Tailored two-dimensional finite-element formulations for ad-hoc analysis of waveguiding and mode-matching problems
Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/369504
Tipus de documentText en actes de congrés
Data publicació2022
EditorUniversitat Politècnica de Catalunya. Remote Sensing, Antennas, Microwaves and Superconductivity Group (CommSensLab)
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 4.0 Internacional
Abstract
The analysis of homogeneous closed waveguides is known to be one of the first, if not the very
first, problems to be addressed with the finite element method (P. Silvester, “Finite element solution
of homogeneous waveguide problems”, Alta Frequenza, vol. 38, pp. 313–317, 1969) in the
framework of computational electromagnetics. Since this two-dimensional scalar case, many
developments have followed: extension to three-dimensional analysis, derivation of curlconforming
edge and higher-order elements, domain decomposition approaches, hybridization with
other numerical or analytical methods, etc. This has led the finite element method to be considered
one of the most well-established, reliable techniques to address cutting-edge problems in
computational electromagnetics, with many reference books (G. Pelosi, R. Coccioli, S. Selleri,
Quick Finite Elements for Electromagnetic Waves, Norwood, MA, USA: Artech House, 2009; J.
Jin, The Finite Element Method in Electromagnetics, Hoboken, NJ, USA: Wiley, 2015).
Despite these long-known advancements, resorting to solving the afore-mentioned (and, at first
glance, simple) problem of computing the modes in any waveguiding cross-section still plays a key
role in computer-aided design methodologies that rely on the modal description of the fields, as is
the case of the mode-matching method. In this case, not only an accurate calculation of these modal
fields is required, but also the capability to compute as many modes (without skipping a single one)
as necessary to ensure convergence. If the problem demands for it, it is also imperative to have a
straightforward division into different classes or types of modes according to symmetries and
possible excitations, as well as a proper identification of degenerate modes.
In this work, we will review some strategies and tailored two-dimensional finite-element
formulations proposed by the authors to address some of the issues arising when analyzing
waveguiding structures, especially focusing on obtaining proper modal decompositions of the fields
to be used in further computer-aided design of waveguide devices through mode-matching
techniques. Some of these strategies and formulations include the comparison of different types of
meshes (structured quadrilateral vs. unstructured triangular) when the waveguide cross-sections
have 90º corners, as well as the development of specific boundary conditions to model novel
materials enclosing the waveguide (such as graphene) or to account for higher-order symmetries
(such as rotational ones) in structures with a high number of degenerate modes. In the latter case,
this is especially useful for devices conceived to operate with circular polarization.
CitacióHosein Rasekhmanesh, M. [et al.]. Tailored two-dimensional finite-element formulations for ad-hoc analysis of waveguiding and mode-matching problems. A: EIEC 2022. "XIV Iberian Meeting on Computational Electromagnetics". Universitat Politècnica de Catalunya. Remote Sensing, Antennas, Microwaves and Superconductivity Group (CommSensLab), 2022,
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