Optical waveguides, quantum dot emitters, and flat top beam shapers were designed and fabricated by two soft lithographic techniques; micro transfer molding (microTM) and vacuum assisted microfluidics (VAM). Optical waveguides were fabricated through a microTM technique that utilizes a poly dimethylsiloxane (PDMS) stamp. Generation of the flexible stamp required development of a channel waveguide pattern mask, defined by maskless lithography, and followed by construction of a three dimensional channel waveguide master, acquired through contact lithography on a glass substrate coated with SU-8 photoresist. Creation of a positive imprint replicating mold was accomplished through prepolymer PDMS solution settling and curing around the master. Waveguide fabrication was achieved through PDMS conformal contact on, and subsequent curing of, ultraviolet (UV) polymer resins on a silicon substrate. A slight modification of the microTM PDMS stamp, whereby inlet and outlet tunnels were incorporated, resulted in a novel VAM structure and correspondingly waveguides. Waveguide propagation losses were determined to be 1.14 dB/cm and 0.68 dB/cm for the microTM and VAM fabricated waveguides, respectively. A lithographic approach employing quantum dots doped in SU-8 photoresist has led to the realization of a new quantum dot emitter. Uniform coating of a doped material on a silver coated substrate was followed by contact mask lithography. Evaporation of a thin silver layer, upon development of the resultant quantum dot doped channel waveguide structure, facilitates confined emission. Successful edge emitting was demonstrated with blue laser pumping. The lithographic fabrication of such quantum dot emitter is successfully replaced by soft lithographic VAM technique. A flat top beam shaper, whose profile was developed on cured UV polymer resins, was fabricated by microTM technique. The master used for the development of the PDMS stamp was produced through an iterative wet etching process capable of achieving etching depths as small as a few nanometers. Comparisons between the reference wet etched beam shaper and the microTM based beam shaper produced near identical output flat top beams from incident Gaussian beams. Through this research work, successful soft lithographic fabrication of optical waveguides, quantum dot emitters, and flat top beam shapers were demonstrated. The vast potential exhibited by these and other related technologies show great promise for cost-effective mass production of various micro optics and integrated photonic components.

>Magister Scientiae - MSc / This dissertation consists of two main sections. The first section focuses on generating zero order Bessel beams using axicons. An axicon with an opening angle y = 5⁰ was illuminated with a Gaussian beam of width ω₀ = 1.67 mm from a cw fiber laser with central wavelength λ = 1064 nm to generate zero order Bessel beams with a central spot radius r₀ = 8.3 ± 0.3 μm and propagation distance ½zmax = 20.1 ± 0.5 mm. The central spot size of a Bessel beam changes slightly along the propagation distance. The central spot radius r₀ can be varied by changing the opening angle of the axicon, y, and the wavelength of the beam. The second section focuses on applications of the generated Bessel beams in laser microdrilling. A Ti:Sapphire pulsed femtosecond laser (λ = 775 nm, ω₀ = 2.5 mm, repetition rate kHz, pulse energy mJ, and pulse duration fs) was used to generate the Bessel beams for drilling stainless steel thin sheets of thickness 50 μm and 100 μm and microscopic glass slides 1 mm thick. The central spot radius was r₀ = 15.9 ± 0.3 μm and ½zmax = 65.0 ± 0.5 mm. The effect of the Bessel beam shape on the quality of the holes was analysed and the results were discussed. It was observed that Bessel beams drill holes of better quality on transparent microscopic glass slides than on stainless steel sheet. The holes drilled on stainless steel sheets deviated from being circular on both the top and bottom surface for both thicknesses. However the holes maintained the same shape on both sides of each sample, indicating that the walls are close to being parallel. The holes drilled on the glass slides were circular and their diameters could be measured. The measured diameter (15.4±0.3 μm) of the hole is smaller than the diameter of the central spot (28.2 ± 0.1 μm) of the Bessel beam. Increasing the pulse energy increased the diameter of the drilled hole to a value close to the measured diameter of the central spot.

No description available.

