Thesis (MSc)--University of Stellenbosch, 2005. / ENGLISH ABSTRACT: The beam quality factor (M2) of a laser is important because it describes both the quality of a laser beam as well as its propagation. Particular applications require that the beam radii (from which the M2 factor is determined) be defined in a specific way. The International Standards Organisation (ISO) recently standardised the theoretically correct, but practically difficult second moment definition of the beam radius. This thesis aims to establish correlations between the second moment definition and other more practical definitions. Chapter 2 presents a systematic introduction of moment theory for general beams. Beam centre and radius definitions as well as beam classification are derived by means of second and mixed moments. In Chapter 3 simple laser beams are modelled by means of a resonator approach. The infinite number of solutions of this model is called Gaussian solutions, which are found to be different for rectangular and cylindrical symmetric resonators. The zero order solution for both symmetries is identified as the ideal solution to which all others can be compared to for quality determinations. Chapter 4 presents different beam scanning devices, beam radius definitions and correlations between these definitions. The theoretical basis for a new correlation theory is also given. Chapter 5 describes programs and computations used to verify existing correlation methods and to calculate correlation factors for a newly proposed theory. Chapter 6 presents the results of the computations for both circular and rectangular symmetric beams. The ISO’s correlation theories are tested first. Newly proposed correlation functions between the second moment and alternative definitions as well as theoretical error graphs are given for various beams. A novel method to correlate several important beam subclasses is also presented. Chapter 7 describes the experimental setup, automation software and post processing techniques that were used to characterise a modified CO2 TEA laser. It is further shown how the theory developed in previous chapters could be applied to the experimental data. Chapter 8 presents the experimental results of the beam characterisation measurements performed on two different beams that emanated from the CO2 TEA laser. Existing and newly developed correlation theories are applied to the experimental data and the corresponding results are compared. In Chapter 9, conclusions and suggestions with respect to the initial aims identified in the first chapter are made. Several suggestions for future work are also made. / AFRIKAANSE OPSOMMING: Die bundel kwalitietsfaktor (M2) is baie belangrik omdat dit beide die kwaliteit en voortplanting van ‘n laser bundel beskryf. Bundel radiusse (waarvan die M2 faktor bepaal word) word verskillend gedefinieer vir spesifike toepassings. Die teoreties korrekte, maar minder praktiese tweede moment definisie is onlangs deur die Internasionale Standaard Organisasie (ISO) gestandariseer. Hierdie tesis se hoofdoel is om die tweede moment definisie en ander meer praktiese definisies te korreleer. Hoofstuk 2 stel die moment teorie van bundels sistematies bekend. Dit word gewys hoe die senter en radius van ‘n bundel deur tweede en gemengde momente gedefinieer kan word. In Hoofstuk 3 word laser bundels gemodeleer deur middel van resonator aanslag. Die oneindige aantal oplossings wat verkry word heet Gaussiese oplossings en is verskillend vir reghoekige en silindriese simmetriese resonators. Dit word gewys dat die ideale bundel, waarmee alle ander bundels vergelyk word, die zero orde oplossing van beide simmetrieë is. Hoofstuk 4 stel verskillende bundel skanderings apparaat, bundel radius definisies en korrelasies tussen die definisies bekend. Die teoretiese basis vir ‘n nuwe korrelasie teorie word ook gegee. Hoofstuk 5 beskryf die rekenaarprogramme en berekeninge wat gebruik word om huidige korrelasie teorie mee te toets asook om nuwes mee te skep. Hooftuk 6 gee die resultate van die berekeninge van die rekenaarprogramme vir beide reghoekig en silindriese simmetrie. Die ISO se korrelasies word eerste getoets voordat nuwe teorieë bekend gestel word. In Hoofstuk 7 word die eksperimentele opstelling, outomisasie sagteware en postprosessering tegnieke gewys wat gebruik was om ‘n aangepaste CO2 TEA laser te karakteriseer. Verder word dit gewys hoe die teorie wat in voorafgaande hoofstukke ontwikkel is op eksperimentele data toegepas kan word. Hoofstuk 8 gee die eksperimentele resultate van die bundel karakterisering van twee verskillende bundels vanaf die CO2 TEA laser. Bestaande en nuwe korrelasie metodes word gebruik om die bundels te korreleer en die resultate van elke metode word dan met mekaar vergelyk. In Hoostuk 9 word afleidings gemaak. Daar word ook voorstelle gemaak vir potensiële toekomstige werk.

