Thesis (Ph. D.)--Worcester Polytechnic Institute. / Keywords: vortex; coherence. Includes bibliographical references (p. 127-151).

Thesis (Ph. D.)--Worcester Polytechnic Institute. / Keywords: singularity; vortex; phase; diffraction; interference; nulling; singularities; coherence; dislocation; optical vortex. Includes bibliographical references (p. 123-146).

"Optical vortices are singularities in phase fronts of optical beams. They are characterized by a dark core in the center and by a helical wave front. Owing to azimuthal components of wave vectors, an optical vortex carries orbital angular momentum. Previously, optical vortices were studied only in coherent beams with a well-defined phase. The object of this dissertation is to explore vortices in partially coherent systems where statistics are required to quantify the phase. We consider parametric scattering of a vortex beam and a vortex placed on partially coherent beam. Optical coherence theory provides the mathematical apparatus in the form of the mutual coherence function describing the correlation properties of two points in a beam. Experimentally, the wave-front folding interferometer allows analysis of the cross-correlation function, which may be used to study partial coherence effects even when traditional interferometric techniques fail. We developed the theory of composite optical vortices, which can occur when two coherent beams are superimposed. We then reported the first experimental observation of vortices in a cross-correlation function (which we call spatial correlation vortices). We found numerically and experimentally how the varying transverse coherence length and position of a vortex in a beam may affect the position and existence of spatial correlation vortices. The results presented in this thesis offer a better understanding of the concept of phase in partially coherent light. The spatial correlation vortex presents a new tool to manipulate coherence properties of an optical beam."

xiii, 129 p. : ill. (some col.) A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / Surface plasmon polaritons (SPPs) are collective electron excitations with attendant electromagnetic fields which propagate on a metal-dielectric interface. They behave, in many ways, as model two-dimensional electromagnetic waves. However, because the evanescent field of the SPPs extends a short distance outside the interface, a near-field probe can modify the wave propagation. We use this behavior to study both SPP scattering within the plane of the interface and also the transition to free-space propagation out of the plane. We have, in particular, studied the multiple scattering of SPPs excited on rough silver films. Our laboratory possesses apertureless near-field scanning optical microscopes (A-NSOMs), the probes of which can act as an in-plane scatterer of SPPs. Subsequent momentum-conserving decays of the SPPs generate an expanding hollow cone of light to which information about the direction and phase of the SPPs on the surface is transferred. A focus of our studies has been SPP multiple scattering when one of the scatterers (the tip) can move. This problem is very closely related to a similar problem in mesoscopic electronic transport, involving "universal conductance fluctuations". It is also related to various radar-detection, microwave communications and medical imaging problems. In parallel with actual experimental measurements, we have also conducted extensive Monte Carlo simulations of the scattering. Multiple scattering leads to the appearance and detection of "speckle" in the far field. A speckle field, however, is more properly considered in terms of its embedded optical vortices and so we have used holographic techniques to study these. We have demonstrated that vortices can be manipulated, created and destroyed by movement of the STM probe tip. Optical vortices are an example of the effect of "geometric" or "topological" phase in physics and as such link the trajectory of a parameter in one space to the phase observed in another. In our case, the trajectory of the A-NSOM tip parallel to the sample surface plane generates topological phase in the far field, manifestations of which are vortices. / Committee in charge: Stephen Kevan, Chairperson, Physics; Stephen Gregory, Advisor, Physics; Michael Raymer, Member, Physics; David Strom, Member, Physics; Mark Lonergan, Outside Member, Chemistry

It is well known that light can carry two different kind of angular momentum that together form the total angular momentum of photons. These two forms are the spin orbital angular momentum, associated with the circular polarisation of light, and the orbital angular momentum of light associated with a wavefront tilted with respect to the propagation axis. Any tilted wavefront generates an orbital component of the angular momentum but there are some special cases in which this property becomes particularly interesting. It is the case of optical vortices which form when the waveform is continuously and uniformly tilted to the propagation axis forming a spiral structure.