Magnetic resonance imaging (MRI) has become one of the premier non-invasive diagnostic tools, with around 60 million MRI scans applied each year. However, there is a risk of thermal injury due to radiofrequency (RF) induction heating of the tissue and implanted metallic device for the patients with the implanted metallic devices. Especially, MRI of the patients with implanted elongated devices such as pacemakers and deep brain stimulation systems is considered contraindicated. Many efforts, such as determining preferred MRI parameters, modifying magnetic field distribution, designing new structure and exploring new materials, have been made to reduce the induction heating. Improving the MRI-compatibility of implanted metallic devices by modifying the properties of the existing materials would be valuable. To evaluate the temperature rise due to RF induction heating on a metallic implant during MRI procedure, an electromagnetic model and thermal model are studied. The models consider the shape of RF magnetic pulses, interaction of RF pulses with metal plate, thermal conduction inside the metal and the convection at the interface between the metal and the surroundings. Transient temperature variation and effects of heat transfer coefficient, reflectivity and MRI settings on the temperature change are studied. Laser diffusion is applied to some titanium sheets for a preliminary study. An electromagnetic and thermal model is developed to choose the proper diffusant. Pt is the diffusant in this study. An electromagnetic model is also developed based on the principles of inverse problems to calculate the electromagnetic properties of the metals from the measured magnetic transmittance. iv This model is used to determine the reflectivity, dielectric constant and conductivity of treated and as-received Ti sheets. The treated Ti sheets show higher conductivity than the as-received Ti sheets, resulting higher reflectivity. A beam shaping lens system which is designed based on vector diffraction theory is used in laser diffusion. Designing beam shaping lens based on the vector diffraction theory offers improved irradiance profile and new applications such as polarized beam shaping because the polarization nature of laser beams is considered. Laser Pt diffusion are applied on the titanium and tantalum substrates using different laser beam polarizations. The concentration of Pt and oxygen in those substrates are measured using Energy Dispersive X-Ray Spectroscopy (EDS). The magnetic transmittance and conductivity of those substrates are measured as well. The effects of laser beam polarizations on Pt diffusion and the magnetic transmittance and conductivity of those substrates are studied. Treated Ti sheets show lower magnetic transmittance due to the increased conductivity from diffused Pt atoms. On the other hand, treated Ta sheets show higher magnetic transmittance due to reduced conductivity from oxidation. Linearly polarized light can enhance the Pt diffusion because of the excitation of local vibration mode of atoms. Laser Pt diffusion and thermo-treatment were applied on the Ta and MP35N wires. The Pt concentration in laser platinized Ta and MP35N wires was determined using EDS. The ultimate tensile strength, fatigue lives and lead tip heating in real MRI environment of those wires were measured. The lead tip hating of the platinized Ta wires is 42 % less than the as-received Ta wire. The diffused Pt increases the conductivity of Ta wires, resulting in more reflection of magnetic field. In the case of the platinized MP35N wire, the reduction in lead tip heating was only 1 °C v due to low concentration of Pt. The weaker ultimate tensile strength and shorter fatigue lives of laser-treated Ta and MP35N wires may attribute to the oxidation and heating treatment.

