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This thesis covers a set of works pertaining to the generation and the characterization of structured waves defined by exotic topologies. It first presents a method to fabricate devices that can be used to arbitrarily shape the wavefronts of optical waves by means of a geometric phase. These devices can be used to shape the transverse polarization pattern of a light beam as well. Two new extensions to characterization schemes known as orbital angular momentum (OAM) sorters are then introduced and demonstrated. The first extension consists of a sorting scheme able to characterize both the OAM and the polarization content of an optical wave. As demonstrated, this feature could be of use in high-dimensional quantum cryptography. The other extension consists of an OAM sorter for electron waves whose use in materials science is also demonstrated by employing it to characterize a magnetic structure. A proposal on how to measure the OAM carried by an electron by minimally perturbing it is also discussed. The thesis then moves on towards works describing more exotic types of structured waves. On one hand, it explores the stability of space-varying polarized light beams upon propagation through a nonlinear medium. Namely, their propagation is found to be more stable than what is experienced by beams with phase singularities. On the other hand, the effect of twisting a neutron’s wavefunction is also explored and is suggested to affect some of its electromagnetic properties. Finally, a method used to knot the transverse polarization profile of optical beams is presented. The structure of these optical polarization knots is then accurately characterized to reconstruct some of its topological features.

M.Ing. (Mechanical Engineering) / An experimental investigation has been carried out to study the influence of sound waves on the transition from laminar to turbulent flow in the boundary layer associated with natural convection from a vertical flat plate with uniform surface heat flux. A relationship exists between frequency and Grashof number at transition. Buckling flow theory provides a means of explaining this relationship. Numerical solutions for the temperature and velocity distributions in an enclosed cavity with one heated vertical wall have been obtained. The frequency of applied sound waves at which transition in the boundary layer would occur, is predicted.

M.Ing. / The heating and drying of products is a process which is essential to improve the quality. This process has been around since the beginning of the industrial age. Most industries use natural energy sources, e.g. coal, to generate the energy that is needed. This energy is then used to heat air and this in turn is used to dry the products. Heat transfer is used to dry the materials and it is a known fact that this mechanism is not effective due to huge losses. A certain company identified this problem and decided to investigate microwave energy as an alternative energy source. The aim of the project was to determine if microwave energy could dry the phosphate and to do an economic feasibility study on such a microwave oven. The operation of microwave sources was examined and the magnetron was found to be the most effective source. Magnetrons that operate at a frequency of 2.45GHz, are easily obtainable and therefore also more economical than magnetrons that operate at other frequencies. The loss mechanisms that are associated with microwave heating as well as the parameters associated with volumetric heating were then investigated. It was found that the complex permittivity and permeability of the material to be heated, are important properties associated with microwave heating and these were not known and needed to be determined. After examlnlng several methods to determine these properties, the measurements were done by means of a network analyser. From the results it was evident that the phosphate losses were relatively high enabling most of the microwave energy to be absorbed. These results were confirmed after further tests were done.

The directional spectrum of wind-driven surface waves has been measured under conditions of well-defined fetch in Burrard Inlet, which separates the cities of Vancouver and West Vancouver in British Columbia, Canada, and extends seaward to Howe Sound and Strait of Georgia. This investigation was undertaken to check the predictions of two recent theories concerning the mechanism by which the wind acts on the water surface to produce waves. These theories, one due to Phillips and the other to Miles, were first advanced in 1957, and have since been combined into a unified theory by the latter author. The unified theory yields an expression for the directional spectrum of the waves in terms of wind speed and direction, the duration of the wind (or alternatively the fetch available), and the two-dimensional spectrum of the turbulent pressure fluctuations in the wind. The fetch is the distance from the shore to the point of observation. The pressure spectrum has never been measured; it appears, indeed, that even single point pressure measurement is a matter of considerable difficulty. However, it is possible even without knowledge of the pressures, to obtain theoretical estimates of the major features of the directional spectrum. Thus, given the wind speed and direction, and the fetch as a function of azimuth, it is possible to predict the frequency at which the power spectrum should peak; and for this and higher frequencies to predict the range of azimuth over which high spectral values should be observed. Further, when the fetch is small, so that the waves are not fully developed, there is a range of frequencies below that of the spectral peak in which only Phillips’ resonance waves should be present. For these, the theory indicates a bimodal distribution in azimuth, and it also predicts the angle of travel relative to the wind as a function of frequency. The results of the measurements made in the present investigation are in fairly good agreement with the theoretical predictions for the higher frequencies, from the frequency of the peak of the power spectrum up (referred to here as the Miles’ regime; the lower frequencies will be referred to as the Phillips' regime). The asymmetrical fetch results in the prediction that these waves will travel at an angle to the wind which varies with frequency, and this was observed. The range of azimuth over which the spectral density is high is also close to the theoretical expectation. In the Phillips’ regime, the bimodal distribution was not observed; the waves were found to have a single predominant direction of travel at each frequency. However, this direction conformed closely to that of one of the two wave trains predicted by Phillips, and its variation with frequency was also that given by the theory. It is suggested that peculiarities of the experimental site may be responsible for the absence of the second wave train, since the observed effects would be difficult to account for on any basis other than that of Phillips’ theory. In order to demonstrate the physical reality of resonance waves in an absolutely decisive way it would be necessary to measure a spectrum exhibiting the characteristic bimodal form. Further investigations at a more suitable site are planned by the Institute of Oceanography, University of British Columbia, (IOUBC) to determine whether this second wave train is actually present. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

