<p> A detailed theoretical analysis of the propagation constant and the field components in rectangular waveguide completely filled with a semiconductor subjected to an external transverse applied magnetic field, has been carried out. A numerical solution of the transcendental equation for the propagation constant has been obtained for the n-type germanium samples with different conductivities and magnetic fields. </p> <p> An experimental verification of this theoretical analysis has been made with a 22.2 ohm-em, n-type germanium sample at 9.46 GHz. The applied transverse magnetic field was varied from 0 to 10 Kilogauss. Measurements of the reflection co efficients at the air-semiconductor interface for different values of the applied magnetic field have been made with a high precision microwave reflection bridge. The experimental results agree well with the theoretical results. </p> / Thesis / Master of Engineering (MEngr)

Materials with resonant features can have a rapidly changing refractive index spectrally or temporally that gives rise to a changing group index. Depending on the wavelength of the input light, this light can see regimes of normal or anomalous dispersion. Within these regions, the group index can become large, depending on the optical effect used, and give rise to slow or fast light effects. This thesis covers two platforms that exhibit the use of slow and fast light. Slow and fast light are used to manipulate and enhance other optical effects in question. As the focus of this thesis, we examine a rotating ruby rod and spaceplates based on multilayer stacks, both considered as slow- and fast-light media. Light propagation through each platform is modelled and simulated to compare to the experiment. The simulation results for both platforms match well with the measured experimental effects and show the feasibility and utility of slow or fast light to manipulate or enhance optical effects. We simulate light propagation in a rotating ruby rod as a rotating, anisotropic medium with thermal nonlinearity using generalized nonlinear Schrodinger equations, modelling the interplay of many optical effects, including nonlinear refraction, birefringence, and a nonlinear group index. The results are fit to experimentally measured results, revealing two key relationships: The photon drag effect can have a nonlinear component that is dependent on the motion of the medium, and the temporal dynamics of the moving birefringent nonlinear medium create distorted figure-eight-like transverse trajectories at the output. We observe light propagation through a rotating ruby rod where the light is subject to drag. Light drag is often negligible due to the linear refractive index but can be enhanced by slow or fast light, i.e., a large group index. We find that the nonlinear refractive index can also play a crucial role in the propagation of light in moving media and results in a beam deflection. An experiment is performed on the crystal that exhibits a very large negative group index and a positive nonlinear refractive index. The negative group index drags the light opposite to the motion of the medium. However, the positive nonlinear refractive index deflects the beam along with the motion of the medium and hinders the observation of the negative drag effect. Therefore, it is deemed necessary to measure not only the transverse shift of the beam but also its output angle to discriminate the light-drag effect from beam deflection. This work could be applied to dynamic control of light trajectories, for example, beam steering and velocimetry. For the following two chapters, we will focus on a different slow-light platform. This platform focuses on optics that we developed and tested that compress the amount of free-space propagation using multilayered stacks of thin films known as spaceplates. We design and characterize four multilayer stack-based spaceplates based on two design philosophies: coupled resonators and gradient descent. Using the transfer-matrix method, we simulate and extract the angular and wavelength dependence of the transmission phase and transmittance to extract and predict compression factors for each device. A brief theoretical investigation is developed to predict resonance positions, spacing, and bandwidth. We measure the transverse walk-off to extract the compression factor of four multilayer stack-based spaceplates as a function of angle and wavelength. One of the devices was found to have a compression factor of $R=176\pm14$, more than ten times larger than previous experimental records. We increased the numerical aperture of one of the devices by ten times, and we still observed a compression factor of $R=30\pm3$, two times larger than the most recent experimental measurements. We also measured focal shifts up to 800 microns, more than 40 times the device size, typically 10-12 microns thick. The multilayer stack-based spaceplates we studied here show great promise for ultrathin flat optical systems that can easily be integrated into a modern-day imaging system.

Elastic-plastic finite element analyses were performed to predict the crack opening level profiles in semi-elliptical surface cracks. A script was written to use the commercial finite element code ANSYS to predict opening levels in cracked geometries. The functionality of the scripts was verified by comparing predicted opening levels in two and three-dimensional center-cracked geometries to experimental results. In addition, a parameter study was performed in which various aspects of the modeling routine were modified. This included a mesh refinement study as well as a study into the effect of a strain hardening material. The main focus of the current research, however, is to compare finite element predicted opening levels with published opening levels determined experimentally. Due to the complexities and long run-times involved with these models, no attempt was made at growing the cracks from initial length to final length. Instead, discrete crack lengths at which experimental opening levels were published were instead used. Also, no attempt was made to predict the crack aspect ratio evolution. The finite element predicted opening levels were in all cases significantly lower than those reported experimentally, however, similar trends in both crack opening level profile along the crack front, and opening level variations with crack growth were shown.

An investigation has been made of the propagation characteristics of magnetostatic waves with frequencies in the range 890-990 MHz in a crystal of Yttrium Iron Garnet. The sample was mounted in a two port strip line assembly and magnetised axially along the (100) direction. The experiments were performed at room temperature. Magnetostatic waves were observed in external magnetic fields in the neighbourhood of 500 Cersteds. and to explain the experimental results a non-uniform distribution of magnetisation along the axial direction is proposed for the unsaturated sample. Theoretical results for the demagnetising field and the time delay have been computed using this model to explain the excitation and transmission of the observed magnetostatic waves. / Thesis / Master of Engineering (ME)

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