Laser drilling of microvias for organic packaging applications is studied in present research. Thermal model is essential to understand the laser-materials interactions and to control laser drilling of blind micro holes through polymeric dielectrics in multilayer electronic substrates. In order to understand the profile of the drilling front irradiated with different laser beam profiles, a transient heat conduction model including vaporization parameters is constructed. The absorption length in the dielectric is also considered in this model. Therefore, the volumetric heating source criteria are applied in the model and the equations are solved analytically. The microvia drilling speed, temperature distribution in the dielectric and the thickness of the residue along the microvia walls and at the bottom of the microvia are studied for different laser irradiation conditions. An overheated metastable state of material is found to exist inside the workpiece. The overheating parameters are calculated for various laser drilling parameters and are used to predict the onset of thermal damage and to minimize the residue. As soon as a small cavity is formed during the drilling process, the concave curvature of the drilling front acts as a concave lens that diverges the incident laser beam. This self-defocusing effect can greatly reduce the drilling speed. This effect makes the refractive index of the substrate at different wavelengths an important parameter for laser drilling. A numerical thermal model is built to study the effect of self-defocusing for laser microvias drilling in multilayer electronic substrates with Nd:YAG and CO2 lasers.. The laser ablation thresholds was calculated with this model for the CO2 and Nd:YAG lasers respectively. Due to the expulsion of materials because of high internal pressures in the case of Nd:YAG laser microvia drilling, the ablation threshold may be far below the calculated value. A particular laser beam shape, such as pitch fork, was found to drill better holes than the Gaussian beam in terms of residue and tapering angle. Laser beam shaping technique is used to produce the desired pitchfork beam. Laser beam shaping allows redistribution of laser power and phase across the cross-section of the beam for drilling perfectly cylindrical holes. An optical system, which is comprised of three lenses, is designed to transform a Gaussian beam into a pitchfork beam. The first two lenses are the phase elements through which a Gaussian laser beam is transformed into a super Gaussian beam. The ray tracing technique of geometrical optics is used to design these phase elements. The third lens is the transform element which produces a pitchfork profile at the focal plane due to the diffraction effect. A pinhole scanning power meter is used to measure the laser beam profile at the focal plane to verify the existence of the pitchfork beam. To account for diffraction effect, the above mentioned laser beam shaping system was optimized by iterative method using Adaptive Additive algorithm. Fresnel diffraction is used in the iterative calculation. The optimization was target to reduce the energy contained in the first order diffraction ring and to increase the depth of focus for the system. Two diffractive optical elements were designed. The result of the optimization was found dependent on the relation between the diameter of the designed beam shape and the airy disk diameter. If the diameter of the designed beam is larger, the optimization can generate better result. Drilling experiment is performed with a Q-switched CO2 laser at wavelength of 9.3 μm. Comparison among the drilling results from Gaussian beam, Bessel beam and Pitchfork beam shows that the pitchfork beam can produce microvias with less tapering angle and less residue at the bottom of the via. Laser parameters were evaluated experimentally to study their influences on the via quality. Laser drilling process was optimized based on the evaluation to give high quality of the via and high throughput rate. Nd:YAG laser at wavelengths of 1.06 μm and 532 nm were also used in this research to do microvias drilling. Experimental result is compared with the model. Experimental results show the formation of convex surfaces during laser irradiation. These surfaces eventually rupture and the material is removed explosively due to high internal pressures. Due to the short wavelength, high power, high efficiency and high repetition rate, these lasers exhibit large potentials for microvias drilling.

