  The intention of this manuscript is twofold. First, the mode-width
probability density function (PDF) is introduced as a powerful statistical tool
to study and compare the transverse Anderson localization properties of a
disordered one dimensional optical waveguide. Second, by analyzing the scaling
properties of the mode-width PDF with the transverse size of the waveguide, it
is shown that the mode-width PDF gradually converges to a terminal
configuration. Therefore, it may not be necessary to study a real-sized
disordered structure in order to obtain its statistical localization properties
and the same PDF can be obtained for a substantially smaller structure. This
observation is important because it can reduce the often demanding
computational effort that is required to study the statistical properties of
Anderson localization in disordered waveguides. Using the mode-width PDF,
substantial information about the impact of the waveguide parameters on its
localization properties is extracted. This information is generally obscured
when disordered waveguides are analyzed using other techniques such as the beam
propagation method. As an example of the utility of the mode-width PDF, it is
shown that the cladding refractive index can be used to quench the number of
extended modes, hence improving the contrast in image transport properties of
disordered waveguides.