Ce travail de thèse consiste en l’étude de la mise en forme topologique de la lumière et de la matière et s’articule autour de deux axes de recherche. Le premier concerne la mise en forme topologique de la lumière à partir d’interfaces spin-orbite à base de cristaux liquides. En l’occurrence, nous montrons dans ce manuscrit que différents systèmes de défauts topologiques naturels permettent de générer des vortex optiques par interaction spin-orbite de la lumière, de manière efficace, accordable en longueur d’onde et reconfigurable en temps réel et donnant accès à des charges topologiques diverses. Tout ceci nous a permis de travailler à des échelles microscopiques et de manière spatialement contrôlée. Ces avancées ouvrent la voie au contrôle de l’état orbital de la lumière sur une large bande spectrale.Le second axe concerne la mise en forme topologique d’un film de cristal liquide cholestérique dans le cadre du stockage de l’information de nature topologique. Nous avons démontré la possibilité de générer une grande diversité de défauts topologiques métastables, de manière contrôlée et reconfigurable, à la fois dans le temps et dans l’espace. Nous avons développé une approche permettant de réduire drastiquement le coût énergétique d’écriture de ces défauts. Nous avons également montré qu’il était possible d’obtenir un nouveau type de mémoire réinscriptible contrôlé par le degré de liberté «spin» du photon. / The enclosed work deals with the study of the topological shaping of light and matter and will bedivided into two categories of research. The first focuses on the topological shaping of light from liquid-crystal based spin-orbit interfaces. In particular, we show in this manuscript, that different systems based on the use of natural topological defects behave as highly efficient natural optical spin-orbit encoders, for distinct topological charges, at the micron scale and with spatial control.The operating wave length and operation mode of such interfaces can be tuned in real-time using low voltage electric fields. This breakthrough opens the path to the ultra-broadband control of the light’sorbital state. The second category concerns the topological shaping of a cholesteric liquid crystal film in context of mass data storage. We show the potential to generate metastable topological mi-crostructures in a controlled and reconfigurable way, both in time and space and with a low energy cost. We also demonstrated a new, unique type of rewritable memory, controlled by the«spin»ofthe laser-generated incident photon

The growth of data capacity in optical communications links, which form the critical backbone of the modern internet, is facing a slowdown due to fundamental nonlinear limitations, leading to an impending "capacity crunch" on the horizon. Current technology has already exhausted degrees of freedom such as wavelength, amplitude, phase and polarization, leaving spatial multiplexing as the last available dimension to be efficiently exploited. To minimize the significant energy requirements associated with digital signal processing, it is critical to explore the upper limit of unmixed spatial channels in an optical fiber, which necessitates ideally packing spatial channels either in real space or in momentum space. The former strategy is realized by uncoupled multi-core fibers whose channel count has already saturated due to reliability constraint limiting fiber sizes. The later strategy is realized by the unmixed multimode fiber whose high spatial efficiency suggest the possibility of high channel-count scalability but the right subset of mode ought to be selected in order to mitigate mode coupling that is ever-present due to the plethora of perturbations a fiber normally experiences. The azimuthal modes in ring-core fibers turn out to be one of the most spatially efficient in this regard, by exploiting light’s orbital angular momentum (OAM). Unmixed mode counts have reached 12 in a ~1km fiber and 24 in a ~10m fiber. However, there is a fundamental bottleneck for scalability of conventionally bound modes and their relatively high crosstalks restricts their utility to device length applications. In this thesis, we provide a fundamental solution to further fuel the unmixed-channel count in an MMF. We utilize the phenomenon of topological confinement, which is a regime of light guidance beyond conventional cutoff that has, to the best of our knowledge, never been demonstrated till publications based on the subject matter of this thesis. In this regime, light is guided by the centrifugal barrier created by light’s OAM itself rather than conventional total internal reflection arising from the index inhomogeneity of the fiber. The loss of these topologically confined modes (TCMs) decreases down to negligible levels by increasing the OAM of fiber modes, because the centrifugal barrier that keeps photons confined to a fiber core increases with the OAM value of the mode. This leads to low-loss transmission in a km-scale fiber of these cutoff modes. Crucially, the mode-dependent confinement loss of TCMs further lifts the degeneracy of wavevectors in the complex space, leading to frustration of phase-matched coupling. This thus allows further scaling the mode count that was previously hindered by degenerate mode coupling in conventionally bound fiber modes. The frustrated coupling of TCMs thus enables a record amount of unmixed OAM modes in any type of fiber that features a high index contrast, whether specially structured as a ring-core, or simply constructed as a step-index fiber. Using all these favorable attributes, we achieve up to 50 low-loss modes with record low crosstalk (approaching -45 dB/km) over a 130-nm bandwidth in a ~1km-long ring-core fiber. The TCM effect promises to be inherently scalable, suggesting that even higher modes counts can be obtained in the future using this design methodology. Hence, the use of TCMs promises breaking the record spectral efficiency, potentially making it the choice for transmission links in future Space-Division-Multiplexing systems. Apart from their chief attribute of significantly increasing the information content per photon for quantum or classical networks, we expect that this new light guidance may find other applications such as in nonlinear signal processing and light-matter interactions.