In vielen Anwendungsgebieten der Lasermesstechnik kann eine adaptive örtliche und zeitliche Lichtfeldformung völlig neue Perspektiven eröffnen. In der Optogenetik sind beispielsweise sowohl schnell in drei Dimensionen adressierbare Einzelpunkte mit einem maximalen Durchmesser von 10 μm für die Stimulation einzelner Zellen als auch komplexe Muster für die Aktivierung oder Inhibierung ganzer Zellgruppen notwendig, um fortgeschrittene Analysen neuronaler Netzwerke durchzuführen. Computergenerierte Hologramme (CGH) sind durch die vielseitigen Möglichkeiten der Amplituden- und Phasenmodulation für die Mustererzeugung am besten geeignet. Zur Darstellung von CGH weit verbreitete Flüssigkristall-Flächenlichtmodulatoren besitzen oft eine Megapixelauflösung aber eine Bildrate von nur wenigen Hertz. Durch Innovationen im Consumer-Bereich stehen mit mikroelektromechanischen Scannerspiegeln und ferroelektrischen binären Phasenmodulatoren neuartige Bauelemente zur Verfügung, die gleichzeitig hohe Orts- und Zeitauflösung vereinen. Aufbauend auf solchen Geräten mit 250 Hz bzw. 1,7 kHz Bildrate wurden in dieser Arbeit computergestützte adaptive optische Systeme für den Bereich des lasergenerierten Ultraschalls sowie für die Optogenetik entwickelt und angewendet. Anhand von Computersimulationen wurden Methoden zur schnellen Erzeugung binärer Phasenhologramme verglichen. Für Fresnelhologramme führt eine Fehlerdiffusionsmethode zu rekonstruierten Bildern ähnlicher der gewünschten Intensitätsverteilung und ist dabei mehr als 10× schneller als die zweitbeste Methode, welche auf dem Gerchberg-Saxton-Algorithmus beruht. Im Bereich des lasergenerierten Ultraschalls konnten durch einen mikroelektromechanischen Senkspiegel-Modulator ringförmige Beleuchtungsmuster unterschiedlichen Durchmessers generiert werden, die eine Fokussierung von Scherwellen in verschiedenen Tiefen in einem Aluminiumwerkstück bewirkten. So können potenziell Materialeigenschaften kontaktfrei mit hoher Bandbreite erfasst werden. Für die optogenetische Netzwerkanalyse wurden zwei Systeme zur zellulären und subzellulären dreidimensionalen Stimulation und Inhibierung entwickelt. Durch ein iteratives Korrekturverfahren mit Zernike-Polynomen konnte durch die Korrektur systeminhärenter Aberrationen eine nahezu beugungsbegrenzte laterale Ortsauflösung erreicht werden. Abschließend wurde die zeitliche Entwicklung der Konnektivität neuronaler Netze mit diesen Systemen beobachtet. Durch die gezielte Einzelzellstimulation konnten dabei allein mit elektrischer Stimulation nicht sichtbare Effekte wie distanzabhängige Signalgeschwindigkeiten und Verknüpfungen zwischen nicht anhand elektrischer Signale erfassbaren Neuronen beobachtet werden. Dies eröffnet neue Wege z.B. für pharmakologische Untersuchungen und die Analyse neurodegenerativer Krankheiten.:Abkürzungsverzeichnis V Symbolverzeichnis VII Abbildungsverzeichnis XI Tabellenverzeichnis XV 1 Motivation/Einleitung 1 2 Grundlagen der Strahlformung 5 2.1 Physikalisch-mathematische Grundlagen 5 2.1.1 Von den Maxwellgleichungen zur Helmholtzgleichung 5 2.1.2 Die Winkelspektrumsmethode zur Beschreibung der Lichtausbreitung 6 2.1.3 Phasen-Beschreibung einer Linse 8 2.1.4 Zernike-Polynome 10 2.2 Computergenerierte Hologramme 10 2.2.1 Direkte Berechnung 11 2.2.2 Fourier- und Fresnelhologramme 12 2.2.3 Simulated Annealing 16 2.2.4 Phase retrieval mittels Gerchberg-Saxton-Algorithmus 19 3 Binäre Phasenhologramme 21 3.1 Gerchberg-Saxton 23 3.2 Thresholding 23 3.3 Error Diffusion 24 3.4 Methodenvergleich - Fresnelhologramme 28 3.5 Methodenvergleich - Fourierhologramme 31 3.6 Zusammenfassung 33 4 Anwendung I: Laserultraschall 35 4.1 Einleitung 35 4.2 Problemstellung 35 4.3 Strahlformung beliebiger Wellenfronten mit Phase Retrieval 37 4.4 Versuchsaufbau 40 4.5 Durchgeführte Messungen 42 4.6 Zusammenfassung 45 5 Anwendung II: Optogenetik 47 5.1 Problemstellung und Stand der Technik 47 5.2 Versuchsaufbau für Fresnelhologramme 53 5.2.1 Versuchsaufbau für die Verwendung von Fresnelhologrammen 53 5.2.2 Ferroelektrischer binärer räumlicher Phasenmodulator 54 5.2.3 Berechnung computergenerierter Fresnelhologramme 56 5.2.4 Verwendete Zellkultur 57 5.2.5 Minimale Ortsauflösung 58 5.2.6 Framerate