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Multicore microstructure fibers have emerged as promising components in ultrahigh capacity transmissions, biomedical imaging, quantum computing and signal-processing applications like wavelength conversion, and optical amplification. For long-haul transmission they are attractive due to low differential group delay and nonlinear impairment reduction depending on the number of cores. In this thesis we explore the linear-optical and nonlinear-optical properties of single and triple-core microstructure fibers with the goal of using them in parametric devices based on the four-wave mixing (FWM) nonlinearity Although the presence of multiple cores in a fiber produces drawbacks as well as advantages, we experimentally demonstrate that FWM and parametric oscillation are possible in multicore microstructure fibers. One such advantage is the ability to increase the power conversion efficiency of a fiber optical parametric oscillator (FOPO). We also present results for a FOPO built using a single-core microstructure fiber and demonstrate a higher power extraction using a polarization-based output coupling method compared with a polarization-independent method.We discuss measurements of the group velocity dispersion over a wavelength range from 1064-1600 nm. We study the mode coupling among the cores as a function of input power, polarization, wavelength, and spectral broadening. We demonstrate FWM in a triple core microstructure fiber at 1064 nm and study the transition between the case where FWM happens primarily in a single core and the case where FWM is distributed among multiple cores. We find that the effective nonlinear coefficient is reduced by a factor of 3 (the number of cores) when the coupling length is short compared with the nonlinear length, and that this leads to a three-fold reduction in the FWM bandwidth.

Intra mode coupling effects and degeneracy conditions are thoroughly investigated in the scenario of multilayer waveguide structures with grating. Propagating modes in uniform slab waveguides are exactly solved by a transfer matrix method, with modes’ profiles and dispersion characteristics illustrated. Modes coupling phenomena in parallel slab waveguides is studied through inspecting the spatial evolution of single mode’s profile as well as superimposed field distribution. Floquet-Bloch analysis is implemented to accurately solve the modes in single slab waveguides with periodic grating. Dispersion relations are obtained for both propagating modes and evanescent modes in the structure, where second order mode degeneracy is demonstrated at the regular photonic band edge. Through examining the fields’ distribution and spatial evolution, the fundamental harmonic and the -1st Floquet harmonic are illustrated. Finally coupled mode theory is implemented to support better understandings of the various coupling phenomena. Moreover, a coupled mode model is developed for the parallel slab waveguides with a grating structure in between, and the existence of the degenerate band edge in such stricture is qualitatively demonstrated.

We study acoustic waveguides with varying cross sections and slowly bending axes. In particular, we consider waveguides with rough walls and cross sectional width that varies slowly. Roughness means fast and small fluctuations that occur on the scale of the wavelength. The roughness in the walls is unknown in applications and so we model it as a random process to study the propagation of uncertainty in the walls to uncertainty in the wavefield. The slow variations occur on a scale much larger than the wavelength and cause jumps in the number of propagating modes supported by the guide. Here we present a mathematical analysis from first principles of waves in waveguides with an arbitrary but finite number of turning points. We use our analysis to quantify randomization of the wavefield and transport of power in the guide. This is accomplished by obtaining a statistical description of coupled complex waveguide mode amplitudes in terms of the statistics of the fluctuations in the walls. Randomization is captured by decay of the means of the mode amplitudes with distance from the source. Transport of power is studied through differential equations for the second moments of the mode amplitudes. We show using these equations that the random fluctuations in the wall may increase or decrease net transmitted power depending upon the source excitation.

Mode coupling due to periodic index perturbation is a phenomenon which has many applications in optical fiber communications. Coherent coupling between co-propagating modes is one of the most important outcomes of this index perturbation. This property has been utilized to create frequency selective filters, sensors and frequency shifters just to name a few of the applications. This index perturbation is created by a periodic microbending along the longitudinal direction of the optical fiber. Two of the most commonly utilized methods are Fiber Bragg Gratings (FBG) and Long Period Fiber Gratings (LPFG). LPFGs can be utilized to couple forward propagating core and cladding modes.In this work, we have investigated how to generate LPFGs by using acoustic vibrations and utilize these vibrations to facilitate mode coupling in newly developing multicore optical fibers. The hypothesis of this work states that the presence of acoustic vibrations can couple core modes to cladding modes, and then couple that cladding mode to the adjacent core mode. This thesis investigates the optimum coupling conditions based on magnitude and frequency of acoustic vibrations and measures potential core-to-core crosstalk.In our analysis, we used commercial simulation tools to simulate multicore optical fiber core and cladding modes and to calculate coupling coefficient for various modes. As a result, we got the coupling length and crosstalk values between multiple modes under periodic perturbation conditions for two different multicore fiber configurations and concluded that the amount of crosstalk between adjacent cores is not significant in terms of practical optical communications purposes.

The linear variable stability Transfer Function Simulation Model (TFSM), inspired by the United States Air Force's NF-16D Variable stability In-flight Simulator Test Aircraft (VISTA) and created by Henrik Pettersson, can simulate any desired aircraft. The TFSM represents a non-linear aircraft model with its stability parameters - a collection of gain constants, time constants, damping ratios, and natural frequencies. Stability parameters for aircraft generally fall into two uncoupled modes: longitudinal and lateral-directional. Unfortunately, flight tests using the TFSM exhibited undesired lateral-directional coupling in the longitudinal responses. An S-turn maneuver, formation flight test, and an uncontrolled simulation with an initial bank angle of 60 degrees were the foundation for the investigation to pinpoint the TFSM's errors. The flight tests and subsequent analysis showed that although this model is highly versatile, it has three fundamental problems. First, the original creation of the TFSM incorrectly assumed that the time rate of change for the pitch angle (in the local-horizontal reference frame) is equal to the body-axis pitch-rate for all flight conditions. Second, the TFSM's dynamics do not contain gravity terms. Third, the TFSM cannot generate the angular rates needed in a turn. Integrating the aircraft's pitch, roll, and yaw angles with the equations of motion for aircraft fixed the first problem. Unfortunately, resolving this issue only intensified the second two problems. The results from this thesis show that the last two problems are part of the TFSM and cannot be fixed explicitly.