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The Multimodal Transfer Matrix Method: And its application to higher-symmetric periodic structures
KTH, School of Electrical Engineering and Computer Science (EECS), Electrical Engineering, Electromagnetic Engineering.ORCID iD: 0000-0003-2095-121x
2022 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis focuses on the understanding and computation of the dispersion properties of periodic structures possessing higher symmetries with the multimodal transfer matrix method (MMTMM). Periodic structures with higher symmetries are invariant after additional symmetry operations over the translation operation. To demonstrate the potential of the MMTMM, three structures with spatial higher symmetries are proposed and their operation explained based on the constituent modes. 

In this thesis, I propose, analyze and explain the operation of two structures possessing glide symmetry and one with twist symmetry. Glide-symmetric structures remain invariant after a mirroring and a translation whereas twist-symmetric structures remain invariant after n rotations and translations. These structures inherently have low dispersion due to the interactions of the fundamental mode with higher order modes.

The MMTMM has been implemented in order to efficiently compute the complex propagation constant of these structures. This is a hybrid method that models a unit cell as a multiport network. Each port accounts for one mode, so the coupling between modes is considered. Commercial software is used to compute the ABCD-matrix, then post-processing is used to get both the phase and attenuation constant due to material losses, electromagnetic bandgaps and/or radiation. This method permits the study of complex structures while enabling a fundamental understanding of the modes that contribute to the dispersion properties, as well as their interactions. 

The first periodic structure analyzed in this thesis is a dielectric-filled corrugated waveguide. It allows the propagation of a backward mode in a wide frequency band. A discussion on the convergence of the method concludes that it is needed families of TE/TM modes with the same number of variations in the x direction. 

The second structure is a glide-symmetric dielectric unit cell placed in a parallel plate waveguide. This unit cell can be used to produce planar lens antennas that can be cost-effectively manufactured with dielectric 3D-printers. The attenuation constant due to material losses in two different directions is computed using the MMTMM.

Finally, a 3-fold twist-symmetric dielectric open waveguide is analyzed. Its interest lies in its inherent circular polarization selectivity. Here, the MMTMM is used to compute the attenuation constant from material losses and the stopband, as well as to understand the interaction between linear and circularly polarized modes.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2022. , p. 38
Series
TRITA-EECS-AVL ; 2022:39
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-318520ISBN: 978-91-8040-247-7 (print)OAI: oai:DiVA.org:kth-318520DiVA, id: diva2:1697765
Presentation
2022-10-21, H1 room, Teknikringen 33, floor 5, Stockholm, 15:00 (English)
Opponent
Supervisors
Note

QC 20220926

Available from: 2022-09-26 Created: 2022-09-21 Last updated: 2022-10-28Bibliographically approved
List of papers
1. Study of Forward and Backward Modes in Double-Sided Dielectric-Filled Corrugated Waveguides
Open this publication in new window or tab >>Study of Forward and Backward Modes in Double-Sided Dielectric-Filled Corrugated Waveguides
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2021 (English)In: Sensors, E-ISSN 1424-8220, Vol. 21, no 18, article id 6293Article in journal (Refereed) Published
Abstract [en]

This work studies the propagation characteristics of a rectangular waveguide with aligned/misaligned double-sided dielectric-filled metallic corrugations. Two modes are found to propagate in the proposed double-sided configuration below the hollow-waveguide cutoff frequency: a quasi-resonant mode and a backward mode. This is in contrast to the single-sided configuration, which only allows for backward propagation. Moreover, the double-sided configuration can be of interest for waveguide miniaturization on account of the broader band of its backward mode. The width of the stopband between the quasi-resonant and backward modes can be controlled by the misalignment of the top and bottom corrugations, being null for the glide-symmetric case. The previous study is complemented with numerical results showing the impact of the height of the corrugations, as well as the filling dielectric permittivity, on the bandwidth and location of the appearing negative-effective-permeability band. The multi-modal transmission-matrix method has also been employed to estimate the rejection level and material losses in the structure and to determine which port modes are associated with the quasi-resonant and backward modes. Finally, it is shown that glide symmetry can advantageously be used to reduce the dispersion and broadens the operating band of the modes.

Place, publisher, year, edition, pages
MDPI AG, 2021
Keywords
corrugated waveguide, glide symmetry, higher symmetries, Bloch analysis
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-303193 (URN)10.3390/s21186293 (DOI)000701124000001 ()34577500 (PubMedID)2-s2.0-85115142355 (Scopus ID)
Note

QC 20211011

Available from: 2021-10-11 Created: 2021-10-11 Last updated: 2022-09-21Bibliographically approved
2. Two-Dimensional Glide-Symmetric Dielectric Structures for Planar Graded-Index Lens Antennas
Open this publication in new window or tab >>Two-Dimensional Glide-Symmetric Dielectric Structures for Planar Graded-Index Lens Antennas
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2021 (English)In: IEEE Antennas and Wireless Propagation Letters, ISSN 1536-1225, E-ISSN 1548-5757, Vol. 20, no 11, p. 2171-2175Article in journal (Refereed) Published
Abstract [en]

In this letter, we propose and study a 2-D glide-symmetric dielectric periodic structure. We demonstrate that glide symmetry broadens the bandwidth of operation and achieves lower effective refractive indices when compared to non-glide configurations. These two properties are beneficial for producing graded-index lens antennas. To demonstrate the potential of the proposed unit cell, we designed a Luneburg lens operating in the K- and K-a-bands. The lens was manufactured with conventional additive manufacturing and it has a potential use for future wireless communications given its low-cost and low-profile.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2021
Keywords
Additive manufacturing, dielectric lens antennas, glide symmetry, Luneburg lens
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-305769 (URN)10.1109/LAWP.2021.3092169 (DOI)000719561800023 ()2-s2.0-85112065139 (Scopus ID)
Note

QC 20211206

Available from: 2021-12-06 Created: 2021-12-06 Last updated: 2024-05-08Bibliographically approved
3. Dispersion Analysis of Twist-Symmetric Dielectric Waveguides
Open this publication in new window or tab >>Dispersion Analysis of Twist-Symmetric Dielectric Waveguides
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2021 (English)In: Photonics, E-ISSN 2304-6732, Vol. 8, no 6, p. 206-206Article in journal (Refereed) Published
Abstract [en]

 We propose a circular twist-symmetric dielectric waveguide that is polarization-selective.In the practical implementation of optical fibers, a selective circular polarization is more convenientthan its linearly polarized counterpart where previous knowledge of the emitted polarization fromthe transmitter is unknown. The analysis of the waveguide was conducted with three methods: aneigenmode approach, simulation of a truncated structure, and the so-called multimodal transfermatrix method (MMTMM). The presented simulations demonstrate that the operational band canbe manipulated by tuning the parameters of the structure. Furthermore, the MMTMM allows for adirect and accurate calculation of the attenuation constant of the rejected circular polarization.

Place, publisher, year, edition, pages
MDPI AG, 2021
Keywords
: higher symmetries, twist symmetries, frequency dispersion, multimodal analysis, circular polarization
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-318193 (URN)10.3390/photonics8060206 (DOI)000665886300001 ()2-s2.0-85108431990 (Scopus ID)
Note

QC 20220920

Available from: 2022-09-16 Created: 2022-09-16 Last updated: 2022-09-21Bibliographically approved

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