des Modulators 60 5.2.7 Erzeugung mehrerer Fokusse 61 5.2.8 Beispielhafte Einzelzellstimulation 63 5.3 Versuchsaufbau für die Verwendung von Fourierhologrammen 65 5.3.1 Experimenteller Aufbau 66 5.3.2 Abschätzung der Ortsauflösung 68 5.3.3 Erzeugung von Lichtmustern und Aberrationskorrektur 69 5.3.4 Erzeugung mehrerer Fokusse 72 5.3.5 Testmessungen mit Fluoreszenzpartikeln in 2d/3d 73 5.3.6 Zusammenfassung 77 5.4 Untersuchung der Konnektivität neuronaler Netze 78 5.4.1 Zellkultur 80 5.4.2 Lokalisierung einzelner Neuronen 80 5.4.3 Experimentelles Vorgehen 81 5.4.4 Ergänzungen zum holographischen Stimulationsaufbau 83 5.4.5 Spike-Sorting 84 5.4.6 Vergleich von Aktivitätsprofilen von Weitfeld- und holographischer Stimulation 85 5.4.7 Peri-Event-Raster und -Zeithistogramme 86 5.4.8 Post-Stimulus-Zeit-Histogramm (PSTH) der holographischen Stimulation 86 5.4.9 Entfernungsabhängige Reaktionen der Neuronen auf holographische Stimulation 86 5.4.10 Funktionellen Konnektivität der Spontanaktivität (Baseline) 87 5.4.11 Kartierung funktioneller Konnektivität durch Einzelzellstimulation 88 5.4.12 Holographische Einzelzellstimulation 90 5.4.13 Zeitliche Dynamik der Konnektivität 95 5.4.14 Diskussion 99 5.4.15 Zusammenfassung 101 6 Zusammenfassung 103 Literaturverzeichnis 107 / In many application areas of laser measurement technology, adaptive local and temporal light field shaping can open up completely new perspectives. In optogenetics, for example, single foci with a maximum diameter of 10 μm, addressable in three dimensions, as well as complex light patterns are necessary for the the activation or inhibition of single cells or whole cell groups, respectively, to perform in-depth analyses of neuronal networks. Computer-generated holograms (CGH) are best suited for this purpose due to their versatile possibilities of amplitude and phase modulation. To display these, fast spatial light modulators (SLM) with a large number of pixels are required. Widely used liquid crystal SLMs, however, often have a megapixel resolution but a frame rate of only a few Hertz. Due to innovations in the consumer sector, microelectromechanical scanner mirrors and ferroelectric binary phase modulators are available, which offer high spatial and temporal resolution at the same time. Building on such devices with 250 Hz and 1.7 kHz frame rate, respectively, this work presents the development and application of computer-aided adaptive optical systems for laser-generated ultrasound and optogenetics. Based on computer simulations, methods for the fast generation of binary phase holograms were compared. For Fresnel holograms, an error diffusion method led to reconstructed images with highest similarity to the desired intensity distributions and was more than 10× faster than the second best method, which was based on the Gerchberg-Saxton algorithm. In the field of laser-generated ultrasound, a microelectromechanical modulator was used to generate ring-shaped illumination patterns of different diameters, which allow a focussing of shear waves in varying depths in an aluminium workpiece. This way, material properties can potentially be detected without contact and with a high bandwidth. For optogenetic network analysis, two systems for cellular and subcellular three-dimensional stimulation and inhibition were developed. Using ferroelectric liquid crystal modulators, frame rates up to the kilohertz range can be achieved. An iterative correction procedure with Zernike polynomials was able to correct system-inherent aberrations to achieve almost diffraction-limited lateral spatial resolution. Applying these systems, the temporal evolution of neural network connectivity was observed. Through targeted single-cell stimulation, effects not visible with electrical stimulation alone, such as distance-dependent signal velocities and connections between neurons undetectable by electrical recording, were observed. This opens up new ways for pharmacological investigations and the analysis of neurodegenerative diseases.:Abkürzungsverzeichnis V Symbolverzeichnis VII Abbildungsverzeichnis XI Tabellenverzeichnis XV 1 Motivation/Einleitung 1 2 Grundlagen der Strahlformung 5 2.1 Physikalisch-mathematische Grundlagen 5 2.1.1 Von den Maxwellgleichungen zur Helmholtzgleichung 5 2.1.2 Die Winkelspektrumsmethode zur Beschreibung der Lichtausbreitung 6 2.1.3 Phasen-Beschreibung