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A higher-order spectral element method for modeling eccentric anisotropic multilayered waveguides via transformation optics

Published online by Cambridge University Press:  19 February 2025

Raul O. Ribeiro Open the ORCID record for Raul O. Ribeiro [Opens in a new window] ,
Guilherme S. Rosa Open the ORCID record for Guilherme S. Rosa [Opens in a new window] ,
José R. Bergmann Open the ORCID record for José R. Bergmann [Opens in a new window]  and
Fernando L. Teixeira Open the ORCID record for Fernando L. Teixeira [Opens in a new window]
Raul O. Ribeiro*
Affiliation:
School of Engineering, São Paulo State University (UNESP), São João da Boa Vista, SP, Brazil
Guilherme S. Rosa
Affiliation:
School of Engineering, São Paulo State University (UNESP), São João da Boa Vista, SP, Brazil
José R. Bergmann
Affiliation:
Department of Electrical Engineering, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil
Fernando L. Teixeira
Affiliation:
ElectroScience Laboratory, The Ohio State University, Columbus, OH, USA
*
Corresponding author: Raul O. Ribeiro; Email: [email protected]
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Abstract

We present a higher-order spectral element method (SEM) for analyzing eccentric anisotropic multilayered waveguides. The formulation uses conformal transformation optics to map the original eccentric waveguide to an equivalent concentric one. This transformation is extended to handle anisotropic non-reciprocal media characterized by non-symmetric and non-Hermitian tensors. In the transformed concentric domain, higher-order two-dimensional basis functions associated with the zeros of the completed Lobatto polynomial are used to expand the fields. To simulate radially unbounded problems, we employ a complex-stretched perfectly matched layer to mimic open space. The method is validated with radially bounded two-layer and three-layer waveguides and radially unbounded three-layer waveguides. Comparisons with the finite element method (FEM) demonstrate that our SEM approach requires significantly fewer degrees of freedom than FEM.

Keywords

anisotropic non-reciprocal mediaeccentric multilayered waveguidespectral element methodtransformation optics
Type
Research Paper
Information
International Journal of Microwave and Wireless Technologies , First View , pp. 1 - 8
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Copyright
© The Author(s), 2025. Published by Cambridge University Press in association with The European Microwave Association.