In this thesis we consider the propagation of internal waves in a rotating stratified unbounded ocean with randomly varying Brunt-Väisälä frequency, N. Keller's method is used to obtain the dispersion relation for the mean wave field correct to second order in Є when N is of the form N² = Nօ² (1+Єμ) where Nօ = constant, 0<Є²<< 1 and μ is a centered stationary random function of either depth or time separately. From the dispersion relation there are derived general formulas for the change in phase speed and growth or attenuation rates due to the random fluctuations μ . These formulas are dependent on the statistics of μ only through the autocovariance function. The phase speed change and growth rate formulas for depth dependent μ , which constitutes a model of the temperature and salinity fine-structure in the ocean, are presented for various special cases including the limiting cases of correlation lengths of μ that are long or short with respect to the wavelength. Observations at station P (50°N, 145° W) indicate that, to a good approximation, the μ are "white noise" and a close examination is made of the theoretical results for this case. With the aid of the station P data it is estimated that, although the phase speed changes are generally small, the amplitude of a wave increases (decreases) significantly in propagating upward (downward) through a depth of a few kilometers. In addition it is found that the mean effect of the depth dependent fluctuations μ is to increase the effective Brunt-Väisälä frequency, or "stiffen" the fluid. This may explain why some recently observed frequency spectra of internal waves do not exhibit a sharp cut-off at Nօ, the deterministic theoretical upper bound for the wave frequency. Finally an attempt is made to asses the range of validity of Keller's method in the context of the present problem. / Science, Faculty of / Mathematics, Department of / Graduate