einer Linse 8 2.1.4 Zernike-Polynome 10 2.2 Computergenerierte Hologramme 10 2.2.1 Direkte Berechnung 11 2.2.2 Fourier- und Fresnelhologramme 12 2.2.3 Simulated Annealing 16 2.2.4 Phase retrieval mittels Gerchberg-Saxton-Algorithmus 19 3 Binäre Phasenhologramme 21 3.1 Gerchberg-Saxton 23 3.2 Thresholding 23 3.3 Error Diffusion 24 3.4 Methodenvergleich - Fresnelhologramme 28 3.5 Methodenvergleich - Fourierhologramme 31 3.6 Zusammenfassung 33 4 Anwendung I: Laserultraschall 35 4.1 Einleitung 35 4.2 Problemstellung 35 4.3 Strahlformung beliebiger Wellenfronten mit Phase Retrieval 37 4.4 Versuchsaufbau 40 4.5 Durchgeführte Messungen 42 4.6 Zusammenfassung 45 5 Anwendung II: Optogenetik 47 5.1 Problemstellung und Stand der Technik 47 5.2 Versuchsaufbau für Fresnelhologramme 53 5.2.1 Versuchsaufbau für die Verwendung von Fresnelhologrammen 53 5.2.2 Ferroelektrischer binärer räumlicher Phasenmodulator 54 5.2.3 Berechnung computergenerierter Fresnelhologramme 56 5.2.4 Verwendete Zellkultur 57 5.2.5 Minimale Ortsauflösung 58 5.2.6 Framerate des Modulators 60 5.2.7 Erzeugung mehrerer Fokusse 61 5.2.8 Beispielhafte Einzelzellstimulation 63 5.3 Versuchsaufbau für die Verwendung von Fourierhologrammen 65 5.3.1 Experimenteller Aufbau 66 5.3.2 Abschätzung der Ortsauflösung 68 5.3.3 Erzeugung von Lichtmustern und Aberrationskorrektur 69 5.3.4 Erzeugung mehrerer Fokusse 72 5.3.5 Testmessungen mit Fluoreszenzpartikeln in 2d/3d 73 5.3.6 Zusammenfassung 77 5.4 Untersuchung der Konnektivität neuronaler Netze 78 5.4.1 Zellkultur 80 5.4.2 Lokalisierung einzelner Neuronen 80 5.4.3 Experimentelles Vorgehen 81 5.4.4 Ergänzungen zum holographischen Stimulationsaufbau 83 5.4.5 Spike-Sorting 84 5.4.6 Vergleich von Aktivitätsprofilen von Weitfeld- und holographischer Stimulation 85 5.4.7 Peri-Event-Raster und -Zeithistogramme 86 5.4.8 Post-Stimulus-Zeit-Histogramm (PSTH) der holographischen Stimulation 86 5.4.9 Entfernungsabhängige Reaktionen der Neuronen auf holographische Stimulation 86 5.4.10 Funktionellen Konnektivität der Spontanaktivität (Baseline) 87 5.4.11 Kartierung funktioneller Konnektivität durch Einzelzellstimulation 88 5.4.12 Holographische Einzelzellstimulation 90 5.4.13 Zeitliche Dynamik der Konnektivität 95 5.4.14 Diskussion 99 5.4.15 Zusammenfassung 101 6 Zusammenfassung 103 Literaturverzeichnis 107

Reflector design stemmed from the need to shape the light emitted by candles or lamps. Over 2,000 years ago people realized that a mirror shaped as a parabola can concentrate light, and thus significantly boosts its intensity, to the point where objects can be set afire. Nowadays many applications require an accurate control of light, such as automotive headlights, streetlights, projection displays, and medical illuminators. In all cases light emitted from a light source can be shaped into a desired target distribution with a reflective surface. Design methods for systems with rotational and translational symmetry were devised in the 1930s. However, the freeform reflector shapes required to illuminate targets with no such symmetries proved to be much more challenging to design. Even when the source is assumed to be a point, the reflector shape is governed by a set of second-order partial non-linear differential equations that cannot be solved with standard numerical integration techniques. An iterative approach to solve the problem for a discrete target, known as the method of supporting ellipsoids, was recently proposed by Oliker. In this research we report several efficient implementations of the method of supporting ellipsoids, based on the point source approximation, and we propose new reflector design techniques that take into account the extent of the source. More specifically, this work has led to three major achievements. First, a thorough analysis of the method of supporting ellipsoids was performed that resulted in two alternative implementations of the algorithm, which enable a fast generation of freeform reflector shapes within the point source approximation. We tailored the algorithm in order to provide control over the parameters of interest to the designers, such as the reflector scale and geometry. Second, the shape generation algorithm was used to analyze how source flux can be mapped onto the target. We derived the condition under which a given source-target mapping can be achieved with a smooth continuous