Analytical Study of Light Propagation in Highly Nonlinear Media

The present dissertation is devoted to the construction of exact and approximate analytical solutions of the problem of light propagation in highly nonlinear media. It is demonstrated that for many experimental conditions, the problem can be studied under the geometrical optics approximation with a sufficient accuracy. Based on the renormalization group symmetry analysis, exact analytical solutions of the eikonal equations with a higher order refractive index are constructed. A new analytical approach to the construction of approximate solutions is suggested. Based on it, approximate solutions for various boundary conditions, nonlinear refractive indices and dimensions are constructed. Exact analytical expressions for the nonlinear self-focusing positions are deduced. On the basis of the obtained solutions a general rule for the single filament intensity is derived; it is demonstrated that the scaling law (the functional dependence of the self-focusing position on the peak beam intensity) is defined by a form of the nonlinear refractive index but not the beam shape at the boundary. Comparisons of the obtained solutions with results of experiments and numerical simulations are discussed.

Fabrication of diamond nanostructures and investigation of the imbedded NV centers

Diamant ist ein Material mit vielen außerordentlichen Eigenschaften, die ihn zu einem äußerst vielversprechenden Kandidaten für Anwendungen in Wissen-schaft und Technik machen. In den letzten Jahren wurde Diamant häufig als einzigartige Plattform für neue Anwendungen beispielsweise in der Quanteninformationstechnologie (QIT) oder in der Magnetometrie im Nanometermaßstab eingesetzt, wobei einer der wichtigsten lumineszierenden Gitterdefekte im Diamantgitter eingesetzt wird. Dabei handelt es sich um die sogenannten Stickstoff/Fehlenstellen-Farbzentren (NV-Zentren), die im sichtbaren Bereich mit einer absoluten Photostabilität bei Raumtemperatur emittieren. In dieser Arbeit wurden NV-Zentren in Diamantnanokristalliten und –nanosäulen untersucht, die während des Wachstumsprozesses erzeugt wurden. Einzelne Diamantnanokristallite und nanokristalline Diamantschichten (NCD), aus denen Nanosäulen geätzt wurden, wurden mithilfe der Hot Filament Chemical Vapour Deposition (HFCVD) abgeschieden. Zu Vergleichszwecken wurden auch ultrananokristalline Diamantschichten (UNCD) mittels Mikrowellen-CVD (MWCVD) hergestellt. Die Filme wurden sorgfältig in Bezug auf ihre Morphologie, kristallinen Eigenschaften und Zusammensetzung untersucht. Um die Möglichkeit einer Integration dieser Diamantschichten mit temperaturempfindlichen Materialien wie III/V-Halbleitern, Metallen mit niedrigem Schmelzpunkt oder Polymeren zu untersuchen, wurde der Einfluss der Substrattemperatur ermittelt. Eindimensionale NCD- und UNCD-Diamantnanostrukturen wurden mithilfe der Elektronenstrahllithographie (EBL) und reaktivem Ionenätzen in einem induktiv gekoppelten O2-Plasma (ICP-RIE) hergestellt. Zur Vorbereitung wurden zunächst die Ätzraten in Abhängigkeit von den vier wichtigsten Parametern ermittelt. Weitere Erkenntnisse über die Ätzmechanismen wurden durch Ätzexperiment mit unstrukturierten NCD- und UNCD-Schichten erhalten Mittels der EBL konnten mithilfe von Gold-Ätzmasken Nanosäulen mit Durchmessern von 50 nm bis zu 1 μm hergestellt werden.Eine optische Charakterisierung der NCD- und UNCD-Nanosäulen erfolgte mithilfe von Fluorenzenz-Mapping und Photomumineszenz-Spektroskopie. Diese Messungen ergaben, dass in beiden Arten von Säulen NV-Zentren vorhanden sind. Allerdings wurden nur in NCD-Säulen die gewünschten NV--Zentren gefunden, in UNCD-Säulen hingegen nur NV0-Zentren.

Surface modifications of nanocrystalline diamond films and their functionalization with phthalocyanines

Boron-doped diamond is a promising electrode material for a number of applications providing efficient carrier transport, a high stability of the electrolytic performance with time, a possibility for dye-sensitizing with photosensitive molecules, etc. It can be functionalized with electron donor molecules, like phthalocyanines or porphyrins, for the development of light energy conversion systems. For effective attachment of such molecules, the diamond surface has to be modified by plasma- or photo-chemical processes in order to achieve a desired surface termination. In the present work, the surface modifications of undoped and boron-doped nanocrystalline diamond (NCD) films and their functionalization with various phthalocyanines (Pcs) were investigated. The NCD films have been prepared by hot filament chemical vapor deposition (HFCVD) on silicon substrates and were thereafter subjected to modifications with O2 or NH3 plasmas or UV/O3 treatments for exchange of the H-termination of the as-grown surface. The effectiveness of the modifications and their stability with time during storage under different ambients were studied by contact angle measurements and X-ray photoelectron spectroscopy (XPS). Furthermore, the surface roughness after the modifications was investigated with atomic force microscopy (AFM) and compared to that of as-grown samples in order to establish the appearance of etching of the surface during the treatment. The as-grown and the modified NCD surfaces were exposed to phthalocyanines with different metal centers (Ti, Cu, Mn) or with different side chains. The results of the Pc grafting were investigated by XPS and Raman spectroscopy. XPS revealed the presence of nitrogen stemming from the Pc molecules and traces of the respective metal atoms with ratios close to those in the applied Pc. In a next step Raman spectra of Ti-Pc, Cu-Pc and Mn-Pc were obtained with two different excitation wavelengths (488 and 785 nm) from droplet samples on Si after evaporation of the solvent in order to establish their Raman fingerprints. The major differences in the spectra were assigned to the effect of the size of the metal ion on the structure of the phthalocyanine ring. The spectra obtained were used as references for the Raman spectra of NCD surfaces grafted with Pc. Finally, selected boron doped NCD samples were used after their surface modification and functionalization with Pc for the preparation of electrodes which were tested in a photoelectrochemical cell with a Pt counter electrode and an Ag/AgCl reference electrode. The light sources and electrolytes were varied to establish their influence on the performance of the dye-sensitized diamond electrodes. Cyclic voltammetry measurements revealed broad electrochemical potential window and high stability of the electrodes after several cycles. The open circuit potential (OCP) measurements performed in dark and after illumination showed fast responses of the electrodes to the illumination resulting in photocurrent generation.