We propose a new method to measure the localization length. The width of a resonant mode can be related to the diffusion time. By means of this new method, the localization length can be determined with a single sample of size comparable to, or even smaller than, the localization length itself. The measurement of localization length for the randomly layered media and the randomly layered systems that are periodic on average is demonstrated explicitly. Experimental support for this approach is also presented....[ Read more ]

We propose a new method to measure the localization length. The width of a resonant mode can be related to the diffusion time. By means of this new method, the localization length can be determined with a single sample of size comparable to, or even smaller than, the localization length itself. The measurement of localization length for the randomly layered media and the randomly layered systems that are periodic on average is demonstrated explicitly. Experimental support for this approach is also presented.

Furthermore, the light amplification and localization behaviors in randomly layered systems that are periodic on average are studied with both matched and mismatched boundary conditions. In the case of matched boundary condition, the Blochwave functions are used in the leads, and the system follows the same two-parameter scaling behaviors as that of a homogeneously random system. However, non-universal behaviors are found if the mis-matched boundary condition is used. In both cases, the threshold length L_s where the reflection coefficient reaches a stationary distribution follows the same relation L_s[approximately equal to][approximately equal to] (ζ₀ι_g) [to power of half]. Here ζ₀ is the localization length in the absence of gain, and ι_g, is the gain length. The localization length ζ in the presence of gain is shown to obey a simple relation l/zeta = l/ζ₀ + l/ι_g.