In radio-astronomy, spectra of noisy signals are often computed using digital auto-correlation techniques. To simplify the design of the many high-speed multipliers and averagers, coarse quantization is employed, using only a few digital levels. This thesis is a theoretical study of the penalty paid for such coarse quantization in the form of increased output noise. A degradation factor is defined and is calculated for a variety of logic schemes which have been used or proposed. For each scheme, results are given as a function of sampling rate and it is demonstrated that there is often significant improvement in sampling at rates faster than the Nyquist rate. A computer simulation technique was developed for verifying the computed results, and for extending the results to complicated schemes where analysis is very difficult. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The operation of a diaphragm shock tube of 5 cm inside diameter in which the driver gas is heated by the discharge of electrical energy ( ~ 10³ joules) is analyzed in detail. A technique is described for the measurement of the heated driver gas pressure and empirical relations are obtained which enable the shock speed to be calculated from a knowledge of the discharge voltage and test gas pressure. Using helium driver gas initially at atmospheric pressure, shock Mach numbers of about 20 are obtained in argon at an initial pressure of about 1 Torr. The separation of shock front and contact surface is analyzed by means of a convenient shock reflection technique using a smear camera. The properties of the shock-heated gas are shown to agree with the predictions of standard shock wave theory, which yields a temperature of about 1.3•10⁴°K and an electron density of about I0¹⁷ cm⁻³ for the case of a Mach 20 shock in argon at 0.5 Torr. In this case the shock-heated gas sample is observed to be about 5 cm in length at a position 1.2 meters from the diaphragm. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The objectives of this study were to show how far the statistical assumptions usually made when dealing with the theory of continuum nonlinear interactions were relevant to the case of fetch limited wind generated wave fields, and to observe some consequence of the nonlinearity as a check on the other results. The usual assumption, that the first order wave field is composed of Gaussian random wave components stationary in space and time, is shown to require that the real and imaginary parts of the complex Fourier coefficients of the observed surface elevation at a fixed point are normally distributed with zero mean, and that the real and imaginary parts of the complex coefficient for a given frequency band are independent. Coefficients from different frequency bands must also be independent. Four wave fields were observed and described in terms of their power spectra and frequency-wavenumber spectra. Although their directional spectra were found to be strongly influenced by the particular arrangement of fetch at the observing site, their power spectra agreed well with both theory and other observations, at least after correction for the observed currents. This agreement is important from the point of view of establishing the relevance of the results of this work to other field situations. Observations of the frequency domain statistics for these four wave fields indicated that the assumptions of stationarity and of normal distributions for the Fourier coefficients were correct to good accuracy. Two methods were tried for observing direct evidence of nonlinear effects in the wave field. One of these, the attempt to detect products of second order interactions in the frequency-wavenumber spectra, failed because of the poor resolution of the array of sensors. The other, the bispectrum, succeeded, with reasonable agreement being achieved between the observed bispectra and bispectra predicted from the power spectra using the results of perturbation of theory. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Theoretical and experimental studies have been made of the propagation characteristics of helicon waves in metallic spheres; the helicon wave is a branch of the magnetoplasma wave spectrum in the presence of a uniform, static magnetic field. Our theoretical considerations have shown that for an infinitely conducting sphere the helicon wave inside the sphere can be described to good approximation by a single cylindrical wave. This model leads to a simple, approximate, analytic understanding of the resonant mode structure and of the helicon field distribution inside the sample. The resonant modes can be described as a doubly infinite series, labelled by (m,n), where m indicates the number (odd) of half wavelengths along the magnetic field direction nearly equalling the sample diameter and n indicates the same condition perpendicular to the magnetic field. An exact numerical calculation for a sphere of finite scalar resistivity has been carried out by representing the helicon wave inside the sphere by a superposition of cylindrical waves. In this way one is able to calculate the absorption peak heights and widths as well as the resonant frequencies for the first few modes. These results are found to be in good agreement with those calculated independently by Ford and Werner using vector spherical harmonics throughout. Whereas the formalism of Ford and Werner is preferred for computational accuracy, their approach is physically less transparent. Experimentally, we have substantiated the results of the calculations by using single-crystal spheres of aluminium with a residual resistance ratio of about 4000. The resonant modes were studied for two distinct geometries of the excitation and detection coils: the "parallel" geometry had the axes of the coils collinear but at right angles to the static magnetic field, whereas the "perpendicular" geometry had the excitation coil, the detection coil and the magnetic field all mutually perpendicular. The anisotropy of the fundamental (1,1) absorption peak amplitude is about 20% and that of the resonant frequency is about 1% for an applied magnetic field of 35 k0e. The helicon data are interpreted in terms of the anisotropics of the transverse magnetoresistivity (20%) and of the Hall coefficient (1%). For the first time in a helicon experiment an adequate sampling of crystallographic orientations has been made using the same sample throughout. The principal feature of the (1,1) peak height anisotropy is the presence of a narrow trough - typically 1° wide - whenever the static magnetic field lies in a {100} plane. This feature, which corresponds to an equally sharp ridge in the anisotropy of the transverse magnetoresistivity, has escaped detection in all previous studies of the magnetoresistivity (by helicons and otherwise), and it is a consequence of the magnetic breakthrough which is required by the Ashcroft model of the Fermi surface of aluminium. The transverse magnetoresistivity oscillates (periodically in 1/B) whenever the magnetic field is parallel to a <100> direction and this feature is likewise consistent with the Ashcroft model. Other quantum oscillations have been observed superimposed on the helicon resonance and their periodicities are found to agree closely with those in the de Haas-van Alphen effect. / Science, Faculty of / Physics and Astronomy, Department of / Graduate