Dissertation (PhD)--University of Stellenbosch, 2006. / ENGLISH ABSTRACT: The formation of Ni-, Co- and Fe-silicides through different diffusion barrier interlayers was investigated. The diffusion barrier layers examined were Ta, Ti and Cr. In some cases the thickness of the barrier layer and the influence of a capping layer was also investigated. The thin-film structures were prepared on single crystal Si-substrates by Electron Beam Vacuum Deposition. The samples were vacuum annealed for times ranging from 10 to 60 min at temperatures ranging from 340 - 800°C and sample characterization was carried out by conventional RBS, dynamic RBS, channeling RBS and X-ray diffraction (XRD). The use of a thin (20Å) Ta diffusion barrier in the Ni-Si system allowed no reaction even after annealing for 10 min at 400°C, but RBS measurements showed that after annealing for 15 min at 400°C uniform NiSi formed suddenly as first phase. XRD as well as dynamic RBS measurements confirmed this abrupt formation of NiSi instead of the normal first phase Ni2Si. According to the Effective Heat of Formation (EHF) model this shows that the diffusion barrier reduces the effective concentration of the Ni atoms to a value where the effective heat of formation of NiSi is more negative than that of Ni2Si and first phase formation of NiSi is thus thermodynamically favoured. The thickness uniformity of the first phase NiSi that formed through the thin Ta barrier improved at higher annealing temperatures. A thicker (100Å) Ta barrier also retarded the Ni diffusion and first phase, non-uniform NiSi only started to form at 500°C. The uniformity of this NiSi also improved with increased temperature but the use of the 20Å Ta barrier produced more uniform first phase NiSi in the 400 to 700°C temperature range. The use of a thin (30-50Å) Cr barrier also allowed the formation of mainly NiSi at 400°C, although XRD spectra indicated the presence of some Ni2Si. The uniformity of NiSi improved at higher temperature anneals. Similar results were obtained from samples with a thicker (100Å) Cr barrier layer at lower temperatures, i.e. the formation of NiSi as first phase at 400°C, but the first phase NiSi that formed at 500 to 700°C was non-uniform. In the case of Ti-barriers, the thicker (100Å) Ti barrier seems less effective than the thinner Ti barriers in delivering uniform first phase NiSi in the 500 to 700°C temperature range. The use of a thin (30-50Å) Ti barrier produced a mixture of Ni2Si and NiSi as first reaction at 400°C, but a 10 min anneal at 500°C formed uniform NiSi as confirmed by RBS and XRD measurements. The uniformity of the NiSi improved with an increase in annealing temperature up to 700°C. In the case of the thicker Ti interlayer no reaction occured at 400°C and non-uniform first phase NiSi formed at 500°C. All three thin barriers formed NiSi2 at temperatures of 750°C and above, but the thin Ti barrier formed the most uniform di-silicide. The NiSi2 that formed at 800°C through all three of the thicker barriers was non-uniform. The use of a thin (10-30Å) Ta diffusion barrier prevented Co-silicide formation up to 560°C. The effective Co concentration at the growth interface is lowered, thus skipping the usual first phase formation of Co2Si at 450°C. At 560°C a mixture of CoSi and CoSi2 formed, as was confirmed by XRD. The CoSi2 that formed at 640°C (a higher formation temperature than without barrier) was of quite uniform thickness, but XRD measurements indicated that some CoSi was present as well. The use of thicker (100Å) Ta barrier layers retarded the diffusion of Co atoms for temperatures of up to 600°C. Annealing at 700°C formed CoSi2 and some CoSi