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The intention of this manuscript is twofold. First, the mode-widthprobability density function (PDF) is introduced as a powerful statistical toolto study and compare the transverse Anderson localization properties of adisordered one dimensional optical waveguide. Second, by analyzing the scalingproperties of the mode-width PDF with the transverse size of the waveguide, itis shown that the mode-width PDF gradually converges to a terminalconfiguration. Therefore, it may not be necessary to study a real-sizeddisordered structure in order to obtain its statistical localization propertiesand the same PDF can be obtained for a substantially smaller structure. Thisobservation is important because it can reduce the often demandingcomputational effort that is required to study the statistical properties ofAnderson localization in disordered waveguides. Using the mode-width PDF,substantial information about the impact of the waveguide parameters on itslocalization properties is extracted. This information is generally obscuredwhen disordered waveguides are analyzed using other techniques such as the beampropagation method. As an example of the utility of the mode-width PDF, it isshown that the cladding refractive index can be used to quench the number ofextended modes, hence improving the contrast in image transport properties ofdisordered waveguides.

Scaling analysis of transverse Anderson localization in a disordered optical waveguide