Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The experimental observation of the quantum Hall effect in a two-dimensional electron gas posed an intriguing question to theorists: Why is the quantization of conductance so precise, given the imperfections of the measured samples? The question was answered a few years later, when a connection was uncovered between the quantum Hall effect and topological quantities associated with the band structure of the material in which it is observed. The Hall conductance was revealed to be an integer topological invariant, implying its robustness to certain perturbations. The topological theory went further than explaining only the usual integer quantum Hall effect in a perpendicular magnetic field. Soon it was realized that it also applies to certain systems in which the total magnetic flux is zero. Thus it is possible to have a quantized Hall effect without Landau levels. We study a carbon nanotube in a magnetic field perpendicular to its axial direction. Recent studies suggest that the application of an electric field parallel to the magnetic field would induce a gap in the electronic spectrum of a previously metallic carbon nanotube. Despite the quasi onedimensional nature of the carbon nanotube, the gapped state supports a quantum Hall effect and is associated with a non zero topological invariant. This result is revealed when an additional magnetic field is applied parallel to the axis of the carbon nanotube. If the flux due to this magnetic field is varied by one flux quantum, exactly one electron is transported between the ends of the carbon nanotube. / AFRIKAANSE OPSOMMING: Die eksperimentele waarneming van die kwantum Hall effek in ’n twee-dimensionele elektron gas laat ’n interessante vraag aan teoretiese fisikuste: Waarom sou die kwantisasie van die geleiding so presies wees al bevat die monsters, waarop die meetings gedoen word, onsuiwerhede? Hierdie vraag word ’n paar jaar later geantwoord toe ’n konneksie tussen die kwantum Hall effek en topologiese waardes, wat verband hou met die bandstruktuur van die monster, gemaak is. Dit is aan die lig gebring dat die Hall geleiding ’n heeltallige topologiese invariante is wat die robuustheid teen sekere steurings impliseer. Die topologiese teorie verduidelik nie net die gewone kwantum Hall effek wat in ’n loodregte magneetveld waargeneem word nie. Dit is ook moontlik om ’n kwantum Hall effek waar te neem in sekere sisteme waar die totale magneetvloed nul is. Dit is dus moontlik om ’n gekwantiseerde Hall effek sonder Landau levels te hˆe. Ons bestudeer ’n koolstofnanobuis in ’n magneetveld loodreg tot die aksiale rigting. Onlangse studies dui daarop dat die toepassing van ’n elektriese veld parallel aan die magneetveld ’n gaping in die elektroniese spektrum van ’n metaliese koolstofnanobuis induseer. Ten spyte van die een-dimensionele aard van die koolstofnanobuis ondersteun die gapings-toestand steeds ’n kwantum Hall effek en hou dit verband met ’n nie-nul topologiese invariante. Hierdie resultaat word openbaar wanneer ’n bykomende magneetveld parallel tot die as van die koolstofnanobuis toegedien word. Indien die vloed as gevolg van hierdie magneetveld met een vloedkwantum verander word, word presies een elektron tussen die twee kante van die koolstofnanobuis vervoer.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Crossing symmetry relates scattering and annihilation processes to each other. Its derivation is straightforward in perturbative approaches to quantum field theory: it merely reflects the exchange of in- and outgoing states in Feynman diagram computations. In soliton models, the situation is much more complicated because the scattering and the annihilation processes concern distinct topological sectors that are not related by any continuous transformation. In this thesis a simple soliton model will be employed to address this problem numerically. First, in the unit topological sector we extract asymptotically the phase shift of the scattering process of a wave packet off the kink-solution. To this end we solve the time-dependent equation of motion of the non-integrable '4 field model in (1+1) spacetime dimensions for two distinct initial conditions: the wave packet in a trivial vacuum background and in the background of the kink-solution. Second, in the topologically trivial sector we present numerical solutions of the kink– antikink interaction in the same model. We find that the final state of this interaction varies dramatically with the impact velocity. As result, we analyze our numerical solutions for the kink–antikink collisions system in two regimes. For the initial velocity of the system less than some critical velocity, vc 0:26, the kink and the antikink either annihilate or