Minimum wave-localization length in a one-dimensional random medium

The frequency dependence of the localization length l for acoustic and electromagnetic waves in a one-dimensional randomly layered medium is studied both numerically and analytically. Through the consideration of different types of random-media models characterized by abrupt or continuous variation of the material parameters, it is shown that beyond the low-frequency behavior of l-2, where denotes the angular frequency, the localization length either approaches a constant or diverges at high frequencies. In all cases, the value of l for a given random medium is found to exhibit a well-defined lower bound whose value is generally several orders of magnitude times the correlation length of the inhomogeneities. The dependence of this minimum localization length on the amount of randomness, plus a comparison with the Schrödinger wave-localization length behavior, are presented and discussed.