Thesis (MS)--Montana State University--Bozeman, 2008. / Typescript. Chairperson, Graduate Committee: Christopher H. M. Jenkins. Includes bibliographical references (leaves 54-55).

A pair of light beams that have orthogonal polarizations and equal intensity can be generated through reflection and refraction of a monochromatic light at a dielectric surface. Sytematic procedures to design beam splitters which can produce such output light beams are described in this thesis. Two designs that are of particular interest are prismatic substrates coated by a single layer and a double layer of thin films. Specific examples of each beam splitter in the visible and infrared are included. The performance of each beam splitter as a function of incidence angle, film thickness, and wavelength is also discussed.

Thesis (M.S.)--University of Missouri-Columbia, 2004. / Typescript. Includes bibliographical references (leaves 65-67). Also available on the Internet.

Thesis (M.S.)--University of Missouri-Columbia, 2004. / Typescript. Includes bibliographical references (leaves 65-67). Also available on the Internet.

Στην παρούσα εργασία μελετάμε τη λειτουργία των διαχωριστών δέσμης, καθώς και τη στατιστική κατανομή ενός και δύο σωματιδίων σε απλό και διπλό πηγάδι δυναμικού. Εξετάζουμε υπό ποιες συνθήκες τα δύο αυτά συστήματα μας δίνουν σύμπλεκτες καταστάσεις. Για τους διαχωριστές δέσμης καταλήγουμε στο συμπέρασμα ότι η καταλληλότερη διάταξή τους για να έχουμε μέγιστη απόδοση σύμπλεκτων καταστάσεων, είναι αυτοί να βρίσκονται σε διαδοχική σειρά μεταξύ τους. Από την άλλη μεριά, η μελέτη πηγαδιών δυναμικού, που έγινε γραφικά και αριθμητικά, μας έδειξε ότι τα γεωμετρικά χαρακτηριστικά τού κάθε πηγαδιού, δηλαδή το πάχος και το ύψος του, καθορίζουν τις ιδιοενέργειες τού συστήματος, τις πυκνότητες πιθανότητας των κυματοπακέτων και τελικά την πιθανότητα δημιουργίας σύμπλεκτων καταστάσεων. Γνωρίζοντας τη στατιστική κατανομή των σωματιδίων, ελέγχουμε τη συμπεριφορά τους άρα και την πληροφορία που αυτά μεταφέρουν. Τα παραπάνω βρίσκουν εφαρμογή στα qubits και τους κβαντικούς υπολογιστές. / In the current project we study the function of the beam splitters as well as the statistical behavior of one and two particles in a single and a double quantum well. We examine the conditions under which these two systems provide us with entangled states. For the beam splitters we come to the conclusion that the most appropriate array for having entangled states, is to put them in successive line. On the other hand, the graphical and numerical study of the quantum wells showed that the geometrical characteristics of a quantum well, that is to say thickness and height, define the energy of the system, the density probability of the wave packets and finally the probability for having entangled states. Having knowledge of the statistical behavior of the particles, we may then control the informations that they carry. All the above have many applications in qubits and quantum computers.

Quarter-wave retarders (QWR) that employ total internal reflection (TIR) and interference of light in a transparent thin-film coating at the base of a prism are presented. Explicit equations that guide the optimal design are provided. The optimal refractive index and normalized thickness of QWR coatings on glass and ZnS prisms are determined as functions of the internal angle of incidence from 45o to 75o. An achromatic QWR that uses an Si3N4- coated N-BK10-Schott glass prism is also presented with retardance error of 3o over the 400-600 nm wavelength range. An iterative procedure for the design of a polarizing beam splitter (PBS) that uses a form-birefringent, subwavelength-structured, one-dimensional photonic-crystal layer (SWS 1-D PCL) embedded in a high-index cubical prism is presented. The PBS is based on index matching and total transmission for the p polarization and total internal reflection for the s polarization at the prism-PCL interface at a 45o angle of incidence. A high extinction ratio in reflection ( 50 dB) over the 4-12 μm IR spectral range is achieved using a SWS 1-D PCL of ZnTe embedded in a ZnS cube within an external field of view (FOV) of ±6.6o and in the presence of grating filling factor errors of up to ±10%. Comparable results, but with a wider field of view, are also obtained with a Ge PCL embedded in a Si prism. A design for visible spectrum (553–713 nm) PBS SWS 1-D PCL of ZnTe embedded in a ZnS cube is also presented. The PBS shows a FOV of ±7o. A circular polarizing beam splitter (CPBS) with equal throughput for p and s polarization using SWS 1-D PCL embedded in a high-index cubical prism is introduced. A dual QWR in transmission and reflection with 50–50% CPBS is designed using the PCL. Such a CPBS shows large deviation from the design point as a result of small changes in the design parameters; e.g. a change of 10% in the filling factor results in 12o shift from the 90o phase shift between p and s polarizations, which limits the practical utility of the device.

This thesis is concerned with the guiding of cold atoms using optical forces, which is of great importance in the field of atom optics. Atomic beams can be used for precision sensor equipment, building nano-scale structures, construction of quantum computers and to further the understanding of the properties of atoms. Atoms are guided along light beams using the dipole force; there are two regimes under which this force works. Typically red-detuned guides are used (atoms are attracted towards the light) such guides, however, require large detuning and high powers. In this thesis we investigate the use of blue-detuned (atoms are repelled from the light) hollow light beams of moderate power (a few hundred mW) and confine atoms in the dark centre of the beams. Several magneto-optical traps (MOTs) have been constructed to exploit different guiding geometries. Hollow beams have been generated using a variety of methods; in particular the use of a computer controlled spatial light modulator (SLM) has provided great versatility and simplicity to the experimental arrangements. First, experiments were performed with a low-velocity intense source (LVIS) of atoms. A co-linear LG beam significantly enhances the observed flux, however, considerable difficulties are encountered loading atoms into oblique guides. Imaging a hole in the walls of the light tube was used to improve the loading efficiency. Second, guiding a free-falling atom cloud is performed using a non-diffracting Bessel beam. It is found that while the potential of the Bessel beam is steeper than equivalent LG beams the power distribution across the beam severely limits its usefulness. The next study investigated higher-order LG guide beams generated with an SLM. High order modes have a narrower profile so confine the atoms with less interaction with the guide beam, leading to a more natural guide (as opposed to a pushing force). Finally the SLM was used to create non-trivial beam shapes for beam splitters and interferometers.