surface, referred as the integrability condition. We proposed a method to derive mappings that satisfy the integrability condition. We then use these mappings to quickly generate reflector shapes that create continuous target distributions as opposed to reflectors generated with the method of supporting ellipsoids that create discrete sets of points on the target. We also show how mappings that do not satisfy the integrability condition can be achieved by introducing step discontinuities in the reflector surface. Third, we investigated two methods to design reflectors with extended sources. The first method uses a compensation approach where the prescribed target distribution is adjusted iteratively. This method is effective for compact sources and systems with rotational or translational symmetry. The second method tiles the source images created by a reflector designed with the method of supporting ellipsoids and then blends the source images together using scattering in order to obtain a continuous target distribution. This latter method is effective for freeform reflectors and target distributions with no sharp variations. Finally, several case studies illustrate how these methods can be successfully applied to design reflectors for general illumination applications such as street lighting or luminaires. We show that the proposed design methods can ease the design of freeform reflectors and provide efficient, cost-effective solutions that avoid unnecessary energy consumption and light pollution.

No description available.

No description available.

Thesis (PhD (Physics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: There are many applications where a Gaussian laser beam is not ideal, for example, in areas such as medicine, data storage, science, manufacturing and so on, and yet in the vast majority of laser systems this is the fundamental output mode. Clearly this is a limitation, and is often overcome by adapting the application in mind to the available beam. A more desirable approach would be to create a laser beam as the output that is tailored for the application in mind – so called intra-cavity laser beam shaping. The main goal of intra-cavity beam shaping is the designing of laser cavities so that one can produce beams directly as the output of the cavity with the required phase and intensity distribution. Shaping the beam inside the cavity is more desirable than reshaping outside the cavity due to the introduction of additional external losses and adjustment problems. More elements are required outside the cavity which leads to additional costs and larger physical systems. In this thesis we present new methods for phase and amplitude intra– cavity beam shaping. To illustrate the methods we give both an analytical and numerical analysis of different resonator systems which are able to produce customised phase and intensity distributions. In the introduction of this thesis, a detailed overview of the key concepts of optical resonators is presented. In Chapter 2 we consider the well–known integral iteration algorithm for intra–cavity field simulation, namely the Fox–Li algorithm and a new method (matrix method), which is based on the Fox–Li algorithm and can decrease the computation time of both the Fox–Li algorithm and any integral iteration algorithms. The method can be used for any class of integral iteration algorithms which has the same calculation integrals, with changing integrants. The given method appreciably decreases the computation time of these algorithms and approaches that of a single iteration. In Chapter 3 a new approach to modeling the spatial intensity profile from Porro prism resonators is proposed based on rotating loss screens to mimic the apex losses of the prisms. A numerical model based on this approach is presented which correctly predicts the output transverse field distribution found experimentally from such resonators. In Chapter 4 we present a combination of both amplitude and phase shaping inside a cavity, namely the deployment of a suitable amplitude filter at the Fourier plane of a conventional resonator configuration with only spherical curvature optical elements, for the generation of Bessel–Gauss beams as the output. In Chapter 5 we present the analytical and numerical analyses of two new resonator systems for generating flat–top–like beams. Both approaches