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.

This thesis investigates lens antennas for future wireless applications. The aim is to provide robust and cost-effective antenna solutions with wide-angle beam steering capabilities. The wide-angle beam steering is obtained using rotationally symmetric inhomogeneous lenses, such as the Luneburg lens. The derivation of the inhomogeneous refractive index using geometrical optics is outlined. Parallel plate waveguide (PPW) lens antennas and volumetric lens antennas are investigated. 

The studied PPW lens antennas are designed to be robust to manufacturing and assembly errors while enabling a high radiation efficiency and wide-angle steering of a fan-shaped beam. The refractive index distribution is mimicked using quasi-periodic structures or by shaping the PPW. Specifically, two robust and cost-effective glide-symmetric quasi-periodic structures are proposed. First, glide-symmetric substrate-integrated holes (SIHs) are proposed, since they enable a larger PPW spacing compared to previously reported fully-metallic designs. This large PPW spacing translates into a robust antenna solution, and the SIH structure can be cost-effectively manufactured. The presence of the dielectric introduces losses, but it is shown that these added losses are sufficiently low for many applications at K_a-band. Secondly, a glide-symmetric perforated dielectric slab is proposed to enable an even larger PPW spacing. The slab is produced using additive manufacturing and it is shown that by arranging the perforations glide-symmetrically, a wider range of effective refractive indices can be accurately realized. Again, it is shown that the added losses due to the dielectric are sufficiently low for practical applications at K_a-band. Fully-metallic (and therefore highly efficient) PPW lens antennas can be based on geodesic lenses. These lenses do not require the realization of any small features and can therefore be robust. A geodesic lens antenna demonstrator at V-band is presented, and techniques of reducing the sensitivity to manufacturing errors are proposed. These techniques are later used in the design of a geodesic lens antenna with reduced gain variation within the beam steering range compared to the reference works. This geodesic lens is based on the generalized Luneburg lens. Providing a low gain variation in the steering range ensures a good quality of service to all end users. 

Additive manufacturing provides attractive opportunities for the realization of volumetric inhomogeneous lens antennas capable of producing directive pencil beams that can be steered in a wide angular range. However, the effective refractive index range of quasi-periodic dielectric structures is often limited by the smallest realizable geometrical detail, and the reported volumetric inhomogeneous lenses are often truncated, which impacts their focusing properties. In this thesis, the impact of the lattice arrangements is discussed and it is demonstrated that by using highly symmetric lattice arrangements, the realizable effective refractive index range can be increased. Furthermore, a new lens, accounting for the manufacturing constraints, is also proposed. This lens operates similarly to the Luneburg lens, but it has a refractive index distribution that can be tuned to alleviate the manufacturing.

Denna avhandling undersöker linsantenner för framtida trådlösa tillämpningar. Målet är att tillhandahålla robusta och kostnadseffektiva antennlösningarmed bred strålstyrningsförmåga. Den breda strålstyrningen uppnås med hjälp av rotationsymmetriska inhomogena linser, såsom Luneburg-linsen. Härledningen av det inhomogena brytningsindexet med geometrisk optik beskrivs. Linsantenner implementerade i planvågledare (PPW) och volymetriskalinsantenner undersöks.

De studerade PPW-linsantennerna är konstruerade för att vara robusta mot tillverknings- och monteringsfel samtidigt som de möjliggör hög strålningseffektivitet och strålstyrning i ett brett vinkelspann. Linsens brytningsindex realiseras med hjälp av kvasiperiodiska strukturer eller genom att modifiera vågledaren. Specifikt föreslås två robusta och kostnadseffektiva glidsymmetriska kvasiperiodiska strukturer. För det första används glidsymmetriska substratintegrerade hål (SIHs) för att möjliggöra ett större PPW-avstånd jämfört med tidigare rapporterade helt metalliska konstruktioner. Detta stora PPW-avstånd leder till en robust antennlösning, och SIH-strukturen kan tillverkas kostnadseffektivt. Närvaron av dielektrikat medför förluster, men det visar sig att dessa uppkomna förluster är tillräckligt låga för många tillämpningar i K_a-bandet. För det andra används en glidsymmetrisk perforerad dielektrisk skiva för att möjliggöra ett ännu större PPW-avstånd. Skivan tillverkas additivt genom att arrangera perforationerna glidsymmetriskt vilket möjliggör att fler effektiva brytningsindex kan realiseras. Återigen visas det att de tillkomna förlusterna på grund av dielektrikat är tillräckligt låga för praktiska tillämpningar i K_a-bandet. Helt metalliska (och högeffektiva) PPW-linsantenner kan baseras på geodesiska linser. Dessa linser kräver inte realisering av små detaljer och kan därför vara robusta. En demonstrator av en geodesisk linsantenn för V-bandet presenteras, och tekniker för att minska känsligheten för tillverkningsfel föreslås. Dessa tekniker används senare i designen av en geodesisk linsantenn med reducerad variation i antennförstärkningen inom strålstyrningsintervallet jämfört med referensverk i litteraturen. Denna geodesiska lins baseras på den generaliserade Luneburg-linsen.

Additiv tillverkning erbjuder attraktiva möjligheter för realisering av volymetriska inhomogena linsantenner som kan producera hög-direktiva strålar som kan styras över ett brett vinkelspann. Dock begränsas det realiserbara spannet av det effektiva brytningsindexet för kvasiperiodiska dielektriskastrukturer av den minsta realiserbara geometriska detaljen, och volymetriska inhomogena linser i litteraturen är ofta trunkerade, vilket påverkar deras fokuseringsegenskaper. I denna avhandling diskuteras inverkan av kristallstrukturen på det effektiva brytningsindexet, och det visas att genom att använda symmetriska kristallstrukturer kan fler effektiva brytningsindex realiseras. Dessutom föreslås en ny lins som tar hänsyn till tillverkningsbegränsningarna. Denna lins fungerar på ett liknande sätt som Luneburg-linsen, men den har ett brytningsindex som kan justeras för att lättare kunna tillverkas.