0; here k denotes the wavenumber and λ = k 22 . Propagating modes occur at values λ1 ≤ λ2 ≤ λ3 ≤ ... of λ generating non-trivial solutions of the Helmholtz equation; the cutoff wavenumbers correspond to setting γ to zero. Now suppose that axially aligned PEC structures of cross-section Γ are inserted in the waveguide. The propagation constants are perturbed to values that may be denoted λ1+Δλ1,λ2+Δλ2,...; the cutoff wavenumbers of the empty waveguide are correspondingly perturbed. In this paper we present a reliable, effective and efficient method to obtain the perturbed propagation constants. It allows us to examine the inclusion of multiple strips aligned with the z-axis, with the potential for characterizing propagation in structures with a number of small strip inserts, metamaterial-filled waveguides and so on.

LanguageEnglish
Title of host publicationProceedings of the 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA)
Place of PublicationPiscataway, NJ
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages1049
Number of pages1
ISBN (Electronic)9781728105635, 9781728105628
ISBN (Print)9781728105642
DOIs
Publication statusPublished - 2019
Event21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019 - Granada, Spain
Duration: 9 Sep 201913 Sep 2019

Conference

Conference21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019
CountrySpain
CityGranada
Period9/09/1913/09/19

Fingerprint

Conductor
Waveguide
Waveguides
Helmholtz equation
Propagation
Helmholtz Equation
Strip
Cross section
Metamaterials
Nontrivial Solution
Harmonic
Inclusion
Denote
Zero

Cite this

Smith, P. D., Vinogradova, E. D., & Shestopalov, Y. V. (2019). Accurate cutoff wavenumbers of a waveguide perturbed by axially aligned inner conductors. In Proceedings of the 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA) (pp. 1049). Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/ICEAA.2019.8879114
Smith, Paul D. ; Vinogradova, Elena D. ; Shestopalov, Yu V. / Accurate cutoff wavenumbers of a waveguide perturbed by axially aligned inner conductors. Proceedings of the 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA). Piscataway, NJ : Institute of Electrical and Electronics Engineers (IEEE), 2019. pp. 1049
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abstract = "Time-harmonic propagating modes in a perfectly electrically conducting waveguide with constant cross-section ∂D and axis aligned with the z-axis have the form u(x,y)e -iωt-iγz where the cross-sectional function u satisfies the two-dimensional Helmholtz equation (Δ+λ)u=0; here k denotes the wavenumber and λ = k 2 -γ 2 . Propagating modes occur at values λ1 ≤ λ2 ≤ λ3 ≤ ... of λ generating non-trivial solutions of the Helmholtz equation; the cutoff wavenumbers correspond to setting γ to zero. Now suppose that axially aligned PEC structures of cross-section Γ are inserted in the waveguide. The propagation constants are perturbed to values that may be denoted λ1+Δλ1,λ2+Δλ2,...; the cutoff wavenumbers of the empty waveguide are correspondingly perturbed. In this paper we present a reliable, effective and efficient method to obtain the perturbed propagation constants. It allows us to examine the inclusion of multiple strips aligned with the z-axis, with the potential for characterizing propagation in structures with a number of small strip inserts, metamaterial-filled waveguides and so on.",
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Smith, PD, Vinogradova, ED & Shestopalov, YV 2019, Accurate cutoff wavenumbers of a waveguide perturbed by axially aligned inner conductors. in Proceedings of the 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA). Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, pp. 1049, 21st International Conference on Electromagnetics in Advanced Applications, ICEAA 2019, Granada, Spain, 9/09/19. https://doi.org/10.1109/ICEAA.2019.8879114

Accurate cutoff wavenumbers of a waveguide perturbed by axially aligned inner conductors. / Smith, Paul D.; Vinogradova, Elena D.; Shestopalov, Yu V.

Proceedings of the 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA). Piscataway, NJ : Institute of Electrical and Electronics Engineers (IEEE), 2019. p. 1049.

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionResearchpeer-review

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N2 - Time-harmonic propagating modes in a perfectly electrically conducting waveguide with constant cross-section ∂D and axis aligned with the z-axis have the form u(x,y)e -iωt-iγz where the cross-sectional function u satisfies the two-dimensional Helmholtz equation (Δ+λ)u=0; here k denotes the wavenumber and λ = k 2 -γ 2 . Propagating modes occur at values λ1 ≤ λ2 ≤ λ3 ≤ ... of λ generating non-trivial solutions of the Helmholtz equation; the cutoff wavenumbers correspond to setting γ to zero. Now suppose that axially aligned PEC structures of cross-section Γ are inserted in the waveguide. The propagation constants are perturbed to values that may be denoted λ1+Δλ1,λ2+Δλ2,...; the cutoff wavenumbers of the empty waveguide are correspondingly perturbed. In this paper we present a reliable, effective and efficient method to obtain the perturbed propagation constants. It allows us to examine the inclusion of multiple strips aligned with the z-axis, with the potential for characterizing propagation in structures with a number of small strip inserts, metamaterial-filled waveguides and so on.

AB - Time-harmonic propagating modes in a perfectly electrically conducting waveguide with constant cross-section ∂D and axis aligned with the z-axis have the form u(x,y)e -iωt-iγz where the cross-sectional function u satisfies the two-dimensional Helmholtz equation (Δ+λ)u=0; here k denotes the wavenumber and λ = k 2 -γ 2 . Propagating modes occur at values λ1 ≤ λ2 ≤ λ3 ≤ ... of λ generating non-trivial solutions of the Helmholtz equation; the cutoff wavenumbers correspond to setting γ to zero. Now suppose that axially aligned PEC structures of cross-section Γ are inserted in the waveguide. The propagation constants are perturbed to values that may be denoted λ1+Δλ1,λ2+Δλ2,...; the cutoff wavenumbers of the empty waveguide are correspondingly perturbed. In this paper we present a reliable, effective and efficient method to obtain the perturbed propagation constants. It allows us to examine the inclusion of multiple strips aligned with the z-axis, with the potential for characterizing propagation in structures with a number of small strip inserts, metamaterial-filled waveguides and so on.

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Smith PD, Vinogradova ED, Shestopalov YV. Accurate cutoff wavenumbers of a waveguide perturbed by axially aligned inner conductors. In Proceedings of the 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA). Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE). 2019. p. 1049 https://doi.org/10.1109/ICEAA.2019.8879114