This thesis includes a theoretical study of the performance of an optical network system with linear impairments: chromatic dispersion (CD), polarization mode dispersion (PMD), polarization dependent loss (PDL), and amplified spontaneous emission (ASE) noise. Both the a-factor and bit error rate (BER) were used as performance parameters in this study. First, an analytical optical eye diagram evaluation for a system of highly mode coupled PMD/PDL fiber and lumped sections (up to fifteen sections) have been presented in this study. Based on this evaluation we found that with PDL considered as well as PMD, the a-factor of the output becomes higher than that of a Maxwellian fiber having the same total root mean-squared PMD and PDL values, when the mean-square PDL element of the lumped sections makes up the major portion of the total mean-square of the whole system. Whereas without considering PDL, the a-factor becomes higher as the mean-square PMD element of the Maxwellian fiber takes the major portion of the total mean-square PMD element of the whole system. Also the worst case for the a-factor occurred when the lumped sections were in the middle between two equivalent Maxwellian fibers, rether than if the lumped sections were followed by Maxwellian fiber or the Maxwellian fiber is followed by the lumped sections. We also note that two equivalent Maxwellian fibers connected in series will not give the same a-factor as a Maxwellian fiber equivalent calculated by concatenation rules unless they have the same values of PMD, PDL, and polarization direction correlation elements. Second, considering ASE-noise besides CD, PMD, and PDL, improved values of bit error rate (BER) were gotten using the moment generation function for the optical system in cases of ON-OFF modulation format and DPSK modulation format. We found that, even when considering the noise only without the signal, the probability density function of the output current was dependent on the output state of polarization.

Polarization sensitive mode coupling characteristics of tilted fibre Bragg gratings (FBGs) have been exploited to develop a number of useful devices including fibre polarimeters, gain flattening filters, spectrum analyzers, polarization dependent loss (PDL) compensators, reconfigurable optical add / drop multiplexers (ROADM), as well as interferometric, and surface plasmon based sensors. Recently it was demonstrated that a single grating structure could couple the light guided in a fibre to two azimuthally separated, polarization independent, radiated beams. However the reasons for such behaviour had not been fully explained, precluding the complete understanding, exploitation and optimization of this phenomenon. This thesis explains the mechanisms underlying such behaviour through a thorough analytical examination of an existing equation formulated with the Volume Current Method (VCM), quantifying the degree to which a tilted FBG's radiation field is directionally dependent on the phase matching characteristics of a grating's three-dimensional structure as well as the polarization dependent dipole response of the medium itself. Examination of the equation's parameter space, revealed the possibility of three-beam azimuthal responses as well, and resulted in some guidelines for the design and optimization of these devices. Experimental measurements of the out-tapped field are also provided, clearly confirming these theoretical findings and reporting the fabrication of a three-beam azimuthal response grating for the first time. Drawing upon these advances, an improved polarimeter design is proposed that samples more than four detected beams with only two tilted FBGs, theoretically resulting in average Stokes vector error reductions of roughly 20%, facilitating monitoring at lower signal to noise ratios (SNRs). Finally, this thesis undertakes an analysis and re-derivation of the VCM formulation itself, designed to expand its applicability to FBGs written with ultrafast pulsed lasers, address some of the potentially limiting assumptions identified by Li et al, and provide users with computationally efficient formulae that are as accurate as possible.

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