inelastically scatter. On the other hand, the kink and the antikink always inelastically scatter when the initial velocity of the system is higher than this critical velocity. However, the scattering processes of the kink–antikink with initial velocity below and above the critical velocity are different. Below the critical velocity the kink and the antikink collide and always undergo n-bounces (n 2) before they depart to infinity. When the initial velocity of the system is higher than vc, the kink and the antikink depart to infinity after only one bounce. We present a qualitative description for these bounce effects between the kink and the antikink motivated by earlier studies as well as our numerical simulations. We utilize collective coordinates to study the dynamics of the kink–antikink system in two degrees of freedom. In this regime, we modify the ansätze of the kink–antikink system from earlier studies to account for relativistic effects. We perform a comparison between this approximation and the full system. We end our discussion of this sector by discussing the scattering data for the inelastic scattering and the annihilation processes of the kink–antikink. Third, we compare the extracted scattering data for the scattering process of a wave packet off the kink-solution and the annihilation process of the kink–antikink to each other. Finally, these studies of different sectors allow us to make a conjecture about the validity of crossing symmetry within the non-integrable '4 field model. / AFRIKAANSE OPSOMMING: Kruising-simmetrie beskryf ’n verband tussen verstrooiings- en vernietigingsprosesse. Die afleiding daarvan binne die raamwerk van steuringsteorie is eenvoudig: dit behels bloot die omruil van ingaande en uitgaande toestande in die Feynman-diagram. In soliton-modelle is die situasie egter meer ingewikkeld aangesien die verstrooiings- en vernietigingsprosesse in verskillende topologiese sektore plaasvind wat nie deur kontinue transformasies aan mekaar gekoppel is nie. In hierdie tesis word daar van ’n eenvoudige soliton-model gebruik gemaak om hierdie probleem numeries te ondersoek. Eerstens word die faseverskuiwing van die verstrooiingsproses van ’n golfpakkie vanaf ’n kinkoplossing asimptoties in die topologiese eenheidssektor bepaal. Vir hierdie doel word die tydafhanklike bewegingsvergelykings van die klassieke, nie-integreerbare 4-veldeteorie in (1+1) dimensionele ruimte-tyd opgelos. Twee beginkondisies word ondersoek: ’n golfpakkie in die triviale vakuum agtergrond asook in die kinkoplossing agtergrond. Tweedens ondersoek ons ook numeriese oplossings vir die kink-antikink wisselwerking binne die triviale topologiese sektor van dieselfde model. Hier vind ons dat die finale toestand van hierdie wisselwerkingsproses op ’n uiters sensitiewe wyse van die impaksnelheid afhang. Ons ondersoek gevolglik die numeriese oplossings vir die kink-antikink botsings in twee gebiede. Vir beginsnelhede onder die kritieke snelheid vc 0:26 sal die kink en antikink mekaar óf vernietig óf nie-elasties verstrooi. In teenstelling hiermee sal die kink-antikink altyd nie-elastiese verstrooiing ondergaan as die beginsnelheid die kritieke snelheid oorskry. Die aard van die verstrooiingsprosesse vir beginsnelhede bo en onder die kritieke snelheid is egter verskillend. Onder die kritieke snelheid sal die kink en antikink ’n n-bots proses (n 2) ondergaan voor hulle finaal van mekaar weg beweeg. Bo die kritieke snelheid sal die kink-antikink egter net ’n enkele botsing ondergaan en dan uitmekaar beweeg. Ons lewer ’n kwalitatiewe beskrywing vir die bons-effek tussen die kink en antikink wat deur vorige studies asook ons numeriese resultate gemotiveer word. Ons maak gebruik van ’n kollektiewe koördinaatstelsel om die dinamika van die kink-antikink in terme van twee vryheidsgrade te bestudeer. In hierdie gebied pas ons ook die ansatz vir die kink-antikink stelsel aan om relatiwistiese effekte in ag te neem. Ons vergelyk dan hierdie benadering met die oplossing van die volle sisteem. Die bespreking van hierdie sektor word afgesluit met ’n analise van die verstrooiingsdata vir die verstrooiing- en vernietingsprosesse van die kink-antikink. Derdens vergelyk ons die verstrooiingsdata vir die verstrooiing van ’n golfpakkie vanaf ’n kinkoplossing met die van die vernietigingsproses van die kink-antikink. Ons studie van die verskillende sektore laat ons dan toe om ’n vermoede te formuleer oor die geldigheid van kruissing-simmetrie binne die nie-integreerbare 4-model.