Theoretical properties of light wave envelope propagation in optical fibers are presented. Generation of bright and dark optical solitons, excitation of modulational instabilities and their applications to optical transmission systems are discussed together with other non-linear effects such as the stimulated Raman process.

Introduction

The envelope of a light wave guided in an optical fiber is deformed by the dispersive (variation of the group velocity as a function of the wavelength) and non-linear (variation of the phase velocity as a function of the wave intensity) properties of the fiber. The dispersive property of the light wave envelope is decided by the group velocity dispersion (GVD) which may be described by the second derivative of the axial wavenumber k (= 2π/λ) with respect to the angular frequency ω of the light wave, ∂2k/∂ω2 (= k″). k″ is related to the coefficient the group velocity delay D in ps per deviation of wavelength in nm and per distance of propagation in km, through k″ = Dλ2/(2πc) where λ is the wavelength of the light and c is the speed of light. For a standard fiber, D has a value of approximately –10 ps/nm · km for the wavelength of approximately 1.5 μm. D becomes zero near λ = 1.3 μm for a standard fiber and near λ = 1.5 μm for a dispersion-shifted fiber.

The non-linear properties of the light wave envelope are determined by a combination of the Kerr effect (an effect of the increase in refractive index n in proportion to the light intensity) and stimulated Brillouin and Raman scatterings.