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Thesis (MScEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: An investigation into the cause of undesired sidelobes in the 3D radiation pattern of slotted waveguide arrays is conducted. It is hypothesized that the cross-polarization of the antenna is at fault, along with the possibility that an error is made when designing a linear array. In investigating and finding a solution to the problem, the “Z-slot ” is introduced in conjunction with polarizer plates. The base components are used by a custom optimization algorithm to design reference and solution antennas. Results of the antennas are then compared to ascertain the cause and possible solutions for the unwanted sidelobes. The generic nature of the process may be used to characterize other arbitrary aperture configurations and to design larger antennas. / AFRIKAANSE OPSOMMING: ‘n Ondersoek om die oorsaak van ongewensde sylobbe in die 3D uitstraalpatroon van golfleier-antennas vas te stel. Die hipotese is dat die probleem ontstaan uit die kruis-polarisasie van die antenna, tesame met ‘n verkeerdelikke aanname dat die opstelling liniêr is. Die “Z-Gleuf” tesame met polariseringsplate word voorgestel as hulpmiddel om die moontlikke oorsake te ondersoek. ‘n Gespesialiseerde optime erings-algoritme benut hierdie basiskomponente om beide verwysings- en oplossing-antennas te ontwerp. Resultate van die ontwerpde antennas word dan vergelyk om die oorsaak van die ongewensde sylobbe te vas te stel. Die generiese aard van die proses kan toegepas word op enige gleuf-konfigurasie en om groter antennas mee te ontwerp.

The purpose of this thesis is to study the effects of gain and damping on a nonlinear waveguide array with a strong disorder that is driven in the first site, and try to find regimes which have stable stationary solutions. This has been done with a modified DNLS (Discrete nonlinear Schrödinger equation). Stable stationary solutions were mainly found when the damping was stronger than the gain, but some stable stationary regimes were also found when the gain was stronger than the damping.

Discrete models are used in describing various microscopic phenomena in many branches of science, ranging from biology through chemistry to physics. Arrays of evanescently coupled, equally spaced, identical waveguides are prime examples of optical structures in which discrete dynamics can be easily observed and investigated. As a result of discretization, these structures exhibit unique diffraction properties with no analogy in continuous systems. Recently nonlinear discrete optics has attracted a growing interest, triggered by the observation of discrete solitons in AlGaAs waveguide arrays reported by Eisenberg et al. in 1998. So far, the following experiments involved systems with third order nonlinearities. In this work, an experimental investigation of discrete nonlinear wave propagation in a second order nonlinear medium is presented. This system deserves particular attention because the nonlinear process involves two or three components at different frequencies mutually locked by a quadratic nonlinearity, and new degrees of freedom enter the dynamical process. In the first part of dissertation, observation of the discrete Talbot effect is reported. In contrast to continuous systems, where Talbot self-imaging effect occurs irrespective of the pattern period, in discrete configurations this process is only possible for a specific set of periodicities. The major part of the dissertation is devoted to the investigation of soliton formation in lithium niobate waveguide arrays with a tunable cascaded quadratic nonlinearity. Soliton species with different topology (unstaggered – all channels in-phase, and staggered – neighboring channels with a pi relative phase difference) are identified in the same array. The stability of the discrete solitons and plane waves (modulational instability) are experimentally investigated. In the last part of the dissertation, a phase-insensitive, ultrafast, all-optical spatial switching and frequency conversion device based on quadratic waveguide array is demonstrated. Spatial routing and wavelength conversion of milliwatt signals is achieved without pulse distortions.

The propagation dynamics of light in optical waveguide arrays is characteristic of that encountered in discrete systems. As a result, it is possible to engineer the diffraction properties of such structures, which leads to the ability to control the flow of light in ways that are impossible in continuous media. In this work, a detailed theoretical investigation of both linear and nonlinear optical wave propagation in one- and two-dimensional waveguide lattices is presented. The ability to completely overcome the effects of discrete diffraction through the mutual trapping of two orthogonally polarized coherent beams interacting in Kerr nonlinear arrays of birefringent waveguides is discussed. The existence and stability of such highly localized vector discrete solitons is analyzed and compared to similar scenarios in a single birefringent waveguide. This mutual trapping is also shown to occur within the first few waveguides of a semi-infinite array leading to the existence of vector discrete surface waves. Interfaces between two detuned semi-infinite waveguide arrays or waveguide array heterojunctions and their possible applications are also considered. It is shown that the detuning between the two arrays shifts the dispersion relation of one array with respect to the other. Consequently, these systems provide spatial filtering functions that may prove useful in future all-optical networks. In addition by exploiting the unique diffraction properties of discrete arrays, diffraction compensation can be achieved in a way analogous to dispersion compensation in dispersion managed optical fiber systems. Finally, it is demonstrated that both the linear (diffraction) and nonlinear dynamics of two-dimensional waveguide arrays are significantly more complex and considerably more versatile than their one-dimensional counterparts. As is the case in one-dimensional arrays, the discrete diffraction properties of these two-dimensional lattices can be effectively altered depending on the propagation Bloch k-vector within the first Brillouin zone. In general, this diffraction behavior is anisotropic and as a result, allows the existence of a new class of discrete elliptic solitons in the nonlinear regime. Moreover, such arrays support two-dimensional vector soliton states, and their existence and stability are also thoroughly explored in this work.