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Terahertz radiation is currently used in security, information and communication technology (ICT), and biomedical sciences among others. The usability of terahertz (THz) radiation, in many of its applications depends on characteristics of the materials being investigated in the THz range. At the heart of THz usage is a THz spectroscopy system necessary for the generation and detection of the THz radiation. In this thesis, we characterise such a THz spectroscopy system. In our typical THz spectrometric system, we make use of femtosecond (fs) laser technology and pump-probe principles for emission and detection of THz radiation. Background about the principles of generation THz radiation using fs triggered antennas and the principles of the spectroscopy technique and appropriate literature references are presented. Using an assembled commercially available kit, we reproduce known spectra in order to confirm correct functionality (for calibration) of the assembled spectroscopy system and to gain experience in interpreting these spectra. By introducing a suitable x - y scanning device we construct a crude THz imaging device to illustrate the principle. / AFRIKAANSE OPSOMMING: Terahertsstraling word deesdae wyd in die sekuriteits, inligting-en-kommunikasie en biomediese sektore aangewend. Die gepastheid van terahertsstraling (THz) vir ’n spesifieke toepassings hang af van die eienskappe van die materiale wat ondersoek word. Vir die uitvoer van sulke eksperimente word ’n THz-spektroskopie sisteem benodig vir die opwekking en meting van THz-straling. In hierdie tesis word so ’n THz-spektroskopie sisteem beskou en gekarakteriseer. In die sisteem word van ’n femtosekondelaser (fs) gebruik gemaak in ’nn pomp-en-proef opstelling vir die uitstraling en meting van THz-straling. Die beginsels rakende die opwekking van THz-straling, deur gebruik te maak van ’n antenna wat deur ’n fs-laser geskakel word, asook die beginsels van die spektroskopiese tegniek, met toepaslike verwysings, word in die tesis aangebied. Deur gebruik te maak van’n kommersiële THz opstelling is bekende spektra gemeet om die korrekte funksionering (vir kalibrasie doeleindes) na te gaan en om ondervinding op te doen in die interpretasie van hierdie spektra. ’n X-Y-translasie toestel is tot die opstelling bygevoeg om THz-afbeelding moontlik te maak en sodoende hierdie beginsel te illustreer.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The primary circuit components of very high temperature reactors (VHTRs) experience various unwanted fission products such as Kr, Xe, I, Cs, Sr, and Ag. These particle are generated during normal operation of the reactor from abaration, cracks and/or deffects are transported by the helium coolant. The main candidate that has been identified as a cause for concern and the focus of research to minimizing radioactive contamination of the reactor coolant circuit is silver. This is because the design of the coated particles limits the release of fission products into the coolant except for silver(Ag110m). Ag110m is a long lived metallic fission product formed inside the nuclear reactor core and is the only known element released out of the coated particles into the coolant at any temperature above 1150 ◦C when the reactor starts to heat up. The release occurs on intact coated particles, failed particles and also from defective particles. The amount of released silver is initially small and occurs as the pebble heats up and this is strongly dependent on the temperature of the core. It is therefore able to reach the surface of the reactor core and enter into the Helium coolant flowing throughout the reactor. Thus Ag110m will be circulated through the reactor circuit until it reaches the cooler sides of the main power system (MPS) where it will start to plate out. The presence of this radioactive silver in the primary circuit components may result in unwanted maintenance problems from a radiation hazard point of view. The development of a method to remove particles from the helium stream is therefore needed. In this work, two theoretical deflection models used to deflect the silver particles are proposed, namely the stochastic and the deterministic deflection models. The latter describes the deflection of microparticles in a helium medium. It uses the dielectrophoresis (DEP) technique to investigate the deflection of a silver µm moving in a helium medium with the bulk velocity of 0.021 ms−1 and subjected to a dielectrophoretic force only deflect an amount of 0.52039 nm and 4.49882 nm in the x - and z -directions on average. The former (stochastic deflection model) describes the deflection of ions and polarized particles by using probability theory, namely kinetic theory of gases. This model showed that the mean free time that the particle spends while deflected by a uniform electric field is short so much that there is not enough time for a silver particle to be appreciably deflected between collisions. For example, when