lead to closed form expressions for the required cavity optics, but differ substantially in the design technique, with the first based on reverse propagation of a flattened Gaussian beam, and the second a metamorphosis of a Gaussian into a flat–top beam. We show that both have good convergence properties, and result in the desired stable mode. In Chapter 6 we outline a resonator design that allows for the selection of a Gaussian mode by diffractive optical elements. This is made possible by the metamorphosis of a Gaussian beam into a flat–top beam during propagation from one end of the resonator to the other. By placing the gain medium at the flat–top beam end, it is possible to extract high energy in a low–loss cavity. / AFRIKAANSE OPSOMMING: Daar is verskeie toepassings waar ʼn Gaussiese laser bundel nie ideaal is nie, in gebiede soos mediese veld, stoor van data, vervaardiging en so meer, en tog word die meeste laser sisteme in die fundamentele mode bedryf. Dit is duidelik ’n beperking, en word meestal oorkom deur aanpassing van die toepassing tot die beskikbare bundel. ’n Beter benadering sou wees om ʼn laser bundel te maak wat afgestem is op die toepassing - sogenaamde intra-resonator bundel vorming. Die hoofdoel van intra-resonator bundel vorming is om resonators te ontwerp wat direk as uitset kan lewer wat die gewenste fase en intensiteits-distribusie vertoon. Vorming van die bundel in die resonator is voordeliger omdat die vorming buite die resonator tot addisionele verliese asook verstellings probleme bydra. Meer elemente word benodig buite die resonator wat bydra tot hoër koste en groter sisteme. In hierdie tesis word nuwe fase en amplitude intra-resonator bundelvormings metodes voorgestel. Om hierdie metode te demonstreer word analitiese en numeriese analises vir verskillende resonator sisteme wat aangepaste fase en intensiteit distribusies produseer, bespreek. In die inleiding van die tesis word ʼn detailleer oorsig oor die sleutel konsepte van optiese resonators voorgelê. In hoofstuk 2 word die bekende integraal iterasie algoritme vir intraresonator veld simulasie, naamlik die Fox-Li algoritme, en ʼn nuwe metode (matriks metode), wat gebaseer is op die Fox-Li algoritme, en die berekeningstyd van beide die Fox-Li algoritme en enige ander integraal iterasie algoritme verminder. Die metode kan gebruik word om enige klas van integraal iterasie algoritmes wat dieselfde berekenings integrale het, met veranderde integrante (waar die integrand die veld van die lig golf is in die geval van die Fox-Li algoritme, IFTA, en die skerm metode. Die voorgestelde metode verminder die berekeningstyd aansienlik, en is benaderd die van ʼn enkel iterasie berekening. In hoofstuk 3 word ʼn nuwe benadering om die modellering van die ruimtelike intensiteitsprofiel van Porro prisma resonators, gebaseer op roterende verliese skerms om die apeks-verliese van die prismas te benader, voorgestel. ʼn Numeriese model gebaseer op hierdie benadering wat die uitset van die transversale veld distribusie in eksperimentele resonators korrek voorspel, word voorgestel. In hoofstuk 4 word ʼn tegniek vir die generering van Bessel-Gauss bundels deur die gebruik van ʼn kombinasie van amplitude en fase vorming in die resonator en ʼn geskikte amplitude filter in die Fourier vlak van ʼn konvensionele resonator konfigurasie met optiese elemente wat slegs sferiese krommings het, voorgestel. In hoofstuk 5 word die analitiese en numeriese analises van twee nuwe resonator sisteme vir die generering van sogenaamde “flat–top” bundels voorgestel. Beide benaderings lei na ʼn geslote vorm uitdrukking vir die resonator optika wat benodig word, maar verskil noemenswaardig in die ontwerptegniek. Die eerste is baseer op die terug voortplanting van plat Gaussiese bundel, en die tweede op metamorfose van Gaussiese “flat-top” bundel. Ons toon aan dat beide tegnieke goeie konvergensie het, en in die gevraagde stabiele modus lewer. In hoofstuk 6 skets ons die resonator ontwerp wat die selektering van ʼn Gaussiese modus deur diffraktiewe optiese element moontlik maak. Dit word moontlik deur die metamorfose van ’n Gaussiese bundel na ʼn “flat-top” gedurende die voortplanting van die een kant van die resonator na die ander. Deur die wins medium aan die “flat–top” kant van die bundel te plaas word dit moontlik om hoë energie te onttrek in ʼn lae verlies resonator.