and at 800°C non-uniform CoSi2 formed. The addition of a Ta capping layer (of different thicknesses) in conjunction with a 30Å Ta diffusion barrier layer did not significantly improve Co-silicide formation. The use of thin (10-30Å) Ti barrier layers resulted in the skipping of the Co2Si precursor phase and the formation of quite uniform first phase CoSi at 520°C. Uniform CoSi2 started forming at 560°C and the CoSi2 remained uniform at higher temperatures. The presence of a thicker (100Å) Ti barrier lowered the effective concentration of Co at the growth interface to such an extent that CoSi2 started to form as first phase after annealing for 30 min at 600°C. At 700 and 800°C non-uniform CoSi2 formed. For Fe-silicide formation the use of 50Å and 100Å Cr barriers, as well as CrSi2 barriers, delivered very similar results. There was no change in the normal Fe-silicide phase formation sequence, as non-uniform FeSi was the first phase to form at 500°C and thereafter FeSi2 started to form at 600°C. At 700°C the use of Cr barriers resulted in the complete formation of FeSi2 of greater uniformity than was formed in the Si-Fe binary system without the presence of a diffusion barrier. In this study dynamic real-time RBS has been used for the first time to prove without any doubt that diffusion barrier layers can be used to bring about “phase skipping”. These results have been interpreted in terms of the Effective Heat of Formation (EHF) model and are good examples of concentration controlled phase selection (CCPS). In general it was found that the thicker the diffusion barrier layer, the higher the temperature of silicide formation. Furthermore, silicide formation was generally found to be more uniform at higher annealing temperatures and when thinner diffusion barrier layers were used. / AFRIKAANSE OPSOMMING: Die vorming van Ni-, Co- en Fe-silisiedes deur verskillende diffusie sper-tussenlagies is ondersoek. Die diffusie sperlagies onder beskouing was Ta, Ti en Cr. In sommige gevalle is die invloed van die dikte van die sperlagie en van ‘n deklagie ook ondersoek. Die dun-film strukture is voorberei op enkelkristal Si-substrate d.m.v. Elektronbundel Vakuum Deposisie. Die monsters is in vakuum uitgegloei vir tye wat wissel van 10 tot 60 minute by temperature wat wissel van 340 - 800°C en die karakterisering van die monsters is uitgevoer d.m.v. konvensionele RBS, dinamiese RBS, kanaliserings RBS en X-straal diffraksie (XRD). Die gebruik van a dun (20Å) Ta sperlagie in die Ni-Si sisteem het reaksie verhoed selfs na ‘n uitgloei van 10 min. by 400°C, maar RBS resultate het getoon dat uniforme NiSi skielik gevorm het as eerste fase na ‘n 15 min. uitgloei by 400°C. XRD sowel as dinamiese RBS metings het hierdie abrupte formasie van NiSi in plaas van die normale eerste fase Ni2Si bevestig. Volgens die Effektiewe Hitte van Formasie (EHF) model toon dit dat die diffusie sperlagie die effektiewe konsentrasie van die Ni-atome verlaag tot ‘n waarde waar die effektiewe hitte van formasie van NiSi meer negatief is as dié van Ni2Si en sodoende word die eerste fase formasie van NiSi termodinamies bevoordeel. Die dikte uniformiteit van die eerste fase NiSi wat deur die dun Ta sperlaag gevorm het, het verbeter met uitgloei by hoër temperature. ‘n Dikker (100Å) Ta sperlaag het ook Ni diffusie vertraag en nie-uniforme, eerste fase NiSi het eers by 500°C begin vorm. Die uniformiteit van hierde NiSi het ook verbeter met toename in temperatuur, maar die gebruik van die 20Å Ta sperlagie het meer uniforme eerste fase NiSi produseer in die 400 tot 700°C temperatuur gebied. Die gebruik van ‘n dun Cr (30-50Å) sperlagie het ook by 400°C die vorming van hoofsaaklik