  We present a numerical study of electromagnetic wave transport in disordered
quasi-one-dimensional waveguides at terahertz frequencies. Finite element
method calculations of terahertz wave propagation within LiNbO$_{3}$ waveguides
with randomly arranged air-filled circular scatterers exhibit an onset of
Anderson localization at experimentally accessible length scales. Results for
the average transmission as a function of waveguide length and scatterer
density demonstrate a clear crossover from diffusive to localized transport
regime. In addition, we find that transmission fluctuations grow dramatically
when crossing into the localized regime. Our numerical results are in good
quantitative agreement with theory over a wide range of experimentally
accessible parameters both in the diffusive and localized regime opening the
path towards experimental observation of terahertz wave localization.