Slotted waveguide array (SWGA) antennas find application in systems which require planarity, low profile, high power handling capabilities such as radars. In this thesis, a planar, low sidelobe, phased array antenna, capable of electronically beam scanning in E-plane is designed, manufactured and measured. In the design, slot characterization is done with HFSS and by measurements, and mutual coupling between slots are calculated analytically. A MATLAB code is developed for the synthesis of the SWGA antenna. Grating lobe problem in the scanning array, which is caused by the slot positions, is solved using baffles on the array. A high power feeding section for the planar array, having an amplitude tapering to get low sidelobes is also designed using a corrugated E-plane sectoral horn. The power divider is designed analytically, and simulated and optimized with HFSS.

An X band dual polarized slotted waveguide antenna array is designed with very high polarization purity for both horizontal and vertical polarizations. Horizontally polarized radiators are designed using a novel non-inclined edge wall slots whereas the vertically polarized slots are implemented using broad wall slots opened on baffled single ridge rectangular waveguides. Electromagnetic model based on an infinite array unit cell approach is introduced to characterize the slots used in the array. 20 by 10 element planar array of these slots is manufactured and radiation fields are measured. The measurement results of this array are in very good accordance with the simulation results. The dual polarized antenna possesses a low sidelobe level of -35 dB and is able to scan a sector of &plusmn / 35 degrees in elevation. It also has a usable bandwidth of 600 MHz.

Propagation of coherent waves through disordered media, whether optical, acoustic, or radio waves, results in a spatially redistributed random intensity pattern known as speckle -- a statistical phenomenon. The subject of this dissertation is the statistics of monochromatic coherent light traversing disordered photonic lattices and its dependence on the disorder class, the level of disorder and the excitation configuration at the input. Throughout the dissertation, two disorder classes are considered, namely, diagonal and off-diagonal disorders. The latter exhibits disorder-immune chiral symmetry -- the appearance of the eigenmodes in skew-symmetric pairs and the corresponding eigenvalues in opposite signs. When a disordered photonic lattice, an array of evanescently coupled waveguides, is illuminated with an extended coherent optical field, discrete speckle develops. Numerical simulations and analytical modeling reveal that discrete speckle shows a set of surprising features, that are qualitatively indistinguishable in both disorder classes. First, the fingerprint of transverse Anderson localization -- associated with disordered lattices, is exhibited in the narrowing of the spatial coherence function. Second, the transverse coherence length (or speckle grain size) freezes upon propagation. Third, the axial coherence depth is independent of the axial position, thereby resulting in a coherence voxel of fixed volume independently of position. When a single lattice site is coherently excited, I discovered that a thermalization gap emerges for light propagating in disordered lattices endowed with disorder-immune chiral symmetry. In these systems, the span of sub-thermal photon statistics is inaccessible to the input coherent light, which -- once the steady state is reached -- always emerges with super-thermal statistics no matter how small the disorder level. An independent constraint of the input field for the chiral symmetry to be activated and the gap to be observed is formulated. This unique feature enables a new form of photon-statistics interferometry: by exciting two lattice sites with a variable relative phase, as in a traditional two-path interferometer, the excitation-symmetry of the chiral mode pairs is judiciously broken and interferometric control over the photon statistics is exercised, spanning sub-thermal and super-thermal regimes. By considering an ensemble of disorder realizations, this phenomenon is demonstrated experimentally: a deterministic tuning of the intensity fluctuations while the mean intensity remains constant. Finally, I examined the statistics of the emerging light in two different lattice topologies: linear and ring lattices. I showed that the topology dictates the light statistics in the off-diagonal case: for even-sited ring and linear lattices, the electromagnetic field evolves into a single quadrature component, so that the field takes discrete phase values and is non-circular in the complex plane. As a consequence, the statistics become super-thermal. For odd-sited ring lattices, the field becomes random in both quadratures resulting in sub-thermal statistics. However, this effect is suppressed due to the transverse localization of light in lattices with high disorder. In the diagonal case, the lattice topology does not play a role and the transmitted field always acquires random components in both quadratures, hence the phase distribution is uniform in the steady state.