NiSi opgelewer, maar XRD spektra het Ni2Si ook aangedui. Die uniformiteit van NiSi het verbeter by hoër temparatuur uitgloeiings. Soortgelyke resultate is verkry van monsters met ‘n dikker (100Å) Cr sperlaag by laer temperature, d.w.s die vorming van NiSi as eerste fase by 400°C, maar die eerste fase NiSi wat by 500 tot 700°C gevorm het, was nie-uniform. In die geval van Ti-sperlagies was die dikker (100Å) Ti minder effektief as die dunner Ti sperlagies vir die verkryging van uniforme eerste fase NiSi in die 500 tot 700°C temperatuur gebied. Die gebruik van ‘n dun (30-50Å) Ti sperlagie het ‘n mengsel van Ni2Si en NiSi as eerste reaksie gevorm by 400°C, maar ‘n 10 min. uitgloei by 500°C het uniforme NiSi gevorm, soos bevestig is deur RBS en XRD metings. Die uniformiteit van die NiSi het verbeter met toename in uitgloei-temperatuur tot by 700°C. In die geval van die dikker Ti sperlagie het geen reaksie by 400°C plaasgevind nie en nie-uniforme eerste fase NiSi het by 500°C gevorm. Al drie dun sperlagies het NiSi2 gevorm by temperature van 750°C en hoër, maar die dun Ti sperlaag het die mees uniforme di-silisied gevorm. Die NiSi2 wat deur al drie die dikker sperlae by 800°C gevorm het, was nie-uniform. Die gebruik van ‘n dun (10-30Å) Ta diffusie sperlagie het Co-silisied formasie voorkom tot by 560°C. Die effektiewe Co-konsentrasie by die groei-intervlak is verlaag, derhalwe word die gewone eerste fase formasie van Co2Si by 450°C oorgeslaan. By 560°C het ‘n mengsel van CoSi en CoSi2 gevorm, soos bevestig deur XRD. Die CoSi2 wat by 640°C gevorm het (‘n hoër formasie temperatuur as sonder ‘n sperlagie) se dikte was redelik uniform, maar XRD metings het getoon dat daar ook CoSi teenwoordig was. Die gebruik van dikker (100Å) Ta sperlae het die diffusie van Co-atome vertraag tot by temperature so hoog as 600°C. Uitgloei by 700°C het CoSi2 sowel as CoSi gevorm en by 800°C het nie-uniforme CoSi2 gevorm. Die toevoeging van ‘n Ta deklagie (van verskillende diktes) in samehang met ‘n 30Å Ta diffusie sperlagie het nie Co-silisied formasie wesentlik beïnvloed nie. Die gebruik van dun (10-30Å) Ti sperlagies het gelei tot die oorslaan van die Co2Si voorloper fase en die vorming van redelik uniforme eerste fase CoSi by 520°C. Uniforme CoSi2 het by 560°C begin vorm en by hoër temperature was die CoSi2 steeds uniform. Die teenwoordigheid van ‘n dikker (100Å) Ti sperlagie het die effektiewe konsentrasie van Co by die groei-intervlak so verlaag dat CoSi2 as eerste fase begin vorm het na ‘n 30 min. uitgloei by 600°C. By 700 en 800°C het nie-uniforme CoSi2 gevorm. Vir Fe-silisied formasie het die gebruik van 50Å en 100Å Cr sperlae, sowel as CrSi2 sperlae, soortgelyke resultate opgelewer. Daar was geen verandering in die gewone Fe-silisied fase formasie volgorde nie, want nie-uniforme FeSi was die eerste fase wat by 500°C gevorm het en daarna het FeSi2 begin vorm by 600°C. Uitgloei by 700°C deur Cr sperlagies het gelei tot die volledige formasie van FeSi2 wat meer uniform was as dié wat in die Fe-Si binêre sisteem gevorm het sonder ‘n diffusie sperlagie. In hierdie studie is dinamiese intydse RBS vir die eerste keer gebruik om bo enige twyfel te bewys dat diffusie sperlae gebruik kan word om die “oorslaan” van fases te bewerkstellig. Hierdie resultate is interpreteer in terme van die Effektiewe Hitte van Formasie (EHF) model en is goeie voorbeelde van konsentrasie-gekontroleerde fase seleksie. In die algemeen is bevind dat hoe dikker die diffusie sperlagie, hoe hoër die temperatuur van silisied-formasie. Bowendien was silisied-formasie oor die algemeen meer uniform by hoër uitgloei-temperature en met die gebruik van dunner diffusie sperlagies.