an electric field of 100kV/m was applied on a single silver ion for a time of 0.1 µs, the deflection distance obtained was 33.38 mm for a free time of 0.189285 ns and under pressure and temperature conditions of 1 bar and 20◦ C. The Brownian motion was then compared to the effects of a nonuniform electric field in polarizing and deflecting an atom. This is done by comparing the Brownian motion and the polarizibility of an atom using nonuniform electric fields. It is found that the silver speed produced from Brownian motion (79.563 ms−1) is far larger than that produced from the polarizibility of an atom (4.69455×106 nms−1). The deterministic and stochastic deflection models using nonuniform electric fields proved that the dielectrophoresis technique is negligibly small in deflecting particles and cannot be used to deflect silver particles as required in a VHTR. / AFRIKAANSE OPSOMMING: Die primˆere siklus komponente van baie ho temperatuur reaktore (VHTRs) word bloodgestel aan verskeie ongewenste fisie produkte soos Kr, Xe, I, Cs, Sr, en Ag. Hierdie deeltjies word gegenereer gedurende normale werking van die reaktor van abarasie, krake en / of defekte word vervoer deur die helium verkoelingsmiddel. Die belangrikste kandidaat wat gedentifiseer is as ’n rede vir kommer en die fokus van navorsing op die minimalisering van radioaktiewe besoedeling van die reaktor verkoelingsmiddel siklus is silwer. Die rede hiervoor is die ontwerp van die omhulsel wat die vrylating van die fisie produkte in die koelmiddel behalwe vir silwer (Ag110m) beperk. Ag110m is ’n metaal fisie-produk met ’n lang leeftyd wat gevorm word binne-in die kern van die reaktor en is sover bekend die enigste element wat vrygestel word deur die bedekte deeltjies in die verkoelingsmiddel by enige temperatuur bo 1150 ◦C wanneer die reaktor begin verhit. Die vrystelling kom voor by ongeskonde brandstofomhulse, nie funksionele deeltjies en ook van gebrekkige deeltjies. Die bedrag van vrygestel silwer is aanvanklik klein en kom voor as die brandstofelemente verhit en heirdie vrystelling is sterk afhanklik van die temperatuur van die kern. Dit is dus in staat om die oppervlak van die reaktor kern te bereik en betree die Helium verkoelingsmiddel vloeistelsel en beweeg regdeur die reaktor. Dus sirkuleer die Ag110m deur die reaktor kring totdat dit die koeler kante van die MPS bereik waar dit sal begin uitplatteer. Die teenwoordigheid van hierdie radioaktiewe silwer in die primˆere stroombaan komponente kan lei tot ongewenste onderhoud probleme van ’n straling gevaar oogpunt. Die ontwikkeling van ’n metode om deeltjies te verwyder uit die helium stroom is dus nodig. In hierdie werk word van twee teoretiese defleksie modelle gebruik gemaak om die silwer partikels se defleksie te beskryf, naamlik die stogastiese en die deterministiese defleksie modelle. Laasgenoemde beskryf die defleksie van mikro grootte partikel in ’n helium medium. Dit maak gebruik van die dielektroflorosensie (DEP) tegniek om ondersoek in te stel na die defleksie van ’n silwer deeltjie met ’n radius van 3 μm. Dit is vanaf hierdie model waargeneemdat ’n silwer mikrodeeltjie met ’n radius van 3 m in ’n helium medium beweeg met die snelheid van 0,021 ms−1 en onderworpe is aan ’n dielektroforetiese krag dit net met ’n gemiddelde van 0,52039 nm en 4,49882 nm in die x - en z -rigtings deflekteer. Die voormalige (stogastiese defleksie model) beskryf die defleksie van ione en gepolariseerde partikels deur gebruik te maak van waarskynlikheidsteorie, naamlik die kinetiese teorie van gasse. Hierdie model toon dat die gemiddelde vrye tyd wat die deeltjie spandeer terwyl dit gedeflekteer word deur ’n uniforme elektriese veld sovel korter is dat daar nie genoeg tyd is vir ’n silwer deeltjie is om aansienlik tussen botsings gedeflekteer kan word nie. Byvoorbeeld, wanneer ’n elektriese veld van 100kV/m toegepas word op ’n enkele silwer ioon vir ’n tyd van 0.1 μs, die defleksie afstand van 33,38 mm verkry word vir ’n vrye tyd van 0.189285 ns en onder druk en temperatuur voorwaardes van 1 bar en 20 ◦C. Die Brown-beweging was dan vergeleke met die uitkoms van n univorme elektriese veld wat n polariserende atoom deflekteer. Dit word gedoen deur die vergelykings van die Brown-beweging en die polariseerbaarheid van ’n atoom met behulp van nie-uniform elektriese veld te gebruik. Daar word gevind dat as die silwer spoed van Brown se beweging (79,563 ms−1) veel groter is as di van die polariseerbare atoom (4,69455 × 10−6 nms−1). Die deterministiese en stogastiese defleksie modelle deur gebruik te maak van nonuniform elektriese velde bewys dat dielectrophoresis tegniek is weglaatbaar klein in defleksie van deeltjies en kan dus nie gebruik word om silwer partikels te buig soos wat in ’n VHTR vereis word nie.

