  A directional random laser mediated by transverse Anderson localization in a
disordered glass optical fiber is reported. Previous demonstrations of random
lasers have found limited applications because of their multi-directionality
and chaotic fluctuations in the laser emission. The random laser presented in
this paper operates in the Anderson localization regime. The disorder induced
localized states form isolated local channels that make the output laser beam
highly directional and stabilize its spectrum. The strong transverse disorder
and longitudinal invariance result in isolated lasing modes with negligible
interaction with their surroundings, traveling back and forth in a Fabry-Perot
cavity formed by the air-fiber interfaces. It is shown that if a localized
input pump is scanned across the disordered fiber input facet, the output laser
signal follows the transverse position of the pump. Moreover, a uniformly
distributed pump across the input facet of the disordered fiber generates a
laser signal with very low spatial coherence that can be of practical
importance in many optical platforms including image transport with fiber
bundles.