Thesis (PhD)--Stellenbosch University, 2001. / ENGLISH ABSTRACT: Please see full text for abstract / AFRIKAANSE OPSOMMING: Sien volteks vir opsomming

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: We investigate the procedure of assigning probabilities to logical statements. The simplest case is that of equilibrium statistical mechanics and its fundamental assumption of equally likely states. Rederiving the formulation led us to question the assumption of logical independence inherent to the construction and speci cally its inability to update probability when data becomes available. Consequently we replace the assumption of logical independence with De Finetti's concept of exchangeability. To use the corresponding representation theorems of De Finetti requires us to assign prior distributions for some general parameter spaces. We propose the use of stability properties to identify suitable prior distributions. The combination of exchangeable likelihoods and corresponding prior distributions results in more general evidence distribution assignments. These new evidence assignments generalise the Shannon entropy to other entropy measures. The goal of these entropy formulations is to provide a general framework for constructing models. / AFRIKAANSE OPSOMMING: Ons ondersoek the prosedure om waarskynlikhede aan logiese stellings toe te ken. Die eenvoudigste geval is die van ewewig-statistiese meganika en die ooreenkomstige fundamentele aanname van ewekansige toestande. Hera eiding van die standaard formulering lei ons tot die bevraagtekening van die aanname van logiese onafhanklikheid en spesi ek die onmoontlikheid van opdatering van waarskynlikheid wanneer data beskikbaar raak. Gevolglik vervang ons die aanname van logiese onafhanklikheid met De Finetti se aanname van omruilbaarheid. Om die ooreenkomstige voorstelling stellings te gebruik moet ons a priori verdelings konstrueer vir 'n paar algemene parameter-ruimtes. Ons stel voor dat stabiliteits-eienskappe gebruik moet word om geskikte a priori distribusies te identi seer. Die kombinase van omruilbare aanneemlikheids funksies en die ooreenkomstige a priori verdelings lei ons tot nuwe toekennings van getuienis-verdelings. Hierdie nuwe getuienesverdelings is n veralgemening van Shannon se entropie na ander entropie-maatstawwe. Die doel van hierdie entropie formalismes is om 'n raamwerk vir modelkonstruksie te verskaf.

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: We investigate a model system for particle diffusion in elastically coupled one-dimensional narrow channels. The elastic coupling of the channels is such that channels mutually affect the stochastic dynamics of particles. This kind of constrained and coupled stochastic diffusion may occur in supramolecular lattices where pore occupancy by guest particles may induce a reversible mechanical deformation of the lattice hence, affecting particle evolution in neighbouring pores. The model is explored first for out-of-equilibrium conditions, where we look mainly at the kinetic properties of the system, and thereafter under equilibrium conditions, where we try to understand the nature of dynamic correlation within the coupled channel system. For an out-of-equilibrium version of the model the focus is placed on the steady state behaviour of the two elastically coupled finite channels. The channels are kept in contact with particle reservoirs at the boundaries. Three current-density regimes of different distinct behaviour are identified using a simulation experiment. The sensitivity of the system mean occupancy profile and the steady state particle flux to small and large coupling parameter strength are explored. We find that, for small coupling strength, the system steady state profile and flux behaviour can be approximated by a simple mean field theory ignoring density-density correlations. We present the analytic description of the system using a cellular automaton formalism and then we generalize the theory for a multi-coupled channel system using a hopping particle dynamics approach. For small coupling parameter values, the analytic results are confirmed by the stochastic simulation. From the equilibrium perspective, we model the elastically coupled channel system as a system of infinite narrow channels having a uniform guest particle occupancy and we calculate density fluctuation correlation functions. The elastic coupling between channels is modelled as