"Optical vortices are ubiquitous features of electromagnetic radiation that are often described as a destructive null in a beam of coherent light. Optical vortices may be created by a variety of different methods, one of which is by the use of a diffractive vortex mask, which is a plate of glass that has been etched in a spiral staircase pattern such that the thickness of the mask varies harmonically in the azimuthal direction. Light passing through the mask gains an azimuthal variation in phase due to the index mismatch between the glass substrate and the surrounding medium and thus an optical vortex is created. There is an implicit assumption that the light is spatially coherent, or in other words, that there is a definite phase relationship between each point in the beam. Optical vortices are not believed to occur in completely incoherent light where the term “phase” no longer holds any meaning. Optical vortices are also poorly understood in partially coherent light where statistics must be used to quantify the phase. The purpose of the research presented in this thesis was to determine how spatial coherence affects the transmission properties of the vortex phase mask. This research enabled us to create a coherence filtering technique based upon the vortex diffractive mask. In this dissertation I will demonstrate the usefulness of this filtering technique in two specific applications. First in the detection of forward-scattered light, where the un-scattered probe beam may blind a detector making detection of the scattered light extremely difficult. Second, in the enhanced resolution of two nearby objects, where the signal from one object may be lost in the glare of a brighter companion. This filtering technique has a wide field of possible applications including the detection of extra-solar planets, the detection of defects in laser optics, and improved methods in optical tomography."

"Optical vortices are singularities in phase fronts of laser beams. They are characterized by a dark core whose size may dramatically affect their behavior upon propagation. Previously, only large-core vortices have been extensively studied. The object of the research presented in this dissertation was to explore ways of generating small-core optical vortices (also called optical vortex filaments), and to examine their propagation using analytical, numerical and experimental methods. Computer-generated holography enabled us to create arbitrary distributions of optical vortex filaments for experimental exploration. We used hydrodynamic paradigms to develop an heuristic model which described the dependence of vortex motion on other vortices and the background beam, both qualitatively and quantitatively. We predicted that pair of optical vortex filaments will rotate with angular rates inversely proportional to their separation distance (just like vortices in a fluid). We also reported the first experimental observation of this novel fluid-like effect. It was found, however, that upon propagation in linear media, the fluid-like rotation was not sustained owing to the overlap of diffracting vortex cores. Further numerical studies and experiments showed that rotation angle may be enhanced in nonlinear self-defocusing media. The results presented in this thesis offer us a better understanding of dynamics of propagating vortices which may result in applications in optical switching, manipulation of micro-particles and optical limiting."

This thesis describes an innovative method for topographic measurement of diffuse surfaces. Tested surface is measured indirectly using nanoparticles distributed across the studied area. An image of every particle is captured by CCD camera as a double helix point spread function whose angular rotation corresponds to local surface height. Used point spread function is the result of an interference of non-diffracting vortex beams that are formed by a spiral phase mask from light originating from a nanoparticle. Diploma thesis presents an overview of current techniques for surface topography measurement. Next, working principle of proposed method is described and its experimental application is discussed. An influence of signal-to-noise ratio and image sampling on reconstruction precision is studied using numerical simulations and, as a result, optimal experimental parameters are proposed. Practical potential of the method is demonstrated by 3D reconstruction of planar and spherical surfaces in the depth range of up to 9 times the depth of focus of used microscope objective.