This thesis concerns the linear properties of solid-core photonic bandgap fibers and the use of their specific properties for guided non-linear optics. Part I focuses on optical properties of the core mode whose guidance mechanism is related to the photonic bandgaps of the microstructured cladding. A numerical tool is developed for bandgap calculation using the plane wave expansion method with the dispersion taken into account. This tool was used for the design of a fiber which allows the photo-writing of a Bragg grating. Then, the stationary perturbation method is applied to the determination of the effective index of the allowed modes at long wavelengths and to the identification of linearly polarized modes towards which they evolve. In part II, the generalized non-linear Schrödinger equation is established. In the case of a tapered fiber, an extra-term appears in the equation allowing the exact conservation of the photons number. Then, the principles of the soliton red-shift and supercontinuum generation are recalled. The usual analytical expression of soliton self-frequency shift rate is extended to the case of short-duration solitons which play an important part in the dynamics of supercontinuum generation. Part III focuses on results obtained in nonlinear regime in solid-core photonic bandgap fibers. We show that the strong value of the third order dispersion term is the cause of the soliton self-frequency shift suppression near the bandgap edge without significant energy loss. Then, this suppression was used to tailor the spectral extent of the supercontinuum and to reduce pulse-to-pulse fluctuations.