short range interacting potential and the particle evolution is modelled through Langevin dynamics. The dynamics are cast into the functional integral formalism expressed in terms of the collective particle number density, current density and the associated density response fields. The resulting generating functional takes these fields into consideration within the random phase approximation (RPA) up to second order. For a short range interaction potential, we uncover the behaviour of the system by looking at the influence of the inter-channel interaction strength on the dynamic density-density correlation functions. We conclude that the system long time limit effective friction coefficient is reduced with increase in the coupling parameter values while the strength of thermal forces for the effective system becomes renormalized. We also find out that the RPA breaks down under certain conditions, signalling a transition to a behaviour that is no longer characterised by a homogeneous density. The work presented here provides the beginnings for microscopic insights into the filling, filtering and storage processes for which certain types of microporous materials can be utilised. / AFRIKAANSE OPSOMMING: Ons ondersoek ’n modelstelsel vir die diffusie van deeltjies in elasties gekoppelde, eendimensionele nou kanale. Die elastiese koppeling is sodanig dat die stogastiese dinamika wedersyds be¨ınvloed word. Hierdie gekoppelde en aan dwangvoorwaardes onderhewig diffusie kan in supermolekulˆere roosters gebeur waar die besetting van holtes deur deeltjies ’n omkeerbare meganiese vervorming van die kristalrooster kan veroorsaak en sodoende die tydontwikkeling in ’n aangrensende porie be¨ınvloed. Die model word eers vir nie-ewewig toestande ondersoek, waar ons hoofsaaklik die kinetiese eienskappe van die stelsel beskou, en daarna word dit vir ewewig ondersoek, waar ons die aard van die dinamiese korrelasie binne die gekoppelde kanaalstelsel probeer verstaan. Vir die nie-ekwilibrium weergawe van die model word die fokus op die gedrag van twee gekoppelde en eindige kanale se bestendige toestand gerig. Die porie¨e bly aan hulle eindpunte in kontak met reservoirs van deeltjies. Daar word drie deeltjiestroom-digtheid gebiede ge¨ıdentifiseer met behulp van ’n simulasieeksperiment. Die sensitiewiteit van die stelsel se gemiddelde deeltjiebesettingsprofiel en die deeltjievloed in ’n bestendige toestand is ondersoek vir groot en klein koppelingsparameters. Vir klein koppelingsterkte vind ons dat die stelsel se bestendige toestand deeltjiebesettingspofiel en deeltjievloed deur ’n eenvoudige gemiddelde-veld teorie beskryf kan word, waar digtheid-degtheids korrelasies verontagsaam kan word. Ons bied die analitiese beskrywing aan vir die gekoppelde stelsel deur van ’n sellulˆere outomaat-formalisme gebruik te maak, en om dan die teorie te veralgemeen vir ’n stelsel bestaande uit vele aanmekaar gekoppelde porie¨e ,deur gebruik te maak van ’n formalisme waarin deeltjies tussen holtes hop. Die analtiese resultate word vir kleine waardes van die koppelingsparameter deur ’n rekenaarsimulasie bevestig. Vir die ekwilibrium gesigspunt modelleer ons die gekoppelde stelsel van kanale as oneindig nou, met ’n homogene verdeling van die deeeltjiebesetting en ons bereken digtheids-korrelasiefunksies. Die elastiese vebinding tussen porie¨e word deur ’n kortrykwydte potensiaal gemodelleer en die deeltjies se dinamika met behulp van Langevindinamika. Die dinamika word met behulp van die funksionaal integraalformalisme uitgedruk in terme van die deeltjiegetaldigtheid-, stroomdigtheid- en meegaande antwoordvelde. Die resulterende genererende funksionaal neem hierdie hoeveelhede tot tweede order binne die “random field approximation” (RPA). Vir ’n potensiaal met kort rykwydte, ondersoek ons die stelsel se gedrag deur die dinamiese digtheid-digtheidskorrelasie te ondersoek. Ons lei af dat die stelsel se langtyd effektiewe wrywingsko¨effisi¨ent afneem met die toename in die koppelingsparameter se waardes terwyl die sterkte van die termiese kragte vir die effektiewe stelsel renormeer word. Ons vind ook dat die RPA onder sekere omstandighede sy geldigheid verloor, wat ’n oorgang kan beteken wat nie meer deur ’n homogene digtheid beskryf kan word nie. Die werk wat hier aangebied word dui die eerste stappe aan vir hoe mikroskopiese insigte vir vul-, filter- en stoorprosesse vir sekere tipes mikroporeuse materiale gebruik kan word.

