We present a detailed analysis of the transverse Anderson localization of light in a one-dimensional disordered optical lattice in the language of transversely localized and longitudinally propagating eigenmodes. The modal analysis allows us to explore localization behavior of a disordered lattice waveguide independent of the properties of the external excitation. Various localization-related phenomena, such as the periodic revival of a propagating Anderson-localized beam, are easily explained in modal language. We characterize the localization strength by the average width of the guided modes and carry out a detailed analysis of localization behavior as a function of the optical and geometrical parameters of the disordered lattice. We also show that in order to obtain a minimum average mode width, the average width of the individual random sites in the disordered lattice must be larger than the wavelength of the light by approximately a factor of two or more, and the optimum site width for the maximum localization depends on the design parameters of the disordered lattice.
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