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Ultra-short laser pulses are useful in materials processing like melting and cutting metals, and medical applications such as surgery and many other fields. In this study, we characterize and control the temporal shape of the ultra-short pulses generated from a Ti:Sapphire femtosecond laser. It operates in the near infra-red spectral region, with a centre wavelength of 800 nm. The 4f pulse shaper is the main setup used to modulate spectral shape and characterize the laser pulse. The shaper consists of two diffraction gratings, two cylindrical lenses and a computer controlled liquid crystal spatial light modulator (LC-SLM). Gratings, lenses and LC-SLM are arranged in a 4f geometry, f being the focal length of the lenses. This setup is first analysed analytically and numerically using Fourier transform and the results obtained are then compared to those obtained from the experiment. The characterization of ultra-short pulses was done using three different autocorrelation techniques such as the intensity autocorrelation, the interferometric autocorrelation, and the pulse shaping autocorrelation which can act as interferometric autocorrelation when a nonlinear crystal ß-barium borate (BBO) is placed exactly at the position of the experiment. These characterization techniques are based on the interaction between the laser pulse and a replica of it with a nonlinear crystal. The setups were implemented and measurements using the last two techniques were successfully conducted, with the pulse duration result in the range from 80-86 fs. / AFRIKAANSE OPSOMMING: Ultrakort laserpulse het baie nut in verskeie velde waaronder materiaalprosessering (soos die smelt en sny van metale) en mediese toepassings (soos chirurgie) maar net twee voorbeelde is. In hierdie studie karakteriseer en beheer ons die vorm van n ultrakort laserpuls, afkomstig vanaf n Ti:Saffier femtosekonde laser, in tyd. Die laser straal in die nabyinfrarooi spektrale gebied uit met n sentrale golflengte van 800 nm. Ons gebruik n sogenaamde 4f-pulsvormer om die spektrum van die laserpuls te moduleer en die laserpuls te karakteriseer. Die vormer bestaan uit twee diffraksieroosters, twee silindriese lense en n rekenaarbeheerde vloeibare kristal ruimtelike-lig-modulator (LC-SLM). Die diffraksieroosters, lense en LC-SLM is in n 4f-geometrie gerangskik, met f die brandpunt van die lense. Die opstelling is eers analities en numeries beskou deur van Fourier-transformasies gebruik te maak waarna die resultate wat verkry is met die van n eksperiment vergelyk is. Die karakterisering van ultrakort laserpulse was met drie verskillende outokorrelasie tegnieke gedoen, naamlik n intensiteits-outokorrelasie, n interferometriese-outokorrelasie en n pulsvormer-outokorrelasie. Die pulsvormer kan as n interferometriese-outokorrelator optree indien n nie-lineêre kristal ß-bariumboraat (BBO) by die uitset van die pulsvormer geplaas word. Hierdie karakteriseringstegnieke is gebaseer op die interaksie tussen die oorspronklike laserpuls en n kopie van die laserpuls in n nie-lineêre kristal. Die nodige opstellings virdie metings is gemaak en die metings was suksesvol uitgevoer. Die pulslengte wat gemeet is, is in die orde van 80-86 fs.

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: A tunable narrow-bandwidth vacuum ultra violet laser source was developed and characterised. Two-photon resonant four-wave sum-frequency mixing of two pulsed dye laser beams in magnesium vapour was used to generate the VUV laser light. A heat pipe oven with a concentric design was incorporated to provide a magnesium vapour column of around 30 cm in length with a sufficiently stable temperature and appropriate vapour pressure for efficient VUV production. This is a longer nonlinear medium length than previously produced in our laboratory using a crossed heat pipe oven. The longer medium facilitated the production of VUV laser light of higher intensity than was previously obtainable. High resolution laser induced fluorescence spectra of carbon monoxide in a supersonic gas jet was recorded using the tunable VUV laser light produced in the crossed heat pipe oven. Experimental parameters were optimised and adjusted for the selective detection of the forbidden singlet-triplet transitions which typically have longer lifetimes than singlet-singlet transitions. Transitions from the X¹Σ⁺(v = 0) ground state to the e³Σ⁻( v = 5) triplet state were recorded, and accurate wavelength for the spectral lines were determined. Laboratory wavelengths for these lines have not been measured previously. Accurate wavelength for the weak forbidden spectral lines of CO are important in astrophysical applications, for example determining column densities of interstellar gas clouds. / AFRIKAANSE OPSOMMING: 'n Afstembare smal bandwydte vakuum ultraviolet laser bron is ontwikkel en gekarakteriseer. Twee-foton resonante vier-golf som-frekwensie vermenging van twee gepulseerde kleurstoflaserbundels in 'n magnesium damp is gebruik om die VUV laser lig te produseer. 