Thesis (MSc)--University of Stellenbosch, 2006. / ENGLISH ABSTRACT: We are studying a possible implementation of an appropriate framework for a proper non- Hermitian quantum theory. We present the case where for a non-Hermitian Hamiltonian with real eigenvalues, we define a new inner product on the Hilbert space with respect to which the non-Hermitian Hamiltonian is Quasi-Hermitian. The Quasi-hermiticity of the Hamiltonian introduces the bi-orthogonality between the left-hand eigenstates and the right-hand eigenstates, in which case the metric becomes a basis transformation. We use the non-Hermitian quadratic Hamiltonian to show that such a metric is not unique but can be uniquely defined by requiring to hermitize all elements of one of the irreducible sets defined on the set of all observables. We compare the constructed metric with specific known examples in the literature in which cases a unique choice is made. / AFRIKAANSE OPSOMMING: Ons ondersoek die implementering van n gepaste raamwerk virn nie-Hermitiese kwantumteorie. Ons beskoun nie-Hermitiese Hamilton-operator met reele eiewaardes en definieer in gepaste binneproduk ten opsigtewaarvan die operator kwasi-Hermitiese is. Die kwasi- Hermities aard van die Hamilton operator lei dan tot n stel bi-ortogonale toestande. Ons konstrueer n basistransformasie wat die linker en regter eietoestande van hierdie stel koppel. Hierdie transformasie word dan gebruik omn nuwe binneproduk op die Hilbert-ruimte te definieer. Die oorspronklike nie-HermitieseHamilton-operator is danHermitiesmet betrekking tot hierdie nuwe binneproduk. Ons gebruik die nie-Hermitiese kwadratieseHamilton-operator omte toon dat hierdie metriek nie uniek is nie, maar wel uniek bepaal kan word deur verder te vereis dat dit al die elemente van n onherleibare versameling operatoreHermitiseer. Ons vergelyk hierdie konstruksiemet die bekende voorbeelde in die literatuur en toon dat diemetriek in beide gevalle uniek bepaal kan word.

Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Two problems in the field of materials-based condensed matter physics, specifically in the field of superconductivity, are studied theoretically. In both problems, where each is of current exper- imental interest, an extension of Ginzburg-Landau theory is used to describe a physical system, with focus on the energy associated to the interface(s) occurring in the respective systems. The first physical system under consideration is that of a two-band superconductor. Using Ginzburg-Landau theory for two-band superconductors, the interface energy ¾s between normal and superconducting states coexisting at the thermodynamic critical magnetic field is determined. From the theoretical and numerical analysis of the interface energy, it is found that close to the transition temperature, where the Ginzburg-Landau theory is applicable, the two-band problem maps onto an effective single band problem. This finding puts into question the possibility of intermediate, so called type-1.5 superconductivity, in the regime where the Ginzburg-Landau theory applies. The second physical system is that of a system with competing superconductivity and anti- ferromagnetism. From Ginzburg-Landau theory for such competing systems in a thermodynamic critical magnetic field, it is shown that two possible interfaces can occur: an interface between a pure anti-ferromagnetic state and a pure superconducting state; and an interface between a state with coexisting superconductivity and anti-ferromagnetism and a pure anti-ferromagnetic state. The energy associated to both these interfaces is analysed theoretically and numerically from which the boundary between type-I and type-II superconductivity is obtained for certain specific cases. / AFRIKAANSE OPSOMMING: Twee probleme in die veld van materiaal-gebaseerde gekondenseerde materie fisika, spesifiek in die veld van supergeleiding, word teoreties bestudeer. In beide probleme, albei tans van eksper- imentele belang, word ’n fisiese sisteem beskryf deur ’n uitbreiding van enkel-band Ginzburg- Landau teorie, met fokus op die energie geassosieer met die koppelvlak(ke) wat in die onderskeie sisteme aangetref word. Die eerste fisiese sisteem wat beskou word is die van ’n twee-band supergeleier. Deur van Ginzburg-Landau teorie vir twee-band supergeleiers gebruik te maak, word die koppelvlak energie ¾s tussen die gelyktydig bestaande normaal- en supergeleidende toestand in die termodinamiese kritieke magneetveld bepaal. Deur beide teoretiese en numeriese analieses word bepaal dat na aan die oorgangstemperatuur, waar Ginzburg-Landau teorie geldig is, die twee-band probleem op ’n effektiewe een-band probleem afbeeld. Hierdie bevinding bevraagteken dus die moontlikheid van onkonvensionele, of sogenaamde tipe-1.5 supergeleiding, vir gevalle waar Ginzburg-Landau teorie geldig is. Die tweede fisiese siteem wat beskou word is ’n sisteem met kompeterende supergeleiding en anti-ferromagnetisme. Met behulp van Ginzburg-Landau teorie vir sulke sisteme in ’n termod- inamiese kritiese magneetveld word gewys dat daar twee moontlike koppelvlakke kan ontstaan: ’n koppelvlak tussen ’n uitsluitlik anti-ferromagnetiese toestand en ’n uitsluitlik supergeleidende toestand; sowel as ’n koppelvlak tussen ’n uitsluitlik anti-ferromagnetiese toestand en ’n toes- tand van beide supergeleiding en anti-ferromagnetisme. Die energie geassosieer met beide hierdie koppelvlakke word teoreties en numeries geanaliseer wat lei tot ’n beskrywing van die grenslyn tussen tipe-I en tipe-II supergeleiding in sekere spesifieke gevalle.

