The transverse Anderson localization (TAL) can always be observed in one-dimensional (1D) disordered systems as long as the transverse dimension is significantly larger than the localization length. This paper presents a detailed modal analysis in one particular realization of the 1D disordered optical waveguides with wavelength-scale feature size based on the imaginary distance beam propagation method (BPM). The localized modes are independent of the physical properties of the external excitation. Additionally, we investigate how the boundaries of disordered waveguides affect the localized modes, which are only related to the design parameters such as feature size, refractive index contrast, and fill-fraction. Finally, we explore the impact of the design parameters on the average localized mode width in the 1D disordered waveguides.
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