'n Hittepyp oond met 'n konsentriese ontwerp is in gebruik geneem om a magnesium damp kollom van ongeveer 30 cm in lengte te voorsien waarvan die temperatuur voldoende stabiel is en die dampdruk toepaslik is vir effektiewe VUV produksie. Dit is 'n langer nie-liniêre medium as wat in die verlede deur 'n kruis-hittepyp oond voorsien is. Die langer medium het dit moontlik gemaak om VUV laser lig van hoër intensiteit te produseer as wat tot dusver bereikbaar was. Hoë resolusie laser geinduseerde fluoresensie spektra van koolstof monoksied in a supersoniese gasstraal is opgeneem met die hulp van die afstembare VUV laser lig geproduseer in die kruis-hittepyp oond. Eksperimentele parameters is geoptimeer en verstel vir die selektiewe waarneming van die verbode singlet-triplet oorgange wat tipies langer leeftye besit in vergelyking met singlet-singlet oorgange. Oorgange vanaf die X¹Σ⁺(v = 0) grond toestand na die e³Σ⁻( v = 5) triplet toestand is opgeneem en akkurate golflengtes vir die spektrale lyne is bepaal. Laboratorium golflengtes het tot dusver nie bestaan vir hierdie lyne nie. Akkurate golflengtes vir die swak verbode spektrale lyne van CO het belangrike toepassings in astrofisika soos die bepaling van die kollom digtheid van interstellêre gas wolke.

Thesis (MSc)--Stellenbosch University, 2013. / This work is a thesis regarding the energy scaling of end-pumped Ho:YLF amplifiers. The work includes: a brief review of laser physics and models, the development of a suitable three dimensional time resolved numerical model, a parametric study of double pass ampli ers simulated using the model, comparison between the simulation and the experimental results of a double pass ampli er system, and simulation of a high energy single pass ampli er. A three dimensional time resolved numerical model of an end-pumped ampli er was developed. A rate equation model was used to simulate the absorption and emission of light, energy transfer upconversion, and spontaneous emission within the gain medium. In the traveling wave approximation the propagation of light through the gain medium was modelled with the use of a split step method that included di raction and gain. A parametric study was performed to nd the design parameters for an end-pumped two pass ampli- er. Limited optimisation of several ampli er parameters was performed. The study focused on the optimisation of the energy per pulse through changes to the following parameters: crystal length, laser beam size, pump beam sizes, and pump wavelength. The nal design speci cations for an experimental system were for a 100 mm long 0.5 % (atm.) doped Ho:YLF gain medium, pump and seed beams with spot sizes with e ective beam sizes of 1 mm and 0.95 mm respectively and a pump wavelength of 1892 nm. The simulation predicted pulse energies above 480 mJ when seeded by a 55 mJ pulse at repetition rates of 50 Hz. The experimentally realised system with similar design parameters produced the highest reported energy, 330 mJ, from an end-pumped Ho:YLF ampli er. Comparison between the simulation and the experimental results showed signi cant deviation. The deviation was explained by the e ect of parameters not included previously in the simulation. These parameters were the power of the continuous component of the seed beam, and the energy transfer upconversion rate. Limitations and delity of the numerical model with respect to the experimental system are discussed, notably the model of the highly divergent pump beam was simplistic. Preliminary simulation results of a high energy single pass ampli er predict that energy scaling in Ho:YLF follows linearly with respect to pump power and that in the ideal case, multi-Joule operation is possible at 50 Hz with optical to optical e ciencies of 19%.

