  Media featuring both optical gain and disorder, such as random lasers,
represent formidable challenges as subjects of research due to the high
complexity of the light propagation within them; however, dramatic advances in
this nascent field have been furnished by the paradigm of applying wavefront
shaping techniques to the beam pumping the system. We present here a
theoretical and experimental study employing this approach in a gain medium
where the disorder arises not from random scattering but rather from the
multimodality of a waveguide: an amplifying multimode fiber. The shaping of the
core-guided pump prior to its injection affects the complex, speckle-like
patterns of excitation within the fiber volume. Thus we are offered the
intriguing prospect of manipulating the spatially heterogeneous gain in a
system where the disorder, albeit highly complex, may be fully understood in
terms of the discrete eigenmodes of a well-known waveguide. We study our medium
in two different configurations: as an optical amplifier, and as a fiber laser.
In the first configuration we show that dependence upon the pump configuration,
of the amplifier transmission function, surprisingly survives several physical
mechanisms which at first sight would appear to severely limit it. This insight
is then carried on to the lasing cavity configuration, where we find striking
parallels between the behavior of the system and that of random lasers; more
importantly, the pump shaping shows a strong ability to control the complex
emission, in particular - to selectively favor individual spectral lines and
stabilize single-mode operation.