Thesis (MSc (Physics))--University of Stellenbosch, 2009. / The exciting field of ultrashort laser optics has experienced tremendous growth since it's inception. One of it's branches that has been of continuous interest is the characterization of ultrashort laser pulses ...

Thesis (MSc (Physics))--Stellenbosch University, 2008. / Third harmonic generation (THG) in a metal vapour is a nonlinear optical interaction that facilitates the generation of light in the vacuum ultraviolet (VUV) portion of the electromagnetic spectrum. The requirement of the metal vapour medium is that it has a suitably large third order nonlinear susceptibility. The third order susceptibility is further enhanced by a two photon resonance. Zinc and magnesium vapours are such nonlinear media. The THG process can be phase matched by mixing the metal vapour with a noble gas in a speci c pressure ratio. The metal vapour noble gas mixture needs to be homogeneous and its temperature needs to be constant to within less than a degree Celsius over a path length of 7 cm. These requirements are satis ed by a crossed heat pipe oven. The heat pipe oven makes use of a dynamic liquid-vapour phase equilibrium in sodium in order to maintain a constant temperature of around 800 degrees Celsius, thus facilitating the generation of a stable homogeneous medium of metal vapour and noble gas that can be used for e cient generation of VUV radiation. The development of such a VUV source using zinc vapour and the application of a similar VUV source using magnesium vapour are discussed. The VUV radiation has been applied to laser induced uorescence spectroscopy of carbon monoxide (12C16O and 13C16O). Spectral lines of 20 spin-forbidden singlet-triplet transitions of the e3 − − X1 +(5 0) band were detected and accurate experimental wavelengths determined for the rst time for ve of these lines.

Thesis (MSc (Physics))--University of Stellenbosch, 2008. / Various autocorrelation techniques are employed to characterize ultrashort laser pulses in both the temporal and spectral domain. These techniques are; interference autocorrelation (IAC), modified spectrum autointerferometric correlation (MOSAIC), background-free autocorrelation (BFA) and frequency resolved optical gating (FROG). All of these techniques are based on the interaction of a pulse with a time delayed copy of itself within a Â(2) medium. Experimental setups for BFA and FROG experiments are developed, which exploit the phenomenon of second harmonic generation (SHG). An existing IAC setup is used for temporal pulse characterization. MOSAIC results are obtained through applying a specific Fourier filter to the IAC data. IAC and MOSAIC measurements performed on a commercially available femtosecond laser, indicate that the emitted pulse has a pulse duration less than 150 fs and possesses positive linear chirp. BFA and FROG measurements carried out on the same laser system mirror these results. Pulses emitted by a 20 Hz chirped pulse amplifier are characterized through BFA and FROG. BFA results suggest that the pulse from the amplifier is actually a double pulse. FROG results indicate that the pulse is highly chirped. The experiments and physical interpretations presented in this work demonstrate the preferred methods of optical pulse characterization for ultrashort laser pulses.