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: An ultra-fast laser pulse can be described in the time or frequency domain. If the timebandwidth product of an ultra-fast pulse is not satisfied, then the pulse is stretched. Stretching can be described in the time or frequency domain. In the time domain, it is called a chirp and in the frequency domain, it is known as the group delay dispersion GDD. Various techniques can be used to stretch and compress laser pulses. In this project, a prism pulse compressor used for compressing stretched pulses was built. A 200nm supercontinnum generated in an all normal dispersion photonic crystal fibre (ANDi-PCF) was compressed using the prism pulse compressor from 2ps to 140fs. The experiment and physical interpretation presented in this project suggest that a shorter pulse duration less than the measured 140fs of the compressed supercontinnum can be obtained. / AFRIKAANSE OPSOMMING: 'n Ultra-vinnige laser puls kan beskryf word in tyd of frekwensie. As die tyd-bandwydte produk van ‘n ultra-vinnige puls nie bevredig is nie, dan is die puls uitgerek. Hierdie uitrekking kan beskryf word in tyd of frekwensie. In tyd word dit tjirp genoem en in frekwensie groep vertraging dispersie. Verskeie tegnieke kan gebruik word om ‘n laser puls te rek of saam te pers. In hierdie projek is ‘n prisma puls kompressor gebou om uitgerekte pulse saam te pers. ‘n 200nm bre e bandwydte puls (“supercontinuum”) is gegenereer in ‘n fotoniese kristal optiese vesel wat uitsluitlik normale dispersie toon (ANDI-PCF) en die puls is toe saamgepers met behulp van die prisma puls kompressor van‘n oorspronklike 2ps na 140fs. Die eksperiment en fisiese interpretasie wat in hierdie projek aangebied word dui daarop dat ‘n nog korter puls, minder as die gemete 140 fs, verkry kan word deur die bre e bandwydte puls verder saam te pers.

Thesis (MSc)-- Stellenbosch University, 2013. / ENGLISH ABSTRACT: A Magneto Optical Trap (MOT) is a configuration formed by three orthogonal pairs of counterpropagating circularly polarized laser beams and a magnetic field gradient. A MOT is used to cool, capture and trap large numbers of atoms in vacuum at very low temperature in K range. In this thesis the development of an experimental setup for realising a MOT of 87Rb atoms is presented. The atomic structure of Rb and the theoretical background of laser cooling and magneto optical trapping was reviewed. The influence of rubidium background pressure in the vacuum system, the laser beam size and the power and frequency on the number of the trapped atoms were studied in literature. The trapping and repumping lasers were characterised experimentally. Six circularly polarised trapping beams with equal power were formed and properly aligned to intersect at the center of the trapping cell. Two optical setups were designed and exploited to investigate and optimise the trapping beam polarisation. The repumping laser beam was successfully aligned and colinearly combined into all the trapping beams. Three different experimental setups for saturated absorption spectroscopy were developed. Saturated absorption spectra showing the hyperfine structure of both 85Rb and 87Rb isotopes were measured and are discussed. Using two saturated absorption spectroscopy setups, the frequencies of both lasers were successfully locked to the trapping and repumping transitions of 87Rb respectively. A rectangular trapping cell was designed and attached to the vacuum system. A pressure of about 10­¯7 mbar was achieved. The magnetic field coils were characterised and affixed on both sides of the cell in an anti-Helmholtz configuration. Setups for imaging and quantification of the 87Rb atoms in the MOT were designed. Finally, the procedures for demonstrating a MOT are presented. In conclusion, the current status of the project is reported, with recommendations for the future work. / AFRIKAANSE OPSOMMING: ’n Magneto optiese val (Magneto Optical Trap, MOT) is ’n konfigurasie wat gevorm word deur drie ortogonale laserbundelpare, wat elk uit twee sirkelvormig gepolariseerde bundels met teenoorgestelde voortplantingsrigtings bestaan, en ’n magneetveld gradient. ’n MOT word gebruik om ’n groot aantal atome af te koel, te vang en vas te hou in vakuum by ’n baie lae temperatuur in die K bereik. In hierdie tesis word die ontwikkeling van ’n eksperimentele optelling vir die realisering van ’n MOT van 87Rb atome voorgelê. Die atoomstruktuur van Rb en die teoretiese agtergrond van laser afkoeling en ’n magneto optiese val is hersien. Die invloed van die rubidium agtergronddruk in die vakuumstelsel, die grootte van die laserbundels en die laser drywing en frekwensie op die aantal gevangde atome is bestudeer uit die literatuur. Die MOT-laser en die optiese pomplaser is eksperimenteel gekarakteriseer. Ses sirkelvormig gepolariseerde MOT-laserbundels met gelyke drywings is gevorm en behoorlik belyn om in die middel van die MOT-sel te kruis. Twee optiese opstellings is ontwerp en gebruik om die polarisasie van die MOT-laserbundels te ondersoek en te optimeer. Die optiese pomplaserbundel is suksesvol belyn en ko-liniêr ekombineer met al die MOT-laserbundels. Drie verskillende eksperimentele opstellings vir versadigde absorpsie spektroskopie is ontwikkel. Versadigde absorpsie spektra wat die hiperfyn struktuur van beide die 85Rb en 87Rb isotope toon is gemeet en bespreek. Deur twee versadigde absorpsie spektroskopie opstellings te gebruik is die frekwensies van beide lasers suksesvol gestabiliseer op die MOT- en optiese pomp-oorgange van 87Rb onderskeidelik. ’n Reghoekige MOT-sel is ontwerp en aangesluit by die vakuumstelsel. ’n Druk van ongeveer 10­¯7 mbar is bereik. Die magneetveld spoele is gekarakteriseer en weerskante van die sel gemonteer in ’n anti-Helmholtz konfigurasie. Ten einde word die prosedures vir die demonstrasie van ’n MOT voorgelê. In die gevolgtrekking word daar verslag gedoen oor die status van die projek, met aanbevelings vir toekomstige werk.