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References

Gholizadeh, M, Baharian, M and Kashani, FH (2019) A simple analysis for obtaining cutoff wavenumbers of an eccentric circular metallic waveguide in bipolar coordinate system. IEEE Transactions on Microwave Theory and Techniques 67, 837–844.CrossRefGoogle Scholar
Gholizadeh, M and Hojjat Kashani, F (2020) A new analytical method for calculating the cutoff frequencies of an eccentrically dielectric-loaded circular waveguide. IEEE Microwave and Wireless Technology Letters 30, 453–456.CrossRefGoogle Scholar
Gholizadeh, M and Hojjat Kashani, F (2021) Analytical solution of higher order modes of a dielectric-lined eccentric coaxial cable. International Journal of Microwave and Wireless Technologies 13, 247–254.CrossRefGoogle Scholar
Gonçalves, JR, Rosa, GS and Teixeira, FL (2021) Perturbative analysis of anisotropic coaxial waveguides with small eccentricities via conformal transformation optics. IEEE Transactions on Microwave Theory and Techniques 69, 3958–3966.CrossRefGoogle Scholar
Gonçalves, JR, Rosa, GS and Teixeira, FL (2022) Perturbation solution for anisotropic circular waveguides loaded with eccentric rods. IEEE Microwave and Wireless Technology Letters 32, 935–938.CrossRefGoogle Scholar
Rosa, GS, Bergmann, JR, Teixeira, FL and Novo, MS (2018) A perturbation-based method to model electromagnetic logging sensors in eccentric boreholes via conformal transformation optics. In 12th Eur. Conf. Antennas Propag. (EuCAP), London, UK, .Google Scholar
Mao, S-C, Wu, Z-S, Zhang, Z, Gao, J and Yang, L (2020) Scattering of a Gaussian beam by an anisotropic-coated eccentric conducting circular cylinder. International Journal of Microwave and Wireless Technologies 12, 900–905.CrossRefGoogle Scholar
Liu, G-S, Teixeira, FL and Zhang, G-J (2012) Analysis of directional logging tools in anisotropic and multieccentric cylindrically-layered earth formations. IEEE Transactions on Antennas and Propagation 60, 318–327.CrossRefGoogle Scholar
Liu, N, Cai, G, Zhu, C, Tang, Y and Liu, QH (2015) The mixed spectral-element method for anisotropic, lossy, and open waveguides. IEEE Transactions on Microwave Theory and Techniques 63, 3094–3102.CrossRefGoogle Scholar
Liu, J, Jiang, W, Liu, N and Liu, QH (2019) Mixed spectral-element method for the waveguide problem with bloch periodic boundary conditions. IEEE Transactions on Electromagnetic Compatibility 61, 1568–1577.CrossRefGoogle Scholar
Ribeiro, RO, Rosa, GS and Bergmann, JR (2022) An improved formulation of the spectral element method in cylindrical coordinates for the analysis of anisotropic-filled waveguide devices. In 2022 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (AP-S/URSI), Denver, CO, USA. .CrossRefGoogle Scholar
Ribeiro, RO, Rosa, GS, Bergmann, JR and Teixeira, FL (2023) A novel high-order spectral element method for the analysis of cylindrical waveguides filled with complex anisotropic media. In 2023 17th Eur. Conf. on Antennas and Propag. (EuCAP), Florence, Italy, .Google Scholar
Ribeiro, RO, Gonçalves, JR, Rosa, GS, Bergmann, JR and Teixeira, FL (2024) Higher order spectral element method for rapid analysis of eccentric coaxial waveguides filled with lossy anisotropic media. IEEE Transactions on Microwave Theory and Techniques 72, 3322–3333.CrossRefGoogle Scholar
Ribeiro, RO, Rosa, GS, Bergmann, JR and Teixeira, FL (2023) Spectral element method for modeling anisotropic circular waveguides loaded with eccentric rods via conformal transformation optics. In 2023 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (USNC-URSI). .CrossRefGoogle Scholar
Ribeiro, RO, Rosa, GS, Bergmann, JR and Teixeira, FL (2024) A higher-order spectral element method to model eccentric anisotropic two-layer waveguides via conformal transformation optics. In 2024 18th Eur. Conf. on Antennas and Propag. (EuCAP), Glasgow, UK, .Google Scholar
Teixeira, F and Chew, W (1999) Differential forms, metrics, and the reflectionless absorption of electromagnetic waves. Journal of Electromagnetic Waves and Applications 13, 665–686.CrossRefGoogle Scholar
Xu, L and Chen, H (2015) Conformal transformation optics. Nature Photonics 9, 15–23.CrossRefGoogle Scholar
Vardapetyan, L and Demkowicz, L (2002) Full-wave analysis of dielectric waveguides at a given frequency. Mathematics of Computation 72, 105–129.CrossRefGoogle Scholar
Monk, P et al. (2003) Finite Element Methods for Maxwell’s Equations. New York, USA: Oxford University Press.CrossRefGoogle Scholar
Ribeiro, RO (2024) Higher-order Spectral Element Methods for Electromagnetic Modeling of Complex Anisotropic Waveguides, Ph.D. Dissertation, Dept. Elect. Eng., Rio de Janeiro, Brazil: Pontifical Catholic University Rio de Janeiro. https://doi.org/10.17771/PUCRio.acad.68605.Google Scholar
Pozrikidis, C (2014) Introduction to Finite and Spectral Element Methods Using MATLAB. Boca Raton, FL, USA: Chapman & Hall Book.CrossRefGoogle Scholar
Teixeira, F and Chew, W (1997) Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates. IEEE Microwave and Wireless Technology Letters 7, 371–373.Google Scholar
Teixeira, F and Chew, W (1998) General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media. IEEE Microwave and Wireless Technology Letters 8, 223–225.Google Scholar
Rosa, GS (2017) Pseudo-analytical Modeling for Electromagnetic Well-logging Tools in Complex Geophysical Formations, Ph.D. Dissertation, Dept. Elect. Eng., Rio de Janeiro, RJ, Brazil: Pontifical Catholic University of Rio de Janeiro.Google Scholar
Chew, WC and Weedon, WH (1994) A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates. Microwave and Optical Technology Letters 7, 599–604.CrossRefGoogle Scholar
Chew, WC, Jin, JM and Michielssen, E (1997) Complex coordinate stretching as a generalized absorbing boundary condition. Microwave and Optical Technology Letters 15, 363–369.3.0.CO;2-C>CrossRefGoogle Scholar
Teixeira, FL and Chew, WC (2000) Complex space approach to perfectly matched layers: A review and some new developments. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 13, 441–455.3.0.CO;2-J>CrossRefGoogle Scholar
, COMSOL, COMSOL Multiphysics reference manual version 5.4, Inc., [Online]. Available: https://doc.comsol.com, 2018.Google Scholar
MATLAB version 9.12.0.2009381 (R2022a) Update 4, The Mathworks, Inc., Natick, Massachusetts, 2022.Google Scholar