This thesis proposes a metallic hole array of a rectangular converging-diverging channel (RCDC) shape with extraordinary transmission. We use a three-dimensional (3D) finite element method to analyze the transmission characteristics of two-dimensional metallic hole arrays (2D-MHA) with RCDC. For a straight channel MHA, when the aperture size is reduced, the transmission peaks have a blue-shift. The same result is observed for a smaller gap throat for the RCDC structure. For the rectangular holes with a high length-width ratio, a similar blue-shift in the transmission peaks as well as a narrower full width at half maximum (FWHM) are observed. The asymmetry from the rectangular shape gives this structure high selectivity for light with different polarizations. Furthermore, the RCDC shape gives extra degrees of geometrical variables to 2D-MHA for tuning the location of the transmission peak and FWHM. The tunable transmission property of this structure shows promise for applications in tunable filters, photonic circuits, and biosensors. / text

Die Arbeit stellt neu entwickelte Röntgenbeugungsmethoden vor, mit deren Hilfe der Verzerrungszustand des Kristallgitters von Halbleiter-Wafern und -Bauteilen im Detail charakterisiert werden kann. Hierzu werden die aussergewöhnlichen Eigenschaften der an modernen Synchrotrons wie der ESRF (Grenoble) verfügbaren Röntgenstrahlung genutzt. <br>Im ersten Teil der Arbeit werden Röntgen-Diffraktometrie und -Topographie zu einer Untersuchungsmethode kombiniert, mit der die makroskopische Krümmung von Halbleiter-Wafern ebenso wie ihre mikroskopische Defektstruktur abgebildet werden kann. Der zweite Teil ist der Untersuchung von epitaktisch gewachsenen und geätzten Oberflächengittern mit Abmessungen im Submikrometer-Bereich gewidmet. Die unterschiedlichen Gitterkonstanten der beteiligten Halbleitermaterialien führen zu einem inhomogenen Verzerrungsfeld in der Probe, das sich im Röntgenbild durch eine charakteristische Verformung des Beugungsmusters in der Umgebung der Bragg-Reflexe äussert. Die Analyse der experimentell gemessenen Beugungsmuster geschieht mit Hilfe eines neu entwickelten Simulationsverfahrens, das Elastizitätstheorie und eine semi-kinematische Röntgenbeugungstheorie miteinander verbindet. Durch quantitativen Vergleich der Simulationsergebnisse mit den Messdaten kann auf den genauen Verlauf des Verzerrungsfeldes in den Proben zurückgeschlossen werden. Dieses Verfahren wird erfolgreich auf verschiedene Halbleiter-Probensysteme angewendet, und schliesslich auch auf die Untersuchung von akustischen Oberflächenwellen in Halbleiterkristallen übertragen. / This thesis presents newly developed X-ray methods which can be used to characterize in detail the state of distortion of the crystal lattice in semiconductor wafers, devices and nanostructures. The methods use the extraordinary properties of the X-rays available from modern synchrotron sources such as the ESRF (Grenoble). <br>In the first part of the thesis, X-ray diffractometry and X-ray topography are combined into a new method, called X-ray rocking curve imaging, which allows to image the macroscopic curvature of semiconductor wafers as well as the underlying microscopic defect structure. The second part of the thesis deals with the investigation of epitaxially grown and subsequently etched semiconductor gratings with lateral periods below the micrometer. The lattice mismatch between the different materials used in heteroepitaxy leads to a non-uniform strain field in the sample, which is reflected in a characteristic distortion of the X-ray diffraction pattern around each Bragg peak. The experimental data are evaluated with the help of a newly developed simulation procedure which combines elasticity theory with a semi-kinematical theory of X-ray diffraction. From a quantitative comparison of measured and simulated data the detailed shape of the strain field in the samples can be deduced. This procedure is used successfully for the structural characterization of different types of semiconductor gratings, and is finally applied also to the investigation of surface acoustic waves in crystals.

In this thesis, an investigation into the modal characteristics of novel beam shapes is presented. Sculpting the phase profile of a Gaussian beam can result in the generation of a beam with unique properties. Described in this thesis are Laguerre-Gaussian (LG), Hermite-Gaussian (HG) and Bessel beams (BBs). The diffraction of LG beam modes from a triangular aperture is explored and this effect can be used for the efficient measurement of the azimuthal mode index l that indicates the number of multiples of 2π of phase changes that the field displays around one circumference of the optical axis. In this study, only LG beams with zero radial mode index p, with p + 1 denoting the number of bright high intensity concentric rings around the optical axis, were considered. Then, a powerful approach to simultaneously determine both mode indices of a pure LG beam using the principal component analysis (PCA) algorithm on the observed far-field diffraction patterns was demonstrated. Owing to PCA algorithm, the shape of the diffracting element used to measure the mode indices is in fact of little importance and the crucial step is ‘training' any diffracting optical system and transforming the observed far-field diffraction patterns into the uncorrelated variables (principal components). Our PCA method is generic and it was extended to other families of light fields such as HG, Bessel and superposed beams. This reinforces the widespread applicability of this method for various applications. Finally, both theoretically and experimentally investigations using interferometry show the definitive linkage between both the radial and azimuthal mode indices of a partially coherent LG beam and the dislocation rings in the far-field cross-correlation function (CCF).