  We investigate and report the optical and laser characteristics of a
ytterbium-doped transverse Anderson localizing optical fiber to develop a
fundamental understanding of the light propagation, generation, and
amplification processes in this novel fiber. Ultimately, the goal based on the
measurements and calculations conducted herein is to design and build a random
fiber laser with a highly directional beam. The measurements are based on
certain observations of the laser pump propagation and amplified spontaneous
emission generation in this fiber. Judicious approximations are used in the
propagation equations to obtain the relevant desired parameters in simple
theoretical fits to the experimental observations, without resorting to
speculations based on the intended construction from the fiber preform.
