In 1920, Leon Brillouin discovered a new kind of light scattering – Brillouin scattering – which occurs as a result of the interaction of light with a transparent material’s temporal periodic variations in density and refractive index. Many advances have since been made in the study of Brillouin scattering, in particular in the field of fiber optics. An in-depth investigation of Brillouin scattering in optical fibers has been carried out in this thesis, and the theory of stimulated Brillouin scattering (SBS) and combined Brillouin gain and loss has been extended. Additionally, several important applications of SBS have been found and applied to current technologies. Several mathematical models of the pump-probe interaction undergoing SBS in the steady-state regime have emerged in recent years. Attempts have been made to find analytical solutions of this system of equations, however, previously obtained solutions are numerical with analytical portions and, therefore, qualify as hybrid solutions. Though the analytical portions provide useful information about intensity distributions along the fiber, they fall short of describing the spectral characteristics of the Brillouin amplification and the lack of analytical expressions for Brillouin spectra substantially limits the utility of the hybrid solutions for applications in spectral measurement techniques. In this thesis, a highly accurate, fully analytic solution for the pump wave and the Stokes wave in Brillouin amplification in optical fibers is given. It is experimentally confirmed that the reported analytic solution can account for spectral distortion and pump depletion in the parameter space that is relevant to Brillouin fiber sensor applications. The analytic solution provides a valid characterization of Brillouin amplification in both the low and high nonlinearity regime, for short fiber lengths. Additionally, a 3D parametric model of Brillouin amplification is proposed, which reflects the effects of input pump and Stokes powers on the level of pump wave depletion in the fiber, and acts as a classification tool to describe the level of similarity between various Brillouin amplification processes in optical fibers. At present, there exists a multitude of electro-optic modulators (EOM), which are used to modulate the amplitude, frequency, phase and polarization of a beam of light. Among these modulators, phase modulation provides the highest quality of transmitted signal. As such, an improved method of phase-modulation, based on the principles of stimulated Brillouin scattering, as well as an optical phase-modulator and optical phase network employing the same, has been developed. Due to its robustness, low threshold power, narrow spectrum and simplicity of operation, stimulated Brillouin scattering (SBS) has become a favourable underlying mechanism in fiber-based devices used for both sensing and telecommunication applications. Since birefringence is a detrimental effect for both, it is important to devise a comprehensive characterization of the SBS process in the presence of birefringence in an optical fiber. In this thesis, the most general model of elliptical birefringence in an optical fiber has been developed for a steady-state and transient stimulated Brillouin scattering (SBS) interaction, as well as the combined Brillouin gain and loss regime. The impact of the elliptical birefringence is to induce a Brillouin frequency shift and distort the Brillouin spectrum – which varies with different light polarizations and pulse widths. The model investigates the effects of birefringence and the corresponding evolution of spectral distortion effects along the fiber, and proposes regimes that are more favourable for sensing applications related to SBS – providing a valuable prediction tool for distributed sensing applications. In recent years, photonic computing has received considerable attention due to its numerous applications, such as high-speed optical signal processing, which would yield much faster computing times and higher bandwidths. For this reason, optical logic has been the focus of many research efforts and several schemes to improve conventional logic gates have been proposed. In view of this, a combined Brillouin gain and loss process has been proposed in a polarization maintaining optical fiber to realize all-Optical NAND/NOT/AND/OR logic gates in the frequency domain. A model describing the interaction of a Stokes, anti-Stokes and a pump wave, and two acoustic waves inside a fiber, ranging in length from 350m-2300m, was used to theoretically model the gates. Through the optimization of the pump depletion and gain saturation in the combined gain and loss process, switching contrasts of 20-83% have been simulated for different configurations.

The algebra of SU(2) is ubiquitous in physics, applicable both to the atomic spin states and the polarisation states of light. The method developed by Majorana and Schwinger to represent pure, symmetric spin-states of arbitrary value as a product of spin-1/2 states is a powerful tool that allows for a great conceptual and practical simplification. Foremost, it allows the representation of a qudit on the same geometry as a qubit, i.e., the Bloch sphere. An experimental implementation of the Majorana representation in the realm of quantum optics is presented. The technique allows the projection of arbitrary quantum states from a coherent state input. It is also shown that the method can be used to synthesise arbitrary interference patterns with unit visibility, and without resorting to quantum resources. In this context, it is argued that neither the shape nor the visibility of the interference pattern is a good measure of quantumness. It is only the measurement scheme that allows for the perceived quantum behaviour. The Majorana representation also proves useful in delineating uncertainty limits of states with a particular spin value. Issues with traditional uncertainty relations involving the SU(2) operators, such as trivial bounds for certain states and non-invariance, are thereby resolved with the presented pictorial solution. / <p>QC 20170428</p>