  Anderson localization lasers exploit resonant cavities formed due to
structural disorder. The inherent randomness in the structure of these cavities
realizes a probability distribution in all cavity parameters such as quality
factors, mode volumes, mode structures etc, implying resultant statistical
fluctuations in the temporal behavior. Here, we provide the first, direct
experimental measurements of temporal width distributions of Anderson
localization lasing pulses in intrinsically and extrinsically disordered
coupled-microresonator arrays. We first illustrate signature exponential decays
in the spatial intensity distributions of the lasing modes that quantify their
localized character, and then measure the temporal width distributions of the
pulsed emission over several configurations. We observe a hitherto-unreported
dependence of temporal widths on the disorder strength, wherein the widths show
a single-peaked, left-skewed distribution in extrinsic disorder and a
dual-peaked distribution in intrinsic disorder. We propose a model based on
coupled rate equations for an emitter and an Anderson cavity with a random mode
structure, which gives excellent quantitative and qualitative agreement with
the experimental observations. The experimental and theoretical analyses bring
to the fore the temporal complexity in Anderson localization based lasing
systems.