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Techniques for estimating a signal in the presence of noise which contains outliers are currently not well developed. In this thesis, we consider a constant signal superimposed by a family of noise distributions structured as a tunable mixture f(x) = α g(x) + (1 − α) h(x) between finitesupport components of “well-behaved” noise with small variance g(x) and of “impulsive” noise h(x) with a large amplitude and strongly asymmetric character. When α ≈ 1, h(x) can for example model a cosmic ray striking an experimental detector. In the first part of our work, a method for obtaining the expected values of the positive and negative pulses in the first resolution level of a LULU Discrete Pulse Transform (DPT) is established. Subsequent analysis of sequences smoothed by the operators L1U1 or U1L1 of LULU-theory shows that a robust estimator for the location parameter for g is achieved in the sense that the contribution by h to the expected average of the smoothed sequences is suppressed to order (1 − α)2 or higher. In cases where the specific shape of h can be difficult to guess due to the assumed lack of data, it is thus also shown to be of lesser importance. Furthermore, upon smoothing a sequence with L1U1 or U1L1, estimators for the scale parameters of the model distribution become easily available. In the second part of our work, the same problem and data is approached from a Bayesian inference perspective. The Bayesian estimators are found to be optimal in the sense that they make full use of available information in the data. Heuristic comparison shows, however, that Bayes estimators do not always outperform the LULU estimators. Although the Bayesian perspective provides much insight into the logical connections inherent in the problem, its estimators can be difficult to obtain in analytic form and are slow to compute numerically. Suboptimal LULU-estimators are shown to be reasonable practical compromises in practical problems. / AFRIKAANSE OPSOMMING: Tegnieke om ’n sein af te skat in die teenwoordigheid van geraas wat uitskieters bevat is tans nie goed ontwikkel nie. In hierdie tesis aanskou ons ’n konstante sein gesuperponeer met ’n familie van geraasverdelings wat as verstelbare mengsel f(x) = α g(x) + (1 − α) h(x) tussen eindige-uitkomsruimte geraaskomponente g(x) wat “goeie gedrag” en klein variansie toon, plus “impulsiewe” geraas h(x) met groot amplitude en sterk asimmetriese karakter. Wanneer α ≈ 1 kan h(x) byvoorbeeld ’n kosmiese straal wat ’n eksperimentele apparaat tref modelleer. In die eerste gedeelte van ons werk word ’n metode om die verwagtingswaardes van die positiewe en negatiewe pulse in die eerste resolusievlak van ’n LULU Diskrete Pulse Transform (DPT) vasgestel. Die analise van rye verkry deur die inwerking van die gladstrykers L1U1 en U1L1 van die LULU-teorie toon dat hul verwagte gemiddelde waardes as afskatters van die liggingsparameter van g kan dien wat robuus is in die sin dat die bydrae van h tot die gemiddeld van orde grootte (1 − α)2 of hoër is. Die spesifieke vorm van h word dan ook onbelangrik. Daar word verder gewys dat afskatters vir die relevante skaalparameters van die model maklik verkry kan word na gladstryking met die operatore L1U1 of U1L1. In die tweede gedeelte van ons werk word dieselfde probleem en data vanuit ’n Bayesiese inferensie perspektief benader. Die Bayesiese afskatters word as optimaal bevind in die sin dat hulle vol gebruikmaak van die beskikbare inligting in die data. Heuristiese vergelyking wys egter dat Bayesiese afskatters nie altyd beter vaar as die LULU afskatters nie. Alhoewel die Bayesiese sienswyse baie insig in die logiese verbindings van die probleem gee, kan die afskatters moeilik wees om analities af te lei en stadig om numeries te bereken. Suboptimale LULU-beramers word voorgestel as redelike praktiese kompromieë in praktiese probleme.