The statistics of transmission through random 1D media are generally presumed
to be universal and to depend only upon a single dimensionless parameter, the
ratio of the sample length and the mean free path, s=L/l. For s much larger
than unity, the probability distribution function of the logarithm of
transmission, P(ln T) is Gaussian with average value -s and variance 2s. Here
we show in numerical simulations and optical measurements that in random binary
systems, and most prominently in systems for which s less than unity, the
statistics of transmission are universal for transmission near an upper cutoff
of unity and depend upon the character of the discrete disorder near a lower
cutoff. The universal behavior of P(ln T) closely resembles a segment of a
Gaussian and arises in random binary media with as few as three binary layers.
Above the lower cutoff, but below the crossover to a universal expression, the
shape of P(ln T) also depends upon the reflectivity of the interface between
the layers. For a given value of s, P(ln T) evolves towards a universal
distribution given by random matrix theory in the dense weak scattering limit
as the numbers of layers increases. P(ln T) found in simulations is compared to
results of random matrix calculations in the dense weak scattering limit but
with an imposed minimum in transmission. Optical measurements in stacks of
glass coverslips are compared to random matrix theory, and differences are
ascribed to transverse disorder in the layers.Comment: 7 pages, 7 figure