We have analyzed numerically the localization length of light $\xi$ fornearly periodic arrangements of homogeneous stacks (formed exclusively byright-handed materials) and mixed stacks (with alternating right andleft-handed metamaterials). Layers with index of refraction $n_1$ and thickness$L_1$ alternate with layers of index of refraction $n_2$ and thickness $L_2$.Positional disorder has been considered by shifting randomly the positions ofthe layer boundaries with respect to periodic values. For homogeneous stacks,we have shown that the localization length is modulated by the correspondingbands and that $\xi$ is enhanced at the center of each allowed band. In thelimit of long-wavelengths $\lambda$, the parabolic behavior previously found inpurely disordered systems is recovered, whereas for $\lambda \ll L_1 + L_2$ asaturation is reached. In the case of nearly periodic mixed stacks with thecondition $|n_1 L_1|=|n_2 L_2|$, instead of bands there is a periodicarrangement of Lorenztian resonances, which again reflects itself in thebehavior of the localization length. For wavelengths of several orders ofmagnitude greater than $L_1 + L_2$, the localization length $\xi$ dependslinearly on $\lambda$ with a slope inversely proportional to the modulus of thereflection amplitude between alternating layers. When the condition $|n_1L_1|=|n_2 L_2|$ is no longer satisfied, the transmission spectrum is veryirregular and this considerably affects the localization length.
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