Efficiency of pump absorption in double-clad fiber amplifiers I Fiber with circular symmetry

The paraxial propagation of spatially random monochromatic light in a fiber with an absorbing core is treated as a model for pump absorption in a double-clad optical fiber amplifier. Mode coupling caused by fluctuations of the index of refraction is considered a mechanism that increases the pump absorption and is analyzed in the speckle-mode approximation for the example of a Kerr nonlinearity. The original method of approximate images is described; it allows the use of a fast Fourier transform for numerical simulations in curvilinear regions. Simulations demonstrate the validity of the speckle-mode estimations. For a continuous-wave pump in silica fibers, the electronic Kerr effect is shown to be too small to enhance pump absorption; however, estimates show that the thermal nonlinearity may have a significant effect. The electronic Kerr nonlinearity in the cladding can be significant for a pulsed pump source.